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Europhysics Letters (EPL)

Momentum Distributions of Nuclear Matter

Majid Modarres

Published May 15, 1987• 11 citations
Publisher

Abstract

The momentum distribution of nuclear matter n(k) is evaluated by using the cluster expansion for the occupation probability. The gap in n(k) at the Fermi surface is found to be about 0.96 compared with 1.0 for the noninteracting Fermi gas model. It is shown that the high-momentum tail of n(k) is very much smaller than it has been thought.

DOI
10.1209/0295-5075/3/10/005

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The momentum distribution of nuclear matter n(k) is evaluated by using the cluster expansion for the occupation probability. The gap in n(k) at the Fermi surface is found to be about 0.96 compared with 1.0 for the noninteracting Fermi gas model. It is shown that the high-momentum tail of n(k) is very much smaller than it has been thought.
The generalized momentum distribution n(p,Q), related to the half-diagonal two-body density matrix ${\mathrm{\ensuremath{\rho}}}_{2\mathrm{h}}$(r1{\mathbf{r}}_{1}r1​,r2{\mathbf{r}}_{2}r2​,${\mathbf{r}}_{1}^{\ensuremath{'}}$) by Fourier transformation in the variables r1{\mathbf{r}}_{1}r1​-${\mathbf{r}}_{1}^{\ensuremath{'}}$ and r1{\mathbf{r}}_{1}r1​-r2{\mathbf{r}}_{2}r2​, plays a key role in the description of final-state interactions in the nuclear medium and other strongly interacting many-body systems. The function n(p,Q) is explored for two Jastrow-correlated models of infinite nuclear matter within a Fermi hypernetted-chain procedure. Significant departures from ideal Fermi gas behavior in certain kinematic domains provide signatures of the strong short-range correlations contained in these models. However, such deviations are less prominent than in earlier calculations based on low-order cluster truncations; correspondingly, violations of the sequential relation are greatly reduced. Simple prescriptions for improved low-cluster-order approximations to n(p,Q) are suggested by analysis of the results of the Fermi hypernetted-chain evaluation. These results are also used to assess the quality of Silver's approximation n(p,Q)\ensuremath{\approx}n(p)[S(Q)-1] for the generalized momentum distribution in terms of the ordinary momentum distribution n(p) and the static structure function S(Q), with findings that have potential implications for the interpretation of data from inclusive electron scattering by nuclei at high momentum transfers.
By the method of ``modes'' introduced by Sawada, the excitation spectra of a fermion system with singular interactions have been obtained in three cases; (1) with one additional particle above and and one hole below the Fermi surface, (2) with one additional particle above the Fermi surface, and (3) with two particles above the Fermi surface. The argument holds not only for the system of low density (nuclear matter with a hard-core repulsion), but also for the case of the interacting electron gas in the high-density region. The results have been compared with the Brueckner-Goldstone perturbation-expansion formulas, by using diagrams in the second- and third-order of the expansion in interaction strength. We show that in the approximation of our treatment, the occupation probability function at temperature T has the same form as the Fermi distribution function.
Valuable information on the correlation structure of the nuclear medium is stored in the generalized momentum distribution n(p,Q), the Fourier transform of the half-diagonal two-body density matrix ρ_{2η}(r_1,r_2,r'). In this paper, we present a numerical calculation of n(p,Q) for two Jastrow-correlated models of symmetrical nuclear matter based on the structural decomposition of n(p,Q) derived by Ristig and Clark and on a Fermi-hypernetted-chain procedure. Results exhibit significant departures from the ideal Fermi gas case in certain kinematic domains; this behaviour indicates the strong short-range correlations present in these models. Nevertheless, such deviations are less prominent than in earlier low- cluster-order calculations. The results are also used to judge the quality of Silver's approximation for n(p,Q).
The natural orbitals (NOs) and natural occupation numbers (NON) of various N = Z, sp and sd shell nuclei are calculated by applying a correlated one-body density matrix (OBDM). The correlated density matrix has been evaluated by considering central correlations of Jastrow type and an approximation named factor cluster expansion. The correlation effects on NOs, NON and the Fermi sea depletion (FSD) are discussed and analyzed. In addition, an approximate expression for the correlated OBDM of the nuclear matter has been used for the evaluation of the relative momentum distribution and FSD. We found that the value of FSD is higher in closed shell nuclei compared to open shell ones and it is lower compared to the case of nuclear matter. This statement could be confirmed by relevant experimental studies.
The formalism based on correlated basis functions and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. To gauge the reliability of this scheme, we perform a systematic comparison between the results of its application to the Fermi hard-sphere system and the predictions obtained from low-density expansions, as well as from other many-body techniques. The analysis of a variety of properties, including the ground-state energy, the effective mass, and the momentum distribution, shows that the effective-interaction approach is quite accurate, thus suggesting that it may be employed to achieve a consistent description of the structure and dynamics of nuclear matter in the density region relevant to astrophysical applications.