# Compilation of isomeric ratios of light particle induced nuclear reactions

A. Rodrigo  E-mail<EMAIL_ADDRESS>N. Otuka  E-mail:
<EMAIL_ADDRESS>S. Takács  A.J. Koning  Nuclear Data Section, Division of
Physical and Chemical Sciences, Department of Nuclear Sciences and
Applications, International Atomic Energy Agency, A-1400 Wien, Austria
Department of Energy Engineering (Division of Nuclear Engineering),
Universidad Politécnica de Madrid, 28006 Madrid, Spain  Institute for Nuclear
Research (ATOMKI), 4026 Debrecen, Hungary

(12.01.2023)

Experimental isomeric ratios of light (A$\leq$4) particle-induced nuclear
reactions were compiled for the product nuclides having metastable states with
half-lives longer than 0.1 sec. The experimental isomeric ratio data were
taken from the EXFOR library and reviewed. When an experiment reports isomer
production cross sections instead of isomeric ratios, the cross sections taken
from the EXFOR library were converted to the isomeric ratios by us. During
compilation, questionable data (e.g.,preliminary data compiled in EXFOR in
parallel with their final data, sum of isomer production cross sections larger
than the total production cross sections) were excluded. As an application of
the new compilation, goodness-of-fit was studied for the isomeric ratios
predicted by the reaction model code TALYS-1.96.

††journal: Atomic Data and Nuclear Data Tables

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##  1 Introduction

A nucleus on an excited level formed as a reaction product is typically
deexcited to the ground state promptly by a series of gamma-ray emissions.
However, this deexcitation may be delayed due to presence of a long-lived
excitation level. Such an excitation level is known as the metastable state,
whose spin is usually not close to the spin of the ground state and it
prevents immediate deexcitation to a lower level. It may further undergo
deexcitation by gamma-ray emission to a lower level (isomeric transition)
and/or by $\alpha$/$\beta$-ray emission or electron conversion to a
neighboring nuclide. Detection of such radiation allows us to measure the
production cross section of the metastable state. Similarly, we can define the
production cross section of the ground state, which corresponds to
deexcitation of the reaction product decayed into the ground state without
going through any metastable state. If there is only one metastable state, the
total production cross section $\sigma_{t}$ is related with the ground state
production cross section $\sigma_{g}$ and metastable state production cross
section $\sigma_{m}$ by $\sigma_{t}=\sigma_{g}+\sigma_{m}$.

The ratio of production cross sections such as $\sigma_{m}/\sigma_{g}$ or
$\sigma_{m}/\sigma_{t}$ is known as the isomeric ratio. From the view of
theoretical reaction modelling, the isomeric ratio is related with the spin
($J$) dependence of the level density of the intermediate and final product
nuclei. This distribution has been theoretically modelled by
$(2J+1)\exp[-(J+1/2)^{2}/(2\sigma^{2})]$ with the square of the distribution
width $\sigma^{2}$ known as the spin cut-off parameter [1, 2]. Huizenga and
Vandenbosch formulated the relationship between $\sigma$ and the isomeric
ratio [3], and various attempts have been made to parameterize $\sigma$ by
using experimental isomeric ratios. Namely, compilation of experimental
isomeric ratios contributes to better model description of the isomer
production cross sections through adjustment of the spin cut-off parameters to
reproduce the compiled isomeric ratios.

The knowledge of the isomeric ratio is also important for nuclear technology.
For example, the 241Am(n,$\gamma$)242Am isomeric ratio is important from the
view of nuclear waste management. This is because 241Am may be produced in
fission energy systems by successive neutron captures and $\beta^{-}$ decay
starting from 238U, and the long-lived metastable state 242mAm can be further
transmuted into the heavier americium isotopes and finally to 244Cm [4] due to
a large thermal neutron capture cross section of 242mAm [5](1290$\pm$300 b
[6]). The isomeric ratios of low-energy neutron-induced reaction products have
been evaluated and compiled in File 9 of the ENDF-6 format [7], and are
utilized in reactor burn-up calculation. The isomeric ratios for production of
some metastable states such as 99mTc and 186mRe in nuclear reactions are also
important from the view of medical isotope production [8, 9]. Accessibility to
the experimental isomeric ratios is, therefore, important for both research of
nuclear reactions and its application.

