# Modeling of deuteron-induced reactions on molybdenum at low energies

M<EMAIL_ADDRESS>E. Šimečková2, J. Mrázek2, C.
Costache1, V. Avrigeanu1 1Horia Hulubei National Institute for R and D in
Physics and Nuclear Engineering, P.O. Box MG-6, 077125 Magurele, Romania
2Nuclear Physics Institute of the Czech Academy of Sciences (NPI CAS), 25068
Řež, Czech Republic

###### Abstract

The activities of the EUROfusion consortium on the development of high quality
nuclear data for fusion applications include evaluations of deuteron induced
reactions and related data libraries for needs of the DEMO fusion power plant
and IFMIF-DONES neutron–source nuclear analyses. Molybdenum is one of the
major constituents of the reference stainless steels used in critical
components of these projects. While the TENDL deuteron data library was the
current reference used by EUROfusion, need of its further improvement has
already been pointed out. The weak binding energy of the deuteron is
responsible for the high complexity of its interaction with nuclei, involving
also a variety of reactions initiated by the nucleons following the deuteron
breakup. Their analysis completed that of the deuteron interactions with Mo
and its stable isotopes, from elastic scattering to pre-equilibrium and
compound–nucleus reactions, up to 50 MeV. A particular attention has been paid
to the breakup, stripping, and pick-up direct interactions which amount to
around half of the deuteron total–reaction cross section. The due account of
most experimental data has validated the present approach, highlighted some
prevalent features, and emphasized weak points and consequently the need for
modeling/evaluation upgrade.

###### pacs:

24.10.Eq,24.10.Ht,25.45.-z,25.60.Gc

##  I Introduction

Accurate cross–section data of deuteron induced reactions are a pre–requisite
also for reliable design of the accelerator–based neutron source facility
IFMIF-DONES (International Fusion Materials Irradiation Facility – DEMO
Oriented NEutron Source), e.g. Bernardi et al. (2022); Królas et al. (2021)
and Refs. therein, and material qualification of the European DEMO fusion
reactor Federici et al. (2017) beyond the ITER fusion–device materials Packer
et al. (2018, 2021). Actually, the suitable account of deuteron-nucleus
interactions is an important test for reaction mechanism models and
nuclear–data evaluation within on-going strategic research programmes at
large-scale facilities using deuteron beams Fischer et al. (2020, 2017);
Ledoux et al. (2017); Mardor et al. (2018); Ledoux et al. (2021). The present
work concerns in this respect the deuteron–induced reactions on Mo, which is
used in stainless steels to provide a greater corrosion resistance Pardo et
al. (2008); Wang et al. (2022). SS-316L steel, being a reference material for
Li loop piping of DONES contains 2-3% of Mo Ibarra et al. (2018). Since the
natural Mo consists of seven stable isotopes, with abundances between 9-24%,
the activation of number of enriched foils in separate experiments would be
preferred but for obvious reasons less feasible. Thus, a new experiment
performed with natMo targets in Center of Accelerators and Nuclear Analytical
Methods (CANAM) infrastructure Nuclear Physics Institute of the Czech Academy
of Sciences (2024) of the Nuclear Physics Institute of the Czech Academy of
Sciences (NPI CAS) and Neutrons for Science Facility at SPIRAL-2 Ledoux et al.
(2017) was less resource-demanding while the analysis (both experimental
Ledoux et al. (2021); Šimečková et al. (2024) and theoretical) becomes a quite
complex task. Apart from the applications in fusion technology, knowledge of
activation cross-sections of deuteron-induced reactions on molybdenum is very
important also for production of the medically relevant radionuclides (e.g.
Tárkányi et al. (2012); Elbinawi et al. (2022); Tárkányi et al. (2011)).

The deuteron sub-library of the TALYS–based evaluated nuclear data library
(TENDL) Koning et al. (2019), related to the output of the TALYS nuclear model
code system Koning et al. (2023), is the current reference within the
EUROfusion Consortium EUROfusion Consortium Research Institutions (2014-2024)
project of the Early Neutron Source (ENS) Ibarra et al. (2019). However, the
need of its further improvement has been pointed out Fischer et al. (2020).
The latest version of the Fusion Evaluated Nuclear Data Library (FENDL)
Forrest et al. (2012, 2013) also includes for structural materials Leichtle
(2019) the data of the first version of FENDL, which are from TENDL-2011.
Meanwhile, recent advancements in deuteron reaction modeling in the TALYS code
Fischer et al. (2018); Avrigeanu et al. (2022) are taken into account to
provide more reliable data for TENDL evaluated files, to be reviewed and
integrated step by step in the future Schnabel et al. (2024).

The recent studies of deuteron activation of elements within the priority list
of the structural materials Fischer (2012); Alba et al. (2022) known to be
problematic (e.g. Sauvan et al. (2017)), namely Al, V, Cr, Mn, Fe, Co, Ni, Cu,
Zr, and Nb Bém et al. (2009); Kreisel et al. (2019); Šimečková et al. (2018);
Avrigeanu et al. (2020, 2014, 2016); Šimečková et al. (2011, 2021); Avrigeanu
et al. (2013), are continued by the present work on Mo. These nuclear–model
analyses of deuteron–induced reactions have been completed with reference to
the short reaction–times direct interactions (DI), i.e. breakup (BU) and
direct reactions (DR), in addition to the statistical processes of pre-
equilibrium emission (PE) and evaporation from compound nucleus (CN) at
continuously increasing reaction times. A careful account of BU and DR
contributions seems essential in this respect due to the still existing
disagreement between recent measurements and calculated data Tárkányi et al.
(2012); Elbinawi et al. (2022), while due consideration has also been given to
the weak points of an eventual evaluation. Moreover, the consistent analysis
of all available data for competitive reaction channels as well as full stable
isotopic chains and even neighboring elements, beyond a particular reaction
analysis for one or only a couple of isotopes (e.g. Kara (2017)), strengthens
the assessment of the model approach.

A consistent energy–dependent optical model potential (OMP) for deuterons on
Mo isotopes is concerned in Sec. II.1 using the computer code SCAT2 Bersillon
(1992). Then, theoretical framework of the deuteron BU mechanism (Sec. II.2)
and the DR analysis (Sec. II.3) involving the computer codes TALYS-1.96 Koning
et al. (2023) and FRESCO Thompson (1988), respectively, is briefly mentioned.
The PE and CN mechanism contributions to the population of various residual
nuclei (Sec. II.4), on the grounds of also TALYS-1.96, are completing the
nuclear model discussion of the present work. The measured and calculated
deuteron activation cross sections of natural Mo and its stable isotopes, as
well as the corresponding evaluated data within the TENDL-2021 library Koning
et al. (2019), are then compared in Sec. III. Conclusions of this work are
given in Sec. IV.

##  II Nuclear model framework

The weak binding energy of the deuteron is responsible for the high complexity
of its interaction with nuclei, involving also a variety of reactions
initiated by the nucleons following the deuteron breakup (breakup nucleons)
Avrigeanu et al. (2022); Avrigeanu and Avrigeanu (2015, 2017). Its importance
increases with the target-nucleus mass and charge, becoming dominant for heavy
target nuclei at incident energies particularly around the Coulomb barrier
Avrigeanu et al. (2012); Avrigeanu and Avrigeanu (2015). Overall, the
accompanying breakup–nucleons induced reactions make substantially different
the deuteron projectile among the other incident particles, with proved
significant impact even for applications in nuclear transmutation of
radioactive waste Wang et al. (2019); Chillery et al. (2023). Additional
comments on systematic uncertainties in DR theories used to analyze
particularly $(d,p)$ reactions are referred to in Sec. II.3.

Figure 1: (Color online) Comparison of measured Zerkin and Pritychenko (2018);
Hjorth et al. (1968); Korostova et al. (1968); Takeda (1973); Peterson et al.
(1977); Wada (1978); Takei et al. (1987) and calculated elastic–scattering
angular distributions of deuterons on 92,94,96,98,100Mo isotopes at 14.5,
17.2, 21.14, 21.5, and 22 MeV, using the global OMP of Daehnick et al.
Daehnick et al. (1980)

###  II.1 Deuteron optical potential assessment

A simultaneous analysis of the deuteron elastic scattering as well as induced
activation cross sections is essential as the deuteron OMP parameters are
obtained by the former data fit, and then used within the analysis of the
latter ones. The demand of a consistent input of nuclear model calculations of
deuteron activation of Al, V, Cr, Fe, Co, Ni, Zr, Nb, Pa, U Bém et al. (2009);
Kreisel et al. (2019); Šimečková et al. (2018); Avrigeanu et al. (2020, 2014,
2016); Šimečková et al. (2011, 2021); Avrigeanu et al. (2013, 2012); Avrigeanu
and Avrigeanu (2015) was satisfied by the deuteron OMP of Daehnick et al.
Daehnick et al. (1980). It has been a first option of the present work, being
obtained by use of a large experimental basis including the angular
distributions of elastic scattered deuteron on the above–mentioned elements as
well as on 100Mo isotope.

Figure 2: (a,d) Excitation functions of deuteron $\sigma_{R}$ (dotted curves),
total breakup $\sigma_{BU}$=2$\sigma^{n/p}_{BF}$+$\sigma_{EB}$ (thick solid
curves), $nucleon$-$emission$ total breakup
$\sigma^{n/p}_{BU}$=$\sigma^{n/p}_{BF}$+$\sigma_{EB}$ (thin solid curves) and
inelastic-breakup $\sigma^{n/p}_{BF}$ (dashed curves), and elastic breakup
$\sigma_{EB}$ (dash-dot-dotted curves) cross sections Avrigeanu and Avrigeanu
(2017); (b,e) DI excitation functions (thick solid curves) and its components:
total BU (thin curves), DR (dashed curves), stripping $(d,p)$ (dash-dotted
curves) and $(d,n)$ (dash-dot-dotted curves), and pick-up $(d,\alpha)$ (short-
dotted curve) and $(d,t)$ (dotted curves); (c,f) $\sigma_{R}$ fractions of BU
(thin solid curves), DR (dashed curves), DI (solid thick curves), and PE+CN
(thick dotted curves) cross sections of deuteron interactions with (a,b,c)
92Mo and (d,e,f) 100Mo (see text)

Unfortunately, the systematics of elastic–scattering angular distributions of
deuterons on the stable isotopes of Mo is scarce, despite the number of these
isotopes. There is also no related measurement of the deuteron total–reaction
cross section $\sigma_{R}$. The comparison of the measured angular
distributions of elastic–scattered deuterons on 92,94,96,98,100Mo Zerkin and
Pritychenko (2018); Hjorth et al. (1968); Korostova et al. (1968); Takeda
(1973); Peterson et al. (1977); Wada (1978); Takei et al. (1987) at the
incident energies of 14.5, 17.2, 21.14, 21.5, and 22 MeV, and the calculated
values using the computer code SCAT2 Bersillon (1992) and Daehnick et al.
Daehnick et al. (1980) OMP is shown in Fig. 1. The good description of the
measured data provided thus confidence in the further use of this potential
within a consistent analysis of the deuteron activation cross sections of Mo
isotopes through the BU, DR, PE, and CN reaction mechanisms.

###  II.2 Deuteron breakup

A detailed overview of the specific deuteron breakup in the Coulomb and
nuclear fields of the target nucleus, including its complexity given by the
addition to the primary deuteron–nucleus interaction of various nuclear
reactions initiated by the breakup nucleons, was given recently Avrigeanu et
al. (2022); Šimečková et al. (2021). Therefore, only particular points are
mentioned hereafter concerning the two distinct BU processes, i.e. the elastic
breakup (EB) in which the target nucleus remains in its ground state and none
of the deuteron constituents interacts with it, and the inelastic breakup or
breakup fusion (BF), where one of these constituents interacts nonelastically
with the target nucleus.

Empirical parametrization Avrigeanu et al. (2022, 2009); Avrigeanu and
Avrigeanu (2015, 2017) has concerned the fractions $f_{BU}^{n/p}$ and $f_{EB}$
of cross sections for the total breakup (EB+BF) $nucleon$-$emission$
$\sigma^{n/p}_{BU}$ and elastic breakup $\sigma_{EB}$, respectively, to
$\sigma_{R}$. The experimental systematics of deuteron-induced reactions on
target nuclei from 27Al to 232Th Pampus et al. (1978); Wu et al. (1979);
Kleinfeller et al. (1981); Matsuoka et al. (1980); Mustafa et al. (1987) was
involved in this respect. Moreover, since equal BF nucleon–emission cross
sections $\sigma^{n}_{BF}$ and $\sigma_{BF}^{p}$ were assumed Mustafa et al.
(1987), the total breakup (BF+EB) cross section becomes
$\sigma_{BU}$=2$\sigma^{n/p}_{BF}$+$\sigma_{EB}$, while the total breakup
(BF+EB) $nucleon$-$emission$ cross section is
$\sigma^{n/p}_{BU}$=$\sigma^{n/p}_{BF}$+$\sigma_{EB}$. At the same time, the
BF fractions for each of the breakup nucleons are given by the difference
$f_{BF}^{n/p}$=$f_{BU}^{n/p}$-$f_{EB}$.

An overall view of the incident–energy dependence of the BU, BF, and EB cross
sections for deuterons on 92,100Mo target nuclei is shown in Fig. 2(a,d). It
is thus apparent the change of these excitation functions with the
target–nucleus mass number, too. There are shown also both the BU and BF
nucleon–emission excitation functions. These results as well as the earlier
ones Bém et al. (2009); Kreisel et al. (2019); Šimečková et al. (2018);
Avrigeanu et al. (2020, 2014, 2016); Šimečková et al. (2011, 2021); Avrigeanu
et al. (2013, 2012); Avrigeanu and Avrigeanu (2015) point out the dominant
role of the BF component, to be concerned in connection with the two opposite
effects of the deuteron breakup on the deuteron activation cross sections
Avrigeanu et al. (2022); Avrigeanu and Avrigeanu (2015, 2017). At first, the
total–reaction cross section shared among various outgoing channels, is
reduced by the value of the total breakup cross section $\sigma_{BU}$. Next,
this component brings contributions to different reaction channels through
breakup–neutrons/protons interactions with target nucleus Avrigeanu et al.
(2022); Bém et al. (2009); Kreisel et al. (2019); Šimečková et al. (2018);
Avrigeanu et al. (2020, 2014, 2016); Šimečková et al. (2011, 2021); Avrigeanu
et al. (2013, 2012); Avrigeanu and Avrigeanu (2015) leading to the enhancement
of the corresponding $(d,xp)$ or $(d,xn)$ reaction cross sections,
respectively.

