# Photoproduction of the 55-57Co nuclei on natNi
at the bremsstrahlung end-point energy of 35–94 MeV

I.S. Timchenko1,2<EMAIL_ADDRESS>
<EMAIL_ADDRESS>O.S. Deiev2, S.M. Olejnik2, S.M. Potin2,
V.A. Kushnir2, V.V. Mytrochenko2, S.A. Perezhogin2, A. Herzáň1 1 Institute of
Physics, Slovak Academy of Sciences, SK-84511 Bratislava, Slovakia  2 National
Science Center ”Kharkov Institute of Physics and Technology”,
1, Akademichna St., 61108, Kharkiv, Ukraine

###### Abstract

Production of the 55-57Co nuclei on natNi in photonuclear reactions using
bremsstrahlung gamma photon irradiation with end-point energy $E_{\rm{\gamma
max}}$ between 35 and 94 MeV has been studied. The experiment was performed at
the electron linear accelerator LUE-40 NSC KIPT using the methods of $\gamma$
activation and off-line $\gamma$-ray spectroscopy. The obtained experimental
flux-averaged cross-sections $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$
agree with the data found in literature. The theoretical flux-averaged cross-
sections $\langle{\sigma(E_{\rm{\gamma max}})}\rangle_{\rm{th}}$ for the
production of 55-57Co and 55-57Ni were estimated using the cross-section
values $\sigma(E)$ from the TALYS1.95 code and bremsstrahlung spectra of gamma
photons calculated by GEANT4.9.2. The experimental results for 56,57Co agree
with the cumulative $\langle{\sigma(E_{\rm{\gamma max}})}\rangle_{\rm{th}}$.
However theoretical prediction fails to reproduce the measured cross-sections
for the production of 55Co.

photonuclear reactions, natNi, 55Co, 56Co, 57Co, flux-averaged cross-section,
bremsstrahlung end-point energy of 35–94 MeV, $\gamma$ activation and off-line
$\gamma$-ray spectroscopy, TALYS1.95, GEANT4.9.2.

##  I Introduction

Most of the data on cross-sections for photonuclear reactions are important
for traditional studies of the Giant Dipole Resonance (GDR), mechanisms of its
excitation and decay including competition between statistical and direct
processes in decay channels, GDR configurational and isospin splitting, sum
rule exhaustion, etc. Experimental cross-sections for photonuclear reactions
are also widely used in various applications, primarily in astrophysics [1],
medicine [2], design of fast reactors [3] and accelerator driven sub-critical
systems [4, 5].

Such data were obtained in experiments using high-intensity $\gamma$-fluxes
either quasi-monoenergetic annihilation photons [6, 7, 8, 9, 10, 11], or high-
energy electron bremsstrahlung [12, 13, 14, 15]. Data on these cross-sections
can be found in the international digital databases [16].

Despite the significant amount of experimental data available in international
databases, there is still an insufficiency of data for the cross-sections of
many-particle photoneutron reactions. Mainly, data for reactions resulting in
the release of up to 4 neutrons can be found. In addition, experimental data
from different laboratories do not always agree with each other, even in the
GDR range [17, 18, 19]. Data for photonuclear reactions involving charged
particles in the output channel are mainly limited to the region of light
nuclei and energies within the GDR range.

Experimental research into photonuclear reactions is currently being performed
in several directions. Thus, in a number of works, previously measured results
are revised and criteria of data reliability are developed [20, 19]. Repeated
systematic measurements of cross-sections for previously studied reactions are
performed, as noted in [21]. Studies are being carried out on high-threshold
photoneutron reactions [22, 23], photoproton [24, 25], and photonuclear
reactions with the emission of charged particles/clusters [26, 27, 28].

Theoretical estimates of cross-sections for photonuclear reactions are
commonly performed now using the TALYS code [29, 30]. This code is constantly
being improved and is used to simulate the processes of interaction of
particles with the atomic nuclei. Additionally, it is employed in calculations
relating to astrophysics, fission yields, medical isotopes production, and
thermal scattering data. The results for the output files from TALYS, which
are based on default parameters, adjusted calculations and data from different
sources, are placed in the TENDL tables [31].

It should be noted that theoretical estimates of photonuclear cross-sections
in TALYS do not always agree with experimental data. Discrepancies occur for
many-particle photoneutron reactions [22, 23], as well as in the case of
reactions with the emission of charged particles (including clusters) [24, 25,
27, 28].

The photonuclear cross-sections on natNi are important because nickel is of
practical interest as an important structural and surface material, which is
often used in structural materials for accelerator and nuclear technology
[32]. The physical and mechanical properties of nickel are suitable for the
manufacture of heat-resistant and corrosion-resistant alloys [33]. Nickel is
an important structural material not only for modern reactors, but also for
generation IV reactors and future fusion reactors [34]. From a medical and
research point of view, the photon-induced reaction cross-sections of Co and
Ni can be used to produce important isotopes such as 55-58Co, 56Ni, and 57Ni
due to their suitable decay characteristics. For example, the 55Co isotope is
useful for diagnostics by positron emission tomography, and could be used for
the diagnostics of lung cancer and for the visualization of tumours [35]. The
57Co isotope general use is as a calibration standard for
$\gamma$-spectrometers and single photon emission tomographs [35], the 56Co
isotope is used as a calibration source up to 3.5 MeV for $\gamma$-ray
detectors [36].

