Activation cross sections of gamma-emitters produced in deuteron induced reactions on 209 Bi up to 50 MeV

Deuteron induced reactions on natural bismuth targets were investigated with the stacked foil activation technique up to 50 MeV. Excitation functions for the reactions 209 Bi(d,xn) 207 , 206 , 205 Po,Bi(d,x) 207 , 205 Biand 209 Bi(d,x) 203 Pb obtained from gamma-spectra of decay products were compared with the results of our ALICE-D and EMPIRE-D modelcalculations,withtheresultofTALYScodetakenfrom TENDL-2019 on-line library and the results of the only measurement performed earlier. Thick target yields were deduced from the ﬁtted experimental cross sections.


Introduction
We perform a systematic investigation of the activation crosssections of deuteron induced nuclear reactions in all elements since years. The investigation has covered 65 elements (individual stable isotopes or elemental targets with natural isotopic composition): Be, B, C, N, Ne, Mg, Al, Si, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, Se, Kr, Rb, Sr, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Xe, Cs, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl and Pb. The investigations are connected to different projects on activation analyses, medical isotope production, radiation safety of accelerator elements, nuclear reaction theory and more. In the present work we investigated the activation cross-sections on bismuth up to 50 MeV deuteron energy. Lead-bismuth eutectics are under consideration as a target material with high-energy protons and deuterons for generating spallation neutrons and for nuclear coolant material in reactor technology. For this purposes deuteron activation cross-sections are already collected in the Fusion Evaluated Data Library a e-mail: ditroi@atomki.hu (corresponding author) (FENDL-3 library [1]), presently based mainly on results of TALYS model calculations.
A throughout literature survey resulted in only one experimental dataset on 209 Bi for production cross-sections of gamma-emitter radionuclides by Gonchar et al. [2], studying the deuteron induced reactions up to 47 MeV incident particle energy. In our earlier study of alpha particle induced reactions on Bi (Hermanne et al. [3]) we investigated both gamma and alpha particle emitting reaction products. In the present study we had studied only the activation cross sections of radionuclides with gamma emission.

Experiment and data evalution
For determination of the cross section data the activation method, by using stacked-foil target technique and off-line gamma-ray spectrometry were used. The bismuth targets were prepared by vacuum evaporation onto Al backing. The surface thickness of the Bi layer of each target was determined by measuring the weight of the foils before and after evaporation of the bismuth layer. The average thickness of the evaporated bismuth layers was about 1.8 µm. The thickness of the Al-backings was 51 µm, and 13 mm in diameter. The diameter of the evaporated spot was 8 mm. The evaporated samples were ordered according to their Bi-weight and the smallest and highest weight samples were paired and created an Al-Bi-Al sandwiched target putting the bismuth layers face-to-face. This way 20 bismuth targets were created with an overall Bi layers of 2.5-3.7 µm. The Al backings served as recoil catchers and as monitor foils for exact determination of beam parameters (intensity and energy) along the stack. Additionally, 102.6 µm thick Al energy degrader foils were inserted into the high energy part of the stack and 10.9 µm  Table 1) Ti foils for beam monitoring in the low energy segment of the stack (see Fig. 1).
The stacked target was irradiated in a Faraday cup like target holder equipped with a collimator of 3 mm in diameter, which determined beam size. The beam current was kept constant at about 20 nA during the 40 min irradiation. The details of the target stack, the experimental technique and the data evaluations are summarized in Table 1. The decay data used in data analysis are collected in Table 2. Effective beam intensities and the energy scale were determined by using the excitation functions of the 24 Al(d,x) 22,24 Na and nat Ti(d,x) 48 V monitor reactions. The excitation functions of these reactions, in comparison with the IAEA recommended data for monitors [4] are shown in Fig. 2. For estimation of the uncertainty of the effective beam energy in the target foils, cumulative effects of possible uncertainties in primary energy and target thickness were taken into account together with the effect of the energy straggling and of the correction for the monitor reaction (0.3-1.1 MeV). The uncertainties of cross sections were obtained from the sum in quadrature of all individual contributions (beam current (7%), beam-loss corrections (maximum 1.5%), target thickness (3%), detector efficiency (5%), photo peak area determination and counting statistics (1-20%) [5]. The main individual source of the uncertainties is the uncertainty of the counting statistics. The uncertainties of the non-linear contributing time related processes and parameters were not considered.
The activities of the detected radioisotopes were calculated from the spectrometry of the corresponding gammalines (Eq. 1) [6]: where A E O B denotes the activity at End of Bombardment (EOB), T is the net count in the gamma-peak, λ is the decay constant, t real , t live and t c are the real-time, live-time of the measurement and the cooling time, respectively I γ is the gamma-line absolute intensity and ε is the detector efficiency. From the activities the corresponding cross section was calculated by using Eq. 2.
where z denotes the projectile charge, I (A)is the beam current, N A is Avogadro's number (6.02214×10 23 mol −1 ), M (g/mol) is the molar mass of the chemical compound forming the target material, eis the electron charge (1.6 × 10 −19 C), ρ(g/cm 3 )is the density of the target material, s (cm) is the thickness of the target foil, ν is the number of atoms of the target element in the molecule and. σ (E)(cm 2 )is the cross section at E median energy in the particular foil in the stack. When complex particles are emitted instead of individual protons and neutrons the Q-values have to be decreased by the respective binding energies of the compound particles: np-d, +2.2 MeV; 2np-t, +8.48 MeV; n2p-3 He, +7.72 MeV; 2n2p-α, +28.30 MeV.