It should be noted that the BF cross–section partition among various
residual–nuclei population is triggered by the energy spectra of the breakup
nucleons as well as the excitation functions of the reactions induced by these
nucleons on the target nucleus Avrigeanu and Avrigeanu (2015, 2017), while the
atomic mass and maybe also the atomic number of the related compound nuclei
differ by one unit from that in deuteron-induced reactions. The BF related
formalism involved in the present work is described in Sec. 3.4 of Ref.
Avrigeanu et al. (2022), the corresponding reaction cross sections being
calculated with the code TALYS-1.96 Koning et al. (2023) and its second option
for the breakup model, i.e. including the BF enhancement (Koning et al.
(2023), p. 40).

The enhancements due to $(p,x)$ and $(n,x)$ reactions induced by the breakup
nucleons on 92,94,96,98,100,natMo are discussed in Sec. III and distinctly
showed in Figs. 9–23. It has been thus proved that BF enhancements are
particularly important for the suitable description of the maximum as well as
the high–energy side of the excitation functions for second and third chance
emitted-particle channels Avrigeanu et al. (2022).

###  II.3 Direct reactions

Apart from the breakup contributions to deuteron interactions, an increased
attention has to be paid to the direct reactions so far poorly considered
within deuteron activation analysis. For low– and medium–mass target nuclei
and deuteron energies below and around the Coulomb barrier, the interaction
process proceeds largely through DR mechanism, while PE+CN component become
important with the incident–energy increase. Nevertheless, the assessment of
DR cross sections is subject to available information on spectroscopic factors
for populated states, outgoing particle angular distributions, or at least
differential cross–section maximum values.

The appropriate assessment of stripping – $(d,p)$, $(d,n)$, and $(^{3}He,d)$ –
and pick-up – $(d,t)$, $(d,\alpha)$, and $(d,^{3}He)$ – DR mechanism
contributions has been performed through the distorted-wave Born approximation
(DWBA) method, with the code FRESCO Thompson (1988). The $post/prior$ form
distorted–wave transition amplitudes for stripping and pick-up reactions,
respectively, and the finite–range interaction have been considered. A note
may concern the finite range (FR) effects in deuteron stripping process which
were formerly shown to be very small around the incident energy of 10 MeV, so
that a zero–range (ZR) approximation was expected to be reasonable Buttle and
Goldfarb (1964) and eventually completed (e.g. Shinsuke Nakayama and Ogata
(2021)) by an usual FR correction Liu et al. (2004); Tsang et al. (2005). More
recently, ZR calculation has led to results very close to the full FR-DWBA
calculation for deuteron reactions while FR effects become important for
incident 6Li ions Lei and Moro (2015). Nevertheless, it was also found these
effects are important in $(d,p)$ reactions at intermediate energies (20 MeV/u)
Nguyen et al. (2010) while they are not however among the actual major sources
of uncertainties in a variety of reaction theories used to analyze $(d,p)$
nuclear reactions in the incident energy range 10-20 MeV Lovell and Nunes
(2015).

At the same time, a simple Gaussian form was considered for the $n$-$p$
interaction in the deuteron Iseri et al. (1986), which reproduces well the
binding energy of deuteron and the low–energy $n$-$p$ scattering phase shifts.
It is yet widely used (e.g. Lei and Moro (2015, 2018)), DWBA as well as BU
cross sections being modified by a few percent when including a realistic NN
interaction for the reaction at low energy, while at higher energy the cross
section is not affect by details of the NN interaction Moro et al. (2009);
Upadhyay et al. (2012); Deltuva et al. (2016); Gomez-Ramos and Moro (2017);
Neoh et al. (2020). Following the original data analysis, similar form has
been used for the $d$-$n$ interaction in the triton Guazzoni et al. (2011), at
the same time with a Woods-Saxon shape of the $d$-$p$ interaction Iseri et al.
(1986) in 3He, as well as the $d$-$d$ interaction DelVecchio (1973) in the
$\alpha$ particle. The transferred–nucleon and –deuteron bound states were
generated in a Woods-Saxon real potential Bém et al. (2009); Avrigeanu et al.
(2014).

The number of $N$ nodes corresponding to an $L$ transferred angular momentum
in the radial wave function was determined by the harmonic–oscillator energy
conservation rule:

$2N+L=2(n_{n/p}-1)+l_{n/p}\>,$ (1)

where $n_{n/p}$ and $l_{n/p}$ are the single–particle (neutron/proton)
shell–model state quantum numbers. Particularly for the FRESCO code, the
number of nodes includes the origin, so that $N$$>$0.

Figure 3: (Color online) Comparison of measured Riley et al. (1971) and
calculated (solid curves) neutron angular distributions of 92Mo$(d,n)^{93}$Tc
(top) and 94Mo$(d,n)^{95}$Tc (bottom) stripping transitions to states with
excitation energies in MeV, at the incident energy of 12 MeV. For the measured
angular distributions of unresolved doublets it is shown the sum of the
calculated contributions corresponding to the spectroscopic factors for each
state of the doublet given in the Appendix A. Figure 4: (Color online) As Fig.
3 but for deuteron angular distributions of 95Mo$(^{3}He,d)^{96}$Tc Emigh et
al. (1979) (top) and 96Mo$(^{3}He,d)^{97}$Tc (bottom) Cheung et al. (1975)
stripping transitions, at 33.6 and 18 MeV, respectively Figure 5: (Color
online) As Fig. 4 but for 98Mo$(^{3}He,d)^{99}$Tc Cheung et al. (1977) at 18
MeV Figure 6: (Color online) As Fig. 3 but for $\alpha$-particle angular
distributions of 92Mo$(d,\alpha)^{90}$Nb pick-up transitions Comfort et al.
(1974), at 17 MeV Figure 7: (Color online) As Fig. 3 but for triton angular
distributions of 92,94,98,100Mo$(d,t)^{90,92,94,98,100}$Mo pick-up transitions
Kozub and Youngblood (1973); Bindal et al. (1977); Ohnuma and Yntema (1969);
Habib et al. (1982), at 40.6 (top), 23 (middle), and 16 (bottom) MeV Figure 8:
(Color online) As Fig. 3 but for 3He angular distributions of
96,98Mo$(d,^{3}He)^{95,97}$Nb pick-up transitions Bindal et al. (1974), at
40.7 MeV

The energy, spin, and parity of the residual–nuclei discrete levels within the
ENSDF Brookhaven National Laboratory (2024) and RIPL Capote et al. (2009)
libraries were used as starting input of the DWBA calculations for the
stripping and pick-up reactions Basu and McCutchan (2020); Baglin (2013);
Abriola and Sonzogni (2008); Nica (2010); Browne and Tuli (2017); McCutchan
and Sonzogni (2014); Blachot (1998).

####  II.3.1 Stripping reactions

$(d,n)$ reactions.
The analysis of the neutron angular distributions from
92,94Mo$(d,n)^{93,95}$Tc reactions Riley et al. (1971) is shown in Fig. 3 for
transitions to discrete levels of residual nuclei. There were thus provided
the spectroscopic factors (given in the Appendix A) and then the corresponding
calculated stripping cross sections, e.g. Fig. 2(b), Fig. 13(e,j,o), and Fig.
15(d,h,l) in Sec. III.

$(^{3}He,d)$ reactions.
There are so scarce or even lacking measured neutron angular distributions for
95,96,98Mo$(d,n)^{96,97,99}$Tc stripping reactions, in order to obtain the
stripped–proton spectroscopic factors for the assessment of the DR
contributions Because of that, these spectroscopic factors have been got
through deuteron angular-distribution analysis of $(^{3}He,d)$ stripping
reaction populating the same residual nucleus as the $(d,n)$ process. Thus,
description of the deuteron angular distributions from
95,96,98Mo$(^{3}He,d)^{96,97,99}$Tc stripping reactions Emigh et al. (1979);
Cheung et al. (1975, 1977) (Figs. 4 and 5) validates the extracted
stripped–proton spectroscopic factors. Then, they were involved in
95,96,98Mo$(d,n)^{96,97,99}$Tc stripping cross–sections calculations whose
contributions to the total activation cross sections are shown in Figs. 10(b),
11(b), and 12(b,g,l) of Sec. III.

Moreover, for calculations of 100Mo$(d,n)^{101}$Tc stripping cross sections we
made use of the spectroscopic factors reported by Freeman et al. Freeman et
al. (2017) (Table XXVII) for deuteron distributions of
100Mo$(^{3}He,d)^{101}$Tc stripping reaction. The corresponding stripping
100Mo$(d,n)^{101}$Tc excitation function is shown in Fig. 2(e) and Fig. 9(b)
of Sec. III. The same discrete levels schemes are involved for the residual
nuclei within both $(d,n)$ and $(^{3}He,d)$ reaction calculations, e.g. 33
levels of 96Tc Brookhaven National Laboratory (2024); Abriola and Sonzogni
(2008), 30 levels of 96Tc Brookhaven National Laboratory (2024); Nica (2010),
35 levels of 99Tc Brookhaven National Laboratory (2024); Browne and Tuli
(2017), and 17 levels of 101Tc Freeman et al. (2017).

$(d,p)$ reactions.
The $(d,p)$ stripping reaction cross sections corresponding to the residual
nuclei of interest for this work have been calculated using the spectroscopic
factors provided by the more recent analyzes of 92Mo$(d,p)^{93}$Mo Sharp et
al. (2013) (Table III), and 98,100Mo$(d,p)^{99,101}$Mo reactions Freeman et
al. (2017) (Tables XXIV and XXIII, respectively). The related
92,100Mo$(d,p)^{93,101}$Mo excitation functions are shown in Figs. 2(b,e) and
16(b) of Sec. III. At the same time, the excitation function of the
98Mo$(d,p)^{99}$Mo stripping reaction is shown in Fig. 17(b).

####  II.3.2 Pick-up reactions

$(d,\alpha)$ reactions.
Even worse than the scarce systematics of neutron angular distributions
corresponding to $(d,n)$ stripping processes, there exist measured
$\alpha$-particle angular distributions only for the
${}^{92}Mo(d,\alpha)^{90}$Nb pick-up reaction Comfort et al. (1974). Their
analysis shown in Fig. 6 has allowed to extract the spectroscopic factors of
the picked deuteron. The corresponding $(d,\alpha)$ excitation function is
included also in Fig. 2(b), but particularly in Fig. 22(l) of Sec. III.

On the other hand, spectroscopic factors corresponding to
94,97,98Mo$(d,\alpha)^{92,95,96}$Nb pick-up reactions have been obtained
following due consideration of the measured $\alpha$-particle angular
distributions Schoonover et al. (1974) maxima. The corresponding $(d,\alpha)$
pick-up excitation functions are shown in Figs. 20(k), 21(d,i,n), and 22(c) of
Sec. III.

$(d,t)$ reactions.
The analysis of measured triton angular distributions Kozub and Youngblood
(1973); Bindal et al. (1977); Ohnuma and Yntema (1969); Habib et al. (1982) of
the 92,94,98,100Mo$(d,t)^{91,93,97,99}$Mo pick-up reactions has provided the
spectroscopic factors for the corresponding transitions to discrete levels of
residual nuclei. The suitable account of the available $(d,t)$ angular
distributions shown in Fig. 7 provides the modeling support of the calculated
pick-up excitation functions shown in Figs. 2(b,e) and 17(c).

$(d$,3$He)$ reactions.
The analysis of measured outgoing 3He angular distributions of the
96,98Mo$(d$,3$He)$95,97Nb pick-up processes Bindal et al. (1974) made possible
further calculations of the corresponding pick-up cross–section contributions
to the total activation cross sections of 95,97Nb residual nuclei. Thus,
appropriate description of these angular distributions (Fig. 8) validated the
extracted spectroscopic factors which have led to pick-up excitation functions
in Figs. 20(f) and 21(c,h,m) of Sec. III.

The DR contributions, which have proved essential for describing the measured
excitation functions corresponding to the first–chance emitted particles Bém
et al. (2009); Kreisel et al. (2019); Šimečková et al. (2018); Avrigeanu et
al. (2020, 2014, 2016); Šimečková et al. (2011, 2021); Avrigeanu et al.
(2013), are furthermore discussed in Sec. III. Nevertheless, it should be
pointed out the significant effect of the maximum of the stripping excitation
functions around 8-12 MeV, shown in Fig. 2(b,e), on the increasing low–energy
side and the maximum of the corresponding total activation excitation
functions.

To sum up, the deuteron total-reaction cross section that remains available
for the PE+CN mechanisms has followed the due consideration of the incident
flux leakage through the breakup, stripping and pick-up DI processes. Using
the present work notation as well as its first assessment of the deuteron
break-up and DR transitions, the composite–formation cross section, e.g. Eq.
(164) Koning et al. (2023), becomes
$\sigma_{PE}$+$\sigma_{CN}$=$\sigma_{R}$-$\sigma_{BU}$-$\sigma_{DR}$. In
brief, similarly to the depletion factor to account for the direct and PE
effects within the default TALYS computation, Eq. (127) Koning et al. (2023),
we have used finally a normalization factor of the deuteron total-reaction
cross section, of the form:

$\displaystyle 1-\frac{\sigma_{BU}+\sigma_{DR}}{\sigma_{R}}\>$ (2)

for the final assessment of the PE+CN cross section. The energy dependence of
this factor is shown in Fig. 2(c,f) for deuteron interaction with 92,100Mo
target nuclei, at once with the fractions of the DI cross section and its BU
and DR components to $\sigma_{R}$. One may note a steep increase with energy
of PE+CN fraction, while the BU increase is much lower than that of
${\sigma_{R}}$. Next, PE+CN fraction reaches its maximum at deuteron energies
of 15–20 MeV, and continues with a slow decrease due to the continuous BU
increase with the incident energy.

