Shell-Model Calculations forV51andCr52

Employing ${\mathrm{Ca}}^{48}$ as the core and the reaction matrix elements of Kuo and Brown for the residual interaction among the three valence protons, the nuclear energy levels of ${\mathrm{V}}^{51}$ are calculated within the spherical shell-model framework. All the $0f-1p$ configurations are included. The wave functions obtained on diagonalizing the Hamiltonian matrices are used to calculate the transition rates and spectroscopic factors for the reaction ${\mathrm{Ti}}^{50}({\mathrm{He}}^3,d){\mathrm{V}}^{51}$. Good agreement with experiments is found suggesting that it is not necessary to include deformation in ${\mathrm{V}}^{51}$ as in the papers of Scholz and Malik. The consequences of mixing effective interaction matrix elements of Lips and McEllistrem and realistic Kuo-Brown matrix elements are studied and it is pointed out that such a mixture does not yield a successful effective interaction model. Our results are further supported by similar calculations on ${\mathrm{Cr}}^{52}$.