Re-visiting thermal effects on stellar neutron capture reactions using a novel quantum dynamical approach

TL;DR

Temperature has a critical impact on neutron capture cross sections in heavy nuclei under astrophysical conditions. The authors introduce a time-dependent coupled channels wave-packet (TDCCWP) method that incorporates thermal effects directly in the initial state and compare it against CCDM and Hauser-Feshbach style treatments for the $n+^{188}$Os system. Key findings show that increasing $kT$ can reduce capture probability and reaction rates (up to ~10% at high $kT$) in TDCCWP, contrasting with Hauser-Feshbach results and underscoring the role of initial-state dynamical couplings. This work highlights the importance of thermalisation at the initial state for accurate astrophysical reaction rates and has implications for the Re-$^{187}$Re to Os-$^{187}$Os chronometer and r-process isotopes.

Abstract

The neutron capture process plays a vital role in creating the heavy elements in the universe. The environments involved in these processes are, in general, high in temperature and are characterized by two distinct reaction mechanisms: the slow and rapid neutron capture processes. In this work, the slow neutron capture process is described with the time-dependent coupled channels wave-packet (TDCCWP) method that uses both a many-body nuclear potential and an initial temperature-dependent state to account for the thermal environment. To evaluate the role of a mixed and entangled initial state in the temperature-dependent neutron capture cross section, TDCCWP calculations are compared with those from the coupled-channels density matrix (CCDM) method based on the Lindblad equation. The importance of including temperature in the initialisation is compared to a thermalisation of the capture cross section using a Hauser-Feshbach style approach. Finally, a decrease of the n+$^{188}$Os reaction with an increasing temperature is present, along with a decrease of $10\%$ in reaction rates for the highest thermal energies studied, which are contrary to previous results and important in the rapid neutron capture process.

Figures (8)

• Figure 1: The nuclear interaction potential between a neutron and the $^{188}$Os target is generated from the Sky3D code with a Woods-Saxon shaped line fitted to the data for $^{188}$Os+n using a Newtonian least-squares regression. The parameterisation data for $^{188}$Os+n is shown in Table \ref{['tab:my_label']}.
• Figure 2: All of the different potentials in the model for the $^{188}$Os+n reaction are presented, including the coupling potential. Note the positioning of the absorption potential, which is more central than the coupling potential and well inside the nuclear interaction region. The 0-2 shows the coupling between the ground and first excited state.
• Figure 3: Transmission coefficients from TDCCWP calculations are compared to those from the CCDM model for the $l=0$ partial wave for the $^{188}$Os+n reaction. Two thermal energies are displayed, these being 0 and 500 keV in thermal energy (KT). The shaded region around the 500 keV TDCCWP results shows the error in the TDCCWP calculation found by finding the percentage change from a wider wave-packet calculation.
• Figure 4: Temperature-dependent capture cross sections for a $l=0$ neutron on the $^{188}$Os target as a function of neutron energy using a Hauser-Feshbach and TDCCWP style calculation. A thermal energy of 250 keV is used in both implementations of thermal effects.
• Figure 5: Temperature-dependent capture cross sections for a l=0 neutron on the $^{188}$Os target as a function of the neutron incident energy in the range 140-500 keV. The shaded regions highlight errors associated with the energy variance of the neutron energy (i.e., the differences in the TDCCWP calculations using a spatial width of the initial wave-packet of 50 and 80 fm). The change from the kinematically closed energy region to the open one happens at the $^{188}$Os first excited state energy (155 keV).