Experimental data on cross-sections for photonuclear reactions on nickel at
energies of 12–40 MeV were obtained in a number of studies [37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49]. In [20] estimated cross-section values
for the reactions of photoproduction of Co nuclei on 58,60Ni are presented,
and obtained on the basis of the model of the phenomenological description of
the main GDR decay channel competition at energies of 10–40 MeV. At higher
energies, the study of cross-sections on natural nickel using electron
bremsstrahlung was performed in [50, 51]. The flux-averaged cross-sections of
natNi($\gamma$,$x$np)55-58Co reactions were measured in these studies using
the $\gamma$-activation technique at bremsstrahlung end-point energies of
55–65 MeV [50] and 65–75 MeV [51].

This paper presents results of the experimental study of the 55-57Co
production in photonuclear reactions on natural nickel measured using
bremsstrahlung spectra of gamma photons with end-point energy $E_{\rm{\gamma
max}}$ between 35 and 94 MeV. The obtained data are compared both with the
theoretical calculation performed using partial cross-sections $\sigma(E)$
from the TALYS1.95 code [29, 30], and with the experimental data available in
the literature [50, 51, 48].

##  II Experimental setup and procedure

The photoproduction of the 55-57Co nuclei was experimentally studied via
measurement of residual $\gamma$-activity of the irradiated targets. This
technique has been described in many studies of photonuclear reactions, e.g.
[52, 53, 54, 55]. The schematic block diagram of the experiment is presented
in Fig. 1.

Figure 1: Schematic block diagram of the experiment. The upper part shows the
measurement room. The lower part shows the electron accelerator LUE-40, Ta
converter, Al absorber, and exposure reaction chamber.

In the experiment, the LUE-40 electron linear accelerator of Research and
Development Center ”Accelerator” of the National Science Center ”Kharkov
Institute of Physics and Technology” [56, 57] was employed. To generate the
bremsstrahlung $\gamma$-flux, electrons with the initial energy $E_{\rm e}$
were impinging on the converter made of a natural tantalum square plate of 20
mm and a thickness of 1.05 mm. To stop the electrons, a cylindrical aluminum
absorber, 100 mm in diameter and 150 mm in length, was used. The studied
target and target-monitor, placed in the thin aluminum capsule, were
positioned behind the Al absorber on the electron beam axis. For transporting
the targets to the irradiation point and back for induced activity
measurement, the pneumatic tube transfer system was used. After the irradiated
targets are delivered to the measurement room, the targets are extracted from
the aluminum capsule and transferred one by one to the detector for the
measurements. The semiconductor High-Purity Germanium (HPGe) detector with the
energy resolution (FWHM) of 0.8 and 1.8 keV at 122 and 1332.5 keV,
respectively, was used. Its detection efficiency, $\varepsilon$, at 1332.5 keV
was 20% relative to the NaI(Tl) scintillator, 3 inches in diameter and 3
inches in thickness. The detector was equipped with passive Pb shielding to
suppress natural background. The detection efficiency calibration was done
using a standard set of $\gamma$ sources: 22Na, 60Co, 133Ba, 137Cs, 152Eu, and
241Am.

To investigate the photonuclear reactions of the production of 55-57Co nuclei
on nickel, targets made of natural Ni were used. Isotopic composition of the
natNi material (%) is: 58Ni – 68.077, 60Ni – 26.223, 61Ni – 1.140, 62Ni –
3.634, 64Ni – 0.926 [30, 58]. The admixture of other elements in the targets
did not exceed 0.1% by weight. The targets had a disk-like shape with a
diameter of 8 mm and a weight of $\sim$80 mg.

The bremsstrahlung $\gamma$-flux was monitored by the yield of the
100Mo$(\gamma,{\rm n})^{99}$Mo reaction and calculated using the GEANT4.9.2
code [58, 59, 60]. For this purpose, the natMo and the natNi targets were
closely placed to each other and simultaneously irradiated. The natMo targets
had a form of 8 mm diameter disks with a mass of approximately 60 mg. The
monitoring procedure was performed by comparing the measured flux-averaged
cross-section values with the calculated data using the procedure described in
[15]. In the case of the 100Mo isotope, the isotopic abundance of 9.63 % [30,
58] was used in our calculations.

In the experiment, the natNi and natMo targets were exposed to bremsstrahlung
radiation with end-point energy $E_{\rm{\gamma max}}$ ranging from 35 to 94
MeV with an energy step of $\sim$5 MeV. The irradiation time $t_{\rm irr}$ was
30 min for each $E_{\rm{\gamma max}}$ value.