When the ground and metastable states are unstable and their activities are
measurable, the isomeric ratio is related with the counts of the ground and
metastable state decays $N_{g}$ and $N_{m}$ by

$\frac{\sigma_{g}}{\sigma_{m}}=\frac{f_{m}}{f_{g}}\left[\frac{N_{g}I_{\gamma
m}\epsilon_{m}}{N_{m}I_{\gamma
g}\epsilon_{g}}-p\frac{\lambda_{g}}{\lambda_{g}-\lambda_{m}}\right]+p\frac{\lambda_{m}}{\lambda_{g}-\lambda_{m}}$
(1)

[10], where $N$, $I_{\gamma}$, $\epsilon$, $p$ and $\lambda$ are the number of
gamma-rays counted, gamma emission probability, gamma-ray detection
efficiency, isomeric transition probability and decay constant, respectively.
The time factor $f$ is defined by $f=[1-\exp(-\lambda t_{i})]\exp(-\lambda
t_{c})[1-\exp(-\lambda t_{m})]/\lambda$ with the irradiation time $t_{i}$,
cooling time $t_{c}$ and measurement time $t_{m}$. This equation does not
require determination of the incident particle flux, which may be a major
source of the uncertainty and error in determination of the production cross
section. Similarly, prediction of the isomeric ratio by a reaction model is
free from the absolute normalization (e.g.,total reaction cross section
constrained by the optical potential). These facts show an advantage to do
comparison between measurements and model predictions for the isomeric ratio
rather than for the isomer production cross sections.

The experimental isomeric ratios of nuclear reaction products have been
compiled in the EXFOR library by the International Network of Nuclear Reaction
Data Centres (NRDC) [11]. The compiled data are included in database systems
and disseminated to the end users by the data centres [12, 13, 14, 15].
However, the isomeric ratios compiled in EXFOR have not been fully utilized
because they are published in various expressions
(e.g.,$\sigma_{m}/\sigma_{t}$, $\sigma_{m}/\sigma_{g}$), and the EXFOR library
compiles these ratios as they are published without unification of the
expression. When an experimentalist reports $\sigma_{g}$ and $\sigma_{m}$
without their ratios, the ratios are not compiled in the EXFOR library, and
this also makes the experimental information on the isomeric ratio less
accessible.

In the past, assignment of the ground and metastable states has not been done
in a consistent manner in EXFOR since assignments may depend on the decay
scheme referred to by the experiment (e.g.,the 69 min state of 110In, which
was known as the ground state in the past but now considered as a metastable
state). However, this inconsistency was analysed and improved by the data
centres in 2010s [16]. Considering these situations of EXFOR, we decided to
compile experimental isomeric ratios which are derived from but are more
accessible than those in the EXFOR library. In the following sections, we
discuss procedure of compilation and its application to benchmark of the
TALYS-1.96 reaction model code [17].

##  2 Procedure

###  2.1 Criteria of data selection

We defined the scope of our compilation by the following criteria:

  * 1.

Experimental isomeric ratios or production cross sections compiled in EXFOR as
of 23 August 2022.

  * 2.

Data not superseded. (i.e.,preliminary data are excluded if their final data
are also in EXFOR.)

  * 3.

Data measured with a monoenergetic photon, neutron, proton, deuteron, triton,
helion, or alpha particle beam.

  * 4.

Data for production of nuclides having ground state and only one metastable
state with its half-life longer than 0.1 sec.

The EXFOR data were extracted not directly from the original EXFOR files but
from the X4Pro database [18].

In the EXFOR library, the quantity of each dataset is expressed by a REACTION
code. For example, the REACTION code (79-AU-197(N,3N)79-AU-195-M,,SIG)
expresses the 197Au(n,3n)195mAu cross section. The two codes 79-AU-195-M and
,SIG express the product nuclide and quantity, respectively. The combinations
of the reaction product and quantity within our scope are summarized in Table
A. Note that the code ELEM/MASS indicates that the atomic and mass numbers of
the reaction product are independent variables of the EXFOR dataset. See
Chapter 6 of EXFOR Formats Manual [19] for more details about the EXFOR
REACTION formalism. The EXFOR library also compiles the ground state
production cross section including partial feeding via isomeric transition
from a metastable production cross section (e.g.,34-SE-73-G,M+,SIG) and the
production cross section including feeding by decay of another nuclide
(e.g.,13-AL-27,CUM,SIG). Such datasets are not for direct use of isomeric
ratio construction and were excluded in the present compilation.

