Abstract
The present work shows our academic investigation of the role of the binary cluster model in probing the states of even–even mid-mass stable isotopes like \({}^{70,72,74,76}\) Ge and \({}^{84,86,88}\) Sr. The even- \(Z\) stable nuclei are significant in number. Although light even- \(Z\) stable isotopes have been studied extensively in terms of cluster models, there are fewer studies of mid-mass stable isotopes. Thus, we applied a cluster model to characterize some static properties of \({}^{70,72,74,76}\) Ge and \({}^{84,86,88}\) Sr. The eigenvalues and wave functions have been calculated for even–even stable nuclei in the germanium and strontium isotopic chains by analytically solving the time-independent Schrödinger equation involving a phenomenological potential. We have shown that the available experimental data of the charge radius and ground state energy can be well described by assuming a binary structure of \(\alpha\) cluster and a core and using an analytical solution. We applied Zn and Kr isotopes as cores of \({}^{70,72,74,76}\) Ge and \({}^{84,86,88}\) Sr, respectively.
