Examination of n-T_9 conditions required by N=50,82,126 waiting points in r-process

We examined the conditions of neutron density (n) and temperature (T₉) required for the N = 50, 82, and 126 isotopes to be waiting points (WP) in the r-process. The nuclear mass based on experimental data presented in the AME2020 database (AME and AME ± Δ) and that predicted using FRDM, WS4, DZ10, and KTUY models were employed in our estimations. We found that the conditions required by the N = 50 WP significantly overlap with those required by the N = 82 ones, except for the WS4 model. In addition, the upper (or lower) bounds of the n − T₉ conditions based on the models are different from each other due to the deviations in the two-neutron separation energies. The standard deviations in the nuclear mass of 108 isotopes in the three N = 50, 82, and 126 groups are about rms = 0.192 and 0.434 MeV for the pairs of KTUY-AME and WS4-KTUY models, respectively. We found that these mass uncertainties result in a large discrepancy in the n_n − T₉ conditions, leading to significant differences in the conditions for simultaneously appearing all the three peaks in the r-process abundance. The newly updated FRDM and WS4 calculations can give the overall conditions for the appearance of all the peaks but vice versa for their old versions in a previous study. The change in the final r-process isotopic abundance due to the mass uncertainty is from a few factors to three orders of magnitude. Therefore, accurate nuclear masses of the r-process key nuclei, especially for ⁷⁶Fe, ⁸¹Cu, ¹²⁷Rh, ¹³²Cd, ¹⁹²Dy, and ¹⁹⁷Tm, are highly recommended to be measured in radioactive-ion beam facilities for a better understanding of the r-process evolution.