Photonuclear reactions on stable isotopes of cadmium and tellurium at bremsstrahlung end-point energies of 10-23 MeV

In order to learn more about how the population of nuclear shells affects unique aspects of the decay of excited nuclear states, it is interesting to investigate the photodisintegration of nuclei located close to the Z = 50 closed proton shell. The yields of different channels of the photodisintegration of isotopes compared to the ratio of the numbers of neutrons and protons in nuclei can highlight the mechanisms of excitation and decay of nuclear states in the energy region between 10 and 50 MeV.

Cadmium (Z = 48) and tellurium (Z = 52) isotopes are convenient objects of investigation, since under natural conditions, there exist several stable isotopes, which allows to obtain the dependence of the yields of various reactions on the number of neutrons in a nucleus. The main decay channels of giant dipole resonance (GDR) are the emission of neutrons or protons. Currently, there is an extensive database of experimental data on photoneutron reactions in the stable isotopes of natural mixture of cadmium and tellurium [1-22]. Nevertheless, these data are not yet complete and properly explained. The proton channel, despite a small cross section of the (γ,p) reaction, is interesting in connection with isospin splitting of GDR [23].

Natural cadmium consists of eight stable isotopes with following mass numbers and isotopic abundances: ¹⁰⁶Cd (1.25%), ¹⁰⁸Cd (0.89%), ¹¹⁰Cd (12.49%), ¹¹¹Cd (12.80%), ¹¹²Cd (24.13%), ¹¹³Cd (12.22%), ¹¹⁴Cd (28.73%) and ¹¹⁶Cd (7.49%). The photoneutron reaction cross sections σ(γ,n) + σ(γ, np) and σ(γ, 2n) as well as the total absorption cross section σ(γ, sn) = σ(γ,n) + σ(γ, np) + σ(γ, 2n) for a target from a natural mixture of cadmium isotopes were measured by using a beam of quasimonochromatic photons without separating the contributions from the reactions on individual isotopes [1]. Absolute majority of photonuclear reaction data on cadmium isotopes has been obtained in experiments using bremsstrahlung photons, namely, relative yields of multiparticle reactions on natural cadmium were studied using end-point energy of 23 MeV [2,3], 55 MeV [4-6], the flux-averaged cross section were determined using end-point energies of 50 and 60 MeV [7], isomeric ratios were determined using electron bremsstrahlung for pairs ^115m,gCd [7-15] and ^104m,gAg [13].

Natural tellurium consists of eight stable isotopes with following mass numbers and isotopic abundances: ¹²⁰Te (0.09%), ¹²²Te (2.55%), ¹²³Te (0.89%), ¹²⁴Te (4.74%), ¹²⁵Te (7.07%), ¹²⁶Te (18.84%), ¹²⁸Te (31.74%) and ¹³⁰Te (34.08%). Although all of these isotopes can undergo photodisintegration via different reaction channels, only a small number have been studied so far, namely, photoneutron reactions [10-12,16-22]. The cross sections for the (γ,n) [22], (γ,n) + (γ,pn) [16] and (γ,2n) + (γ,2np) [16] reactions on the isotopes ^{120,124,126,128,130}Te induced by bremsstrahlung photons and positron annihilation in flight were determined by detecting neutrons in the energy range of γ quantum 8.03-26.46 MeV. Isomeric ratios have been measured for the pairs ^119m,gTe [10,17,19,20], ^121m,gTe [10,11,19,20], ^123m,gTe [10,18], ^127m,gTe [11,19,21] and ^129m,gTe [10-12,17,19,21].

This work aims to obtain new data on fundamental photonuclear reactions on cadmium and tellurium isotopes using a bremsstrahlung γ-radiation beam with energies between 10 and 23 MeV. We used TALYS-2.0 [24] and combined model of photonucleon reactions (CMPR) [25] for simulations and the γ-activation method with bremsstrahlung photons from the electron accelerator to obtain our experimental data. Furthermore, the photoproton reaction product the ¹¹¹Ag is prospective medicinal isotope [26-29]; thus, examining the reaction yields is a beneficial for both research and application.

The paper is organized as follows. In Sec. 2 the experimental set-up and procedures are described. In Sec. 3 the methods of data analysis are outlined. In Sec. 4, the results for Cd and Te isotopes are presented and discussed. In Sec. 5, the conclusions are drawn. In Appendix 1, the tabulated experimental results are presented. In Appendix 2, The TALYS options and GDR isospin splitting are inspected.

This experiment was carried out using the MT-25 microtron's output electron beam [30]. The electron energies ranged from 10 to 23 MeV, with an energy step of 1 MeV. Table 1 lists the main parameters of the experiments. To generate γ-radiation, a tungsten radiator target, a common convertor material, was employed. The tungsten target was thick enough (3 mm) to maximise the amount of photons in the energy range of the giant dipole resonance (GDR), which dominates the photonuclear cross section between the nucleon separation threshold and 20-30 MeV. To eliminate the leftover electrons from the bremsstrahlung beam, a 30 mm thick aluminium absorber was positioned behind the tungsten converter. The Cd and Te targets were located perpendicular to the electron beam and 1 cm away from the converter. The target of natural cadmium had dimensions 10×10×0.5 mm (at 10–19 MeV) and 5×5×0.5 mm (at 20–23 MeV). The natural tellurium target in a form of a powder in an aluminium foil in the form of a square envelope with a size of 15×15×2 mm (at 10-15 MeV), 8×8×2 mm (at 16-19 MeV) and 6×6×2 mm (at 20-23 MeV).