Isomeric ratios of fission products are also excluded for all spontaneous
fission datasets, majority of the neutron-induced fission datasets and some
other fission datasets. This is because they are compiled in EXFOR as fission
product yield ratios FY/RAT rather than the cross section ratios SIG/RAT, and
their REACTION coding rule is slightly different (e.g.,the code indicating
partial feeding M+ is not combined with FY/RAT). The readers are reminded that
compilation of experimental isomeric fission yield ratios has been recently
published by the US National Nuclear Data Center (NNDC) [20]. Sometimes we
found an experiment showing completely different trend from the other
experiments. When appearance of such an outlier was due to a typo in the EXFOR
library, we fixed it. Otherwise, we included such outliers in the present
compilation without exclusion.

We also sometimes meet an experiment reporting $\sigma_{t}$ smaller than
$\sigma_{m}$, and such an experiment was excluded from our compilation unless
it was resolved by communication with the experimentalist. This is often due
to presence of a ground state production cross section without clear
indication of the state in the nuclide symbol in documentation. For example,
we experienced this problem for the cross sections tabulated with not 148gPm
but 148Pm published by Lebeda et al. [21, 22], for which the author kindly
confirmed that they are not the total but the ground state production cross
sections, and we were able to keep them in our compilation. The EXFOR datasets
corrected and excluded in the above-mentioned procedures are summarized in
NRDC technical memos [23, 24]. Another possible reason of the unexpected
relation between $\sigma_{g}$ and $\sigma_{m}$ is due to large uncertainties
in the cross sections (e.g., 85Rb(p,x)84Rb cross sections of Kastleiner et
al.[25], where we see $\sigma_{m}>\sigma_{t}$ at some incident energies though
their error bars overlap.).

E.A. Skakun et al. measured (p,n) and (p,$\gamma$) isomer productions below 10
MeV with the Kharkiv proton linear accelerator and published several times
(e.g.,[26, 27, 28]). Though they are compiled as independent results in EXFOR,
we assumed they are from the same measurements and selected one of them for
compilation as summarized in NRDC technical memo [31]. Unfortunately the
isomeric ratios in its final publication [28] are compiled in EXFOR by
digitization from the figure images and we did not adopt them.

A reference value (e.g.,monitor cross section, gamma emission probability)
adopted by the experimentalist may be different from the currently recommended
value. We did not update the originally published data compiled in EXFOR
during the present compilation except for the proton-induced activation cross
sections published by Levkovskii [29], for which we renormalized the
originally published cross sections and compiled in EXFOR A0511 by
192.8/252$\sim$0.77 where 252 mb is the natMo(p,x)96Tc cross section at 30 MeV
adopted by Levkovskii while 192.8 mb is the value recommended by an IAEA
Coordinated Research Project [30].

###  2.2 Ground and metastable state assignments

The ground and metastable state assignments may depend on the decay data
adopted by the experimentalist. During the comprehensive review and
improvement of isomeric flagging in EXFOR performed in 2010s [32, 16], we
followed the assignment seen in Nuclear Wallet Cards [33].

Some experimentalists do not consider a short-lived metastable state as an
isomer. For example, the first metastable state of 196m1Au (8.1 sec) is
usually not detectable in an activation measurement designed for detection of
196gAu (6.2 d) and 196m2Au (9.6 hr) activities. Consequently, an
experimentalist may report their 196m2Au production cross sections just as
196mAu production cross sections, which may be wrongly entered in EXFOR as
79-AU-196-M,,SIG though this must be 79-AU-196-M2,,SIG. In order to exclude
such a dataset compiled with improper isomeric flagging, the reaction product
code of each EXFOR dataset was checked against NUBASE [34], and the dataset
was excluded when NUBASE defines two or more metastable states or no
metastable state for the product nuclide. Typical examples of such nuclides
are (1) 124m2Sb 20 min states (denoted as 124mSb in the literature(e.g.,[35,
36]) and (2) 30mAl 72.5 sec state, whose production cross sections were
reported in the past (e.g.,[37, 38]) but this state is currently unknown.

###  2.3 Conversion of cross sections to isomeric ratios

After extraction of the EXFOR datasets within our scope and filtered by the
above-mentioned procedures, we converted the extracted data to the isomeric
ratios $\sigma_{m}/\sigma_{t}$. When an experimental work does not provide an
isomeric ratio in EXFOR but provide at least two of $\sigma_{g}$, $\sigma_{m}$
and $\sigma_{t}$ at the same incident energy, we converted them to
$\sigma_{m}/\sigma_{t}$ for compilation. When all these three types of the
cross sections are available, we did not use $\sigma_{g}$. If an experiment
does not provide any pair of the cross sections at the same incident energy,
we simply discarded the experiment.

