The generalized momentum distribution n(p,Q), related to the half-diagonal two-body density matrix ${\mathrm{\ensuremath{\rho}}}_{2\mathrm{h}}$(
r1,
r2,${\mathbf{r}}_{1}^{\ensuremath{'}}$) by Fourier transformation in the variables
r1-${\mathbf{r}}_{1}^{\ensuremath{'}}$ and
r1-
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.
The short-range and tensor components of the bare nucleon-nucleon interaction induce a sizable depletion of low momenta in the ground state of a nuclear many-body system. The self-consistent Green's function method within the ladder approximation provides an ab initio description of correlated nuclear systems that accounts properly for these effects. The momentum distribution predicted by this approach is analyzed in detail, with emphasis on the depletion of the lowest momentum state. The temperature, density, and nucleon asymmetry (isospin) dependence of the depletion of the Fermi sea is clarified. A connection is established between the momentum distribution and the time-ordered components of the self-energy, which allows for an improved interpretation of the results. The dependence on the underlying nucleon-nucleon interaction provides quantitative estimates of the importance of short-range and tensor correlations in nuclear systems.
An elaborate cluster analysis of the single-particle occupation probability ${n}_{\stackrel{^}{q}}$ and associated one-body density matrix
n(r) is performed for a Fermi system described by a Jastrow wave function. A diagrammatic formalism rooted in Ursell-Mayer theory facilitates the analysis. It is conjectured, and demonstrated to convincingly high cluster order, that ${n}_{\stackrel{^}{q}}$ may be written as
n[N(q)+N1(q)], where
n is a strength factor independent of wave number
q and the quantities
N(q) and
N1(q) may be expressed as series of irreducible cluster contributions. The strength factor
n has the form
n=eQ, where
Q may also be expressed as a series of irreducible cluster contributions. Massive partial summations on the latter series yield a compact expression for
Q in terms of the spatial distribution functions corresponding to the Jastrow wave function. Working with the Fourier inverse of ${n}_{\stackrel{^}{q}}$, it is further demonstrated that
n(r) may be cast in the form $\ensuremath{\rho}n[{N}_{1}(r)+{N}_{2}(r)]\mathrm{exp}\mathcal{Q}(r)$, where $\ensuremath{\rho}$ is the particle density and the functions
N1(r),
N2(r), and
Q(r) are all given by irreducible cluster series. Massive partial summations are executed in the
Q(r) series to achieve a compact expression of this quantity in terms of the aforementioned spatial distribution functions. One has
Q(0)=Q. The leading diagrams necessary for a quantitative evaluation of the momentum distribution of liquid
3He and nuclear matter are displayed. Specialization to infinite degeneracy of the single-particle levels, while shrinking the Fermi wave number to zero (Bose limit), allows liquid
4He to be treated as well. In this limit off-diagonal long-range order appears, the condensate fraction ${\ensuremath{\rho}}^{\ensuremath{-}1}n(\ensuremath{\infty})={n}_{c}$ being just the strength factor
n. It may also be shown (under certain reasonable assumptions) that the customary ${r}^{\ensuremath{-}2}$ long-range behavior of the two-body correlations implies a singular behavior ${n}_{q}={n}_{c}(\frac{\mathrm{mc}}{2\ensuremath{\hbar}}){q}^{\ensuremath{-}1}$ of the Bose momentum distribution for small
q.
The one-body density matrix, momentum distribution, natural orbits, and quasihole states of
16O and
40Ca are analyzed in the framework of the correlated basis function theory using state-dependent correlations with central and tensor components. Fermi hypernetted chain integral equations and single operator chain approximation are employed to sum cluster diagrams at all orders. The optimal trial wave function is determined by means of the variational principle and the realistic Argonne ${v}_{8}^{\ensuremath{'}}$ two-nucleon and Urbana IX three-nucleon interactions. The correlated
16O momentum distribution is in good agreement with the variational Monte Carlo results and shows the well-known enhancement at large momentum values with respect to the independent-particle model. A similar behavior is found in
40Ca. The relative importance of the different types of correlations (mainly Jastrow and tensor) on the momentum distribution appears to be similar in the nuclei and in nuclear matter. Diagonalization of the density matrix provides the natural orbits and their occupation numbers. Correlations deplete the occupation number of the first natural orbital by more than
10 The orbitals following the first one result instead, occupied by a few percent, or less. The single particle overlap functions and the spectroscopic factors are computed in the correlated model for both nuclei and compared with previous estimates. Jastrow correlations lower the spectroscopic factors of the valence states by a few percent $(\ensuremath{\sim}1--3%)$ with respect to unity. An additional $\ensuremath{\sim}8--12%$ depletion is provided by spin-isospin tensor correlations. It is confirmed that a variational treatment of short-range correlations does not explain the spectroscopic factors extracted from ${(e,e}^{\ensuremath{'}}p)$ experiments. Such an approach corresponds to the zeroth order of the correlated basis function theory and two-hole one-particle perturbative corrections in the correlated basis are expected to provide most of the remaining strength, as in nuclear matter.
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).