Systematic calculations of $alpha$-decay half-lives with an improved empirical formula

Based on the recent data in NUBASE2012, an improved empirical formula for evaluating the $alpha$-decay half-lives is presented, in which the hindrance effect resulted from the change of the ground state spins and parities of parent and daughter nuclei is included, together with a new correction factor for nuclei near the shell closures. The calculated $alpha$-decay half-lives are found to be in better agreements with the experimental data, and the corresponding root-mean-square (rms) deviation is reduced to $0.433$ when the experimental $Q$-values are employed. Furthermore, the $Q$-values derived from different nuclear mass models are used to predict $alpha$-decay half-lives with this improved formula. It is found that the calculated half-lives are very sensitive to the $Q$-values. Remarkably, when mass predictions are improved with the radial basis function (RBF), the resulting rms deviations can be significantly reduced. With the mass prediction from the latest version of Weizs{a}cker-Skyrme (WS4) model, the rms deviation of $alpha$-decay half-lives with respect to the known data falls to $0.697$.

Nuclear $beta$-decay half-lives in the relativistic point-coupling model

The self-consistent proton-neutron quasiparticle random phase approximation approach is employed to calculate $beta$-decay half-lives of neutron-rich even-even nuclei with $8leqslant Z leqslant 30$. A newly proposed nonlinear point-coupling effective interaction PC-PK1 is used in the calculations. It is found that the isoscalar proton-neutron pairing interaction can significantly reduce $beta$-decay half-lives. With an isospin-dependent isoscalar proton-neutron pairing strength, our results well reproduce the experimental $beta$-decay half-lives, although the pairing strength is not adjusted using the half-lives calculated in this study.

Constraint on the cosmic age from the solar $r$-process abundances

The cosmic age is an important physical quantity in cosmology. Based on the radiometric method, a reliable lower limit of the cosmic age is derived to be $15.68pm 1.95$ Gyr by using the $r$-process abundances inferred for the solar system and observations in metal-poor stars. This value is larger than the latest cosmic age $13.813pm 0.058$ Gyr from Planck 2013 results, while they still agree with each other within the uncertainties. The uncertainty of $1.95$ Gyr mainly originates from the error on thorium abundance observed in metal-poor star CS 22892-052, so future high-precision abundance observations on CS 22892-052 are needed to understand this age deviation.