An experiment may report two or more data points at the same incident energy.
When an average value from several measurements is reported, we adopted it
while discarded the individual results. For example, Meierhofer et al. [39]
reports 6 $\sigma_{t}$ and 12 $\sigma_{m}$ values for the 74Ge(n,$\gamma$)75Ge
reaction at the thermal energy, and one may construct 72
$\sigma_{m}/\sigma_{t}$ values from various combinations of $\sigma_{t}$ and
$\sigma_{m}$. However, they also report the average of the $\sigma_{t}$ and
$\sigma_{m}$ values and we adopted only these averages to obtain a single
$\sigma_{m}/\sigma_{t}$ value from this measurement. When the authors report
only individual results without their averages, we compiled the isomeric
ratios derived from all combinations of the cross sections, and tabulated them
with a flag for caution.

Filatenkov et al. performed systematic measurements of neutron activation
cross sections and documented their results around 2000 [40, 41]. Later the
cross sections were revised with the updated reference data (e.g.,decay data)
and published in 2016 [42]. During our compilation, we found some isomeric
ratios in the two original reports are not seen in the 2016 report even in
revised forms though the corresponding cross sections are there. We adopted
the isomeric ratios derived from the cross sections published in the 2016
report rather than the isomeric ratios published in the original reports.
(c.f. [43, 44]). Similarly, we found that an isomeric ratio derived from the
high energy (above 660 MeV) cross sections measured by A.R.Balabekyan et al.
at JINR (e.g.,[45, 46, 47, 48, 49, 50]) and compiled in an EXFOR entry is
often very close to an isomeric ratio compiled in another EXFOR entry. We
carefully identified such pairs to avoid appearance of the isomeric ratios
from the same experiment twice (c.f. [51]).

###  2.4 Uncertainty

The EXFOR library may provide several types of the uncertainties such as the
total uncertainty (ERR-T), statistical uncertainty (ERR-S), total systematic
uncertainty (ERR-SYS), partial uncertainty (ERR-1, ERR-2 etc.) or uncertainty
without further specification (DATA-ERR). When several of them are in EXFOR,
we always selected the largest one in our tabulation. When an isomeric ratio
was derived from the respective cross sections, we propagated the
uncertainties in the cross sections to the isomeric ratio assuming that the
uncertainties in the cross sections are independent. This may overestimate the
actual uncertainty since a partial uncertainty (e.g.,uncertainty in the
incident particle flux) may be shared in both cross sections and cancelled
when they are converted to the isomeric ratio.

The isomeric ratio plus (minus) its uncertainty in our compilation is
sometimes higher (lower) than 1 (0). There are a few such ratios directly
taken from the original publication (e.g.,, 75As(n,p)75Ge isomeric ratio in
Ref. [52]) but the majority of them are $\sigma_{m}/\sigma_{t}$ values derived
by us. Such values are flagged in the main table for caution.

##  3 Results

Table B summarizes the number of reactions and isomeric ratios for each
projectile. Very few photon-induced reaction isomeric ratios were found for
inclusion in the current compilation. This is because usually photoactivation
isomeric ratio measurements are done with bremsstrahlung photon sources, which
are not monoenergetic and not for our compilation.

It is not an intention of this article to discuss various findings in
individual cases. Nevertheless, we discuss activation measurements of two
reactions just to demonstrate what kind of discussion we can do based on the
new compilation.

###  3.1 93Nb(n,$\alpha$)90Y

Figure 1 shows the 93Nb(n,$\alpha$)90Y isomeric ratios as well as the ground
and metastable state production cross sections [42, 53, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77,
78]. The 3.2 hr metastable state has two intense gamma lines at 203.53 and
479.51 keV [79] and measurement of its production cross section is
straightforward. On the other hand, the 64 hr ground state does not have such
a suitable gamma line, and it makes measurement of the ground state production
cross section difficult. Filatenkov carefully determined the isomeric ratio by
decay-curve analysis for an energetic ($E_{\mathrm{max}}$=2280 keV)
$\beta^{-}$-ray by a HPGe detector considering the fact that there are few
other reaction products and they do not emit $\gamma$-rays at the high energy
region. See Sect. 2.7.2 of Ref. [42] for more details. The isomeric ratios
reported by Filatenkov are lower than the majority of the isomeric ratios
published by others but consistent with the prediction by TALYS. On the other
hand, the TALYS calculation with the same default parameters underestimates
both ground and metastable state production cross sections.

