Activation Cross Section Measurement of the (n,2n) Reaction on 203Tl at 16.4 MeV, 18.9 MeV and Theoretical Calculations via the EMPIRE code

The aim of the present work is to study the cross section of the (n,2n) and (n,3n) reactions on 203 Tl, by irradiating a natural TlCl pellet target with monoenergetic neutron beams at 16.4 and 18.9 MeV. The cross section measurements were carried out using the activation method, with respect to the 197 Au(n,2n) 196 Au and 27 Al(n,α) 24 Na reference reactions. The monoenergetic neutron beams were generated in the 5.5 MV Tandem accelerator of NCSR “Demokritos”, using the 3 H(d,n) 4 He reaction. Monte Carlo simulations have been performed to take into account the γ-ray self-absorption results as well as the estimation of the neutron flux through the reference foils. Theoretical calculations with the EMPIRE code have also been performed, using the same parameterization implemented in the theoretical study of Ir and Au nuclei in an attempt to find a suitable model for the description of all the experimental results in this mass region.


INTRODUCTION
The significance of studying neutron-induced reactions lies in their importance to basic research and their relevance for practical applications in medicine, nuclear technology and industry [1][2][3].Thallium is widely used in electronics, pharmaceuticals, nuclear medicine, infrared detectors and fiber optics.Nevertheless, little available information exists in literature for neutron-induced reactions on Tl isotopes.Especially in the case of the 203 Tl(n,2n) 202 Tl reaction, many discrepancies among the existing experimental data exist, mainly in the energy region above 12 MeV [4,5], as can be seen in Fig. 1.

Reaction
The impingement of the highly energetic neutron beams on the 203 Tl isotope produced the highly excited compound nucleus 204 Tl*, while among the possible exit channels, the (n,2n) channel opens just above 8 MeV and the (n,3n) channel well above 15 MeV.The experimental spectra of the thallium foils after activation are shown in Fig. 2 for the 16.4 and 18.9 MeV along with their background spectra.The characteristic γ-line peak of the 203 Tl(n,2n) 202 Tl reaction lies at 439.5 keV, while the one of 203 Tl(n,3n) 201 Tl reaction at 167.5 keV, with half-lives of 12.31 d and 3.04 d for the two residual nuclei respectively, as shown in Table 1. .

Experimental setup
The experiments were conducted at the 5.5 MV tandem accelerator of N.C.S.R. "DEMOKRITOS".The neutron beam that irradiated the natural ΤlCl pellet, in each irradiation (see Table 2), was produced via the 3 H(d,n) 4 He reaction, using a Ti-T solid target.For the determination of the neutron flux, the reference samples that were used were Al and Au foils of the same diameter (13 mm diameter) as the thalium target.The target and reference foil assembly were placed at approximately 1.5-2 cm from the tritium target, where the neutron beam is practically isotropic and monoenergetic.A BF3 detector was placed at 3 m from the tritium flange for the monitoring of the neutron beam fluctuations.The induced radiation of the samples was measured using High Purity Germanium (HPGe) detectors, with 80% and 100% relative efficiency depending on each irradiation, which were properly shielded with lead blocks.The irradiated samples were placed at a distance of 10 cm from the entrance window of the HPGe detectors.The absolute efficiency of the detectors was deduced with the use of a calibrated 152 Eu point source of (217 ± 3) kBq activity, placed at the same distance as the samples.

CROSS SECTION MEASUREMENT
The cross section σ of the 203 Tl(n,2n) 202 Tl and 203 Tl(n,3n) 201 Tl reactions was measured with respect to the 197 Au(n,2n) 196 Au and 27 Al(n,α) 24 Na reference reactions (see Fig. 3), implementing the activation method, and was calculated by the formula:  The de-excitation of the produced nuclei from the end of the irradiation until the end of the activity measurement, as well as the balance between production and de-excitation of nuclei during the irradiation, were taken into account for the calculation of the number of nuclei produced by the neutron irradiation.

RESULTS AND DISCUSSION
The preliminary experimental cross section results are presented in Table 3 and Fig. 4, along with the existing experimental data in literature [5], as well as the ENDF-VIII, JENDL-5 and TENDL-2019 evaluations [4] of the 203 Tl(n,2n) 202 Tl and 203 Tl(n,3n) 201 Tl reactions.

THEORETICAL CALCULATIONS -EMPIRE CODE
The theoretical calculations in the framework of the Hauser-Feshbach compound nucleus theory using the code EMPIRE (version 3.2.3)[7] and the comparison with the available experimental cross section data were carried out, with the aim of finding a suitable model for the description of the reaction cross sections under study.The best agreement between theoretical calculations with the EMPIRE code and experimental data, especially in the high energy region (see Fig. 5), was achieved with the parameters below: o Optical Model: Wilmore, 1964 [8] o Enhanced Generalized Superfluid Model (EGSM) nuclear level densities [9] o Enabled MSD o Enabled MSC o Disabled Direct input Furthermore, these parameters describe very well the 205 Tl(n,2n) 204 Tl reaction, thus confirming their suitability, as shown in Fig. 6.The same parameters were used in the case of the investigation of neutron-induced reactions on Ir and Au [10,11] and the fair agreement between theoretical calculations and experimental data provides an indication of how successfully the theoretical models can reproduce the experimental results in this mass region with the same parametrization.However, further theoretical investigation is needed in order to achieve better agreement between theoretical calculations and experimental data, mainly for the 203 Tl(n,2n) reaction below 15 MeV and the 203 Tl(n,3n) reaction above 20 MeV.Further measurements are also planned in the near future to cover the energy range from 15 up to 20 MeV and also at lower energies, below 12 MeV, where only the data by Frehaut et al. [12] are available.

Figure 1 .Figure 2 .
Figure 1.Existing experimental data of the 203 Tl(n,2n) 202 Tl reaction number of unstable nuclei produced by the neutron irradiation Nτ: the number of target nuclei irradiated Φ: neutron flux calculated with Monte Carlo simulations applying the MCNP code [6] along with the experimental results from the reference reactions.

Figure 3 .
Figure 3. Schematic configuration of the targets

Table 2 .
Characteristics of the two performed irradiations