Nuclear Properties ofMn5525(Semiatomic Model)

Abstract

The nuclear properties of ${}_{25}{}^{}{}_{}{}^{}\mathrm{Mn}_{}^{55}{}_{}{}^{}$ and some other nuclei in the region of ($1f_{\frac{7}{2}}$) shell are investigated in detail by using a new model (called semiatomic model) which is essentially an extremely weak-coupling formulation of the unified model in contrast to the semimolecular formulation of Bohr and Mottelson. By restricting the variation range of the deformation variable $\gamma$ to the interval $0<~\gamma <\frac{\pi }{3}$, a "zero-point" surface-particle interaction which does not exist in the usual weak-coupling theory is naturally introduced. The theoretical basis for this interaction and the problem of the range of $\gamma$ are discussed. A theoretical relation for the magnetic moment ratio of two odd-$A$ nuclei with conjugate configurations is tested in the region of the ($1f_{\frac{7}{2}}$) shell. The theoretical predictions are in good agreement with the experimental results. An explanation for the positive-negative asymmetry of the quadrupole moment distribution of odd-$A$ nuclei is suggested. It seems that this asymmetry has been so far overlooked without explanation. It is shown that the $E2\mathrm{}$ reduced transition probability in the semiatomic model is given by the following expression: $B(E2; J_i\to J_f)=\frac{2J_f+1\mathrm{}}{2J_i+1\mathrm{}}{B}^s(E2; J_i\to J_f),$ where $B^s(E2; J_i\to J_f)$ is the value which one obtains in the usual shell theory. The calculated $E2\mathrm{}$ reduced transition probability for ${}_{23}{}^{}{}_{}{}^{}\mathrm{V}_{}^{51}{}_{}{}^{}$ in the transition $J_0=\frac{5}{2}\to J=\frac{7}{2}$ is in excellent agreement with the value from Coulomb excitation measurements.