Actually, the weight of PE+CN versus DI fractions for an isotopic chain is
triggered by the increase of the BU mechanism importance with increase of the
target–nucleus mass number. Overall, the DI and statistical processes
fractions vary around half of $\sigma_{R}$ Šimečková et al. (2018); Avrigeanu
et al. (2014, 2016); Šimečková et al. (2021) along the actual incident–energy
range, pointing out the quite important DI role.

###  II.4 Statistical emission

The statistical PE+CN mechanisms, which complete the deuteron interaction
analysis along an enlarged nuclear-interaction time scale, become important
with the increase of the incident energy above the Coulomb barrier. The
corresponding reaction cross sections have been calculated using TALYS-1.96
code Koning et al. (2023), taking into account also the above–discussed BU
approach as well as the stripping and pick–up mechanisms through the
normalization factor of the OMP total–reaction cross section. Another
particular issue of the present calculations is the use of the same model
parameters to account for different reaction mechanisms, as the same OMP
parameters for calculation of the distorted waves in the ingoing/outgoing DR
channels, the PE transition rates, and the transmission coefficients of
various CN channels.

The following input options of the TALYS code were used in the current work:
(a) the OMPs of Koning-Delaroche Koning and Delaroche (2003), Daehnick et al.
Daehnick et al. (1980), Becchetti–Greenlees Becchetti and Greenlees (1969),
and Avrigeanu et al. Avrigeanu et al. (2014) for neutrons and protons,
deuterons, tritons, and $\alpha$-particles, respectively, (b) the model for
breakup reactions including the BF enhancement Avrigeanu et al. (2022);
Avrigeanu and Avrigeanu (2017), (c) the back-shifted Fermi gas formula for the
nuclear level density (NLD), and (d) the PE exciton model with analytical
transition rates with energy–dependent matrix element, and spin distribution
based on particle–hole state densities. Furthermore, likewise to the analysis
of 87Ym,g activation by deuterons incident on natZr Šimečková et al. (2021),
better account of the measured ground and isomeric state excitation functions
of 91Nb, 93Mo, and 93,94,96,97Tc residual nuclei has been obtained within
actual state-of-art TALYS calculations by amending the spin distribution cut-
off parameter by a factor of 0.25.

Next to the above–mentioned sharing of around half of the deuteron
total–reaction cross section by the PE+CN mechanisms (Fig. 2), the weight of
every reaction mechanism is concerned in the following analysis of the
available data for deuteron–induced reactions on 92,94,95,96,97,98,100,natMo
at energies up to 50 MeV.

Figure 9: (Color online) Comparison of NPI Šimečková et al. (2024) (solid
circles) and previous Řanda and Svoboda (1976) measurements, TENDL–2021
evaluation Koning et al. (2019) (short dashed curves), and presently
calculated (thick solid curves) cross sections of (a) natMo$(d,n)^{101}$Tc,
and (b) 100Mo$(d,n)^{101}$Tc+ (see text), along with BF enhancement (dashed),
$(d,n)$ stripping DR (dash-dotted), and PE+CN components (dash-dot-dotted),
and contribution of 101Mo decay (dotted) to cumulative population of 101Tc
(thin curves + cross)

##  III Results and Discussion

The excitation functions of residual nuclei from deuterons interaction with
natMo are compared in Figs. 9–23 with the available data corresponding also to
irradiation of all Mo stable isotopes Zerkin and Pritychenko (2018), the
similar TENDL–2021 evaluation Koning et al. (2019), and the results of
calculations using FRESCO Thompson (1988) and TALYS Koning et al. (2023)
codes. A particular attention is given, beyond the more recent data Tárkányi
et al. (2012); Elbinawi et al. (2022); Lebeda and Fikrle (2010); Tárkányi et
al. (2011); Chodash et al. (2011), to new measured excitation functions at NPI
CAS in Řež Šimečková et al. (2024) for the activation of 97Nb, 98Nbm, 97Tcm,
and 101Tc residual nuclei.

The higher number of Mo stable isotopes, i.e. 92Mo (14.7%), 94Mo (9.2%), 95Mo
(15.9%), 96Mo (16.7%), 97Mo (9,6%), 98Mo (24.2%) and 100Mo (9.7%), made
necessary the analysis of their detailed contributions to the activation of a
certain residual nucleus. The involved reaction mechanisms are particularly
illustrated in order to compare their strength. While some contributions are
not shown for all Mo stable isotopes in Figs. 9–23, they were all considered
within the cross-section calculation for the natural Mo target.

The activation of a certain residual nucleus is presented following four
reaction sequences: natMo$(d,xn)^{93-101}$Tc (Figs. 9–15),
natMo$(d,xnp)^{90-101}$Mo (Figs. 16–19), natMo$(d,xn2p)^{90-98}$Nb (Figs.
20–22), and natMo$(d,xn3p)^{88,89}$Zr (Fig. 23). The following discussion
concerns firstly the heavier residual nuclei since fewer stable isotopes of Mo
contribute to their population, while more isotopes, processes, and emitted
particles are involved going towards the lighter products.

###  III.1 natMo$(d,xn)^{93-101}$Tc reactions

####  III.1.1 natMo$(d,n)^{101}$Tc

The analysis of 101Tc residual nucleus activation by deuterons incident on
natMo concerns only the deuteron interaction with the neutron-richest stable
isotope 100Mo. Moreover, 101Tc excitation function has been for the first time
reported Šimečková et al. (2024) for a natural molybdenum target [Fig. 9(a)],
in addition to the previously measured 100Mo$(d,n)^{101}$Tc activation cross
sections Řanda and Svoboda (1976) [Fig. 9(b)].

In fact, there are two ways of 101Tc residual nucleus population, i.e. via
$(d,n)$ reaction and $\beta^{-}$ decay of 101Mo ($T_{1/2}$=14.61 min) which is
activated through natMo$(d,p)$ reaction (Sec. III.2.1). The NPI–reported 101Tc
activation cross sections Šimečková et al. (2024) have been corrected for the
101Mo decay contribution, while the same correction was noticed also by Randa
et al. within their reported data for the activation of 100Mo isotope.
Moreover, amending Randa et al. data by 100Mo natural abundance, it results a
good agreement of the two data sets below the incident energy of 10 MeV.
However, the maximum of the wholly resulting excitation function in Fig. 9(a)
is maybe followed by a too sharp decrease at the higher incident energies of
the NPI measurement Šimečková et al. (2024).

The calculated cross sections for 100Mo$(d,n)^{101}$Tc reaction have proved a
significant DR stripping $(d,n)$ contribution only for incident energies above
20 MeV, becoming larger than the statistical PE+CN from $\sim$30 MeV [Fig.
9(b)]. At the same time the inelastic breakup enhancement through $(p,\gamma)$
reaction remains much lower in the whole energy range. Overall, it results a
notable underestimation of the measured cross–section maximum Řanda and
Svoboda (1976), at the energies where PE+CN component is prevailing. A rather
similar trend has the TENDL evaluation Koning et al. (2019), particularly at
the energies where the DR weight is larger.

On the other hand, the addition of the 101Mo decay has led for the cumulative
calculated cross sections to an improved account of the reported
100Mo$(d,n)^{101}$Tc excitation–function maximum Řanda and Svoboda (1976). Its
further decrease is however less quick, as it is that of the cumulative
TENDL-2021 evaluation in Fig. 9(b), too.

Nevertheless, the present approach has provided the rather good agreement of
the newly measured natMo$(d,n)^{101}$Tc cross sections shown in Fig. 9(a).
This suitable description stands also as a proof of the appropriate correction
for the removal of the 101Mo decay contribution. The apparent underestimation
of both data sets by the TENDL evaluation points out the effects of neglecting
especially the stripping $(d,n)$ contribution which is larger than TENDL-2021
data above 15 MeV [Fig. 9(b)].

Figure 10: (Color online) As Fig. 9 but for 99Tcm activation Tárkányi et al.
(2012); Elbinawi et al. (2022); Zerkin and Pritychenko (2018); Lebeda and
Fikrle (2010); Tárkányi et al. (2011); Šimečková et al. (2024); Řanda and
Svoboda (1976); Zarubin et al. (1978) and (a) natMo$(d,xn)^{99}$Tcm, (b)
98Mo$(d,n)^{99}$Tcm, and (c) 100Mo$(d,3n)^{99}$Tcm reaction cross sections,
with (a) contributions of $(d,n)$ and $(d,3n)$ reactions (dash-dotted and
dashed, respectively), and (c) an arrow at threshold energy (see text) Figure
11: (Color online) As Fig. 9 but for 97Tcm activation Šimečková et al. (2024)
and (a) natMo$(d,xn)^{97}$Tcm, (b) 96Mo$(d,n)^{97}$Tcm, (c)
97Mo$(d,2n)^{97}$Tcm, (d) 98Mo$(d,3n)^{97}$Tcm, and (e) 100Mo$(d,5n)^{97}$Tcm
reaction cross sections, with (a) contributions of $(d,n)$, $(d,2n)$,
$(d,3n)$, and $(d,5n)$ reactions (dash-dot-dotted, dash-dotted, dashed, and
thin solid curves, respectively)

####  III.1.2 natMo$(d,xn)^{99}$Tcm

The natMo$(d,xn)^{99}$Tcm activation cross sections measured most recently at
NPI Šimečková et al. (2024) are in the good agreement with the recent data
Tárkányi et al. (2012); Elbinawi et al. (2022); Lebeda and Fikrle (2010) shown
in Fig. 10(a). It should be noted again that the population of 99Tcm is also
cumulative, including the $\beta^{-}$ decay of 99Mo ($T_{1/2}$=65.9 h)
activated through 98Mo$(d,p)$ reaction (Sec. III.2). The appropriate
correction has been carried out within the NPI–measured values Šimečková et
al. (2024), as well as reported by Lebeda et al. Lebeda and Fikrle (2010),
Elbinawi et al. Elbinawi et al. (2022), and Tárkányi et al. Tárkányi et al.
(2012) on both natMo and 100Mo Tárkányi et al. (2011). The same correction was
noticed by Randa et al. Řanda and Svoboda (1976) for 98Mo$(d,n)^{99}$Tcm
reaction, but not by Zarubin et al. Zarubin et al. (1978) for a similar
measurement [Fig. 10(b)].

The calculated results of this work for the natMo$(d,xn)^{99}$Tcm activation
are in a rather good agreement with all data available until an incident
energy of $\sim$20 MeV [Fig. 10(a)]. More important within this energy range
is firstly the $(d,n)$ reaction on 98Mo nucleus which, however, becomes half
of order of magnitude lower than that of $(d,3n)$ reaction at 20 MeV. The
statistical PE+CN component is the major one for the former reaction, below
$\sim$30 MeV, while then this role is taken by the stripping DR [Fig. 10(b)].
It is not the same case of the latter reaction, where BF contribution
increases significantly at higher energies but yet below the PE+CN one shown
in Fig. 10(c).

Thus, it has been of interest to understand a sizable underestimation of
98Mo$(d,n)^{99}$Tcm data of Zarubin et al. Zarubin et al. (1978) at the same
time with a suitable account of the similar data of Randa et al. Řanda and
Svoboda (1976) in Fig. 10(b). Addition of the above–mentioned decay of 99Mo
residual nucleus, in a similar way to 100Mo$(d,p)^{101}$Tc reaction analysis,
has led anyhow to a cumulative excitation function in agreement with the
former data, too.

However, a suitable account of the measured 100Mo$(d,3n)^{99}$Tcm excitation
function Tárkányi et al. (2011) is found only until $\sim$30 MeV, the arrow in
Fig. 10(c) pointing out the threshold of this reaction. Moreover, an
overestimation is then apparent by even the statistical PE+CN component alone.
The BF enhancement being already comparable with the experimental data, its
strong importance becomes obvious for the third–chance particle emission
channel, in comparison to $(p,\gamma)$ BF added to $(d,n)$ one–particle
emission. Overall, the model calculations lead to better data account versus
TENDL evaluation while a particular extension of the measurements to incident
energies over 30 MeV is highly requested.

####  III.1.3 natMo$(d,xn)^{97}$Tcm

The measured natMo$(d,xn)^{97}$Tcm excitation function has recently been
reported for the first time Šimečková et al. (2024) while no measurement
exists for 96,97,98,100Mo isotopes involved in this respect. Its account by
the present calculations is related firstly to results for the $(d,n)$ and
$(d,2n)$ reactions on 96Mo and 97Mo isotopes, respectively [Fig. 11(a)]. The
$(d,3n)$ reaction channel for 98Mo target nucleus becomes also significant
close to the incident energy of 20 MeV, while the $(d,5n)$ reaction on 100Mo
is relevant for 97Tcm activation only above 50 MeV.

A routine comment may concern the PE+CN major contribution to the population
of 97Tcm. However, the $(d,n)$ stripping component is shown in Fig. 11(b) to
be even more important at incident energies over $\sim$25 MeV. These DR
results are, at their turn, exceeded at the low energies $\leq$9 MeV by the BF
contribution through the $(p,\gamma)$ reaction even though followed by a fast
decrease.