In the trials, a bremsstrahlung flux generated in the tungsten converter was utilised to irradiate metallic natural cadmium and tellurium samples. The fluctuations in beam current were measured using a Faraday cup and a calibrated ionisation chamber in the beam, and then recorded into a web-accessible database for use in the study with LabView software and an analog-to-digital converter card. [31]. Along with the Faraday cup and ionisation chamber, the beam current was determined by digitising the electrical charge accumulated on the target. During irradiation, the electron current of the accelerator was measured using a Faraday cup. A 0.15-mm-thick copper monitor was positioned behind the irradiation target. The absolute value of the current was calculated by comparison of experimentally measured and theoretical yields at the monitor on the basis of the ⁶⁵Cu(γ,n)⁶⁴Cu reaction. The experimental cross sections of the partial photoneutron reactions for the ⁶⁵Cu nucleus, obtained on quasimonoenergetic annihilation photon beams [32] using the neutron multiplicity sorting method display considerable systematic uncertainties and do not satisfy the specially introduced objective physical data reliability criteria. We used the corrected theoretical cross sections which were used to evaluate the cross sections of the partial reactions using their experimental-theoretical approach [33]. The yield of the ⁶⁵Cu(γ,n)⁶⁴Cu reaction was determined using the expected cross section [33], and the bremsstrahlung spectrum was generated using Geant4 [34].

Once the radiation levels in the experimental hall were safe, the targets were transferred to a different measurement room and the induced activity in the irradiated target was measured. We used a high purity germanium (HPGe) γ-detector with a resolution of 16 keV at 1332 keV, together with standard measurement electronics and a 16K ADC/MCA (Multiport II Multichannel Analyser, CANBERRA). The energy and efficiency of the HPGe detector were calibrated using standard γ-ray sources. A thorough explanation of the γ-activation measurement method used in this study can be found in [35,36].

The duration that elapsed between the end of the irradiation process and the beginning of the measurement was between 10 and 15 minutes, designated as the cooling period. The spectra of each sample were taken many times over a total of 0.5, 1, 12, and 24 hours. Fig. 1 and Fig. 2 display typical γ-ray spectra of the chemical products generated from the ^natCd and ^natTe, respectively. A background spectrum (red line) is also shown in Fig. 1. Bremsstrahlung radiation with end-point energy of 23 MeV was used to irradiate the samples.

Figure 1.  (color online) Spectra of residual activity of the irradiated sample of ^natCd (top-to-bottom) 3 h (a) and 4 days (b) after irradiation. The spectra measurement duration was 1 h (a) and 1 day (b), respectively

Figure 2.  (color online) Spectra of residual activity of the irradiated sample of ^natTe (top-to-bottom) 6 h (a) and 11 days (b) after irradiation. The spectra measurement duration was 1 h (a) and 3 days (b), respectively

The γ-ray spectra were processed using the DEIMOS32 code [37]. This code uses the Gaussian function to fit the count area of full-energy peaks. The processed peaks were identified using the half-life of residual nuclei, γ-ray energy, and intensity. The radionuclides were identified based on their different γ-ray energies and half-lives. Table 2 provides the key γ-ray energies and intensities used to compute the reaction product yield. Table 2's columns 4-5 contain nuclear data from Ref. [38].

The half-lives of previously investigated radionuclides ranged from 20 min (¹¹⁵Ag) to 461.9 days (¹⁰⁹Cd) as well as from 69.6 min (^129gTe) to 164.2 days (^121mTe). To compute radioactive half-lives and select appropriate spectra for each isotope's activity, γ-ray spectra were collected throughout a range of waiting times, from minutes to a day after irradiation. The activity is typically measured using the highest intensity, well-separated, interference-free, and correctable γ-ray.

The experimental yields of the reactions Y_exp were normalized to one electron of the accelerated beam incident on the bremsstrahlung target and calculated using the following formula:

where $ {S}_{p} $ is the full-energy-peak area; $ \varepsilon $ is the full-energy-peak detector efficiency; $ {I}_{\gamma } $ is the γ- emission probability; $ {C}_{abs} $ is the correction for self-absorption of γ-rays in the sample; $ {t}_{real} $ and $ {t}_{live} $ are the real time and live time of the measurement, respectively; $ N $ is the number of atoms in the activation sample; $ {N}_{e} $ is the integral number of incident electrons; $ \lambda $ is the decay constant; $ {t}_{cool} $ is the cooling time; and $ {t}_{irr} $ is the irradiation time.

The experiment determined the yields Y_theor of photonuclear reactions, which reflect the convolution of the photonuclear reactions cross section σ_i(E), and the distribution density of the number of bremsstrahlung photons over energy per one electron of the accelerator W(E, E_γmax). The outcome of measuring the yield of isotope generation in all possible reactions on a natural mixture of isotopes is as follows:

where E_γmax is the kinetic energy of electrons hitting the tungsten radiator, E is the energy of bremsstrahlung photons produced on the radiator, E_th is the threshold of the studied photonuclear reaction, η_i is the percentage of the studied isotope in the natural mixture, and the index i corresponds to the number of the reaction contributing to the production of the studied isotope.

Figure 3 illustrates the distribution density of the number of bremsstrahlung photons W(E, E_γmax) per one electron of the accelerator for accelerated electron energies from 10 to 23 MeV, determined using Geant4 for the bremsstrahlung target made of tungsten with a thickness of 3 mm.

