Abstract
The eigenvalues of a prolate cavity (with axial symmetry) are studied as a function of the deformation for an ellipsoidal shape by using the adiabatic switching method (ASM). The method uses, as the only quantum mechanical ingredients, trajectories which obey the Einstein-Brillouin-Keller rules in the spherical case. The cavity is then adiabatically deformed and the energy change results from work done by the force exerted by the cavity on the particle. The resulting spectrum is in excellent agreement with the exact spectrum as well as with the semiclassical one calculated by the EBK method. The crossing of a separatrix for Lz=0 (Lz is the z-component of the orbital angular momentum) does not affect the authors' results significantly. The method is used to calculate the total energy of a system of independent nucleons as a function of deformation. Comparison with the Balian-Bloch formula shows that the ASM is producing correctly shell effects which are absent in the formula.
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