Evidence of Deformation inV51

Abstract

The energy levels, static moments, and transition rates of ${\mathrm{V}}^{51}$ have been investigated using the strongcoupling symmetric-rotator model. Nilsson's energy levels and wave functions in the $1f-2p$ shell are recomputed for a well depth corresponding to $\hslash {\omega }_0=\frac{41}{A^{\frac{1}{3}}}$ MeV and for a spin-orbit strength $C=-0.26\mathrm{}\hslash {\omega }_0$ appropriate to the $1f-2p$ shell. The shell-model level ordering at zero deformation requires a well-flattening parameter $D=-0.035\mathrm{}\hslash {\omega }_0$. Band-head energies are not adjusted, but determined strictly from the appropriate summation over the occupied states. The final spectrum is obtained by diagonalizing the Coriolis coupling term with the rotational wave function based on the ten available single-particle or single-hole states in the $1f-2p$ shell. The same moment of inertia has been used for all bands and is determined from a least-squares fit to the experimental level scheme. Both for a deformation parameter $\beta =-0.32\mathrm{}$ and for $\beta =0.20\mathrm{}$, the calculated spectrum is in reasonable agreement with the experiment. The rotational bands are mixed to a high degree. As a consequence the band structure is destroyed and the lowest eigenvalue of the spectrum becomes $\frac{7}{2}$. The wave functions corresponding to the optimal deformation are used in predicting (a) the magnetic moment of the ground and the first excited state, (b) the ground-state quadrupole moment, and (c) the magnetic dipole and the electric quadrupole transition probabilities. The agreement with the experiment, especially for the oblate deformation, is good and is achieved without using an effective charge and an effective gyromagnetic ratio.