###  3.2 197Au(d,2n)197Hg

Figure 2 shows the 197Au(d,2n)197Hg isomeric ratios as well as the ground and
metastable state production cross sections [80, 81, 82, 83, 84, 85, 86, 87,
88]. Not only the 24 hr metastable state but also the 64 hr ground state have
characteristic gamma-rays, and it is possible to measure the production cross
sections of both states in principle. Similar to the 93Nb(n,$\alpha$)90Y case,
however, the ground state production cross sections are more scattered than
the metastable state production cross sections in the literature. Furthermore,
we see several groups in the energy dependence of the isomeric ratios.

When the half-life of the ground state is longer than the half-life of the
metastable state and the measurement was done after long cooling time allowing
complete decay of the co-produced metastable state to the ground state
(i.e.,$t_{c}\gg 1/\lambda_{m}$), the cross section derived from the
measurement of the ground state activity $\sigma_{c}=N_{g}/(f_{g}I_{\gamma
g}\epsilon_{g}n\phi)$ with the sample areal density $n$ and beam flux $\phi$
is sometimes assumed to be $\sigma_{c}\sim\sigma_{g}+p\sigma_{m}$. This leads
to

$\sigma_{g}\sim\sigma_{c}-p\sigma_{m}$ (2)

for determination of $\sigma_{g}$ from $\sigma_{c}$ and $\sigma_{m}$. Below we
demonstrate that this equation is valid only when $\lambda_{m}\gg\lambda_{g}$
or $\sigma_{m}\ll\sigma_{g}$.

Since $\sigma_{m}=N_{m}/(f_{m}I_{\gamma m}\epsilon_{m}n\phi)$, Eq. (1) can be
rewritten to

$\sigma_{c}=\sigma_{g}+p\left(\frac{f_{m}}{f_{g}}\frac{\lambda_{g}}{\lambda_{g}-\lambda_{m}}-\frac{\lambda_{m}}{\lambda_{g}-\lambda_{m}}\right)\sigma_{m}.$
(3)

If $t_{c}\gg 1/\lambda_{m}$,
$\exp(-\lambda_{m}t_{c})/\exp(-\lambda_{g}t_{c})\to 0$, namely $f_{m}/f_{g}\to
0$ and

$\sigma_{c}\to\sigma_{g}+p\frac{\lambda_{m}}{\lambda_{m}-\lambda_{g}}\sigma_{m}.$
(4)

Therefore, one can determine $\sigma_{g}$ after long cooling by

$\sigma_{g}\sim\sigma_{c}-p\frac{\lambda_{m}}{\lambda_{m}-\lambda_{g}}\sigma_{m}.$
(5)

in general as long as $\lambda_{m}>\lambda_{g}$.

It follows from Eq. (5) that Eq. (2) is valid only when (1)
$\lambda_{m}\gg\lambda_{g}$ or (2) $\sigma_{m}\ll\sigma_{g}$, and use of Eq.
(2) adds an extra term $p[\lambda_{m}/(\lambda_{m}-\lambda_{g})-1]\sigma_{m}$
to the actual ground state production cross section in general. As
$p[\lambda_{m}/(\lambda_{m}-\lambda_{g})-1]\sim 0.53$ and $\sigma_{m}$ is not
negligible for the 197Au(d,2n)197Hg reaction, some experiments showing high
$\sigma_{g}$ values in Fig. 2 may include this extra term. We notice that
similar problems may occur in pairs of the metastable and ground states having
close half-lives (e.g.,198Tl, 198Au) and we wish our compilation will
contribute to discussion on this problem.

