A simple approximation for the nuclear density matrix

R. Parthasarathy

R. Reif, G. Kiessig

QiRi MaiLaTu

Lu Jia

A new microscopic theory for nuclear pairing is proposed through the generalized density matrix formalism. Instead of the variation principle, we start from the Heisenberg equations of motion for density matrix operators ${K}_{12}\ensuremath{\equiv}{a}_{2}{a}_{1}$. The theory generalizes the well-known particle-particle random-phase approximation. Its analytical equations are as simple as that of the BCS theory and can be solved within a similar computer time if the model space is not too large. The current theory conserves the exact particle number and is valid at arbitrary pairing strength (including those below the BCS critical strength). It is also of interest to other mesoscopic systems such as ultrasmall metallic grains.

F. David Peat, R. J. C. Brown

Μ. Petraki, Eirene Mavrommatis, J. W. Clark

The half-diagonal two-body density matrix ${\ensuremath{\rho}}_{2h}({\mathbf{r}}_{1},{\mathbf{r}}_{2},{\mathbf{r}}_{{1}^{\ensuremath{'}}})$ is a key quantity in theoretical descriptions of nucleon knockout reactions at intermediate energies, due to its central role in treatments of the propagation and final-state interactions of ejected nucleons in the nuclear medium. This quantity is calculated for a simple model of the ground state of infinite symmetrical nuclear matter, based on a Jastrow-correlated wave function and a Fermi hypernetted-chain analysis. The dependence of ${\ensuremath{\rho}}_{2h}$ on the variables ${r}_{{11}^{\ensuremath{'}}}=|{\mathbf{r}}_{1}\ensuremath{-}{\mathbf{r}}_{{1}^{\ensuremath{'}}}|,$ ${r}_{12}=|{\mathbf{r}}_{1}\ensuremath{-}{\mathbf{r}}_{2}|,$ and the angle $\ensuremath{\theta}$ between ${\mathbf{r}}_{1}\ensuremath{-}{\mathbf{r}}_{{1}^{\ensuremath{'}}}$ and ${\mathbf{r}}_{1}\ensuremath{-}{\mathbf{r}}_{2}$ is investigated in some detail. Significant departures from ideal Fermi gas behavior in certain domains reflect the importance of short-range correlations and their interplay with statistical correlations. The quality of approximations to ${\ensuremath{\rho}}_{2h}$ proposed by Gersch et al., Rinat, and Silver is assessed by comparison with the Fermi hypernetted-chain results.