Figure 3.  The distribution density of the number of bremsstrahlung photons at the energies of 10-23 MeV

The total and partial cross sections σ(E) of photonuclear reactions on cadmium and tellurium isotopes were estimated for monochromatic photons using the TALYS code [24] with standard parameters, and CMPR [25]. The TALYS program examines all processes in the nucleus and transitions between states. As a result, it is possible to calculate not only the total cross sections of photonuclear reactions, but also the cross sections of reactions involving the production of certain states, particularly isomeric states. The standard (default) TALYS option uses Simple Modified Lorentzian (SMLO) model for photon strength functions (PSF). This model is used to calculate E1, M1, and upbend components, generally providing more accurate, temperature-dependent resonance shapes than older models.

As compared with TALYS, the CMPR accurately takes into account the GDR isospin splitting, which is of a crucial importance for description of the proton decay channel. The basics of the GDR isospin splitting and some relevant CMPR results are presented in Appendix 2. This Appendix also provides the information on TALYS options as well as examples of comparison of TALYS and CMPR results

The yield measurement for a natural mixture of isotopes yields gives the amount of isotope produced in all potential reactions on the natural mixture. The primary problem of bremsstrahlung beam experiments is that the yield of photonuclear reaction depends on both the investigated cross section of the reaction σ_i(E) and the form of the bremsstrahlung spectrum W(E, E_γmax), which is often known with inadequate accuracy. The use of relative yields allows us to determine the dependency of the yield of photonuclear reactions on the maximal energy of bremsstrahlung under various experimental settings. The overall photon absorption cross section is not taken into account when calibrating the yield of one of the most likely reactions. The the most probable and well-studied ¹¹⁶Cd(γ,n)¹¹⁵Cd and ¹³⁰Te(γ,n)¹²⁹Te reactions were chosen as a primary reaction in case of cadmium and tellurium, respectively. Also there are no other channels (for example, (γ,2n) reaction on heavier stable nuclei) for product formation of ¹¹⁵Cd and ¹²⁹Te since the nuclei ¹¹⁶Cd and ¹³⁰Te are the heaviest stable nuclei in the natural mixture of Cd and Te, respectively.

Theoretical values of the relative yields can be calculated using the following formula:

where η is the percentage of the ¹¹⁶Cd and ¹³⁰Te isotopes in the natural mixture of cadmium and tellurium isotopes, respectively. Owing to the assumption on the unchanged shape of the bremsstrahlung spectrum, the bremsstrahlung spectrum W(E, E_γmax) can be replaced by the photon production cross section σ(E, E_γmax) calculated using Seltzer-Berger tables [39]:

To represent the experimental photonuclear reaction data, the cross section per equivalent quantum σ_q is used determined by the expression:

The cross section per equivalent quantum for a natural mixture of isotopes includes all possible channels of the final isotope production with account for the percentage of initial nuclei is:

The experimental points along the cross sections of the (γ,n) [22] and (γ,n) + (γ,pn) [16] reactions on the isotopes ^120,128,130Te were approximated by the Lorentz function, the relative yields Y_rel and cross sections per equivalent quantum σ_q were calculated based on the least squares approximation. In Fig. 4-10 these points are indicated by open circles [22] and open rectangles [16], respectively.

Figure 4.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 11.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹²Cd(γ, p)¹¹¹Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 12.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹³Cd(γ, p)¹¹²Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 13.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁴Cd(γ, p)¹¹³Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 14.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, p)¹¹⁵Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 15.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹²⁰Te(γ, n)¹¹⁹Te as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [22] (open circles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 16.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of the ¹²²Te(γ,n)¹²¹Te and ¹²³Te(γ,2n)¹²¹Te reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 17.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe and ¹²⁵Te(γ, 2n)^123mTe reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using TALYS code

Figure 18.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using TALYS code

Figure 19.  Relative yields (a) and cross section per equivalent quantum (b) of ¹²⁸Te(γ, n)¹²⁷Te reaction as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [22] (open rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 20.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹³⁰Te(γ, n)¹²⁹Te as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [22] (open rectangles) as well as simulated values using the CMPR (solid line) and TALYS code (dashed lines)

Figure 21.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²³Te(γ, p)¹²²Sb and ¹²⁴Te(γ, np)¹²²Sb reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 22.  The ratio of the cross section per equivalent quantum $ \sigma _{qexp}^{nat}/\sigma _{qtheory}^{nat} $ for the ¹²³Te(γ, p)¹²²Sb reaction

Figure 23.  Relative yields (a) and cross section per equivalent quantum (b) of the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 24.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹²⁸Te(γ, p)¹²⁷Sb as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 25.  Relative yields (a) and cross section per equivalent quantum (b) of the reaction ¹³⁰Te(γ, p)¹²⁹Sb as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 5.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁸Cd(γ, n)¹⁰⁷Cd as a function of bremsstrahlung end-point energy from the present work (solid rectangles) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 6.  Relative yields (a) and cross section per equivalent quantum (b) of reactions ¹¹⁰Cd(γ, n)¹⁰⁹Cd and ¹¹¹Cd(γ, 2n)¹⁰⁹Cd as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) as well as simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 7.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangle) and simulated values using TALYS code (dashed lines)

Figure 8.  (color online) Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹¹⁶Cd(γ, n)¹¹⁵Cd as a function of bremsstrahlung end-point energy from the present work (solid rectangles), literature data [3] (open rectangles) as well as simulated values using the CMPR (solid line) and TALYS code (dashed lines)

Figure 9.  Relative yields (a) and cross section per equivalent quantum (b) of reaction ¹⁰⁶Cd(γ, p)¹⁰⁵Ag as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

Figure 10.  (color online) Cross section per equivalent quantum of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as a function of bremsstrahlung end-point energy from the present work (solid rectangles) and simulated values using the CMPR (solid lines) and TALYS code (dashed lines)

The measured relative yields to the yield of the reaction ¹¹⁶Cd(γ,n)¹¹⁵Cd (in the case of ^natCd) and ¹³⁰Te(γ,n)¹²⁹Te (in the case of ^natTe) and cross sections per equivalent quantum for a natural mixture of isotopes are shown in Fig. 4-25 and Tables 1-2 in Appendix, along with theoretical computations using the TALYS and CMPR programs and previously published data.