During irradiation of the natNi targets, products of the ($\gamma$,$x$n$y$p)
reaction channels and their decay products accumulate in the targets. The
55-57Co nuclei are formed as an result of the natNi($\gamma$,$x$np) reaction.
Also after the EC/$\beta^{+}$ (100%) decay of the 55-57Ni nuclei, which are
formed in targets as a result of ($\gamma$,$x$n) reactions. Accordingly, in
the case of the study of the 55-57Co nuclei, we need to take into account two
production channels of the accumulation. Decay characteristics of the 55-57Co
and 55-57Ni nuclei are listed in Table 1 according to [61]. In addition, also
data for the monitor reaction 100Mo$(\gamma,{\rm n})^{99}$Mo are given.

Measurement time, $t_{\rm meas}$, of the residual $\gamma$-activity of the
natMo targets was 30 min. Before measuring the 55Co activity, the natNi
targets were first cooled for a minimum of 60 min, and then measured for 30
min. The prolonged cooling time of 32 up to 53 days was chosen in the case of
the 56,57Co photoproduction study, and the energy spectra of the induced
activity were measured for 20 up to 95 hours.

The uncertainty in measurements of experimental values of the flux-averaged
cross-sections $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ was determined as
a quadratic sum of statistical and systematical errors.

The systematical errors are due to the following uncertainties: 1) exposure
time and the electron current $\sim$0.5%; 2) detection efficiency of the HPGe
detector $\sim$2–3%, which is generally associated with the radiation source
error and the choice of the approximation curve; 3) the half-life, $T_{1/2}$,
of the reaction products and the intensity, $I_{\gamma}$, of the analyzed
transition are noted in Table 1; 4) the number of target atoms $\sim$0.2%; 5)
normalization of the experimental data to the yield of the monitoring reaction
100Mo$(\gamma,{\rm n})^{99}$Mo made up to 6%.

The statistical error in the observed $\gamma$-activity is mainly due to
statistics calculation in the full absorption peaks of the corresponding
transitions, which varies from 0.15% to 7.65%. The peak area measurements
showed the highest statistics in the production of the 57Co nucleus, with a
statistical error of 0.15–0.65%. The most difficult measurements were
performed for the 55Co nucleus, with a statistical error of 2.15–7.65%.

Table 1:  Spectroscopic data of the products of specific reaction channels adopted from [61]: spin ($J$) and parity ($\pi$) of the ground state of the studied Nucleus, their half-life ($T_{1/2}$); Decay mode is the type of decay of the studied Nucleus, $E_{\gamma}$ and $I_{\gamma}$ are the energies and intensities of the $\gamma$-ray transitions associated with the decay of the nucleus, respectively. In the column ”Contributing reactions” lists of possible reactions of production 55-57Co and 55-57Ni on stable isotopes of natNi. $E_{\rm{thr}}$ denotes threshold energy of the reactions (calculated by TALYS1.95 [29, 30]).  | Nucleus ($J^{\pi}$)
---
$T_{1/2}$ |  | Decay mode (%)
---
$E_{\gamma}$ (keV) |  $I_{\gamma}$ (%) |  | Contributing
---
reactions
$E_{\rm{thr}}$ (MeV)
55Co ($7/2^{-}$) | 17.53 3 h | EC/$\beta^{+}$ (100%) | 931.1 | 75 4 | ${}^{58}\rm{Ni}(\gamma,2np)$ | 29.63
|  |  |  |  | ${}^{60}\rm{Ni}(\gamma,4np)$ | 50.02
|  |  |  |  | ${}^{61}\rm{Ni}(\gamma,5np)$ | 57.84
|  |  |  |  | ${}^{62}\rm{Ni}(\gamma,6np)$ | 68.43
56Co ($4^{+}$) | 77.236 26 d | EC/$\beta^{+}$ (100%) | 846.77 | 99.9399 23 | ${}^{58}\rm{Ni}(\gamma,np)$ | 19.55
|  |  | 1037.84 | 14.05 4 | ${}^{60}\rm{Ni}(\gamma,3pn)$ | 39.94
|  |  | 1238.28 | 66.46 12 | ${}^{61}\rm{Ni}(\gamma,4np)$ | 47.76
|  |  |  |  | ${}^{62}\rm{Ni}(\gamma,5np)$ | 58.35
|  |  |  |  | ${}^{64}\rm{Ni}(\gamma,7np)$ | 74.85
57Co ($7/2^{-}$) | 271.74 6 d | EC (100%) | 122.06 | 85.60 17 | ${}^{58}\rm{Ni}(\gamma,np)$ | 8.17
|  |  | 136.47 | 10.68 8 | ${}^{60}\rm{Ni}(\gamma,2np)$ | 28.56
|  |  |  |  | ${}^{61}\rm{Ni}(\gamma,3np)$ | 36.38
|  |  |  |  | ${}^{62}\rm{Ni}(\gamma,4np)$ | 46.98
|  |  |  |  | ${}^{64}\rm{Ni}(\gamma,6np)$ | 63.47
55Ni ($7/2^{-}$) | 204.7 37 ms | EC/$\beta^{+}$ (100%) | – | – | ${}^{58}\rm{Ni}(\gamma,3n)$ | 39.11
|  |  |  |  | ${}^{60}\rm{Ni}(\gamma,5n)$ | 59.49
|  |  |  |  | ${}^{61}\rm{Ni}(\gamma,6n)$ | 67.31
56Ni ($0^{+}$) | 6.075 10 d | EC/$\beta^{+}$ (100%) | 158.38 | 98.8 10 | ${}^{58}\rm{Ni}(\gamma,2n)$ | 22.46
|  |  |  |  | ${}^{60}\rm{Ni}(\gamma,4n)$ | 42.85
|  |  |  |  | ${}^{61}\rm{Ni}(\gamma,5n)$ | 50.67
|  |  |  |  | ${}^{62}\rm{Ni}(\gamma,6n)$ | 61.27
57Ni ($3/2^{-}$) | 35.60 6 h | EC/$\beta^{+}$ (100%) | 127.16 | 16.7 5 | ${}^{58}\rm{Ni}(\gamma,n)$ | 12.22
|  |  | 1377.63 | 81.7 24 | ${}^{60}\rm{Ni}(\gamma,3n)$ | 32.60
|  |  |  |  | ${}^{61}\rm{Ni}(\gamma,4n)$ | 40.42
|  |  |  |  | ${}^{62}\rm{Ni}(\gamma,5n)$ | 51.02
|  |  |  |  | ${}^{64}\rm{Ni}(\gamma,6n)$ | 67.51
99Mo ($1/2^{+}$) | 65.924 6 h |  $\beta^{-}$ (100%) | 739.50 | 12.2 2 | ${}^{100}\rm{Mo}(\gamma,n)$ | 8.29

