Residual Potential and Nucleon Correlation in the Shell Model. I. $E2\mathrm{}$ Transition in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$

The effect of a class of residual potentials in the Hamiltonian and nucleon-nucleon correlation on calculations in the independent-particle shell-model wave function of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ has been investigated. A method has been developed to give minimum energies of various states of a nuclear system with a somewhat realistic Hamiltonian and wave function. The results on energy calculations are in good agreement with the observed data. The $E2$ transition rate and other relevant observables pertaining to this transition using this wave function and several others have been calculated. Comparison of the results of these calculations with experimental data and other theoretical predictions shows a definite preference for the correlated wave function of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ developed here. The method is convenient for application to other nuclear systems.