Effective masses in relativistic approaches to the nucleon-nucleus mean field

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Abstract
In relativistic descriptions of the mean field in nuclei or in nuclear matter, the expression ‘‘effective mass’’ has been used to denote different quantities. The relationship between these various quantities is clarified. It is exhibited which one among them is most closely related to the effective mass that is derived from nonrelativistic analyses of scattering and bound-state data. This nonrelativistic-type effective mass has a characteristic energy dependence near the Fermi energy whenever one goes beyond the relativistic Hartree or Hartree-Fock approximations. By making use of dispersion relations that connect the real and imaginary parts of the microscopic mean field, it is shown that the occurrence of this ‘‘Fermi surface anomaly’’ is quite general. It has the same origin as in the nonrelativistic case, namely the frequency dependence of the mean field. Despite this qualitative similarity between the relativistic and nonrelativistic cases, a striking difference exists between the size of the Fermi surface anomaly in the two cases. The physical origins of the effective mass are also shown to be very different in the relativistic and nonrelativistic descriptions.