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 $\to$ ${}^{185}$W has the greatest influence on the ${}^{187}$Re-${}^{187}$Os nuclear clock reaction network, and the neutron capture reaction ${}^{186}$W + n $\to$ ${}^{187}$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.