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An analytically solvable model, X(3/2j+1), is proposed to describe odd-A nuclei near the X(3) critical point. The model is constructed based on a collective core described by the X(3) critical point symmetry coupled to a spin-j particle. A detailed analysis of the spectral patterns for cases j=1/2 and j=3/2 is provided to illustrate dynamical features of the model. By comparing theory with experimental data and results of other models, it is found that the X(3/2j+1) model can be taken as a simple yet very effective scheme to describe those odd-A nuclei with an even-even core at the critical point of the spherical to axially deformed shape phase transition. © 2011 American Physical Society.

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Physical Review C - Nuclear Physics