Nuclear model calculations
The cross sections of the investigated reactions were calculated using the modified pre-compound model codes ALICE-IPPE (Dityuk et al. [15]) and EMPIRE-II (Herman et al. [16]). To achieve better description of available data in the used ALIC-IPPE-D and in the EMPIRE-II-D a phenomenological enhancement factor K in these relations was taken as energy dependent and estimated to describe the whole set of the observed (d,p) cross sections for medium and heavy nuclei. The experimental data are also compared with the cross section data in the TENDL-2019 (Koning et al. [17]) nuclear reaction data library. The TENDL-2019 is based on both default and adjusted TALYS [18] calculations. In order to make the results comparable, the default options have been used with each model. Because the models are not perfect, they give results with different accuracy for different reactions. By using the same parameters (default), our results may help to the model developers to improve their description of processes.

Contribution of secondary neutron contribution
As usual by deuteron bombardment of heavy elements a lot of neutrons are produced in the nuclear reaction of direct, pre-equilibrium, compound, stripping, knock-out, break-up, etc. processes. We used the TENDL-2019 on-line library to demonstrate the effects might arise from secondary neutrons. In Fig. 9. The total production yield of neutrons is shown originating from of all nuclear reactions of 50 MeV deuteron bombardment. In order to discuss the possible effect of secondary neutrons we must now the energy distribution of them. A typical neutron spectrum is seen in Fig. 10 also taken from the TENDL-2019 library.
In principle these neutrons might give contribution to our cross sections via the 209 Bi(n,x) 205,207 Bi reactions. The estimated excitation functions of these neutron induced reactions on natural bismuth are shown in Fig. 11. It is obvious from the neutron spectrum in Fig. 10. that only a small fraction of the produced neutrons has an energy above the thresholds of the 209 Bi(n,x) 205,207 Bi reactions (29.6 and 14.4 MeV, respectively).
In order to completely exclude the neutron contribution a short and simple calculation can be made by estimating the number of secondary neutrons. The number of reactions (number of produced nuclei) can be calculated according to Eq. 3.
Where N (t) is the number of produced nuclei (number of reactions occurred) versus time, N t is the number of target nuclei ( 209 Bi) as layer thickness (atom/cm 2 ),N b is the number of bombarding particles (1/s), σ (cm 2 ) is the cross section and. By using Eq. 3. and supposing 1 µA beam current, 1 µm target thickness and an average cross section of 100 mb (overestimation), the number of deuteron induced reactions producing heavy products and neutrons is 1.6 10 9 /s/µA/µm.  The ratio of the number of neutrons and the numbers of the deuterons of 1µA deuteron beam is 2.8 10 −3 . Taking a cross section for the neutron induced reactions an order of magnitude higher (overestimation, 1000 mb), the same number of target atoms and the number of neutrons, estimated above the contribution by secondary neutrons is about two orders of magnitude less than that for the deuterons. Regarding the energy distribution of the secondary neutrons and the threshold energies of the corresponding two reactions only a very small fractions of the secondary neutrons are capable to contribute to the production of the 205,207 Bi radionuclides. Estimating the fraction of high energy neutrons, we found that less than 8% of the secondary neutrons have enough energy for producing 207 Bi and less than 0.5% for producing 205 Bi radionuclides. By combining these two values with production rate of the secondary neutrons it turns out that contributions of the secondary neutrons for the formation of 205,207 Bi is five to six orders of magnitude lower than the deuteron induced part. This small effect of the secondary neutrons is unmeasurable and therefore can be neglected. The secondary neutrons from the parts of the beam transport system, based on our earlier experiences, were not taken into account.

Integral yields
The experimental points were fitted (spline fit) and integral thick target yields were calculated according to the definition given by Otuka et al. [14]. The yields are shown in Fig. 12. No earlier experimental data on 209 Bi(d,x) have been found in the literature.

Summary
In the frame of a systematic investigation of activation cross sections of deuteron induced reactions new experimental cross-sections were measured for the 209 203 Pb reactions. To test the predictivity of the nuclear reaction models, the measured excitation functions were compared to the results obtained with our calculations using ALICE-IPPE -D and EMPIRE-D theoretical codes and the theoretical results of TALYS code taken from TENDL-2019 library. The predictions of the model codes among themselves are significantly different and differ from experimental data.
Funding Open access funding provided by ELKH Institute for Nuclear Research.

Data Availability Statement
This manuscript has associated data in a data repository. [Authors' comment: The associated data of this manuscript will be deposited in the EXFOR on-line Nuclear Data Library (https://www-nds.iaea.org/exfor/exfor.htm) after publication of this paper.] Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecomm ons.org/licenses/by/4.0/.