##  III  Calculation of flux-averaged cross-sections

The cross-section $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ averaged over
the bremsstrahlung $\gamma$-flux $W(E,E_{\rm{\gamma max}})$ from the threshold
energy, $E_{\rm thr}$, of the studied reaction to the end-point energy of the
spectrum, $E_{\rm{\gamma max}}$, was calculated by equation:

$\langle{\sigma(E_{\rm{\gamma
max}})}\rangle=\frac{\int\limits_{E_{\rm{thr}}}^{E_{\rm{\gamma
max}}}\sigma(E)\cdot W(E,E_{\rm{\gamma
max}})dE}{{\int\limits_{E_{\rm{thr}}}^{E_{\rm{\gamma max}}}W(E,E_{\rm{\gamma
max}})dE}}.$ (1)

To calculate the flux-averaged cross-section of the production of a particular
nucleus on a natural element that has several stable isotopes, Eq. (1) must be
transformed into a sum of the flux-averaged cross-sections
$\langle{\sigma(E_{\rm{\gamma max}})}\rangle_{i}$ of the production of the
nucleus on each of the isotopes $i$, where each has its own specific reaction
threshold $E^{i}_{\rm thr}$:

$\langle{\sigma(E_{\rm{\gamma
max}})}\rangle=\sum^{m}_{i=1}\frac{\int\limits_{E^{i}_{\rm{thr}}}^{E_{\rm{\gamma
max}}}A_{i}\cdot\sigma_{i}(E)\cdot W(E,E_{\rm{\gamma
max}})dE}{{\int\limits_{E^{i}_{\rm{thr}}}^{E_{\rm{\gamma
max}}}W(E,E_{\rm{\gamma max}})dE}},\qquad\qquad\qquad\qquad(1\rm a)$

where $m$ is the number of stable isotopes of natural element, on which a
nucleus of interest can be formed. In the case of natNi and the production of
55-57Co nuclei, $m=5$. $A_{i}$ is the abundance of the $i$-th stable isotope.

The flux-averaged cross-section $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$
can also be determined as the sum of the flux-averaged cross-sections on all
stable isotopes $i$-$m$, which are weighted with the integral flux for the
minimum reaction threshold $E^{\rm min}_{\rm thr}$:

$\langle{\sigma(E_{\rm{\gamma
max}})}\rangle=\frac{\sum^{m}_{i=1}\int\limits_{E^{i}_{\rm{thr}}}^{E_{\rm{\gamma
max}}}A_{i}\cdot\sigma_{i}(E)\cdot W(E,E_{\rm{\gamma
max}})dE}{{\int\limits_{E^{\rm min}_{\rm{thr}}}^{E_{\rm{\gamma
max}}}W(E,E_{\rm{\gamma max}})dE}}.\qquad\qquad\qquad\qquad(1\rm b)$

The difference between threshold energies $E^{i}_{\rm{thr}}$ and $E^{\rm
min}_{\rm{thr}}$ leads to different magnitudes ofthe effective integral
bremsstrahlung $\gamma$-flux and $\gamma$-flux from $E^{\rm min}_{\rm thr}$,
respectively. As a result, the estimates given by Eq. (1a) and Eq. (1b) differ
from each other.