On the other hand, a notable BF enhancement corresponds to the $(p,n)$,
$(p,2n)$, and $(p,4n)$ reactions induced by the breakup–protons on the heavier
isotopes 97,98,100Mo, respectively, with additional contributions to $(d,2n)$,
$(d,3n)$, and $(d,5n)$ reactions on the same nuclei [Fig. 11(c-e)].
Nevertheless, the neglected additions of BF and especially DR processes might
contribute to the apparent underestimation of natMo$(d,xn)^{97}$Tcm excitation
function by TENDL-2021 in Fig. 11(a).

Figure 12: (Color online) As Fig. 9 but for (a-e) 96Tc, (f-j) 96Tcg, and (k-o)
96Tcm activation Tárkányi et al. (2012); Elbinawi et al. (2022); Zerkin and
Pritychenko (2018); Lebeda and Fikrle (2010); Šimečková et al. (2024); Řanda
and Svoboda (1976); Wenrong et al. (1998); Sheng et al. (1991), with (a,f,k)
contributions of $(d,n)$, $(d,2n)$, $(d,3n)$, and $(d,4n)$ reactions (dash-
dot-dotted, dash-dotted, dashed, and thin solid curves, respectively)

####  III.1.4 natMo$(d,xn)^{96}$Tcg+m,g,m

The model calculations describe well the recent data Šimečková et al. (2024)
as well as previous measurements of 96Tcg+m,g,m excitation functions Tárkányi
et al. (2012); Elbinawi et al. (2022); Zerkin and Pritychenko (2018); Lebeda
and Fikrle (2010); Řanda and Svoboda (1976); Wenrong et al. (1998); Sheng et
al. (1991) in Fig. 12(a,b,f,k). The contributions of specific outgoing
channels and/or Mo isotopes are shown in Fig. 12(a,f,k), the major role for
96Tcg+m,g,m activation changing from $(d,2n)$ reaction, for incident energies
$\leq$24 MeV, to $(d,3n)$ and, finally, $(d,4n)$ reactions, with the incident
energy increase.

Concerning the involved reaction mechanisms, PE+CN plays an important role
except the $(d,n)$ reaction [Fig. 12(b,g,l)]. In a similar way to the previous
analysis of 97Tcm activation, there is a strong competition of the DR
stripping and PE+CN mechanisms beyond, e.g. 10 MeV. The former becomes
dominant at higher energies. The BF enhancement, due to the $(p,\gamma)$
reaction induced by breakup protons, also exceeds the stripping contribution
at low incident energies, although it decreases faster.

Moreover, there is a sound increase, by about two order of magnitudes, of the
BF contributions through $(p,n)$ and $(p,2n)$ reactions [Fig. 12(c,d)]. They
become comparable with the statistical PE+CN at energies around 50 MeV. The
$(p,3n)$ BF contribution to the $(d,4n)$ forth–chance particle emission is
strong, too [Fig. 12(e,j,o)], but yet lower than $(p,n)$ and $(p,2n)$
reactions. Nevertheless, the lack of data related to specific Mo isotopes
beyond the only one set corresponding to 95Mo$(d,n)^{96}$Tc reaction Řanda and
Svoboda (1976) restrains further comments on the theoretical approach.

Figure 13: (Color online) As Fig. 12 but for (a-e) 95Tc, (f-j) 95Tcg, and
(k-o) 95Tcm activation Tárkányi et al. (2012); Elbinawi et al. (2022); Zerkin
and Pritychenko (2018); Lebeda and Fikrle (2010); Šimečková et al. (2024);
Řanda and Svoboda (1976); Wenrong et al. (1998); Sheng et al. (1991);
Aleksandrov et al. (1991) (see text)

####  III.1.5 natMo$(d,xn)^{95}$Tcg+m,g,m

The 95Tcg+m,m activation cross sections include significant contributions of
94,95,96,97Mo isotopes, through reactions from $(d,n)$ to $(d,4n)$
respectively. The weight of the BU, DR, PE, and CN mechanisms, shown for each
of these reactions in Fig. 13(b-e,g-j,l-o), may prove an appropriate account
and validation of the present analysis for these reactions.

However, similarly to the 96Tcg+m,g,m activation, very scarce related data of
specific Mo isotopes exist only for 95Tcg,m populated through $(d,n)$ reaction
Řanda and Svoboda (1976); Aleksandrov et al. (1991). The present model
analysis describes the measured excitation function for the latter state but
overestimate the former [Fig. 13(g,l)]. At the same time, amending
94Mo$(d,n)^{95}$Tcg activation cross sections Aleksandrov et al. (1991) by
natural abundance of 94Mo isotope, a discrepancy between them and
natMo$(d,xn)^{95}$Tcg data systematics becomes apparent in Fig. 13(f).

Again, the PE+CN dominant role within 95Tcg+m,g,m population at lower energies
is visible at incident energies above 20–30 MeV [Fig. 13(c-e,h-j,m-o)]. It is
yet close to the inelastic breakup enhancement for $(d,xn)$ reactions, with
$x$=2–4. The competition between the inelastic breakup contribution, through
the $(p,\gamma)$ reaction, and the DR stripping into the $(d,n)$ outgoing
channel is also obvious in Fig. 13(b,g,l). The former exceeds the latter one
at low incident energies, with an excitation function maximum higher by an
order of magnitude at $\sim$8 MeV. Then, a faster decrease is leading to the
opposite case around 50 MeV. So, at the same energy, the DR contribution is
however well below the PE+CN one.

Once more, the need to enlarge the data systematics related to Mo stable
isotopes activation, particularly at higher energies, should be pointed out.

Figure 14: (Color online) As Fig. 12 but for (a-d) 94Tc, (e-h) 94Tcg, and
(i-l) 94Tcm activation Tárkányi et al. (2012); Zerkin and Pritychenko (2018);
Lebeda and Fikrle (2010); Šimečková et al. (2024); Řanda and Svoboda (1976);
Aleksandrov et al. (1991), with (a,e,i) contributions of $(d,2n)$, $(d,3n)$,
and $(d,4n)$ reactions (dash-dotted, dashed, and thin solid curves,
respectively).  Figure 15: (Color online) As Fig. 14 but for (a-d) 93Tc, (e-h)
93Tcg, and (i-l) 93Tcm activation Tárkányi et al. (2012); Elbinawi et al.
(2022); Zerkin and Pritychenko (2018); Lebeda and Fikrle (2010); Šimečková et
al. (2024); Řanda and Svoboda (1976), with (a,e,i) contributions of $(d,n)$,
$(d,3n)$, and $(d,4n)$ reactions (dash-dotted, dashed, and thin solid curves,
respectively)

####  III.1.6 natMo$(d,xn)^{94}$Tcg+m,g,m

The actual model analysis shows a very good agreement with the measured
excitation function for 94Tcm activation [Fig. 14(i)]. However, the 94Tcg
activation data are well described just above the threshold as well as at
incident energies above 20 MeV, while there is an overestimation between 10–20
MeV in Fig. 14(e).

As already noticed above, scarce measurements for activation of specific Mo
isotopes consist of two earlier data sets corresponding in Fig. 14(f,j) to
94Mo(d,2n)94Tcg,m reactions Řanda and Svoboda (1976); Aleksandrov et al.
(1991). Unfortunately, they were carried out only at the lower incident
energies $\leq$12 MeV. The present model calculations describe the latter
Řanda and Svoboda (1976) but slightly overestimate the former Aleksandrov et
al. (1991).

It is thus proved that similar overestimation of the 94Tcg activation is due
to the $(d,2n)$ reaction on 94Mo, despite the lowest natural abundance of this
isotope. One may further note the statistical nature of the related difference
between experimental and calculated results, the only additional BF
contribution through the $(p,n)$ reaction being lower by roughly one order of
magnitude. Certainly, any further measurements of 94Tc activation on specific
Mo isotopes as well as measured excitation functions of
natMo$(d,xn)^{94}$Tcg+m,g over 20 MeV incident energy would be most helpful
for detailed analysis of these discrepancies.

####  III.1.7 natMo$(d,xn)^{93}$Tcg+m,g,m

The model calculations describe the excitation functions of 93Tcg+m,g,m
activation by deuterons on natural Mo, as well as the data corresponding to
94Mo$(d,n)^{93}$Tcm reaction Řanda and Svoboda (1976) in Fig. 15(j).

There is however an overestimation of the measured 92Mo$(d,n)^{93}$Tcg+m,g
excitation functions Řanda and Svoboda (1976) in Fig. 15(b,f) below an
incident energy of 12 MeV. Moreover, amending the activation cross sections of
the 92Mo$(d,n)$ reaction Řanda and Svoboda (1976) by the natural abundance of
92Mo, the corresponding derived data in Fig. 15(a,e) are lower, too, than
existing systematics for natural Mo target.

It should be noted also in this case the BF enhancement of the $(d,n)$,
$(d,3n)$, and $(d,4n)$ cross sections through the $(p,\gamma)$, $(p,2n)$, and
$(p,3n)$ reactions, respectively, induced by the breakup protons. However, its
addition to the statistical PE+CN contributions in Fig. 15(b-d,f-h,j-l) is
important only at incident energies higher than 20–30 MeV. At the same time,
the sizable maximum of $(p,\gamma)$ excitation function exceeds the $(d,n)$
stripping DR at $\sim$10 MeV. Nevertheless, its further quick decrease makes
the DR component to have the same role in the $(d,n)$ reaction [Fig.
15(b,f,j)] as the BF one in the $(d,xn)$ reactions, with x$\geq$2 [Fig.
15(c,d,g,h,k,l)].

Figure 16: (Color online) As Fig. 9 but for 101Mo activation cross sections
Zerkin and Pritychenko (2018); Lebeda and Fikrle (2010); Šimečková et al.
(2024); Řanda and Svoboda (1977) of (a) natMo$(d,p)^{101}$Mo, and (b)
100Mo$(d,p)^{101}$Mo reactions (see text)

###  III.2 natMo$(d,xnp)^{101-90}$Mo reactions

####  III.2.1 natMo$(d,p)^{101}$Mo

Similarly to the case of 101Tc residual nucleus, the activation of 101Mo
follows the deuteron interaction with only the neutron–richest 100Mo stable
isotope. The model calculations, taking into account the BU, DR, and
statistical PE+CN mechanisms, describe rather well the two experimental
excitation functions Lebeda and Fikrle (2010); Šimečková et al. (2024) shown
in Fig. 16(a). There are also measured activation cross sections corresponding
to 100Mo$(d,p)^{101}$Mo reaction Řanda and Svoboda (1977), slightly
overestimated in Fig. 16(b). Amending these cross sections by the natural
abundance of 100Mo isotope, it was obtained a derived data set also lower than
both newer measurements in the former figure.

The stripping $(d,p)$ process provides now a much strong contribution to 101Mo
activation comparing with $(d,n)$ one shown in Fig. 9(b) for 101Tc activation.
Actually, the description of natMo$(d,p)^{101}$Mo excitation function, with
contributions only from a single Mo isotope, is relevant for the importance of
the stripping $(d,p)$ mechanism. This proof is just in line with the previous
analyses of the experimental $(d,p)$ excitation functions which can not be
described as long as the substantial DR stripping contribution is neglected
Kreisel et al. (2019); Šimečková et al. (2018); Avrigeanu et al. (2020, 2014,
2016); Šimečková et al. (2021); Avrigeanu et al. (2013). Moreover, the
apparent underestimation by TENDL evaluation of both nat,100Mo$(d,p)^{101}$Mo
reactions (Fig. 16) follows entirely the lack of taking into consideration the
DR stripping process.

####  III.2.2 natMo$(d,xnp)^{99}$Mo

The analysis of 99Mo activation by deuterons interaction with natural Mo and
its stable isotopes 98,100Mo could take advantage of the existing systematics
for Mo target Tárkányi et al. (2012); Elbinawi et al. (2022); Zerkin and
Pritychenko (2018); Lebeda and Fikrle (2010); Chodash et al. (2011); Šimečková
et al. (2024); Wenrong et al. (1998) shown in Fig. 17(a) as well as the
measured excitation functions for 98Mo Zarubin et al. (1978); Řanda and
Svoboda (1977) and 100Mo Tárkányi et al. (2011); Sonck et al. (1999) target
nuclei, respectively [Fig. 17(b,c)]. In fact, it involves two direct reactions
of stripping 98Mo$(d,p)^{99}$Mo and pick-up 100Mo$(d,t)^{99}$Mo, along with
the breakup and PE+CN statistical emission. Their weight is however quite
distinct for each of the two isotopes and even within different energy ranges,
so that their specific discussion is required.

Figure 17: (Color online) As Fig. 16 but for 99Mo activation cross sections
Tárkányi et al. (2012); Elbinawi et al. (2022); Zerkin and Pritychenko (2018);
Lebeda and Fikrle (2010); Tárkányi et al. (2011); Chodash et al. (2011);
Šimečková et al. (2024); Zarubin et al. (1978); Wenrong et al. (1998); Řanda
and Svoboda (1977); Sonck et al. (1999) of (a) natMo$(d,xnp)^{99}$Mo, (b)
98Mo$(d,p)^{99}$Mo, and (c) 100Mo$(d,2np)^{99}$Mo reaction cross sections,
with (a) contributions of $(d,p)$ and $(d,2np)$ reactions (dash-dotted and
dashed, respectively)

Thus, the DR stripping mechanism prevails over PE+CN in the case of
98Mo$(d,p)^{99}$Mo excitation function above the incident energy of 15 MeV,
while at lower energies they are close to each other. The measured
98Mo$(d,p)^{99}$Mo data Zarubin et al. (1978); Řanda and Svoboda (1977) are
thus described rather well [Fig. 17(b)], while the BF enhancement through
breakup–neutron induced reaction 98Mo$(n,\gamma)^{99}$Mo is essentially
negligible. Unfortunately, lack of data at energies above 15 MeV makes not
possible a more detailed analysis.

