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We investigate even-even nuclei in the $A\sim70$ mass region within theframework of the proton-neutron quasi-particle random phase approximation(\mbox{pn-QRPA}) and the interacting boson model-1 (\mbox{IBM-1}). Our workincludes calculation of the energy spectra and the potential energy surfaces$V(\beta,\gamma)$ of Zn, Ge, Se, Kr and Sr nuclei with the same proton andneutron number, $N = Z$. The parametrization of the \mbox{IBM-1} Hamiltonianwas performed for the calculation of the energy levels in the ground statebands. Geometric shape of the nuclei was predicted by plotting the potentialenergy surfaces $V(\beta,\gamma)$ obtained from the \mbox{IBM-1} Hamiltonian inthe classical limit. The \mbox{pn-QRPA} model was later used to computehalf-lives of the neutron-deficient nuclei which were found to be in very goodagreement with the measured ones. The \mbox{pn-QRPA} model was also used tocalculate the Gamow-Teller strength distributions and was found to be in decentagreement with the measured data. We further calculate the electron capture andpositron decay rates for these $N$ = $Z$ waiting point (WP) nuclei in thestellar environment employing the \mbox{pn-QRPA} model. For the $rp$-processconditions, our total weak rates are within a factor two compared with theSkyrme HF+BCS+QRPA calculation. All calculated electron capture rates arecomparable to the competing positron decay rates under $rp$-process conditions.Our study confirms the finding that electron capture rates form an integralpart of the weak rates under $rp$-process conditions and should not beneglected in the nuclear network calculations.

$\beta$-decay half-lives and nuclear structure of exotic proton-rich waiting point nuclei under $rp$-process conditions