Analytically solvable potentials for $\gamma$-unstable nuclei

Abstract

An analytical solution of the collective Bohr equation with a Coulomb-like and a Kratzer-like $\gamma -$unstable potential in quadrupole deformation space is presented. Eigenvalues and eigenfunctions are given in closed form and transition rates are calculated for the two cases. The corresponding SO(2,1)$\times$SO(5) algebraic structure is discussed.

9 pages, 4 figures in one .ps file

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