Influence of nuclear mass uncertainties on radiative neutron-capture rates

Neutron-capture rate plays a crucial role in the rapid neutron-capture process (r-process) and nuclear mass is one of the most important inputs for the estimations of neutron-capture rates. In this work, we employ ten nuclear mass models, including macroscopic, macroscopic-microscopic, and microscopic models, to calculate the radiative neutron-capture rates for the nuclei relevant to the r-process at various temperatures $T={10}^5–{10}^{10}\mathrm{K}$. It is found that the differences in the predictions of neutron-capture rate using these mass models get larger when moving to the neutron-rich and superheavy regions, whereas they generally become smaller with the increase of temperature. Taking the nuclei on the $N=126$ r-process path as examples, we find that the uncertainties of neutron-capture rates at $T={10}^9\mathrm{K}$ range from about one to four orders of magnitude. The influence of the experimental mass errors on neutron-capture rates is investigated as well.

Figure 1

Uncertainties of radiative neutron-capture rates from nuclear mass uncertainties at different temperatures. The boundaries of nuclei with known $Q$ values in AME2016 are shown by the black contours. The r-process path from Ref. [7] is shown for guiding eyes, which is predicted based on the classical r-process model.

Figure 2

Distribution of ${\sigma }_{\mathrm{rms}}$ with respect to the distance from the $\beta$-stability line $Z_{\beta }-Z$ at $T_9=1$, where $Z_{\beta }$ is the proton number of nucleus on the $\beta$-stability line with a given mass number [41]. The average values of ${\sigma }_{\mathrm{rms}}$ are shown by the solid line.

Figure 3

Distributions of the radiative neutron-capture rates for $N=126$ isotones at $T_9=1$ with different mass models. The gray band shows one standard deviations ${\sigma }_{\mathrm{rms}}\left({log}_{10}R\right)$ from the average values for all mass models considered here. The r-process path from Ref. [7] is denoted by the hatched area, which is predicted based on the classical r-process model.

Figure 4

Radiative neutron-capture rates of ${}^{124}\mathrm{Mo}$, ${}^{126}\mathrm{Ru}$, ${}^{194}\mathrm{Er}$, and ${}^{196}\mathrm{Yb}$ as a function of temperature for various nuclear mass models. The gray bands show the deviations in neutron-capture rates, i.e., one standard deviations ${\sigma }_{\mathrm{rms}}\left({log}_{10}R\right)$ among all the ten models, while the hatched area is the same but only for DZ10, ETFSI-2, ETFSI-Q, HFB-31, KTUY, and WS4 models.

Figure 5

Statistical histogram of numbers of nuclei within given ranges of ${\sigma }_{\mathrm{rms}}\left({log}_{10}R\right)$ at $T_9=1$.

Figure 6

Neutron-capture rates of Zr and Sb isotopes and their corresponding uncertainties from experimental mass errors at $T_9=1$. The lower horizontal axis denotes the neutron number of Zr isotopes, while the upper one is for Sb isotopes. The experimental data are taken from AME2016.