Experimental $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ cross-sections are
calculated as following:

$\langle{\sigma(E_{\rm{\gamma max}})}\rangle=\frac{\lambda\triangle
A{\rm{\Phi}}^{-1}(E_{\rm{\gamma max}})}{N_{n}I_{\gamma}\
\varepsilon(1-e^{-\lambda t_{\rm{irr}}})e^{-\lambda
t_{\rm{cool}}}(1-e^{-\lambda t_{\rm{meas}}})},$ (2)

where $\triangle A$ is the number of counts in the full absorption peak,
$\lambda$ is the decay constant (s-1), $N_{n}$ is the number of atoms of the
natural nickel target, $I_{\gamma}$ is the intensity of the measured $\gamma$
quanta, $\varepsilon$ is the absolute detection efficiency at the measured
$\gamma$ quanta energy, ${\rm{\Phi}}(E_{\rm{\gamma max}})={\int\limits_{E^{\rm
min}_{\rm{thr}}}^{E_{\rm{\gamma max}}}W(E,E_{\rm{\gamma max}})dE}$ is the
integrated flux of bremsstrahlung gamma photons in the energy range from the
minimum reaction threshold $E^{\rm min}_{\rm thr}$ up to $E_{\rm{\gamma
max}}$; $t_{\rm{irr}}$, $t_{\rm{cool}}$ and $t_{\rm{meas}}$ are the
irradiation time, cooling time and measurement time, respectively. A more
detailed description of all the calculation procedures necessary for the
determination of $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ can be found in
[15, 23].

The reaction yield is defined as:

$Y(E_{\rm{\gamma max}})=N_{n}\int\limits_{E_{\rm{thr}}}^{E_{\rm{\gamma
max}}}\sigma(E)\cdot W(E,E_{\rm{\gamma max}})dE.$ (3)

To estimate a reaction contribution to the total production of a particular
nuclide (e.q., the 58Ni($\gamma$,p) reaction in the production of the 57Co
nucleus on natNi), the normalized reaction yield $Y_{k}(E_{\rm{\gamma max}})$
was used. The $Y_{k}(E_{\rm{\gamma max}})$ yield can be calculated as follows:

$Y_{k}(E_{\rm{\gamma
max}})=\frac{A_{k}\int\limits_{E^{k}_{\rm{thr}}}^{E_{\rm{\gamma
max}}}\sigma_{k}(E)\cdot W(E,E_{\rm{\gamma
max}})dE}{\sum^{m}_{i=1}A_{i}\int\limits_{E^{i}_{\rm{thr}}}^{E_{\rm{\gamma
max}}}\sigma_{i}(E)\cdot W(E,E_{\rm{\gamma max}})dE}.$ (4)

Equation (4) is useful when the flux-averaged cross-section of the dominant
reaction for the production of the studied nucleus on one of the isotopes in
the natural element need to be obtained. For this purpose, it is necessary to
correct the values calculated by Eq. (2) by using the corresponding value of
the normalized reaction yield $Y_{k}(E_{\rm{\gamma max}})$ and the isotopic
abundance in the target material.

##  IV Results and discussion

###  IV.1 Calculated $\sigma(E)$ and flux-averaged
$\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ cross-sections

The experimental cross-sections of photonuclear production of the 55-57Co and
55-57Ni nuclei on stable nickel isotopes, existing early and obtained in this
study, are compared with theoretical predictions. In this work, the
calculation of the theoretical cross-sections $\sigma(E)$ was performed using
the TALYS1.95 code [29, 30] with default options.

Figure 2 shows the calculated cross-sections $\sigma(E)$ for the production of
57Co (a), 56Co (b) and 55Co (c) nuclei on stable nickel isotopes, taking into
account the isotopic abundance of the elements. To calculate the cross-section
for the production of the studied nucleus on natNi, we summed the cross-
sections for each Ni isotope.

The total cross-sections $\sigma(E)$ for the photoproduction of 57Co and 57Ni,
56Co and 56Ni, 55Co and 55Ni nuclei on natural nickel, respectively, are shown
in Figs. 2 (d-f). The sum of cross-sections of the natNi($\gamma,x$n)55-57Ni
and natNi($\gamma$,$x$np)55-57Co reactions represents the cumulative yield of
the 55-57Co nuclei production on natNi. The contribution of the
natNi($\gamma,x$n)55-57Ni photonuclear reactions is maximal in the case of the
57Co production and negligible in the case of 55Co.