The square root of the quadratic sum of all independent statistical and systematic uncertainties was used to determine the overall uncertainties in the results. The counting statistics from the observed number of counts under the photo-peak of each γ-line (2.5%~10.5%) were the primary contributors to the ensuing statistical uncertainty. Data accumulation for an optimal duration of measurements based on the half-life of the generated nuclides was used to estimate this. The systematic uncertainties, on the other hand, were computed using the uncertainties of the following: the number of target nuclei (~0.3%), the irradiation and cooling time (~0.5%), the current and electron beam energy (~2.5%), the detector efficiency (~3%), the half-life of the reaction products (~2%), the distance between the sample and detector (~2%), the γ-ray abundance (~2%), the flux estimation (~11.5%) and normalization of the experimental data to the ¹¹⁶Cd(γ,n)¹¹⁵Cd and ¹³⁰Te(γ,n)¹²⁹Te monitor reactions’ yield 0.5-2%. Roughly 12.58% is the overall systematic uncertainty. It is determined that the overall uncertainty ranges from about 12% to about 19%.

Five cadmium isotopes are directly generated by ^natCd(γ, n) reactions when natural cadmium is irradiated with bremsstrahlung radiation with end-point energy of 10-23 MeV. In this study, the relative yields and cross section per equivalent quantum of the ^natCd(γ, n)^{105,107,109,111m,115g,115m}Cd reactions at the bremsstrahlung end-point energies of 10-23 MeV are determined and presented in Fig. 4-8. Besides, the tabulated results are given in Appendix 1.

For this reaction, no literature data was available; hence, its measurements were only compared with the theoretical calculations. Fig. 4 shows experimental obtained and simulated values relative yields as well as cross section per equivalent quantum of reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd. In Fig. 4, it is clear that the cross section per equivalent quantum calculated by the TALYS and CMPR codes are almost the same, but they are higher than the currently presented results for the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd reaction.

At an energy of 12 MeV, the theoretical values for the two models are 4 times higher than the experimental point, then with an increase in energy to 20 MeV, the ratio $ \sigma _{qexp}^{nat}/\sigma _{qtheory}^{nat} $ decreases and is equal to approximately 2.5. The apparent disparity between theory and experiment may stem from the fact that statistical models of photonuclear reactions, such as the CMPR and TALYS codes, overlook the unique structural characteristics of cadmium isotopes. Alternatively, the low experimental neutron yield in reaction ¹⁰⁶Cd(γ, n)¹⁰⁵Cd can be partly explained by bypassed character of the nucleus ¹⁰⁶Cd.

Fig. 5 shows that the current results follow the graphical shape but are lower than the theoretical values. The experimental results (γ,n) are two times as less as its theoretical counterparts. This discrepancy indicates the need for further research in the study of photoneutron reactions on ^106,108Cd.

For the production of ¹⁰⁹Cd from the ^natCd(γ, Xn)¹⁰⁹Cd reactions, only one previous experimental data sets in the GDR energy region based on bremsstrahlung photons was available [3]; this was found to be lower than the theoretical values obtained using the TALYS and CMPR codes as shown in Fig. 6. The figure shows that the current results follow the graphical shape but are lower than the theoretical values; they are the closest to the values calculated using TALYS code.

The measured results for the ¹¹¹Cd(γ, γ`)<sup>111m</sup>Cd and <sup>112</sup>Cd(γ, n)<sup>111m</sup>Cd reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 7. For the production of <sup>111m</sup>Cd from the <sup>nat</sup>Cd target, only one previous experimental data set in the GDR energy region based on bremsstrahlung photons were available [3], this was found to be lower than the theoretical values obtained using the TALYS code as shown in Fig. 7. The figure also shows that the theoretical values from both the TALYS and CMPR codes as well as literature data are in agreement with the data from this study. Based on the Fig. 7, it can also be said that in the energy range up to 11 MeV, the <sup>111m</sup>Cd nucleus is formed due to the <sup>111</sup>Cd(γ, γ`)^111mCd reaction, the contributions of the ¹¹¹Cd(γ, γ`)^111mCd and ¹¹²Cd(γ, n)^111mCd reactions to the formation of ^111mCd are equal at 12 MeV, and then the ¹¹²Cd(γ, n)^111mCd reaction plays a dominant role.

The measured results for the ¹¹⁶Cd(γ, n)^115m,gCd reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 8. There is only one literature data for the ¹¹⁶Cd(γ, n)^115m,gCd reaction [3] in 23 MeV. As shown in Fig. 8, it is clear that the theoretical values from both the TALYS and CMPR codes as well as literature data are in agreement with the data from this study.

Five argentum isotopes are directly generated by ^natCd(γ, p) reactions when natural cadmium is irradiated with bremsstrahlung radiation with end-point energy of 10-23 MeV. In this study, the relative yields and cross section per equivalent quantum of the ^natCd(γ, p)^{105,111,112,113,115}Ag reactions at the bremsstrahlung end-point energies of 12-23 MeV are determined for the first time and presented in Fig. 9-14.

