Analytical description of odd-A nuclei near the critical point of the spherical to axially deformed shape transition

A coupling scheme for even-even nuclei with the X(5) critical point symmetry coupled to a single valence nucleon in a j orbit is proposed to approximately describe the critical point phenomena of spherical to axially deformed shape (phase) transition in odd-A nuclear systems. The corresponding scheme, which can be solved analytically, is called the X(5/(2j + 1)) model. A special case with j = 1/2 is analyzed in detail to show its level structure and transition patterns. It is further shown that Au-189 and Tb-155 may be possible X(5/(2j + 1)) symmetry candidates with j = 1/2 and j = 3/2, respectively.