##  4 Application

Global test of reaction model codes is an immediate application of the newly
prepared isomeric ratio table. We can easily check reaction model codes from
the goodness-of-fit of outputs obtained using the new isomeric ratio table. As
an example, we calculated isomeric ratios by TALYS-1.96 with the default
parameter sets but varying the spin cut-off parameter. The spin cut-off
parameter used in TALYS is

$\sigma^{2}=R\frac{\tilde{a}}{a}\frac{I_{\mathrm{rig}}T}{\hslash^{2}}$ (6)

in default setting (“spincutmodel 1”), where $I_{\mathrm{rig}}$ is the rigid
body moment of inertia, $T$ is the nuclear temperature, and $a$ and
$\tilde{a}$ are the level density parameter and its high excitation energy
limit, respectively. In “spincutmodel 2”, this is simplified to

$\sigma^{2}=R\frac{I_{\mathrm{rig}}T}{\hslash^{2}}\equiv\frac{I_{\mathrm{eff}}T}{\hslash^{2}}$
(7)

by omitting the shell effect factor $a/\tilde{a}$. $R$ is an adjustable
parameter in TALYS.111$R$ may be specified by Rspincut (nuclide independent)
or s2adjust (nuclide dependent) in TALYS-1.96. The parameter
$\eta=I_{\mathrm{eff}}/I_{\mathrm{rig}}$ seen in the literature [89, 90, 91]
is equal to $R$ in Eq. (7). To see an appropriate choice of R, we calculated
the isomeric ratios of all reactions in the present compilation from 1 eV
(neutron-induced reactions) or 1 MeV (other reactions) to 200 MeV with the
energy grids hardwired in TALYS. The $R$ values were varied between 0.1 and
1.5, and calculations were done with both spin cut-off parameter models.

For $n\sim 12,000$ experimental isomeric ratios compiled in the present work
with their uncertainties and the isomeric ratios predicted by TALYS, we
calculated the $F$-value [92]:

$F=\exp\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left[\ln\left(\frac{r_{i,\mathrm{cal}}}{r^{\prime}_{i,\mathrm{exp}}}\right)\right]^{2}}$
(8)

with

$r^{\prime}_{i,\mathrm{exp}}=\left\\{\begin{array}[]{ll}r_{i,\mathrm{exp}}-\Delta
r_{i,\mathrm{exp}}&\mathrm{if~{}}r_{i,\mathrm{cal}}<r_{i,\mathrm{exp}}-\Delta
r_{i,\mathrm{exp}}\\\ r_{i,\mathrm{exp}}+\Delta
r_{i,\mathrm{exp}}&\mathrm{if~{}}r_{i,\mathrm{cal}}>r_{i,\mathrm{exp}}+\Delta
r_{i,\mathrm{exp}}\\\ 1&\mathrm{otherwise}\end{array}\right.,$ (9)

where $r_{i,\mathrm{exp}}$ and $\Delta r_{i,\mathrm{exp}}$ are the $i$th
isomeric ratio in our compilation and its uncertainty, and
$r_{i,\mathrm{cal}}$ is the corresponding isomeric ratio predicted by TALYS.
Figure 3 shows $R$ dependence of the $F$-value. This figure suggests that the
best fit is obtained when the spin cut-off parameter is reduced to $\sim$40%
($\sim$50%) of its default value $R=1$ when using the “spincutmodel 1”
(“spincutmodel 2”) setting. For more sophisticated evaluation of isomeric
ratios, $R$ must be adjusted for each nuclide individually. For example, Sudár
et al. [89] reports that the $\eta$ value shows strong mass dependence when it
was adjusted for each nuclide separately.

Figure 4 shows distribution of the $F$-value for prediction by TALYS-1.96 with
default setting (“spincutmodel 1” and $R=1$). Among four reactions getting
high $F$-values, 197Au(n,$\gamma$)198Au and natPb(p,x)198Au could be difficult
ones to get $F\sim 1$ since $\sigma_{m}/\sigma_{t}$ is very low ($\sim
10^{-3}$ or lower) for the former reaction, and the $F$-value is based on only
one experimental $\sigma_{m}/\sigma_{t}$ value at very high energy (150 MeV)
for the latter reaction. On the other hand, we observe systematic deviations
of experimental $\sigma_{m}/\sigma_{t}$ values from those predicted by
TALYS-1.96 for natIr($\alpha$,x)194Ir and 197Au(d,p)198Au, for which the model
predictions could be improved.

##  5 Summary

We extracted the experimental isomer production cross sections and isomeric
ratios from the EXFOR library and compiled the isomeric ratios in the form of
$\sigma_{m}/\sigma_{t}$. Various mistakes in the EXFOR library and original
publications were fixed during compilation. Preliminary experimental results
and experiments reporting unphysical $\sigma_{m}/\sigma_{t}$ values were
discarded during compilation. As an application of the newly created isomeric
ratio table, we studied the spin cut-off parameter dependence of the goodness
of fit for the isomeric ratios predicted by TALYS-1.96.