Comparatively, the BF contribution through $(n,2n)$ and $(p,d)$ reactions is
shown in Fig. 17(c) to be strong for 100Mo$(d,2np)^{99}$Mo reaction. It is
crossing the pick-up $(d,t)$ excitation function at $\sim$20 MeV, becoming
higher by one order of magnitude at $\sim$30 MeV. However, it should be
pointed out this pick-up reaction as the only contribution to 99Mo activation
by deuterons on 100Mo at the incident energies $\leq$ 14 MeV. Nevertheless, it
is by an order of magnitude lower than the $(d,p)$ stripping reaction on 98Mo,
and thus not visible in the case of 99Mo activation by deuterons on the
natural Mo target.

Finally, the sum of BF, DR, and PE+CN contributions overestimates the
dispersed 100Mo$(d,2np)^{99}$Mo activation data Tárkányi et al. (2012); Sonck
et al. (1999). Consequently, a similar overestimation exists above 30 MeV for
the natMo$(d,p)^{99}$Mo excitation function [Fig. 17(a)]. On the other hand,
the suitable account of this excitation function up to $\sim$20 MeV does
validate the $(d,p)$ stripping modeling. New measurement at higher energies
may show if there is a major question of the actual analysis in this respect.

Figure 18: (Color online) As Fig. 16 but for 93Mom activation Tárkányi et al.
(2012); Šimečková et al. (2024) and (a) natMo$(d,xnp)^{93}$Mom, (b)
92Mo$(d,p)^{93}$Mom, (c) 94Mo$(d,2np)^{93}$Mom, and (d) 95Mo$(d,3np)^{93}$Mom
reaction cross sections, with (a) contributions of $(d,p)$, $(d,2np)$, and
$(d,3np)$ reactions (dash-dotted, dashed, and thin curves, respectively)
Figure 19: (Color online) As Fig. 17 but for 90Mo activation Tárkányi et al.
(2012), with contributions of the $(d,3np)$ and $(d,5np)$ reactions (dashed
and thin solid curves, respectively), as well as (a,b) 90Tc decay (dotted) to
cumulative population (thin curves + cross) of 90Mo

####  III.2.3 natMo$(d,xnp)^{93}$Mom

The analysis for activation of the high–spin $21{{}^{+}}$/2 isomeric state of
93Mo, at 2425.9 keV excitation energy, takes advantage of a close agreement
[Fig. 18(a)] between the NPI recent measurement Šimečková et al. (2024) and
the data obtained by Tárkányi et al. Tárkányi et al. (2012) within their
latest irradiation in 2007, during fifteen years (1994–2007) studies at
different accelerators. In fact, a large spread between these results and the
earlier ones (1995) Tárkányi et al. (2012) has been just at the energies of
the latest measurement Šimečková et al. (2024), while more approaching data
were found at higher energies. Otherwise, a model analysis is restrained by
the lack of any measurement of this activation within deuteron–induced
reactions on either 92Mo, 94Mo, or 95Mo isotopes that may have major related
yields.

Furthermore, a complementary modeling should take into consideration the DR
mechanism for the striping 92Mo$(d,p)$ as well as pick-up 94Mo$(d,t)$
reactions, in addition to also more complex BF enhancements and, finally, the
statistical PE+CN emission. However, there is no measured angular distribution
corresponding to this 93Mo isomeric state either in $(d,p)$ stripping, or in
$(d,t)$ pick-up reactions, in order to extract the corresponding spectroscopic
factors of the stripped/picked neutron needed for the calculations of DR
corresponding yield. Moreover, the calculation results for the total stripping
and pick-up cross sections, shown in Fig. 2(b), do not include excited states
of 93Mo which may populate 93Mom through their decay. Therefore, no DR
component has been possible to be added to the BF+PE+CN calculated cross
sections in Fig. 18(b,c). Consequently, an underestimated excitation function
could be expected at low incident energies in the absence of both stripping
and pick-up contributions.

At the same time it should be noted that the model results shown in Fig. 18
have been obtained using an additional factor of 0.25 for the NLD spin cut-off
parameter of the residual nucleus 93Mo. Comparing with the analysis of 87Yg,m
activated by deuteron interaction with natZr target Šimečková et al. (2021),
there is no measurement of 93Mog excitation function to confirm this spin cut-
off adjustment on the basis of the corresponding $g$/$m$ ratio. This
adjustment could be the reason of the apparent differences between the present
and TENDL-2021 predictions in Fig. 18, too.

Nevertheless, one may note that the large amount of measured isomeric cross
sections for the 93Nb$(d,2n)^{93}$Mom Avrigeanu et al. (2013) and
94Mo$(n,2n)^{93}$Mom Reimer et al. (2005) reactions was already well described
using the same breakup approach and no spin cut-off adjustment but the
particle–hole state density (PSD) Avrigeanu and Avrigeanu (1998); Harangozo et
al. (1998) within the geometry-dependent hybrid PE model Blann and Vonach
(1983). This PSD formula has included the PE spin distribution that was early
discussed by Feshbach et al. Feshbach et al. (1980) and further detailed by Fu
Fu (1986). These results are in line with the more recent conclusion that
reduced values of the spin cut-off parameter, obtained from isomeric
cross–section analysis, were artificial and resulted from the improper use of
the CN spin distribution also for the PE spin distribution Fotiades et al.
(2009).

####  III.2.4 natMo$(d,xnp)^{90}$Mo

The present analysis describes the data of Tárkányi et al. Tárkányi et al.
(2012) in Fig. 19(a). While only the 92Mo target nucleus [Fig. 19(b)] plays a
role in this respect, versus 94Mo isotope [Fig. 19(c)], a contribution due to
the decay of 90Tc residual nucleus ($T_{1/2}$=50.7 s) may also be noted. It
follows the $(d,4n)$ reaction on 92Mo, being however lower by at least two
orders of magnitude than 90Mo activation data and the corresponding cumulative
excitation function.

Moreover, there are no measurements of the 90Mo activation by deuterons
incident on the distinct 92,94Mo isotopes. Thus, the analysis corresponding to
the natural Mo is the only way for validation of the contributions from BF and
PE+CN mechanisms, the latter being shown in Fig. 19(b,c) to be obviously the
dominant one.

The TENDL-2021 predictions in Fig. 19(a,b) are also cumulative, including the
90Tc decay. However, the underestimation by the TENDL-evaluation at higher
energies may be just due to the yet neglected contribution of the inelastic
breakup enhancement.

###  III.3 natMo$(d,xn2p)^{98-89}$Nb reactions

Figure 20: (Color online) As Fig. 18 but for (a)-(c) 98Nbm, (d-g) 97Nb, and
(h-l) 96Nb activation Tárkányi et al. (2011); Šimečková et al. (2024); Zarubin
et al. (1978); Řanda and Svoboda (1977), with contributions of (a) the
$(d,2p)$ and $(d,2n2p)$, (d) the $(d,2p)$, $(d,n2p)$, and $(d,3n2p)$, (h) the
$(d,2p)$, $(d,n2p)$, $(d,2n2p)$, and $(d,4n2p)$ reactions (dash-dot-dotted,
dash-dotted, dashed, and thin solid curves, respectively).

####  III.3.1 natMo$(d,xn2p)^{98}$Nbm

A rather equally–well account of the excitation functions measured either
recently Šimečková et al. (2024) for natMo$(d,xn2p)^{98}$Nbm reaction [Fig.
20(a)] or formerly for 100Mo$(d,2n2p)^{98}$Nbm reaction by Tárkányi et al.
Tárkányi et al. (2011) [Fig. 20(c)] has been shown by the actual analysis.
Actually, only the two heaviest Mo isotopes may contribute to the activation
of this isomeric state, through 98Mo$(d,2p)^{98}$Nbm and
100Mo$(d,2n2p)^{98}$Nbm reactions. The latter reaction channel corresponds,
especially at the energies lower than the $(d,2n2p)$ reaction threshold, also
to the $(d,\alpha)$ reaction with a maximum around the incident energy of 16
MeV.

Because of the significantly higher effective threshold of the $(d,2p)$
reaction on 98Mo [Fig. 20(b)], the 98Nbm activation for the natural Mo target
comes fully from this $(d,\alpha)$ reaction. The obvious correspondence
between the two above–mentioned data sets is emphasized within the actual
BF+PE+CN analysis except the less usual steep increase of the latter
excitation function at incident energies over $\sim$45 MeV. However, this
model analysis has been proved difficult due to the lack of any spectroscopic
information concerning the pick-up 100Mo$(d,\alpha)^{98}$Nbm reaction.
Therefore, beyond the dominant PE+CN statistical mechanisms, only the
inelastic breakup has been involved in this particular case. Its
correspondence to a breakup–neutron induced reaction $(n,2np)$ led to
cross–section contribution at incident energies only above 35 MeV and too low
to account for the above–mentioned increase in Fig. 20(c).

On the other hand, the comparison of the $(d,2p)$ and $(d,2n2p)$ interaction
processes points out the dominant inelastic breakup enhancement brought for
the former reaction by breakup neutrons through 98Mo$(n,p)^{98}$Nbm reaction
[Fig. 20(b)]. It exceeds by three times the PE+CN contribution for the
$(d,2p)$ reaction on same target nucleus. This proton–emission enhancement is
essential for the analysis of deuteron radiation–damage estimation in the
structural materials, due to the additional hydrogen accumulation known as the
”gas bubble accumulation”.

####  III.3.2 natMo$(d,xn2p)^{97}$Nb

Similarly to the above, there is a suitable account of 97Nb activation data
first–time recently reported Šimečková et al. (2024) for deuterons incident on
natural Mo [Fig. 20(d)] as well as of the earlier measurement Tárkányi et al.
(2011) of the $(d,3n2p)$ reaction on 100Mo [Fig. 20(g)]. There is also a
correspondence in the last case with a first excitation–function maximum
around the incident energy of 23 MeV due to a $(d,n\alpha)$ reaction component
with an obviously related low–energy side of the data for the natural Mo.

There is also a straightforward strong increase of the BF enhancement, being
by far the dominant mechanism for 97Mo$(d,2p)^{97}$Nb reaction [Fig. 20(e)].
It overcomes the PE+CN contribution in 98Mo$(d,n2p)^{97}$Nb process too, for
the incident energies $\geq$45 MeV shown in Fig. 20(f).

In fact, the availability of spectroscopic data related to the
98Mo$(d,^{3}He)^{97}$Nb pick-up reaction has been followed by a DR
cross–section assessment. It has been thus proved the dominant role of this
mechanism at incident energies $\leq$25 MeV, while it is still higher than the
BF component up to $\sim$37 MeV [Fig. 20(f)].

####  III.3.3 natMo$(d,xn2p)^{96}$Nb

The analysis of the 96Nb activation is of prime interest for the present
analysis due to measured excitation function by Tárkányi et al. Tárkányi et
al. (2011), with the lower incident energies $\leq$20 MeV corresponding fully
to the $(d,\alpha)$ reaction on the most abundant isotope 98Mo [Fig. 20(h,k)].
There are also concerned contributions from 96,97,98,100Mo isotopes Zarubin et
al. (1978); Řanda and Svoboda (1977), through various BF, DR, PE, and CN
mechanisms [Fig. 20(h-l)].

The model calculations describe much better the more recently measured
natMo$(d,xn2p)^{96}$Nb data Tárkányi et al. (2011) than the earlier
98Mo$(d,2n2p)^{96}$Nb excitation function Zarubin et al. (1978); Řanda and
Svoboda (1977) at the energies of the only $(d,\alpha)$ reaction. There are
thus validated the major CN+PE statistical emission as well as the smaller but
yet notable DR component in Fig. 20(k).

Nevertheless, a main point is still the BF mechanism, with the $(n,p)$
enhancement bringing the dominant contribution to the 96Mo$(d,2p)^{96}$Nb
activation. It completes thus the 98,97Nb activation in Fig. 20(b,e,i). The
basic role of inelastic breakup and pick-up reaction contributions is
confirmed also by the data underestimation of TENDL-2021 predictions Koning et
al. (2019) which are yet not including the account of these processes.

Figure 21: (Color online) As Fig. 19 but for (a-e) 95Nb, (f-j) 95Nbg, and
(k-o) 95Nbm activation Tárkányi et al. (2012); Zerkin and Pritychenko (2018);
Lebeda and Fikrle (2010); Šimečková et al. (2024); Řanda and Svoboda (1977);
Anders and Meinke (1960), with (a,f,k) contributions of $(d,2p)$, $(d,n2p)$,
$(d,2n2p)$, $(d,3n2p)$, and $(d,5n2p)$ reactions (short-dotted, dash-dot-
dotted, dash-dotted, dashed, and thin solid curves, respectively), and (a,f)
contribution of the 95Zr decay (short-dash-dotted) to cumulative population
(thin curves + cross) of 95Nb and 95Nbg, respectively

####  III.3.4 natMo$(d,xn2p)^{95}$Nb

The actual BF+DR+PE+CN model results for 95Nb and 95Nbm activation, except for
the points around the deuteron energy of $\sim$7 MeV in Fig. 21(a,k), are
validated by recently measured cross sections through the $(d,xn2p)$ reactions
on natural Mo Šimečková et al. (2024), with well increased accuracy vs
previous data Tárkányi et al. (2012); Lebeda and Fikrle (2010).

The same is true for the data reported more recently by Tárkányi et al.
Tárkányi et al. (2012), including an additional excitation function of
natMo$(d,xn2p)^{95}$Nbg activation [Fig. 21(f)]. A weak contribution of 95Zr
decay ($T_{1/2}$=65.9 h), visible only in Fig. 21(a), has been considered too,
with no real difference for the 95Nbg+m,g cumulative activation. There are
three points of this analysis which demands additional comments.