Figure 2: The theoretical cross-sections $\sigma(E)$ from the TALYS1.95 code.
(a–c) The cross-sections of the photoproduction of 55-57Co nuclei on stable
nickel isotopes, taking into account the isotopic abundance of the elements.
The production of the studied nucleus on natNi is a sum of the cross-sections
for each Ni isotope.
(d–f) The total cross-sections $\sigma(E)$ for the photoproduction of 55-57Co
and 55-57Ni nuclei on natural nickel. The black curves are the sums of the
natNi($\gamma$,$x$np)55-57Co and natNi($\gamma$,$x$n)55-57Ni cross-sections.

###  IV.2 The experimental $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$
cross-sections of the 55-57Co nuclei production on natNi

An energy spectrum of $\gamma$ rays emitted by the reaction products
accumulated in the natNi target after bremsstrahlung gamma photon exposure is
shown in Fig. 3. The bremsstrahlung end-point energy was 89.25 MeV.

Figure 3: A spectrum of $\gamma$ rays emitted by the reaction products
accumulated in the natNi target after bremsstrahlung $\gamma$-flux exposure
with the energy $E_{\rm{\gamma max}}$ = 89.25 MeV. Relevant peaks are labeled
with the $\gamma$-ray transition energies in keV, and their intensities
$I_{\gamma}$ (shown in parentheses). The measurement time, $t_{\rm meas}$, and
cooling time, $t_{\rm cool}$, were 84719 and 2925610 s, respectively.

In natNi targets, photoneutron reaction produce the 57Ni nuclei which decay
via EC/$\beta^{+}$ process (100%). We therefore observe cumulative activity of
57Co, which is the result of two processes: natNi($\gamma$,$x$np)57Co and
natNi($\gamma$,$x$n)57Ni $\xrightarrow{\rm{EC}/\beta^{+}}$ 57Co. The same
applies to the production of the 55,56Co nuclei. Simplified decay schemes of
the 55-57Co nuclei are shown in Figs. 4(a), 5(a), 6(a).

To determine the experimental flux-averaged cross-sections
$\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ we used Eq. (2) and the
bremsstrahlung flux, integrated from the minimum reaction threshold $E^{\rm
min}_{\rm thr}$ ($E_{\rm thr}$ in bold in Table 1). Then, to take into account
the difference between bremsstrahlung $\gamma$-flux from $E_{\rm{thr}}^{\rm
min}$ and effective $\gamma$-flux, which causes the 55-57Co reaction products
on all stable isotopes of natNi, these values were corrected with the
coefficient defined as Eq. (1a)/Eq. (1b). Corrected flux-averaged cross-
sections are larger than results with $E^{\rm min}_{\rm thr}$ by 0.3–2.7 % for
investigated energies.

The obtained experimental cumulative flux-averaged cross-sections are listed
in Tables B–D and graphically shown in Figs. 4(b), 5(b), 6(b).

####  IV.2.1  The photoproduction of 57Co on natNi

To identify the 57Co nuclei, the 122.06 and 136.47 keV transitions with their
intensities of 85.60 and 10.68%, respectively, were used. As can be seen from
Fig. 4(b), the results for two used transitions coincide within the
experimental errors.

The theoretical flux-averaged cross-sections $\langle{\sigma(E_{\rm{\gamma
max}})}\rangle_{\rm th}$ were calculated using Eq. (1a). In Fig. 4(b),
$\langle{\sigma(E_{\rm{\gamma max}})}\rangle_{\rm th}$ for the
natNi($\gamma$,$x$np)57Co reaction are shown, as well as for cumulative
process: natNi($\gamma$,$x$np)57Co + natNi($\gamma$,$x$n)57Ni
$\xrightarrow{\rm{EC}/\beta^{+}}$ 57Co. As can be seen, the difference between
the cumulative flux-averaged cross-section and cross-section for the
natNi($\gamma$,$x$np)57Co reaction is about 33%.

A comparison of the experimental data with the calculation performed for the
cumulative flux-averaged cross-section for the production of 57Co nucleus on
natNi shows a good agreement (see Fig. 4(b)).

The calculated values of $Y_{k}(E_{\rm{\gamma max}})$ revealed that in the
investigated energy region the 57Co nucleus is basically produced from the
58Ni isotope. At $E_{\rm{\gamma max}}$ = 94 MeV the 58Ni isotope contributed
more than 98.3% to the 58Ni($\gamma$,p) reaction. In the case of the
production of the 57Ni nucleus on natNi, the main contribution (more than 99%)
also comes from the reaction on 58Ni, see [62]. With the decrease of energy
$E_{\rm{\gamma max}}$, these contributions smoothly increase and for lower
energies $E_{\rm{\gamma max}}$ are close to 100%.