These measurements were only compared with the theoretical values due to unavailability of published data. In Fig. 9, the measured values are revealed to be higher than the calculated values. No theoretical calculation can describe the experimental data.

The ratio $ \sigma _{qexp}^{nat}/\sigma _{qtheory}^{nat} $ is approximately 10 for the two models. As we discussed in Section A1 that, the proton Fermi surface is significantly higher than the neutron Fermi surface in the ¹⁰⁶Cd nucleus. As a result of a reduction in the effective width of the Coulomb barrier, this must raise the proton penetrabilities and, consequently, the proton yield.

Proton yield on ¹⁰⁶Cd can also be boosted by the direct photoelectric effect, which is predominantly localised at the nucleus’ surface. Protons are expected to dominate in β⁺-radioactive nuclei and nuclei bordering them. The target nucleus's structural (shell) unique features have a significant impact on direct photonuclear reactions. Cadmium isotopes exhibit the most significant single-particle dipole excitations during the 1g_9/2 → 1h_11/2 transitions. The decay of such excitations, which have a probability of about 40% in both the proton and neutron channels, leads to the emission of protons with the maximum possible energy, because the final-state nucleus {Z-1, N} arises in the ground state. The energy carried away by neutrons is 3 to 4 MeV smaller, because the final-state nucleus {Z, N-1} remains in an excited (hole) state. This significantly influences the relative output of protons and neutrons in proton-rich cadmium isotopes.

Fig. 10 shows the relative yields of ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions as well as sum of the ¹⁰⁶Cd(γ, n)¹⁰⁵Cd and ¹⁰⁶Cd(γ, p)¹⁰⁵Ag reactions. The results in Fig. 10 show that the theoretical yields of the (γ,n) and (γ,p) reactions on ¹⁰⁶Cd nuclei differ significantly from their experimental counterparts, but their summed value agrees with the respective experimental value. This means that the original photoabsorption cross section calculated using the TALYS code is unlikely to differ significantly from the true value. The discrepancy in cross sections per equivalent quantum is due to the redistribution of the cross section between the (γ,n) and (γ,p) reactions.

For the ¹¹²Cd(γ, p)¹¹¹Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 11. In Fig. 11, it is shown that the currently measured and theoretical values based on the CMPR code are in good agreement, in terms of not only shape but also magnitude. TALYS predicts results that are about almost 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹³Cd(γ, p)¹¹²Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 12. In Fig. 12, it is shown that the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. TALYS predicts results that are about almost 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

For the ¹¹⁴Cd(γ, p)¹¹³Ag reaction only one previous experimental data sets in 23 MeV [3]; this was found to be lower than the theoretical values obtained using the CMPR code as shown in Fig. 13. In Fig. 13, it is shown that the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. TALYS predicts results that are about almost 5 times lower than CMPR, and this difference increases rapidly with increasing energy.

As can be seen in Fig.11-13, it is clear that a discrepancy in experimental data on the reactions ^natCd(γ, p)^111-113Ag is observed, our results are higher than literature data [3]. The large difference between the results of the work [3] and the present ones on the reactions ^natCd(γ, p)^111-113Ag might arise from the difference in the measuring duration of the irradiated targets.

The measurements from the reaction were only compared with the theoretical values due to unavailability of published data. In Fig. 14, it is shown that the measured values for the reaction are higher than the calculated values; however, they are the closest to the values calculated using the CMPR code. TALYS predicts results approximately 16 times lower than CMPR.

Nine tellurium isotopes are directly generated by ^natTe(γ, n) reactions when natural tellurium is irradiated with bremsstrahlung radiation with end-point energy of 10-23 MeV. In this study, the relative yields and cross sections per equivalent quantum of the ^natTe(γ, n)^{119g,119m,121g,121m,123m,125m,127,129g,129m}Te reactions at the bremsstrahlung end-point energies of 10-23 MeV are determined and presented in Fig. 15-20.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 15. There is only one literature data for the ¹²⁰Te(γ, n)¹¹⁹Te reaction [22] in the energy range of γ quantum 8.03-26.46 MeV. The theoretical values from both the TALYS and CMPR codes align with the literature data; yet, our results are inferior to them, as shown in Fig. 15.

The measured results for the ¹²²Te(γ,n)¹²¹Te and ¹²³Te(γ,2n)¹²¹Te reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 16. The measured values for the reaction are lower than the calculated values, as seen in Fig. 16.

The measured results for the ¹²³Te(γ, γ`)^123mTe, ¹²⁴Te(γ, n)^123mTe and ¹²⁵Te(γ, 2n)^123mTe reactions are compared with the theoretical values obtained with the TALYS code, as shown in Fig. 17. The measured values for the reaction are lower than the calculated values, as seen in Fig. 17.

The measured results for the ¹²⁵Te(γ, γ`)^125mTe and ¹²⁶Te(γ, n)^125mTe reactions are compared with the theoretical values obtained with the TALYS code, as shown in Fig. 18. As can be seen in Fig. 18a, the measured values for the reaction are higher than the calculated values. This may be due to the fact that the nucleus ^125mTe emits a γ-ray with low intensity (109.28 keV (0.28%)). However, with exception data in 10-12 MeV, there is a good agreement between measured data and TALYS value in Fig. 18b.