First, the most abundant isotope 98Mo brings the dominant contribution to
95Nbg+m,g,m activation by $(d,3n2p)$ reaction on natural Mo above the deuteron
energy of $\sim$16 MeV. A first maximum of the $(d,2n2p)$ reaction, at lower
energies, corresponds in fact to the one–particle emission $(d,\alpha)$
reaction on the nearly least abundant isotope 97Mo [Fig. 21(d,i,n)]. Then, the
two–particle emission $(d,n\alpha)$ sort of $(d,3n2p)$ reaction on 98Mo has an
excitation–function maximum at 22-25 MeV [Fig. 21(e,j,o)]. At the same time
there are earlier data sets Řanda and Svoboda (1977); Anders and Meinke (1960)
of $(d,\alpha)$ reaction on 97Mo which are largely overestimated. However, it
should be noted that the closely related recent data for natural Mo are well
accounted for.

Second, it could be again pointed out the important contributions of BF
enhancement to $(d,2p)$ reaction cross sections, for the 95Mo target nucleus
[Fig. 21(b,j,l)], similarly to the above–discussed 96,97,98Nb activation.
Thus, the BF component exceeds the PE+CN statistical emission at the deuteron
energies above 35 MeV. The latter becomes however dominant with the increase
of additional neutron emission in $(d,xn2p)$ reactions with $x$$\geq$2\. This
is true also for deuterons on 100Mo, with results shown only in Fig. 21(a,f,k)
but similar mechanism contributions as for 98Mo isotope.

Third, cross–section increases due to the $(d,^{3}He)$ and $(d,\alpha)$ pick-
up DRs are noteworthy particularly for the former. This one is even larger
than CN+PE component, at the lower energies $\leq$13 MeV, and BF below 30–34
MeV [Fig. 21(c,h,m)]. However, the TENDL-2021 evaluation Koning et al. (2019)
has followed the low–energy side of the earlier measured excitation function
Lebeda and Fikrle (2010); Řanda and Svoboda (1977); Anders and Meinke (1960)
in Fig. 21(a,d,n). Nevertheless, its underestimation of the
natMo$(d,xn2p)^{95}$Nbg,m reaction cross sections could be related to the
missing of BF and DR pick-up contributions.

Figure 22: (Color online) As Fig. 21 but for (a-e) 92Nbm, (f-j) 91Nbm, and
(k-n) 90Nb activation Tárkányi et al. (2012); Zerkin and Pritychenko (2018);
Lebeda and Fikrle (2010); Šimečková et al. (2024); Řanda and Svoboda (1977),
with (a,f,k) contributions of $(d,2p)$, $(d,n2p)$, $(d,2n2p)$, $(d,3n2p)$,
$(d,4n2p)$, and $(d,5n2p)$ reactions (short-dotted, short-dotted, dash-dot-
dotted, dash-dotted, dashed, and thin-solid curves, respectively), and (k)
90Mo decay (short-dash-dotted)

####  III.3.5 natMo$(d,xn2p)^{92}$Nbm

The natMo$(d,xn2p)^{92}$Nbm activation cross sections, measured recently at
NPI with higher accuracy Šimečková et al. (2024), as well as previous similar
data Tárkányi et al. (2012); Lebeda and Fikrle (2010) are rather well
described by the actual model analysis except the lowest deuteron energies
below 4 MeV [Fig. 22(a)]. A similar agreement exists for an earlier
measurement Řanda and Svoboda (1977) at lower energies of the $(d,\alpha)$
reaction in Fig. 22(c), as the first maximum of the 94Mo$(d,2n2p)$ excitation
function, apart from data at $\sim$12 MeV. Nevertheless, there is a valuable
account of the whole natMo systematics at the same energy [Fig. 22(a)], with
the largest contribution of 94Mo isotope in spite of its smallest natural
abundance. The next important and main contribution up to the deuteron energy
of 20 MeV, belongs to 95Mo isotope. It corresponds also to a first maximum of
the two–particle $(d,n\alpha)$ side of the $(d,3n2p)$ reaction channel [Fig.
22(d)].

At the same time, the isotope 92Mo has the main role within 92Nbm activation
above 20 MeV, through the $(d,2p)$ reaction. The corresponding cross sections
are again much increased by the BF enhancement due to the 92Mo$(n,p)$ reaction
induced by breakup neutrons [Fig. 22(b)]. This BF component becomes even
higher than the CN+PE statistical processes at incident energies above 35 MeV.
It is however overridden, up to the same energy, by the pick-up $(d,\alpha)$
reaction on 94Mo nucleus [Fig. 22(c)].

####  III.3.6 natMo$(d,xn2p)^{91}$Nbm

Despite an increased uncertainty above its effective threshold, the available
data of 91Nbm activation Tárkányi et al. (2012); Šimečková et al. (2024) are
rather well described taking into account the contributions of four isotopes
and three reaction mechanisms [Fig. 22(f-j)]. The dominant one in the whole
energy range comes from the semi–magic nucleus 92Mo due to a BF enhancement
close to main CN+PE statistical emission in Fig. 22(g). It is exceeded only at
energies below 20 MeV by the first maximum of the $(d,3n2p)$ excitation
function for the target nucleus 94Mo, corresponding to the sequential emission
of only a neutron and an $\alpha$-particle through actually a $(d,n\alpha)$
reaction (at variance with the sequential five–nucleon emission).

Unfortunately, there is no measurement of this activation on any of the Mo
stable isotopes.

Figure 23: (Color online) As Fig. 22(k-m) but for (a-c) 89Zr, (d-f) 89Zrm, and
(g-i) 88Zr activation Tárkányi et al. (2012); Zerkin and Pritychenko (2018);
Lebeda and Fikrle (2010); Šimečková et al. (2024), with contributions of
(a,d,g) the 94,92Mo target isotopes (dashed and thin-solid curves,
respectively), as well as (a,d) the 89Mo and 89Nb decay (dotted and short-
dotted curves respectively), and (g) the 88Nb decay (short-dotted curve)

####  III.3.7 natMo$(d,xn2p)^{90}$Nb

Overall, the results of this analysis for 90Nb activation are in rather good
agreement with the data measured for natural Mo and 92Mo targets Tárkányi et
al. (2012); Lebeda and Fikrle (2010); Šimečková et al. (2024); Řanda and
Svoboda (1977). A note should concern the main contribution which is by far
given by the two maxima of 92Mo$(d,2n2p)^{90}$Nb excitation–function [Fig.
22(l)]. The former, corresponding to the $\alpha$ emission channel, is also
additionally increased by the $(d,\alpha)$ pick-up DR, while the BF has the
same effect for the latter one, following the sequential nucleons evaporation.
Actually, the CN+PE statistical emission mainly contributes to 90Nb activation
while the breakup and pick-up processes have also a significant addition of
$\sim$15%.

The calculated results for 90Nb activation above 28 MeV had to include a
steady contribution due to the decay of 90Tc ($T_{1/2}$=50.7 s) and
consequently 90Mo ($T_{1/2}$=5.56 h), leading finally to a calculated
cumulative 90Nb excitation function. This addition, involved similarly for the
comparison with the TENDL-2021 evaluation, has been mostly useful to account
for the data at deuteron energies above 20 MeV.

Figure 24: (Color online) Comparison of measured Tárkányi et al. (2012);
Elbinawi et al. (2022); Zerkin and Pritychenko (2018); Lebeda and Fikrle
(2010); Tárkányi et al. (2011); Šimečková et al. (2024); Řanda and Svoboda
(1976); Zarubin et al. (1978); Wenrong et al. (1998); Sheng et al. (1991);
Aleksandrov et al. (1991), TENDL-2021 Koning et al. (2019) evaluated (dotted
curves), and calculated (solid curves) cross sections for
natMo$(d,xn)^{93-101}$Tc excitation functions

###  III.4 natMo$(d,xn3p)^{89,88}$Zr reactions

####  III.4.1 natMo$(d,xn3p)^{89}$Zr

The measured cross sections Tárkányi et al. (2012); Lebeda and Fikrle (2010);
Šimečková et al. (2024) for the activation of the residual nucleus 89Zr [Fig.
23(a)] and 89Zrm state [Fig. 23(d)] are cumulative, i.e. they include the
decays of 89Tc ($T_{1/2}$=12.9 s) and 89Mo ($T_{1/2}$=2.11 min), and 89Nb
($T_{1/2}$=2.03 h) Brookhaven National Laboratory (2024). Consequently, the
present model analysis has taken into account, in addition to the 92,94Mo
isotopes contributions, these decays to 89Zr residual nucleus of 89Mo,
including the 89Tc decay, as well as the decay of 89Nb. Thus, the experimental
data are rather well described in Fig. 23(a,d) while it should be pointed out
the strongest contributions of 89Nb residual–nucleus decay versus the
deuteron–induced reactions on 92,94Mo isotopes. The same addition has been
considered for the comparison with the TENDL-2021 evaluations.

Concerning the reaction mechanisms contributing to 89Zr residual–nucleus
activation, the dominant PE+CN statistical emission is additionally increased
at higher energies by the BF enhancement [Fig. 23(b,c)]. Particularly, this BF
contribution is relevant to 92Mo$(d,2n3p)^{89}$Zr reaction. Actually, the
first maximum of the 89Zr excitation function for both 92,natMo targets
corresponds to $\alpha$-particle emission within $(d,p\alpha)$ reaction
(Q=1.491 MeV), so important for the gas accumulation assessment.

####  III.4.2 natMo$(d,xn3p)^{88}$Zr

The model analysis for the activation of 88Zr residual nucleus involves fewer
issues and thus may have a more reliable outcome. Thus, it concerns
contributions due to deuterons interaction mainly with 92,94Mo isotopes, as
well as following 88Nb decay ($T_{1/2}$=7.78 min) Brookhaven National
Laboratory (2024) taken into account for the present analysis results as well
as well as in the case of the TENDL-2021 evaluations. A further contribution
of 88Mo decay Brookhaven National Laboratory (2024) to 88Zr activation cross
sections is not significant in the energy range of this work.

The modeling results describe satisfactory the measured cumulative 88Zr
excitation function Tárkányi et al. (2012) shown in Fig. 23(g). The largest
contribution is related to the PE+CN mechanisms [Fig. 23(h,i)], and also to
the 92Mo isotope. An yet visible addition is due to the inelastic breakup
enhancement in the case of 92Mo$(d,3n3p)$ reaction. The so weak contribution
of 88Nb decay to 88Zr activation in Fig. 23(g), in addition to 92,94Mo
isotopes components, has pointed out the statistical emission model validation
on this experimental basis.

Figure 25: (Color online) As Fig. 24 but for natMo$(d,xnp)^{90-101}$Mo,
natMo$(d,xn2p)^{90-98m}$Nb, and natMo$(d,xn3p)^{88-89}$Zr reactions, with
(d,h,i,m-o) 90Mo, 95Nbg+m,g, 90Nb, 88Zr, and 89Zr cumulative activation
including the decay of 90Tc, 95Zr, 90Mo, 88Nb, 89Nb (dashed) and 89Mo (dash-
dotted), respectively (see text)

##  IV Conclusions

A consistent analysis has concerned all reaction mechanisms involved in the
complex deuteron interaction process, e.g. elastic scattering, breakup,
stripping, pick-up, pre-equilibrium and compound nucleus, including the
contributions of specific Mo isotopes too. The brief overview of the
activation data for the deuteron–induced reactions on natMo, the related
TENDL–2021 evaluation Koning et al. (2019), and model calculations carried out
within present work is shown in Figs. 24 and 25. It is thus underlined
comparatively the neutron emission natMo$(d,xn)$ and the neutron emission
possibly accompanied by H and He isotopes emission natMo$(d,xnyp)$, if
emerging nucleon clusters are given due consideration. They are related to the
high requests of the radioactivity risks and radiation damages estimation,
critical benchmark for selecting and validating the best structural materials
and a number of key technologies. Thus, accurate estimation of $(d,xn)$
activation is essential for shielding design of nuclear installations while H,
T, and He gas emission leading to ”gas bubbles accumulation”, are of high
interest for damage studies of the structural materials. Overall, the due
account of most experimental data has thoroughly validated the present
theoretical framework and highlighted some prevalent features.

Hence strong neutron emission goes through $(d,2n)$ and $(d,3n)$ reaction
channels (Figs. 10–15), while the charged–particle emission (protons, tritons,
3,4He) is almost an order of magnitude less (Fig. 25). There is only one
different case in this respect, of the strong protons emission within
100Mo$(d,p)^{101}$Mo reaction. Then, higher protons and even tritons emission
leads to 99Mo residual nucleus, with a maximum of $\sim$65 mb for the
corresponding excitation function below 10 MeV [Fig. 25(b)]. Increased
emission of neutrons, protons, 3He and $\alpha$-particles concern the
activation of Nb and Zr isotopes, whose estimation is important for both
theory validation and structural materials comparative analysis.

At the same time, this comparison has emphasized the weak points and
consequently the need for modeling/evaluation upgrade. Most of them were
related to overlooking the deuteron inelastic–breakup enhancement and
appropriate treatment of stripping and pick-up processes shown in Sec. III.
Nevertheless, there may still be present particular discrepancies that are
related to the complexity of the interaction process, not entirely accounted
for in routine evaluation/theoretical analyzes. New data as well as
complementary measurements of $(d,px)$ and $(n,x)$ as well as $(d,nx)$ and
$(p,x)$ reaction cross sections for isotopes of the natural element, presently
very scarce, are essential for validation of the theoretical frame associated
to the deuteron breakup process. The final improvement of evaluation
predictions becomes thus feasible for target nuclei and incident energies
where data are missing, so important for advanced engineering design projects.

## Acknowledgments

This work has been partly supported by OP RDE, MEYS, Czech Republic under the
project SPIRAL2-CZ, CZ.02.1.01/0.0/0.016_013/0001679 and by The Executive Unit
for the Financing of Higher Education, Research, Development and Innovation
(UEFISCDI) under the project No. PN-III-ID-PCE-2021-0642), and carried out
within the framework of the EUROfusion Consortium, funded by the European
Union via the Euratom Research and Training Programme (Grant Agreement No
101052200 — EUROfusion). Views and opinions expressed are however those of the
author(s) only and do not necessarily reflect those of the European Union or
the European Commission. Neither the European Union nor the European
Commission can be held responsible for them.