Figure 4: (a) Simplified decay scheme of 57Co. The nuclear level energies are
in keV. The red-colour arrows represent the $\gamma$-ray transitions used in
this work. (b) The flux-averaged cross-sections $\langle{\sigma(E_{\rm{\gamma
max}})}\rangle$ for the photonuclear production of 57Co on natNi. Experimental
data: empty and full circles – data from this work. Literature values are
adopted from Zaman et al. [50], Naik et al. [51], and Zheltonozhskaya et al.
[48]. Theoretical calculations, performed using Eq. (1a) and cross-sections
from the TALYS1.95 code: dashed curve – natNi($\gamma$,$x$np)57Co, solid curve
– cumulative cross-section. Table 2:  Experimental cumulative flux-averaged
cross-section $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ [mb] of the
photoproduction of 57Co on natNi and 58Ni. The results for the 122.06 keV
transition are presented (see Fig. (3) and (4)).

$E_{\rm{\gamma max}}$ (MeV) |  natNi($\gamma$,$x$np)57Co |  58Ni($\gamma$,p)57Co*
---|---|---
35.55 | 17.6 15 | 25.8 22
40.10 | 17.7 15 | 25.5 21
44.65 | 15.5 13 | 22.2 19
50.20 | 15.3 13 | 21.7 18
54.85 | 17.0 14 | 24.0 20
60.55 | 15.6 13 | 22.0 19
65.05 | 14.2 12 | 20.0 17
70.10 | 14.2 12 | 20.0 17
75.10 | 13.5 11 | 19.0 16
79.95 | 13.7 12 | 19.4 16
85.35 | 13.8 12 | 19.5 16
89.25 | 12.1 10 | 17.0 14
94.00 | 13.6 11 | 19.2 16

* For the calculation of the cumulative photoproduction of 57Co on 58Ni, the normalized reaction yield $Y_{k}(E_{\rm{\gamma max}})$ and the isotopic abundance of 58Ni isotope in natNi were used.

####  IV.2.2  The photoproduction of 56Co on natNi

To identify 56Co nucleus, the 846.77, 1037.84 and 1238.28 keV transitions with
intensities of 99.9399, 14.05 and 66.46%, respectively, were used.

Since the cooling time was 32–53 days, not all of the 56Ni nuclei, formed in
the target at the end of bombarding (EOB), decayed into 56Co. Our estimates
showed that at $t_{\rm cool}$ = 32 days, 2.6% of the 56Ni EOB nuclei remained
in the target. With increasing cooling time, this value quickly decreases and
at $t_{\rm cool}$ = 53 days it is only 0.24%. The experimental data were not
corrected for this contribution. However, to take into account the influence
of the remaining 56Ni nuclei on cumulative yields, the experimental errors
were increased accordingly.

As known, the natural background spectrum contains $\gamma$ ray with
$E_{\gamma}$ = 1238.48 keV. Since the induced activity spectra were recorded
for 20–95 hours, the background radiation makes some additional contribution
to the intensity of the $\gamma$-ray line with $E_{\gamma}$ = 1238.28 keV. Our
estimates showed that the background contribution to the total peak value
ranged from 2.2% to 16.7%. The larger contribution was at low energies
$E_{\rm{\gamma max}}$ where the cross-section for the photonuclear reaction is
smaller. The magnitude of the background contribution was estimated with an
accuracy of no worse than 3.6%, which is taken into account in the total error
of the final results for $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ along
the 1238.28 keV transition.

The obtained experimental data of the bremsstrahlung flux-averaged cross-
sections $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ for the photoproduction
of 56Co are shown in Fig. 5(b). The results for all $\gamma$ rays coincide
within the experimental errors.

All experimental data are slightly lower the calculation result for the
cumulative flux-averaged cross-section (see Fig. 5(b)). As in the case of the
57Co nucleus, the photoproduction of 56Co nucleus in the energy region studied
is basically produced from the 58Ni isotopes. The 58Ni isotope contributed
more than 97.6% to 56Co production at $E_{\rm{\gamma max}}$ = 94 MeV. With the
energy decreasing, this contridution smoothly increases and for lower energies
$E_{\rm{\gamma max}}$ are close to 100%.

Figure 5: (a) Simplified decay scheme of 56Co. (b) The flux-averaged cross-
sections $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ for the photonuclear
production of 56Co on natNi. Experimental data: circles and stars – data from
this work. Literature values are adopted from Zaman et al. [50] and Naik et
al. [51]. Curves are theoretical calculations.  Table 3:  Experimental
cumulative flux-averaged cross-section $\langle{\sigma(E_{\rm{\gamma
max}})}\rangle$ [mb] of the photoproduction of 56Co on natNi and 58Ni. The
results for the 846.77 keV transition are presented (Fig. (3) and (5)).

$E_{\rm{\gamma max}}$ (MeV) |  natNi($\gamma$,$x$np)56Co |  58Ni($\gamma$,pn)56Co*
---|---|---
35.55 | 2.82 19 | 4.14 28
40.10 | 2.93 20 | 4.31 30
44.65 | 2.61 18 | 3.83 26
50.20 | 2.51 17 | 3.67 25
54.85 | 2.82 19 | 4.07 28
60.55 | 2.56 18 | 3.66 25
65.05 | 2.29 16 | 3.25 22
70.10 | 2.28 16 | 3.23 22
75.10 | 2.13 15 | 3.00 20
79.95 | 2.19 15 | 3.08 21
85.35 | 2.09 14 | 2.93 20
89.25 | 1.87 13 | 2.62 18
94.00 | 2.09 14 | 2.92 20

* as in the case of the 58Ni($\gamma$,p)57Co reaction, see Table 2.