The measured results for the ¹²⁸Te(γ,n)¹²⁷Te reaction are compared with the theoretical values obtained with the TALYS, as shown in Fig. 19. The measured values for the reaction are lower than the calculated values, as seen in Fig. 19. There is a good agreement between literature data and theoretical calculations.

The measured results for the ¹²⁰Te(γ, n)^119m,gTe reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 20. There is only one literature data for the ¹³⁰Te(γ, n)¹²⁹Te reaction [22] in the energy range of γ quantum 8.03-26.46 MeV. It is clear that the theoretical values from both the TALYS and CMPR codes are in agreement with the literature data, but our results are below them, as shown in Fig. 20.

Four stibium (¹²²Sb, ¹²⁴Sb, ¹²⁷Sb, ¹²⁹Sb) radioisotopes were directly produced by ^natTe(γ, p) reactions. In this study, the relative yields and cross section per equivalent quantum of the ^natTe(γ, p)^{122,124,127,129}Sb reactions at the bremsstrahlung end-point energies of 10-23 MeV are determined for the first time and presented in Fig. 21-25.

Fig. 21 displays the measured data as well as the computed values. It is evident from the Fig. 21 that there is good agreement between the theoretical values on the basis of CMPR only for 22 and 23 MeV. The remaining experimental points are almost 100 times larger than theoretical calculations.

Since the threshold of the reaction ¹²⁴Te(γ, d)¹²²Sb is 15.33 MeV, then we can assume that up to 19 MeV (taking into account the Coulomb barrier) the nucleus ¹²²Sb is formed as a result of the reaction ¹²³Te(γ, p). Fig. 22 shows the ratios of the cross section per equivalent quantum $ \sigma _{qexp}^{nat}/\sigma _{qtheory}^{nat} $ for the (γ, p) reaction on ¹²³Te. As can be seen in Fig. 22, both models cannot describe the experimental points.

The measured results for the ¹²⁵Te(γ, p)¹²⁴Sb and ¹²⁶Te(γ, np)¹²⁴Sb reactions are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 23. It is clear that there is a discrepancy between theoretical calculations, and the experimental points are higher than the TALYS curve, but lower than the CMPR curve with an exception 19 MeV (this point is in good agreement with the TALYS calculation).

The measured results for the ¹²⁸Te(γ,p)¹²⁷Sb reaction are compared with the theoretical values obtained with the TALYS and CMPR codes, as shown in Fig. 24. It is evident from the Fig. 24 that there is good agreement between the theoretical values on the basis of CMPR and currently measured values in terms of both form and magnitude.

Fig. 25 displays the measured data as well as the computed values. It is clear that there is a discrepancy between theoretical calculations, and the experimental points are higher than the TALYS curve, but lower than the CMPR curve. The experimentally obtained results lie closer to the theoretical curve according to the CMPR.

Since we are irradiating natural mixtures of Cd and Te, this will give us the opportunity to study photonuclear reactions over a wide mass range with A=106-130. The cross section per equivalent quantum of the (γ,p) reaction in a case of monoisotopes σ_q calculated on the basis of the CMPR and TALYS by equation (5) are contrasted against experimental data in Fig. 26. The data in Fig. 26 shows that the measured yields of the (γ,p) reactions on the isotopes ^{112,113,114,116}Cd and ^128,130Te agree within 30% with the results of the calculations based on the CMPR. The (γ,p) yields calculated on the basis of the TALYS code are underestimated with respect to experimental data by one order of magnitude. The reason behind this difference is that the TALYS code disregards special features of the decay of the T_> GDR component, whose decay through the proton channel to low-lying states of the final nucleus is forbidden by isospin-selection rules. As a result, T_> states decay through the proton channel with a higher probability. The cross section per equivalent quantum calculations for the reactions ¹¹⁴Cd(γ,p)¹¹³Ag and ¹²⁸Te(γ,p)¹²⁷Sb using TALYS parameters on the basis of the models of the nuclear level densities and γ-ray strength functions and accounting of isospin splitting in CMPR are given in Appendix 2.

Figure 26.  (color online) Cross section per equivalent quantum of the (γ,p) reaction in a case of monoisotopes σ_q for the stable isotopes of cadmium (a) and tellurium (b)

The measured (γ,p) yields are a few percent of the (γ,n) yields for all nuclei, with the exception of the ¹⁰⁶Cd nucleus, for which the yield of the reaction ¹⁰⁶Cd(γ,p)¹⁰⁵Cd is commensurate with the yield of the reaction ¹⁰⁶Cd(γ,n)¹⁰⁵Cd, but this contradicts the results of the theoretical calculations in [24,25]. In the case of the ¹²³Te(γ,p)¹²²Sb reaction, the situation is completely unclear. In all experiments, the spectra show a line at 564 keV. However, theoretical calculations on the basis of TALYS and CMPR are several orders of magnitude smaller.

For a more thorough analysis of the obtained results, the ratios of the reaction yield (γ,p) to the reaction yield (γ,n) were calculated for the nuclei ¹⁰⁶Cd (¹⁰⁵Ag/¹⁰⁵Cd), ¹¹⁶Cd (¹¹⁵Ag/¹¹⁵Cd), ¹²⁸Te (¹²⁷Sb/¹²⁷Te) and ¹³⁰Te (¹²⁹Sb/¹²⁹Te). Also the ratios of yields (γ,p)/(γ,n) are calculated for the nucleus ⁷⁴Se on the basis of the experimental results of our previously work [41]. Figure 27a shows the ratio of the reaction yield (γ,p) to the reaction yield (γ,n) depending on the electron energy of the accelerator. As shown in Fig. 27a the ratios of yields (γ,p)/(γ,n) are almost equal to 1 for bypassed nuclei ⁷⁴Se and ¹⁰⁶Cd. It can be seen that with the exception of the points for the nucleus ¹⁰⁶Cd, the experimental points are consistent with the calculated curves of CMPR. In the case of ¹⁰⁶Cd (¹⁰⁵Ag/¹⁰⁵Cd), the CMPR and TALYS cannot describe the experimental results. The reason for the observed discrepancy between theory and experiment may be explained by the fact that statistical models of photonuclear reactions do not take into account the individual structural features of Cd isotopes.

