Unified Model in Intermediate Coupling Applied to the Odd-Mass Isotopes of Indium

Abstract

The unified model in intermediate coupling has been applied to the odd-mass isotopes of indium ${\mathrm{In}}^{109\ensuremath{-}117}$. Using three free parameters: the dimensionless interaction parameter, $\ensuremath{\xi}$; the effective ${2}^{+}$ phonon energy of the core, $\ensuremath{\hbar}\ensuremath{\omega}$; and the single-particle energy separations, ${E}_{j}$, theoretical energy spectra were fitted to the experimental spectra. The wave functions obtained during the diagonalization of the Hamiltonian were used in calculating magnetic dipole moments for the ground and first excited states, the quadrupole moments of the ground states, and $M1$ and $E2$ reduced transition probabilities for transitions between the second and first excited states. In reproducing the observed values of the magnetic dipole and electric quadrupole moments, effective values of the spin $g$ factor and interaction strength parameter were employed. These were found to vary remarkably smoothly with the mass number $A$. The following values for the hitherto unmeasured properties of the indium isotopes are predicted: magnetic moment of the ground state of ${\mathrm{In}}^{117}$, $5.516{\ensuremath{\mu}}_{N}$; the quadrupole moment of the ground state of ${\mathrm{In}}^{117}$; 1.057\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$; and the $B(M1)$ and $B(E2)$ values for ${\mathrm{In}}^{113}$ for the decay of the second excited state to the first excited, $0.708{e}^{2}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$ and $0.149{e}^{2}\ifmmode\times\else\texttimes\fi{}{({10}^{\ensuremath{-}24} {\mathrm{cm}}^{2})}^{2}$, respectively. The results compare favorably with those obtained by other investigators using other models.