####  IV.2.3  The photoproduction of 55Co on natNi

To identify 55Co it was used the $\gamma$-ray transition with $E_{\gamma}$ =
931.1 keV and the intensity of 75.0%.

The theoretical flux-averaged cross-sections $\langle{\sigma(E_{\rm{\gamma
max}})}\rangle_{\rm th}$ for the natNi($\gamma$,$x$np)55Co reaction, as well
as for cumulative process are shown in Fig. 6(b). As can be seen, the
difference between these theoretical estimates, direct and cumulative, is less
than 1%. The obtained experimental cumulative cross-sections
$\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ are significantly lower than the
theoretical estimates.

The 55Co nucleus in the investigated energy region is basically produced from
the 58Ni isotopes. The 58Ni isotope contributed more than 98% to 55Co
photoproduction at $E_{\rm{\gamma max}}$ = 94 MeV. With the energy decreasing,
this contribution smoothly increases and for lower energies $E_{\rm{\gamma
max}}$ are close to 100%. The reaction 58Ni($\gamma$,2np)55Co accounts for
more than 98% of the total production of the 55Co nucleus. Thus, the observed
difference between the experimental result and theoretical prediction is
related to the accuracy of the calculation of this reaction.

These are experimental results for photoproduction of the 55-57Co isotopes on
natNi of other authors [50, 51, 48]. These data were obtained using the
$\gamma$-activation method. In all three cases the obtained experimental
cross-sections are in good agreement with those available in the literature
(see Figs. 4(b), 5(b) and 6(b)).

Figure 6: (a) Simplified decay scheme of 55Co. (b) The flux-averaged cross-
sections $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ for the photonuclear
production of 55Co on natNi. Experimental data: circles – data from this work.
Literature values are adopted from Zaman et al. [50] and Naik et al. [51].
Curves are theoretical calculations. Table 4:  Experimental cumulative flux-
averaged cross-section $\langle{\sigma(E_{\rm{\gamma max}})}\rangle$ [mb] of
the photoproduction of 55Co on natNi and 58Ni. The results for the 931.3 keV
transition are presented (Figs. (3) and (6)).

$E_{\rm{\gamma max}}$ (MeV) |  natNi($\gamma$,$x$np)55Co |  58Ni($\gamma$,2np)55Co*
---|---|---
40.10 | 0.152 19 | 0.223 28
44.65 | 0.101 12 | 0.148 18
50.20 | 0.170 19 | 0.250 27
54.85 | 0.226 23 | 0.331 34
60.55 | 0.219 22 | 0.320 32
65.05 | 0.212 22 | 0.308 31
70.10 | 0.215 21 | 0.309 31
75.10 | 0.214 22 | 0.306 31
79.95 | 0.218 22 | 0.310 31
85.35 | 0.215 22 | 0.305 31
89.25 | 0.196 20 | 0.277 28
94.00 | 0.216 22 | 0.305 32

* as in the case of the 58Ni($\gamma$,p)57Co reaction, see Table 2.

##  V Conclusions

In this work, the flux-averaged cross-sections $\langle{\sigma(E_{\rm{\gamma
max}})}\rangle$ of the production of 55-57Co in photonuclear reactions on
natNi have been measured in the bremsstrahlung end-point energy range
$E_{\rm{\gamma max}}$ = 35–94 MeV. The obtained experimental results were
compared with the data available in the literature, and were in a good
agreement.

The theoretical flux-averaged cross-sections $\langle{\sigma(E_{\rm{\gamma
max}})}\rangle_{\rm th}$ were estimated using the cross-section values
$\sigma(E)$ from the TALYS1.95 code. The cumulative experimental and
theoretical cross-sections satisfactory agree in the case of the production of
57Co and 56Co. For the reactions with the production of 55Co nuclei, the
theoretical values differ from experimental ones. It has been shown that the
main contribution (more than 97%) to the production of 55-57Co nuclei in
photoinduced reactions on natural nickel comes from 58Ni.

The obtained experimental results expand the energy range of previously known
data for the cumulative results of natNi($\gamma$,$x$np)55-57Co and can be
used to test various theoretical models.

## Acknowlegment

The authors would like to thank the staff of the linear electron accelerator
LUE-40 NSC KIPT, Kharkiv, Ukraine, for their cooperation in the realization of
the experiment.

This work was supported by the Slovak Research and Development Agency under
No. APVV-20-0532 and APVV-22-0304, and the Slovak grant agency VEGA (Contract
No. 2/0175/24). Funded by the EU NextGenerationEU through the Recovery and
Resilience Plan for Slovakia under the project No. 09I03-03-V01-00069.

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