Figure 27.  (color online) The ratio of the reactions’ yields (γ,p)/(γ,n) as a function of: (a) the electron energy of the accelerator and (b) the proton-neutron ratio N/Z at the electron energy of the accelerator 23 MeV

Figure 27b shows the ratios of yields (γ,p)/(γ,n) as a function of the proton-neutron ratio N/Z at the electron energy of the accelerator 23 MeV. The literature data were calculated using experimentally measured reaction cross sections (γ,p) and (γ,n) on the nuclei ⁹⁰Zr [42,43], ⁸⁹Y [43,44], ¹⁰³Rh [1,45], ¹¹²Sn [46,47] and ¹⁶⁰Gd [48]. With the exception of the points at N/Z = 1.176 (⁷⁴Se) and 1.208 (¹⁰⁶Cd), the experimental points are consistent with the calculated curve on the basis of CMPR. The ratio of yields (γ,p)/(γ,n) decreases with increasing proton-neutron ratio N/Z.

Based on the measured experimental yields of the metastable and ground states from Table 1-2 in Appendix 1, we obtained the isomeric yield ratio (IR=σ_h/σ_l) of ^115gCd (nuclear spin=1/2⁺) and ^115mCd (nuclear spin=11/2^–) in the ^natCd(γ,n) reactions, which are given in Table 3 for various bremsstrahlung end-point energies. The photon induced isomeric ratio values from this study, the literature data in the GDR region [7-15] are shown in Fig. 28a. As seen in Fig. 28a, the experimental isomeric ratio values in the ¹¹⁶Cd(γ, n) reaction are in agreement with the theoretical values. Furthermore, Fig. 28a shows that the isomeric ratio values of ^115m,gCd increase with increasing excitation energy.

Figure 28.  Isomeric yield ratios of the pairs ¹¹⁶Cd(γ,n)^115m,gCd (a), ¹²⁰Te(γ,n)^119m,gTe (b), ¹²²Te(γ,n)^121m,gTe (c) and ¹³⁰Te(γ,n)^129m,gTe (d) as a function of the bremsstrahlung end-point energy from the present work (solid squares), literature data and simulated values using TALYS code (dashed lines)

In the experiments we have registered three isomeric pairs of tellurium ^119,121,129Te. All of the isomeric states are with nuclear spin 11/2^–. Based on the measured experimental yields of the metastable and ground states, we obtained the isomeric yield ratio (IR=σ_h/σ_l) for all of them, which are given in Fig. 28b,c,d for various bremsstrahlung end-point energies.

For the reaction ¹²⁰Te(γ,n)¹¹⁹Te the photon induced isomeric ratio values from this study, the literature data in the GDR region [10,19,20] are shown in Fig. 27b. As seen in Fig. 28b, our experimental isomeric ratio values in the ¹²⁰Te(γ, n) reaction are in agreement with the TALYS curve. Starting from 15 MeV, there is a scatter in our and literature data in isomeric ratios. Moreover, the figure shows that the isomeric ratio values of ^119m,gTe increase with increasing excitation energy.

For the reaction ¹²²Te(γ,n)¹²¹Te the photon induced isomeric ratio values from this study, the literature data in the GDR region [10,11,19,20] are shown in Fig. 28c. As seen in Fig. 28c, our experimental values of isomeric ratios in the reaction ^natTe(γ,n)^121m,gTe are consistent with the literature data, but they diverge from the TALYS curve starting from 11 MeV. Additionally, As the excitation energy increases, the isomeric ratio values of ^121m,gTe rise, as the figure illustrates.

For the reaction ¹³⁰Te(γ,n)¹²⁹Te the photon induced isomeric ratio values from this study, the literature data in the GDR region [10-12,17,19,21] are shown in Fig. 28d. As seen in Fig. 28d, our experimental isomeric ratio values in the ¹³⁰Te(γ,n) reaction are in agreement with the TALYS curve. Starting from 14 MeV, there is a scatter in our and literature data in isomeric ratios. Furthermore, the figure shows that the isomeric ratio values of ^129m,gTe increase with increasing excitation energy.

The present study addressed the measurements of relative yields and cross section per equivalent quantum for the photonuclear reactions on a natural mixture of cadmium and tellurium using bremsstrahlung end-point energies of 10 to 23 MeV. The bremsstrahlung photon flux was computed in the Geant4.11.1 code. The experimental results were compared with calculations using the TALYS model with the standard parameters and the CMPR. For the photoneutron reactions on the nuclei ^112,116Cd(γ,n) and ^{120,122,124,126,130}Te, a good agreement was observed between the experimental data and theoretical calculations.

