Some universal properties of density matrices for finite nuclei (bound systems)

Аннотация

The properties of one-body and two-body density matrices of a nucleus as a nonrelativistic system are studied. Unlike the usual procedure applied in the theory of infinite systems, for a nucleus of A nucleons these quantities are determined as the expectation values of A-body multiplicative operators that depend on the relative coordinates and momenta (Jacobi variables) and affect the intrinsic wave functions. The translational invariance of these operators is thus ensured. An algebraic technique based on the Cartesian representation is developed for handling such operators. Within this technique, the coordinate and momentum operators are linear combinations of production and annihilation operators \(\hat \vec a^ + \) and \(\hat \vec a\) with commutation relations for bosons (oscillators). Each of the multiplicative operators reduces to the normally ordered product of two exponents, one of which depends on set \(\left\{ {\hat \vec a^ + } \right\}\) only and is located to the left of the second, which depends on \(\left\{ {\hat \vec a} \right\}\) only. This procedure offers a new view of the origin of the so-called Tassie–Barker factors and other model-independent results. In addition, the proposed method yields a fair description of the available experimental data and can easily be extended to investigate the role of short-range nucleon-nucleon correlations within these translationally invariant calculations of nucleon density and momentum distributions in light nuclei.