Beta-decay half-lives of the extremely neutron-rich nuclei in the closed-shell N = 50, 82, 126 groups

Abstract

The β--decay half-lives of extremely neutron-rich nuclei are important for understanding nucleosynthesis in the r-process. However, most of their half-lives are unknown or very uncertain, leading to the need for reliable calculations. In this study, we updated the coefficients in recent semi-empirical formulae using the newly updated mass (AME2020) and half-life (NUBASE2020) databases to improve the accuracy of the half-life prediction. In particular, we developed a new empirical model for better calculations of the β--decay half-lives of isotopes ranging in Z = 10 – 80 and N = 15-130. We examined the β--decay half-lives of the extremely neutron-rich isotopes at and around the neutron magic numbers of N = 50, 82, and 126 using either five different semi-empirical models or finite-range droplet model and quasi-particle random phase approximation (FRDM+QRPA) method. The β--decay rates derived from the estimated half-lives were used in calculations to evaluate the impact of the half-life uncertainties of the investigated nuclei on the abundance of the r-process. The results show that the half-lives mostly range in 0.001 < T1/2 < 100 s for the nuclei with a ratio of N/Z < 1.9; however, they differ significantly for those with the ratio of N/Z > 1.9. The half-life differences among the models were found to range from a few factors (for N/Z < 1.9 nuclei) to four orders of magnitude (for N/Z > 1.9). These discrepancies lead to a large uncertainty, which is up to four orders of magnitude, in the r-process abundance of isotopes. We also found that the multiple-reflection time-of-flight (MR-TOF) technique is preferable for precise mass measurements because its measuring timescale applies to the half-lives of the investigated nuclei. Finally, the results of this study are useful for studies on the β-decay of unstable isotopes and astrophysical simulations.

Beta-decay half-lives of the isotopes close to the neutron drip line and astrophysical implications

“…Recently, a few semi-empirical models have been developed using all available experimental data to improve the accuracy of half-life predictions. For example, a few simple linear relations originated from the Sargent law [43] with considerations of shell effects have been proposed in several works by Zhang et al [44,45], Zhou et al [46], and Uyen et al [47]. The validation of these works indicate that the proposed semi-empirical formulae can reproduced well experimental data with simpler computations.…”

“…Since the β-decay half-life was found to depend on the fifth power of the decay energy [43], many semi-empirical models have been developed with small differences from experimental data. According to the examination of theoretical calculations in our previous study [47], we employed four reliable models proposed by Zhang et al [44,45], Zhou et al [46], and Uyen et al [47] for estimating the half-lives of 94 neutron-rich nuclei with Z = 26 − 57 close to the neutron-drip line as follows.…”

Comparative study of neural network and model averaging methods in nuclear β-decay half-life predictions

“…th has been widely used to evaluate the average deviation of the half-life predictions from the experimental data for various models [20,21,56,57], which can roughly reflect the prediction accuracy of nuclear models. In this work, the loss function of the neural network is also set to the rms deviation ( ) s T log rms 10 1 2 th .…”

“…There are mainly four kinds of theoretical models for predicting nuclear β-decay half-lives, i.e. the empirical formula [19][20][21], the gross theory (GT) [22][23][24][25], the quasiparticle random-phase approximation (QRPA) approach [26][27][28][29][30], and the shell model [3,[31][32][33]. The shell model has been successfully applied to the light nuclei and the nuclei near magic numbers, but its calculations for medium and heavy nuclei far from the magic numbers are not feasible due to the limitations of large configuration spaces.…”

Impact of Nuclear β-decay Half-life Uncertainties on the r-process Simulations

“…However, uncertainty analysis with such an intermodel deviation needs a variety of nuclear models, which can be used to make systematic calculations of nuclear physics inputs for all nuclei related to the r-process. Since systematic calculations of nuclear β-decay half-lives are very time consuming, the rprocess uncertainty studies from β-decay half-lives are very scarce; only recently was the uncertainty analysis made based on the β-decay empirical formula (Li et al 2019;Uyen et al 2022).…”