Abstract
A $\gamma$ -rigid solution of the Bohr Hamiltonian is derived for $\gamma=0^{\circ}$ utilizing the Davidson potential in the $\beta$ variable. This solution is going to be called X(3)-D. The energy eigenvalues and wave functions are obtained by using an analytic method which has been developed by Nikiforov and Uvarov. B(E2) transition rates are calculated. A variational procedure is applied to energy ratios to determine whether or not the X(3) model is located at the critical point between spherical and deformed nuclei. The agreement with the experiment is achieved.
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