Nuclear structure and weak rates of heavy waiting point nuclei under rp-process conditions

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