## Data availability

The table of the compiled isomer production cross sections and isomeric ratios
in a plain text file is included in the supplemental material. It is also
available upon request to the authors by email or post. Their graphical
comparison with evaluated data libraries is under preparation for an IAEA
report [93].

## Acknowledgments

The authors are grateful to Viktor Zerkin for his special arrangement of a
X4Pro SQLite database file dedicated to the present work. We also wish to
thank the anonymous reviewer for careful reading of the earlier version of the
manuscript. Sándor Sudár helped us to understand his adjustment of $\eta$
values with TALYS. Ferenc Ditrói, György Gyürky, Alex Hermanne, Mayeen Uddin
Khandaker, Ondřej Lebeda, Rolf Michel, Haladhara Naik, Syed M. Qaim, Yury
Titarenko and Sung Chul Yang helped us to understand the experimental data
published by them. We would like to thank Oscar Cabellos for encouraging us.
Last but not least, we appreciate the managers, compilers and programmers of
the Nuclear Reaction Data Centres (NRDC) for maintenance and development of
the EXFOR library.

## Supplemental material

The compiled cross sections and isomeric ratios in a plain text file and plots
of the experimental cross sections and isomeric ratios along with those
predicted by TALYS-1.96 with default setting can be found online at
https://doi.org/10.1016/j.adt.2023.xxxxxx.

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## Figures

Fig. 1:  93Nb(n,$\alpha$)90Y metastable (top) and ground (middle) state
production cross sections and isomeric ratios (bottom). The asterisk after the
year indicates that the values are not reported by the experimentalists but
derived from the original values compiled in EXFOR (e.g.,isomeric ratio
derived from isomer production cross sections). In addition to the
experimental data [42, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66,
67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78] extracted from the present
compilation, the corresponding data predicted by TALYS-1.96 and evaluated for
the TENDL-2021 library [94] are plotted in curves.  Fig. 2:  197Au(d,2n)197Hg
metastable (top) and ground (middle) state production cross sections and
isomeric ratios (bottom). The asterisk after the year indicates that the
values are not reported by the experimentalists but derived from the original
values compiled in EXFOR (e.g.,isomeric ratio derived from isomer production
cross sections). In addition to the experimental data [80, 81, 82, 83, 84, 85,
86, 87, 88] extracted from the present compilation, the corresponding data
predicted by TALYS-1.96 (with the default deuteron potential and the potential
proposed by Han et al. [95]) and evaluated for the TENDL-2021 library [94] are
plotted in curves.  Fig. 3:  $R$ dependence of the $F$-value for the isomeric
ratios predicted by TALYS-1.96 with two spin cut-off models.  Fig. 4:
Distribution of $F$-value for the isomeric ratios predicted by TALYS-1.96 with
default setting (“spincutmodel 1” and $R=1$).

Table A: Combinations of reaction product and quantity considered in our compilation in EXFOR REACTION formalism. Z-S-A stands for a nuclide symbol (e.g.,79-AU-198). Note that the three underlines code strings are obsolete but still seen in old EXFOR entries. REACTION (SF4-SF6) | Symbols
---|---
Z-S-A,,SIG | $\sigma_{t}$
Z-S-A,IND,SIG |
Z-S-A-G,,SIG | $\sigma_{g}$
Z-S-A-G,M-,SIG |
Z-S-A-M,,SIG | $\sigma_{m}$
Z-S-A-M/T,,SIG/RAT | $\sigma_{m}/\sigma_{t}$
Z-S-A-G/T,,SIG/RAT | $\sigma_{g}/\sigma_{t}$
Z-S-A-M/G,,SIG/RAT | $\sigma_{m}/\sigma_{g}$
ELEM/MASS,,SIG |  $\sigma_{g}$ (coded with ISOMER=0),
ELEM/MASS,IND,SIG |  $\sigma_{m}$ (coded with ISOMER=1) or
|  $\sigma_{t}$ (coded without ISOMER).
Table B: Number of reactions and data points of the isomeric ratios compiled in the present work. projectile | $\gamma$ | n | p | d |  3He | $\alpha$ | total
---|---|---|---|---|---|---|---
reactions | 2 | 186 | 470 | 127 | 34 | 143 | 962
points | 9 | 2229 | 4883 | 1915 | 624 | 2653 | 12313