Calculation of the abundance of \(^{187}Re \)–\(^{187}Os \) nuclear clock nuclides in S-process and sensitivity analysis of Maxwellian-averaged neutron capture cross sections

Abstract

In this paper, the network equations calculation of \(^{187}Re\)–\(^{187}Os\) clock-related nuclide abundance in s-process is studied, and the sensitivities of Maxwellian-averaged neutron capture cross sections for each nuclide are analyzed in detail. Firstly, basing nuclear physical parameters, we give the branching s-process reaction network from \(^{184}W \) to \(^{190}Os \), and establish the corresponding network equations. Using a single path s-process approximation, we obtain an analytical expression of the seed nuclide \(^{183}W \) abundance of our branching network. Because of the stiffness of the system of network equations, we use the semi-implicit Runge–Kutta method to give the numerical solution of the network equations, and thus obtain the abundance of each nuclide related to the \(^{187}Re \)–\(^{187}Os \) nuclear clock in the s-process. Finally, with the numerical solution, the sensitivity analysis of the Maxwellian-averaged neutron capture cross sections of the nuclear reaction involved in the \(^{187}Re \)–\(^{187}Os \) nuclear clock network equations is carried out. Therefore, we find that in s-process, the neutron capture reaction \( ^{184} W+n \rightarrow ^{185}W \) has the greatest influence on the \(^{187}Re \)–\(^{187}Os \) nuclear clock reaction network, and the neutron capture reaction \(^{186} W+n \rightarrow ^{187}W \) has the greatest effect on the particular nuclides \(^{187}Re \) and \(^{187}Os \). So the measurements of these two Maxwellian-averaged neutron capture cross sections deserve the attention of experimental nuclear physicists.