Density matrix of relativistic nuclear matter.

Abstract

We investigate the structure of the density matrix of relativistic nuclear matter at large momentum (k\ensuremath{\gg}${\mathit{k}}_{\mathit{F}}$) making use of the \ensuremath{\sigma}+\ensuremath{\omega} model of Walecka. The density matrix may be written in terms of spinors describing nucleons of modified mass and also has exotic components that contain spinors describing negative-energy states (``antinucleons''). We calculate the modification of the mean-field density matrix due to the admixture of two-particle, two-hole states in the ground state of the relativistic theory and find that the excitation of the exotic components of the density matrix is so strong and coherent as to preclude the use of perturbation theory. We suggest that an expansion in terms of reaction matrices will not improve the situation and conclude that a consistent picture may be obtained only if one limits oneself to a space spanned by positive-energy spinors (describing nucleons of shifted mass). We also consider the exchange of pions in the calculation of high-momentum components of the density matrix. However, in the case of pion exchange, we find that sensible results may not be obtained (even for the nonexotic components) unless we include tensor and short-range correlations. (The latter calculations have not been performed as yet.) Further, we note that a theory without vertex cutoffs (meson-nucleon form factors) leads to totally unacceptable results, as the depletion of the Fermi sea is again much too large.