The measured (γ,p) yields are a few percent of the (γ,n) yields for all nuclei, with the exception of the bypassed nucleus ¹⁰⁶Cd, for which the yield of the reaction ¹⁰⁶Cd(γ,p)¹⁰⁵Cd is commensurate with the yield of the reaction ¹⁰⁶Cd(γ,n)¹⁰⁵Cd, but this contradicts the results of the theoretical calculations. For the reaction ¹²³Te(γ,p)¹²²Sb experimental points are almost 100 times larger than theoretical calculations.

On the heavy isotopes ^{112,113,114,116}Cd and ^128,130Te, the experimental results agree with theoretical relative yields calculated using the CMPR. Including isospin splitting in the CMPR allows for much better description of experimental data on reactions with proton escape in the energy range from 12 to 23 MeV. Therefore, taking into account isospin splitting is necessary for a more reasonable description of the GDR decay. The study of photonuclear reactions on cadmium and tellurium isotopes is important for understanding the formation and decay of bypassed nuclei during nucleosynthesis.

In this Appendix, the tabulated experimental results discussed in Sec. 4 are presented.

The essential components of TALYS calculations for photonuclear reaction cross sections are the nuclear level densities and γ-ray strength functions. The cross sections of the reactions are computed in this work using TALYS 2.0 with standard parameters. For the reactions ¹¹⁴Cd(γ,p)¹¹³Ag and ¹²⁸Te(γ,p)¹²⁷Sb, the effects of altering a number of input options are examined, including level densities (Constant Temperature + Fermi gas model, Back-shifted Fermi gas Model, Generalised Superfluid Model, Skyrme-Hartree-Fock-Bogolyubov level densities from numerical tables, Skyrme-Hartree-Fock-Bogolyubov combinatorial level densities from numerical tables, Temperature-dependent Gogny-Hartree-Fock-Bogolyubov combinatorial level densities from numerical tables) and γ-strength functions (Kopecky-Uhl generalized Lorentzian, Brink-Axel Lorentzian, Hartree-Fock BCS tables, Hartree-Fock-Bogoliubov tables, Goriely’s hybrid model, Goriely T-dependent HFB, T-dependent RMF, Gogny D1M HFB+QRPA, Simplified Modified Lorentzian Model, Skyrme HFB+QRPA).

Using these options, the cross section per equivalent quantum for the reactions ¹¹⁴Cd(γ,p)¹¹³Ag and ¹²⁸Te(γ,p)¹²⁷Sb are displayed in Figures B1 and B2. Changing the parameters LD 1–6 and GSF 1–10 leads to 60 different results for theoretical σ(E) and $ \sigma _{q}^{nat} $(E). As seen in the Fig. B1 and Fig. B2, the change of these input options has no impact on the TALYS results. Thus, it is confirmed that the difference between the TALYS and CMPR results is due to the consideration of isospin splitting in CMPR. A brief description of isospin splitting is given below.

Figure B1.  (color online) Cross sections per equivalent quantum $ \sigma _{q}^{nat} $(E) for the ¹¹⁴Cd(γ,p)¹¹³Ag reaction calculated with the TALYS code for six level density models LD1-LD6 (a-f) and ten gamma strength functions (dashed lines) as well as simulated values using the CMPR (solid lines)

Figure B2.  (color online) Cross sections per equivalent quantum $ \sigma _{q}^{nat} $(E) for the ¹²⁸Te(γ,p)¹²⁷Sb reaction calculated with the TALYS code for six level density models LD1-LD6 (a-f) and ten gamma strength functions (dashed lines) as well as simulated values using the CMPR (solid lines)

In nuclei with N ≠ Z, upon absorption of electric dipole γ photons, two branches of the GDR are excited, T_<= T₀ and T_>= T₀ + 1, where T₀= $ \dfrac{|N-Z|}{2} $ [49]. Fig. B3 shows the excitations of the isospin components T_< and T_> of the GDR in initial nucleus (N, Z) and their decay according to the proton (N, Z − 1) and neutron (N − 1, Z) channels. From Fig. B3, it can be observed that the decay of excited GDR states with isospin T_>= T₀ + 1 according to the neutron channel to low-lying states T = T₀ – 1/2 with neutron emission is forbidden, which leads to an increase in the reaction cross section (γ,p) and to a maximum shift of the reaction cross section (γ,p) with respect to reactions (γ,n) towards higher energies in the nucleus (N, Z).

Figure B3.  Scheme of excitation of states T_< and T_> in the nucleus (N, Z) and their decay along the proton channel (N, Z − 1) and neutron channel (N − 1, Z)

The value of isospin splitting of the GDR is determined by the following relation [50]:

The ratio of the probabilities of excitation of states T_> and T_< is described by the following relation [51]:

Table B1 shows the values of the energy of the GDR isospin energy splitting calculated on the basis of relations (1) for isotopes ^natCd and ^natTe. Also Table B1 contains integral cross sections $ \sigma _{< }^{int} $ and $ \sigma _{> }^{int} $of the isospin components reactions (γ, sn) = (γ, n) + (γ, np) + (γ, 2n) and (γ, sp) = (γ, p) + (γ, np) + (γ, 2p) in the energy region below 40 MeV, the ratio of the reaction cross sections $ \frac{\sigma _{> }^{int}}{\sigma _{< }^{int}} $, calculated on the basis of CMPR for isotopes ^natCd and ^natTe. Table B1 shows that, for ^natCd, the growth of the mass number A from 106 to 116 results in increase of the isospin energy splitting by the value ≈2.29 MeV. For ^natTe, the growth of A from 120 to 130, leads to the increase of energy splitting by the value ≈2.16 MeV. The isospin splitting leads to the shift of the proton cross section of the relatively neutron in the side of the high energy.