##  Appendix A Spectroscopic factors

###  A.1 Table content

The spectroscopic factors obtained through the DWBA analysis of the
experimental outgoing–particle angular distributions (Figs. 3–8) are given
hereafter. The data in the following tables concern the excitation energies
$E$ of the residual–nucleus states (assumed by authors of the
angular–distribution measurements), their spin $J$ and parity $pi$, the
transferred angular momentum $L$, and the corresponding spectroscopic factor
$S$ obtained in the present work by analysis of the experimental
outgoing–particle angular distributions shown in Figs. 3–8. The spectroscopic
factors that have been considered for calculation of the rest of stripping and
pickup reactions were taken from the given references in the text. On the
other hand, the same deuteron OMP Daehnick et al. (1980) as well as the
nucleon Koning and Delaroche (2003), triton Becchetti and Greenlees (1969),
and $\alpha$-particle Avrigeanu et al. (2014) OMPs have been involved within
DWBA calculations as within BU+PE+CN models, for a consistent model analysis.

####  A.1.1 92Mo$(d,n)^{93}$Tc [Fig. 3(top)]

    ----------------------------
    E(MeV)  JΨ  pi Ψ LΨ   S
    ----------------------------
    0.00Ψ  4.5Ψ  1  Ψ4Ψ  0.40
    0.39Ψ  0.5Ψ -1  Ψ1Ψ  0.14
    1.50Ψ  1.5Ψ -1  Ψ1Ψ  0.045
    1.78Ψ  0.5Ψ -1  Ψ1Ψ  0.075
    2.59Ψ  2.5Ψ  1  Ψ2Ψ  0.035
    3.17Ψ  2.5Ψ  1   2Ψ  0.035
    3.36Ψ  2.5Ψ  1Ψ  2Ψ  0.115
    3.90Ψ  0.5Ψ  1Ψ  0Ψ  0.032
    4.11Ψ  0.5Ψ  1Ψ  0Ψ  0.3
    4.76Ψ  2.5Ψ  1Ψ  2Ψ  0.21
    4.90Ψ  1.5Ψ  1Ψ  2Ψ  0.125
    5.01Ψ  2.5Ψ  1Ψ  2Ψ  0.15
    5.18Ψ  2.5Ψ  1Ψ  2Ψ  0.23
    5.30Ψ  2.5Ψ  1Ψ  2Ψ  0.26
    5.44Ψ  0.5Ψ  1Ψ  0   0.3
    5.62Ψ  0.5Ψ  1Ψ  0   0.195
    5.68Ψ  0.5Ψ  1Ψ  0   0.15
    5.78Ψ  2.5Ψ  1Ψ  2   0.22
    5.93Ψ  0.5Ψ  1Ψ  0   0.27
    -----------------------------

####  A.1.2 94Mo$(d,n)^{95}$Tc [Fig. 3(bottom)]

    ----------------------------
    E(MeV)Ψ  JΨ   piΨ LΨ   S
    ----------------------------
    0.000Ψ  4.5Ψ  1Ψ  4Ψ  0.38
    0.040Ψ  0.5Ψ -1Ψ  1Ψ  0.235
    0.064Ψ  1.5Ψ -1Ψ  1Ψ  0.105
    1.084Ψ  2.5Ψ  1Ψ  2Ψ  0.026
    1.276Ψ  1.5Ψ  1Ψ  2Ψ  0.08
    1.281Ψ  3.5Ψ -1Ψ  3Ψ  0.06
    1.450Ψ  2.5Ψ  1Ψ  2Ψ  0.065
    1.639Ψ  1.5Ψ -1Ψ  1Ψ  0.025
    1.750Ψ  1.5Ψ -1Ψ  1Ψ  0.035
    2.320Ψ  2.5Ψ  1Ψ  2Ψ  0.035
    2.550Ψ  0.5Ψ -1Ψ  1Ψ  0.06
    2.830Ψ  2.5Ψ  1Ψ  2Ψ  0.145
    3.210Ψ  0.5Ψ  1Ψ  0Ψ  0.045
    3.490Ψ  2.5Ψ  1Ψ  2Ψ  0.035
    3.630Ψ  2.5Ψ  1Ψ  2Ψ  0.04
    3.810Ψ  0.5Ψ  1Ψ  0Ψ  0.035
    3.920Ψ  0.5Ψ  1Ψ  0Ψ  0.02
    3.990Ψ  1.5Ψ  1Ψ  2Ψ  0.031
    4.400Ψ  1.5Ψ  1Ψ  2Ψ  0.023
    4.500Ψ  1.5Ψ  1Ψ  2Ψ  0.033
    1.660Ψ  0.5Ψ  1Ψ  0Ψ  0.04
    -----------------------------

####  A.1.3 95Mo$(^{3}He,d)^{96}$Tc [Fig. 4(top)]

    -------------------------------
    E(MeV)Ψ  JΨ   piΨ  LΨ    S
    -------------------------------
    0.000Ψ   5Ψ   1Ψ   4Ψ   0.600ΨΨ ΨΨ
    0.046Ψ   5Ψ   1Ψ   4Ψ   0.780ΨΨ
    0.121Ψ   2Ψ  -1Ψ   1Ψ   0.275ΨΨ
    0.177Ψ   4Ψ  -1Ψ   1Ψ   0.150ΨΨ
    0.227Ψ   3Ψ  -1Ψ   1Ψ   0.130ΨΨ
    0.228Ψ   4Ψ   1Ψ   4Ψ   0.292ΨΨ
    0.316Ψ   3Ψ  -1Ψ   1Ψ   0.210ΨΨ
    0.319Ψ   6Ψ   1Ψ   4Ψ   0.300ΨΨ ΨΨ
    0.352Ψ   3Ψ  -1Ψ   1Ψ   0.215ΨΨ
    0.506Ψ   5Ψ   1Ψ   4Ψ   0.235ΨΨ
    0.568Ψ   3Ψ  -1Ψ   1Ψ   0.090ΨΨ
    0.623Ψ   4Ψ   1Ψ   4Ψ   0.201ΨΨ
    0.750Ψ   3Ψ  -1Ψ   1Ψ   0.085ΨΨ
    0.801Ψ   4Ψ  -1Ψ   1Ψ   0.100ΨΨ
    0.815Ψ   4Ψ   1Ψ   4Ψ   0.201ΨΨ
    0.867Ψ   4Ψ  -1Ψ   1Ψ   0.090ΨΨ
    0.933Ψ   3Ψ   1Ψ   2Ψ   0.120ΨΨ
    0.980Ψ   5Ψ   1Ψ   2Ψ   0.077ΨΨ
    1.066Ψ   2Ψ   1Ψ   2Ψ   0.130ΨΨ
    1.158Ψ   4Ψ  -1Ψ   1Ψ   0.083ΨΨ
    1.255Ψ   4Ψ  -1Ψ   1Ψ   0.095ΨΨ
    1.314Ψ   5Ψ   1Ψ   2Ψ   0.115ΨΨ
    1.338Ψ   5Ψ   1Ψ   2Ψ   0.110ΨΨ
    1.408Ψ   4Ψ  -1Ψ   1Ψ   0.125ΨΨ
    1.482Ψ   4Ψ  -1Ψ   1Ψ   0.095ΨΨ
    1.536Ψ   5Ψ   1Ψ   2Ψ   0.090ΨΨ
    1.597Ψ   4Ψ  -1Ψ   1Ψ   0.120ΨΨ
    1.653Ψ   4Ψ  -1Ψ   1Ψ   0.040ΨΨ
    1.670Ψ   5Ψ   1Ψ   2Ψ   0.080ΨΨ
    1.772Ψ   5Ψ   1Ψ   2Ψ   0.115ΨΨ
    1.825Ψ   5Ψ   1Ψ   2Ψ   0.085ΨΨ
    1.884Ψ   5Ψ   1Ψ   2Ψ   0.080ΨΨ
    1.940Ψ   5Ψ   1Ψ   2Ψ   0.074ΨΨ
    ---------------------------------

####  A.1.4 96Mo$(^{3}He,d)^{97}$Tc (Fig. 4)

    ------------------------------
    E(MeV)Ψ JΨ    piΨ  LΨ   S
    ------------------------------
    0.000Ψ  4.5Ψ   1Ψ  4Ψ  0.600ΨΨ
    0.096Ψ  0.5Ψ  -1Ψ  1Ψ  0.350ΨΨ
    0.326Ψ  2.5Ψ   1Ψ  2Ψ  0.080ΨΨ
    0.576Ψ  1.5Ψ  -1Ψ  1Ψ  0.180ΨΨ
    0.655Ψ  2.5Ψ  -1Ψ  3Ψ  0.110ΨΨ
    0.783Ψ  2.5Ψ   1Ψ  2Ψ  0.170ΨΨ
    0.947Ψ  1.5Ψ  -1Ψ  1Ψ  0.145ΨΨ
    1.053Ψ  1.5Ψ  -1Ψ  1Ψ  0.065ΨΨ
    1.316Ψ  4.5Ψ   1Ψ  4Ψ  0.180ΨΨ
    1.374Ψ  2.5Ψ   1Ψ  2Ψ  0.065ΨΨ
    1.537Ψ  0.5Ψ   1Ψ  0Ψ  0.065ΨΨ
    1.599Ψ  1.5Ψ   1Ψ  2Ψ  0.120ΨΨ
    1.649Ψ  2.5Ψ   1Ψ  2Ψ  0.100ΨΨ
    1.712Ψ  0.5Ψ   1Ψ  0Ψ  0.110ΨΨ
    1.847Ψ  0.5Ψ   1Ψ  0Ψ  0.160ΨΨ
    1.951Ψ  1.5Ψ   1Ψ  2Ψ  0.200ΨΨ
    2.013Ψ  2.5Ψ   1Ψ  2Ψ  0.085ΨΨ
    2.111Ψ  1.5Ψ   1Ψ  2Ψ  0.085ΨΨ
    2.151Ψ  0.5Ψ   1Ψ  0Ψ  0.075ΨΨ
    2.264Ψ  0.5Ψ   1Ψ  0Ψ  0.140ΨΨ
    2.307Ψ  2.5Ψ   1Ψ  2Ψ  0.090ΨΨ
    2.653Ψ  0.5Ψ   1Ψ  0Ψ  0.170ΨΨ
    2.713Ψ  1.5Ψ   1Ψ  2Ψ  0.120ΨΨ
    2.783Ψ  2.5Ψ   1Ψ  2Ψ  0.070ΨΨ
    2.878Ψ  1.5    1Ψ  2Ψ  0.085ΨΨ
    2.908Ψ  2.5Ψ   1Ψ  2Ψ  0.100ΨΨ
    3.018Ψ  1.5Ψ   1Ψ  2Ψ  0.100ΨΨ
    3.060Ψ  2.5Ψ   1Ψ  2Ψ  0.110ΨΨ
    3.145Ψ  0.5Ψ   1Ψ  0Ψ  0.160ΨΨ
    3.214Ψ  0.5Ψ   1Ψ  0Ψ  0.105ΨΨ
    ------------------------------

####  A.1.5 98Mo$(^{3}He,d)^{99}$Tc (Fig. 5)

    ------------------------------
    E(MeV)Ψ JΨ    piΨ  LΨ   S
    ------------------------------
    0.000Ψ  4.5Ψ   1Ψ  4Ψ  0.460ΨΨ
    0.142Ψ  0.5Ψ  -1Ψ  1Ψ  0.215ΨΨ
    0.181Ψ  2.5Ψ   1Ψ  2Ψ  0.040ΨΨ
    0.509Ψ  1.5Ψ  -1Ψ  1Ψ  0.130ΨΨ
    0.625Ψ  3.5Ψ   1Ψ  4   0.160ΨΨ
    0.672Ψ  2.5Ψ  -1Ψ  3Ψ  0.090ΨΨ
    0.720Ψ  3.5Ψ   1Ψ  4Ψ  0.107ΨΨ
    0.762   2.5Ψ   1Ψ  2Ψ  0.110ΨΨ
    0.919Ψ  0.5Ψ   1Ψ  0Ψ  0.045ΨΨ
    1.020Ψ  1.5Ψ   1Ψ  2Ψ  0.055ΨΨ
    1.203Ψ  0.5Ψ  -1Ψ  1Ψ  0.050ΨΨ
    1.321Ψ  0.5Ψ  -1Ψ  1Ψ  0.070ΨΨ
    1.435Ψ  1.5Ψ   1Ψ  2Ψ  0.080ΨΨ
    1.505Ψ  1.5Ψ   1Ψ  2Ψ  0.053ΨΨ
    1.560Ψ  0.5Ψ   1Ψ  0Ψ  0.130ΨΨ
    1.679Ψ  1.5Ψ   1Ψ  2Ψ  0.080ΨΨ
    1.760Ψ  1.5Ψ   1Ψ  2Ψ  0.062ΨΨ
    1.803Ψ  0.5Ψ   1Ψ  0Ψ  0.115ΨΨ
    1.825Ψ  1.5Ψ   1Ψ  2Ψ  0.100ΨΨ
    1.911Ψ  1.5Ψ   1Ψ  2Ψ  0.065ΨΨ
    1.982Ψ  1.5Ψ   1Ψ  2Ψ  0.110ΨΨ
    2.000Ψ  1.5Ψ   1Ψ  2Ψ  0.105ΨΨ
    2.111Ψ  2.5Ψ   1Ψ  2Ψ  0.100ΨΨ
    2.160Ψ  1.5Ψ   1Ψ  2Ψ  0.100ΨΨ
    2.176Ψ  0.5Ψ   1Ψ  0Ψ  0.050ΨΨ
    2.203Ψ  1.5Ψ   1Ψ  2Ψ  0.085ΨΨ
    2.281Ψ  0.5Ψ   1Ψ  0Ψ  0.110ΨΨ
    2.396Ψ  1.5Ψ   1Ψ  2Ψ  0.065ΨΨ
    2.414Ψ  1.5Ψ   1Ψ  2Ψ  0.060ΨΨ
    2.466Ψ  0.5Ψ   1Ψ  0Ψ  0.065ΨΨ
    2.486Ψ  0.5Ψ   1Ψ  0Ψ  0.065ΨΨ
    2.522Ψ  1.5Ψ   1Ψ  2Ψ  0.085ΨΨ
    2.581Ψ  1.5Ψ   1Ψ  2Ψ  0.095ΨΨ
    2.653Ψ  0.5Ψ   1Ψ  0Ψ  0.060ΨΨ
    2.675Ψ  0.5Ψ   1Ψ  0Ψ  0.060ΨΨ
    ------------------------------

