Neutron capture cross section measurement of the heaviest s-process branching $^{204}$Tl and of $^{203}$Tl at CERN n_TOF

Neutron capture cross sections are fundamental in the study of the slow neutron capture process of nucleosynthesis, also known as the s-process, which produces half of the observed solar system abundances of elements heavier than iron. Some nuclei along the nucleosynthesis chain are unstable, and there the capture process competes with the decay process, creating a split in the nucleosynthesis path. The nuclear properties of some of these radionuclides change with the conditions of the stellar environment, a fact that influences the local abundance pattern. $^{204}$Tl is a very interesting branching point, because it is shielded from any contribution from other nucleosynthesis processes. The result is that both $^{204}$Tl and its stable daughter isotope $^{204}$Pb are only produced by the s-process. Hence, by competing with the beta decay, the capture cross section of $^{204}$Tl crucially determines the final abundance of $^{204}$Pb. A faithful prediction of the solar abundances of s-only isotopes, like $^{204}$Pb, is one of the key accuracy tests for modern stellar nucleosynthesis calculations. However, until the present work, due to the challenges of performing a capture measurement on $^{204}$Tl, there was no experimental data of its cross section. Thus, large uncertainties existed in its capture cross section, which hampered a more accurate and precise knowledge of the predicted s-process production of $^{204}$Pb. By affecting the abundance of $^{204}$Pb, the cross section of $^{204}$Tl(n,$\gamma$) also influences the ratio of abundances $^{205}$Pb/$^{204}$Pb. $^{205}$Pb is also produced only by the s-process, and it is radioactive, with a long half-life of 17.2 My. Therefore, the ratio of abundances of $^{205}$Pb/$^{204}$Pb has the potential to be used as a chronometer of the s-process. In the year 2013, a sample enriched up to a few percent in $^{204}$Tl was produced by neutron irradiation of a $^{203}$Tl seed sample at the high thermal neutron flux nuclear reactor of the ILL, in Grenoble (France). Two years later, the $^{204}$Tl enriched sample was employed to measure, for the first time, the capture cross section of $^{204}$Tl at the n TOF time-of-flight facility at CERN. The measurement was possible thanks to the unique features of this facility, in particular, its high instant neutron flux low background levels. The measurement was performed employing the well-established Pulse Height Weighting Technique (PHWT), which offers a very low neutron sensibility, and low levels of background, compared to other methods like the Total Absorption technique. The main challenges for the $^{204}$Tl measurement were the very high background due to the activity of the sample, the very low amount of material, and the limited knowledge of the geometry of the sample. Such difficulties required the adoption of specific solutions during the measurement and the posterior data analysis. Related to this, several sources of systematic error were evaluated by means of Monte Carlo simulations. The complications with the $^{204}$Tl sample geometry required to apply an in-sample normalization procedure. For this purpose, an ancillary capture measurement on a $^{203}$Tl sample was also performed in the same experimental campaign. As a stable nuclide, most of the sources of systematic error could be kept under control. This allowed for an accurate R-matrix analysis of the most relevant capture levels in the resolved resonance region of $^{203}$Tl, including the first ever measurement under 3 keV of neutron energy. As a result, the present work has contributed, as well, to improve the $^{203}$Tl stellar capture cross section in the 8 to 25 keV neutron energy range. With the improved $^{203}$Tl(n,$\gamma$) cross section, an R-matrix analysis of several $^{204}$Tl resonances was made possible. These results were employed to experimentally constrain the $^{204}$Tl stellar cross section at low energies, and setting additional limits to the stellar cross section predicted by nuclear data evaluations at s-process temperatures.