Effective Mass and Excitation of Nuclei

More than ten years ago, Gillet and Brown et aI.1) pointed out that RP A calculations yield excitation energies of dipole states not to be high enough to reproduce experimental values, in spite of using reasonable effective interactions and empirical single-particle energies, wo~41/Al/3 (MeV) as unperturbed ones. For the long-standing problem, recently, Brown et aI. 2 ) argued that in discussing high lying nuclear vibrations one should use the unperturbed energies, w, corresponding to the effective mass, m*( < m), instead of Wo determined for the free nucleon mass, m. Since one may obtain the value of w to be higher than Wo, a part of the discrepancy might be resolved. Then, Brown et aI. 2 ) have proposed to use w = wo( m/ m*) as unperturbed energies of dipole excitations. It has been also discussed by many authors2)~6) that the effective mass plays an important role in excitation energies of Quadrupole resonance states. For the arguments in a harmonic oscillator potential model, Bohr and Mottelson ) used the same m* -dependence as w = wo( m/ m*). The scaling factor ( m/ m*) is obtained by adjusting the oscillator frequency so as to retain the spatial dimension, < y2), in a harmonic oscillator potential modeI. 2 ),3)