####  A.1.6 92Mo$(d,\alpha)^{90}$Nb (Fig. 6)

    ----------------------------------
    E(MeV)Ψ JΨ  piΨ  LΨ     S
    ----------------------------------
    0.000 Ψ  8Ψ  1Ψ  8Ψ    0.6Ψ
    0.129 Ψ  4Ψ -1Ψ  3Ψ    0.75
    0.176*Ψ  7   1Ψ  6+8Ψ  0.8+0.1
    0.286*Ψ  5Ψ  1Ψ  4+6   0.4+0.05Ψ
    0.381 Ψ  1Ψ  1Ψ  0Ψ    0.65
    0.655 Ψ  3Ψ  1Ψ  2Ψ    0.365Ψ
    0.819 Ψ  9Ψ  1Ψ  8Ψ    2.2
    0.823 Ψ  2Ψ -1Ψ  1Ψ    0.48
    0.848 Ψ  2Ψ  1Ψ  2Ψ    0.65Ψ
    0.958 Ψ  4Ψ -1Ψ  3Ψ    0.26Ψ
    1.131 Ψ  5Ψ -1Ψ  5Ψ    0.36Ψ
    1.194 Ψ  2Ψ -1Ψ  1Ψ    0.11Ψ
    1.231*Ψ  4Ψ -1Ψ  3+5Ψ  0.25+0.1
    1.255*Ψ  4Ψ -1Ψ  3+5Ψ  0.15+0.1Ψ
    1.289*Ψ  4Ψ -1Ψ  3+5Ψ  0.08+0.12Ψ
    1.350 Ψ  1Ψ  1Ψ  0Ψ    0.25Ψ
    1.370*Ψ  2Ψ -1Ψ  1+3Ψ  0.36+0.24Ψ
    1.415 Ψ  4Ψ -1Ψ  3Ψ    0.8Ψ
    1.492*Ψ  4Ψ -1Ψ  3+5Ψ  1.2+0.3Ψ
    1.552*Ψ  4Ψ -1Ψ  3+5Ψ  0.7+0.75
    1.647 Ψ  4Ψ -1Ψ  3Ψ    0.4Ψ
    1.691 Ψ  4Ψ -1Ψ  3Ψ    0.35Ψ
    1.776*Ψ  1Ψ  1Ψ  0+2Ψ  0.35+0.1Ψ
    1.842*Ψ  1Ψ  1Ψ  0+2Ψ  0.18+0.2Ψ
    1.873 Ψ  3Ψ -1Ψ  3Ψ    0.32Ψ
    2.000 Ψ  4Ψ -1Ψ  3Ψ    0.38
    2.138 Ψ  1Ψ  1Ψ  0Ψ    0.31
    2.311*Ψ  1Ψ  1Ψ  0+2Ψ  0.18+0.05
    ----------------------------------
    *Two possible L values considered.

####  A.1.7 92Mo$(d,t)^{91}$Mo [Fig. 7(top)]

    -----------------------------
    E(MeV)  JΨ   pi Ψ L Ψ  S
    -----------------------------
    0.000Ψ  4.5Ψ  1Ψ  4Ψ  2.96
    0.652Ψ  0.5Ψ -1Ψ  1Ψ  1.29
    1.155Ψ  1.5Ψ -1Ψ  1Ψ  1.4
    1.364Ψ  2.5Ψ  1Ψ  2Ψ  0.436
    1.533Ψ  2.5Ψ -1Ψ  3Ψ  1.61
    1.904Ψ  4.5Ψ  1Ψ  4Ψ  0.93
    2.085Ψ  1.5Ψ -1Ψ  1Ψ  0.387
    2.241Ψ  2.5Ψ  1Ψ  2Ψ  0.15
    2.299Ψ  1.5Ψ -1Ψ  1Ψ  0.292
    2.462Ψ  2.5Ψ -1Ψ  3Ψ  0.387
    2.547Ψ  2.5Ψ  1Ψ  2Ψ  0.188
    2.727Ψ  2.5Ψ -1Ψ  3Ψ  0.806
    2.824Ψ  4.5Ψ  1Ψ  4Ψ  0.755
    2.898Ψ  1.5Ψ -1Ψ  1Ψ  0.31
    3.188Ψ  1.5Ψ -1Ψ  1Ψ  0.21
    3.330Ψ  1.5Ψ -1Ψ  1Ψ  0.243
    3.455Ψ  1.5Ψ -1Ψ  1Ψ  0.346
    2.302Ψ  4.5Ψ  1Ψ  4Ψ  0.316
    3.351Ψ  2.5Ψ -1Ψ  3Ψ  0.387
    -----------------------------

####  A.1.8 94Mo$(d,t)^{93}$Mo (Fig. 7)

    -----------------------------
    E(MeV)   JΨ  pi Ψ L Ψ  S
    -----------------------------
    0.000Ψ  2.5Ψ  1Ψ  2Ψ  1.35
    0.947Ψ  0.5Ψ  1Ψ  0Ψ  0.43
    1.364Ψ  3.5Ψ  1Ψ  4Ψ  0.6
    2.529Ψ  0.5Ψ -1Ψ  1Ψ  0.69
    2.534Ψ  4.5Ψ  1Ψ  4Ψ  1.7
    3.510Ψ  4.5Ψ  1Ψ  4Ψ  0.78
    3.587Ψ  4.5Ψ  1Ψ  4Ψ  1.2
    3.590Ψ  1.5Ψ -1Ψ  1Ψ  0.387
    3.650Ψ  4.5Ψ  1Ψ  4Ψ  0.83
    3.720Ψ  1.5Ψ -1Ψ  1Ψ  0.4
    4.630Ψ  1.5Ψ -1Ψ  1Ψ  0.4
    4.710Ψ  1.5Ψ -1Ψ  1Ψ  0.265
    4.720Ψ  2.5Ψ -1Ψ  3Ψ  0.65
    4.756Ψ  1.5Ψ -1Ψ  1Ψ  0.2
    4.780Ψ  4.5Ψ  1Ψ  4Ψ  0.43
    5.000Ψ  1.5Ψ -1Ψ  1Ψ  0.4
    5.034Ψ  1.5Ψ -1Ψ  1Ψ  0.43
    5.070Ψ  4.5Ψ  1Ψ  4Ψ  0.5
    5.150Ψ  1.5Ψ -1Ψ  1Ψ  0.32
    ------------------------------

####  A.1.9 98Mo$(d,t)^{97}$Mo (Fig. 7)

    -----------------------------
    E(MeV)  JΨ  pi Ψ L Ψ  S
    -----------------------------
    0.00Ψ  2.5Ψ  1Ψ  2Ψ  1.15
    0.68Ψ  0.5Ψ  1Ψ  0Ψ  0.42
    0.72Ψ  1.5Ψ  1Ψ  2Ψ  0.26
    0.89Ψ  0.5Ψ  1   0Ψ  0.182
    1.12Ψ  2.5Ψ  1Ψ  2Ψ  0.24
    1.28Ψ  2.5Ψ  1Ψ  2Ψ  0.48
    2.39Ψ  0.5Ψ -1Ψ  1Ψ  0.47
    2.52Ψ  4.5Ψ  1Ψ  4Ψ  0.82
    2.83Ψ  0.5Ψ -1Ψ  1Ψ  0.3
    ------------------------------

####  A.1.10 100Mo$(d,t)^{99}$Mo (Fig. 7)

    -----------------------------
    E(MeV)    JΨ  pi Ψ L Ψ  S
    -----------------------------
    0.000Ψ   0.5Ψ  1Ψ  0Ψ  0.45
    0.099Ψ   2.5Ψ  1Ψ  2Ψ  0.44
    0.236Ψ   3.5Ψ  1Ψ  4Ψ  0.87
    0.351Ψ   1.5Ψ  1Ψ  2Ψ  0.07
    0.524Ψ   0.5Ψ  1Ψ  0Ψ  0.155
    0.548Ψ   1.5Ψ  1Ψ  2Ψ  0.65
    0.617Ψ   2.5Ψ  1Ψ  2Ψ  0.55
    0.684Ψ   5.5Ψ -1Ψ  5Ψ  0.76
    0.697Ψ   3.5Ψ  1Ψ  4Ψ  0.33
    0.756Ψ   3.5Ψ -1Ψ  3Ψ  0.43
    0.797Ψ   1.5Ψ  1Ψ  2Ψ  0.29
    0.894Ψ   1.5Ψ  1Ψ  2Ψ  0.23
    0.912Ψ   0.5Ψ  1Ψ  0Ψ  0.31
    0.951Ψ   2.5Ψ  1Ψ  2Ψ  0.43
    1.030Ψ   1.5Ψ -1Ψ  1Ψ  0.17
    1.051Ψ   2.5Ψ -1Ψ  3Ψ  0.23
    1.148Ψ   3.5Ψ -1Ψ  3Ψ  0.14
    1.173Ψ   2.5Ψ  1Ψ  2Ψ  0.22
    1.201Ψ   1.5Ψ  1Ψ  2Ψ  0.21
    1.258Ψ   2.5Ψ  1Ψ  2Ψ  0.12
    1.352Ψ   4.5Ψ  1Ψ  4Ψ  0.31
    1.497Ψ   2.5Ψ  1Ψ  2Ψ  0.255
    1.545Ψ   2.5Ψ  1Ψ  2Ψ  0.3
    1.580Ψ   1.5Ψ  1Ψ  2Ψ  0.21
    1.893Ψ   2.5Ψ -1Ψ  3Ψ  0.305
    1.944Ψ   0.5Ψ  1Ψ  0Ψ  0.195
    2.160Ψ   4.5Ψ  1Ψ  4Ψ  0.925
    2.220Ψ   2.5Ψ -1Ψ  3Ψ  0.81
    2.482Ψ   0.5Ψ  1Ψ  0Ψ  0.15
    2.517Ψ   4.5Ψ  1Ψ  4Ψ  0.9
    ------------------------------

####  A.1.11 96Mo$(d,^{3}He)^{95}$Nb (Fig. 8)

    ------------------------------
    E(MeV)Ψ   JΨ  piΨ  LΨ   S
    ------------------------------
    0.000Ψ   4.5Ψ  1Ψ  4Ψ  2.050ΨΨ
    0.232Ψ   0.5Ψ -1Ψ  1Ψ  1.150ΨΨ
    0.792Ψ   1.5Ψ -1Ψ  1Ψ  0.950ΨΨ
    1.000Ψ   2.5Ψ -1Ψ  3Ψ  1.320ΨΨ
    1.221Ψ   1.5Ψ -1Ψ  1Ψ  1.200ΨΨ
    1.623Ψ   1.5Ψ -1Ψ  1Ψ  0.380ΨΨ
    1.635Ψ   2.5Ψ  1Ψ  2Ψ  0.250ΨΨ
    1.980Ψ   2.5Ψ -1Ψ  3Ψ  0.650ΨΨ
    2.230Ψ   1.5Ψ -1Ψ  1Ψ  0.250ΨΨ
    2.328Ψ   2.5Ψ -1Ψ  3Ψ  0.750ΨΨ
    2.340Ψ   1.5Ψ -1Ψ  1Ψ  0.450ΨΨ
    2.481Ψ   2.5Ψ -1Ψ  3Ψ  1.050ΨΨ
    2.786Ψ   2.5Ψ -1Ψ  3Ψ  1.050ΨΨ
    ------------------------------

####  A.1.12 98Mo$(d,^{3}He)^{97}$Nb (Fig. 8)

    ----------------------------
    E(MeV)   JΨ  pi Ψ L Ψ  S
    ----------------------------
    0.000Ψ   4.5Ψ  1Ψ  4Ψ  2.150ΨΨ
    0.746Ψ   0.5Ψ -1Ψ  1Ψ  1.300ΨΨ
    1.251Ψ   1.5Ψ -1Ψ  1Ψ  1.800ΨΨ
    1.438Ψ   2.5Ψ -1Ψ  3Ψ  2.300ΨΨ
    1.764Ψ   1.5Ψ -1Ψ  1Ψ  0.400ΨΨ
    1.774Ψ   2.5Ψ  1Ψ  2Ψ  0.250ΨΨ
    2.090Ψ   2.5Ψ  1Ψ  2Ψ  0.450ΨΨ
    2.100Ψ   2.5Ψ -1Ψ  3Ψ  1.200ΨΨ
    2.244Ψ   1.5Ψ -1Ψ  1Ψ  0.600ΨΨ
    2.386Ψ   1.5Ψ -1Ψ  1Ψ  0.650ΨΨ
    2.550Ψ   1.5Ψ -1Ψ  1Ψ  0.650ΨΨ
    2.948Ψ   1.5Ψ -1Ψ  1Ψ  0.600ΨΨ
    2.963Ψ   2.5Ψ -1Ψ  3Ψ  0.900ΨΨ
    ----------------------------

## References

  * Bernardi et al. (2022) Bernardi D, Ibarra A, Arbeiter F, Arranz F, Cappelli M, Cara P, et al.  The IFMIF-DONES Project: Design Status and Main Achievements Within the EUROfusion FP8 Work Programme.  Journal of Fusion Energy. 2022;41(2):24.  https://doi.org/10.1007/s10894-022-00337-5.
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