Nuclear structure and weak rates of heavy waiting point nuclei under $\mathit{rp}$-process conditions

Abstract

The structure and the weak interaction mediated rates of the heavy waiting point (WP) nuclei ⁸⁰Zr, ⁸⁴Mo, ⁸⁸Ru, ⁹²Pd and ⁹⁶Cd along $N = Z$ line were studied within the interacting boson model-1 (IBM-1) and the proton-neutron quasi-particle random phase approximation (pn-QRPA). The energy levels of the $N = Z$ WP nuclei were calculated by fitting the essential parameters of IBM-1 Hamiltonian and their geometric shapes were predicted by plotting potential energy surfaces (PESs). Half-lives, continuum electron capture rates, positron decay rates, electron capture cross sections of WP nuclei, energy rates of $\beta$-delayed protons and their emission probabilities were later calculated using the pn-QRPA. The calculated Gamow-Teller strength distributions were compared with previous calculation. We present positron decay and continuum electron capture rates on these WP nuclei under $\mathit{rp}$-process conditions using the same model. For the $\mathit{rp}$-process conditions, the calculated total weak rates are twice the Skyrme $\mbox{HF}+\mbox{BCS}+\mbox{QRPA}$ rates for ⁸⁰Zr. For remaining nuclei the two calculations compare well. The electron capture rates are significant and compete well with the corresponding positron decay rates under $\mathit{rp}$-process conditions. The finding of the present study supports that electron capture rates form an integral part of the weak rates under $\mathit{rp}$-process conditions and has an important role for the nuclear model calculations.