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 nucleon momentum distribution
nA(k) for
A=2, 3, 4, 16, and 40 nuclei is systematically analyzed in terms of wave functions resulting from advanced solutions of the nonrelativistic Schr\"odinger equation, obtained within different many-body approaches based upon different realistic bare nucleon-nucleon (
NN) interactions featuring similar short-range repulsion and tensor interactions. Particular attention is paid to the separation of the momentum distributions into the mean-field and short-range correlation (SRC) contributions. It is shown that although at high values of the momentum
k different approaches lead to some quantitative differences, these do not hinder the general conclusion that the high-momentum behavior ($k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$) of all nuclei considered are very similar, exhibiting the well-known scaling behavior with the mass number
A, independently of the used many-body approach and the details of the bare
NN interaction. To analyze and understand the frequently addressed question concerning the relationships between the nucleus,
nA(k), and the deuteron,
nD(k), momentum distributions, the spin (
S)-isospin (
T) structure of few-nucleon systems and complex nuclei is analyzed in terms of realistic
NN interactions and many-body approaches. To this end, the number of
NN pairs in a given (
ST) state, viz.,
(ST)=(10), (00), (01), and (11), and the contribution of these states to the nucleon momentum distributions are calculated. It is shown that, apart from the (00) state, which has very small effects, all other spin-isospin states contribute to the momentum distribution in a wide range of momenta. It is shown that for all nuclei considered the momentum distributions in the states
T=0 and
T=1 exhibit at $k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$ very similar behaviors, which represents strong evidence of the
A-independent character of SRCs. The ratio
nA(k)/nD(k) is analyzed in detail, stressing that in the SRC region it always increases with the momentum and the origin of such an increase is discussed and elucidated. The relationships between the one- and two-body momentum distributions, considered in a previous paper, are discussed and clarified, pointing out the relevant role played by the center-of-mass motion of a correlated pair in the (10) state. Eventually, the values of the the probability of high-momentum components in nuclei and the per nucleon probability
a2 of deuteronlike configurations in nuclei are calculated, and the relationship of the present approach with the many-body methods based upon low-momentum effective interactions is briefly discussed.
Background: The high-momentum distribution of atoms in two spin-state ultracold atomic gases with strong short-range interactions between atoms with different spins, which can be described by using Tan's contact, are dominated by short-range pairs of different fermions and decreases as ${k}^{\ensuremath{-}4}$. In atomic nuclei the momentum distribution of nucleons above the Fermi momentum ($k>{k}_{F}\ensuremath{\approx}250$ MeV/
c) is also dominated by short-range-correlated different-fermion (neutron-proton) pairs.Purpose: Compare high-momentum unlike-fermion momentum distributions in atomic and nuclear systems.Methods: We show that, for
k>kF MeV/
c, nuclear momentum distributions are proportional to that of the deuteron. We then examine the deuteron momentum distributions derived from a wide variety of modern nucleon-nucleon potentials that are consistent with
NN-scattering data.Results: The high-momentum tail of the deuteron momentum distribution, and hence of the nuclear momentum distributions, appears to decrease as ${k}^{\ensuremath{-}4}$. This behavior is shown to arise from the effects of the tensor part of the nucleon-nucleon potential. In addition, when the dimensionless interaction strength for the atomic system is chosen to be similar to that of atomic nuclei, the probability for finding a short-range different-fermion pair in both systems is the same.Conclusions: Although nuclei do not satisfy all of the conditions for Tan's contact, the observed similarity of the magnitude and ${k}^{\ensuremath{-}4}$ shape of nuclear and atomic momentum distributions is remarkable because these systems differ by about 20 orders of magnitude in density. This similarity may lead to a greater understanding of nuclei and the density dependence of nuclear systems.
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.
In this work a unitary correlation operator is presented that explicitly describes the short-ranged central and tensor correlations in the nuclear many-body system. These short-ranged correlations are induced by the repulsive core and the pronounced tensor force of realistic nucleon-nucleon interactions and cannot be described by the simple many-body states of a mean-field or shell model approach. The unitary correlation operator is discussed for the Argonne V18 and the Bonn-A interactions. Applying the correlation operator onto the Hamiltonian a common effective interaction for low momenta is obtained. Calculations for 4He using the one- and two-body part of the correlated Hamiltonian compare favorably with exact many-body methods. Calculations for 16O and 40Ca which are not possible with exact methods are performed using harmonic oscillator shell model states. The observed deviation from the experimental binding energies and radii is attributed to the missing three-body forces. The correlated interaction in a basis-free representation is used in the Fermionic Molecular Dynamics model to calculate the nuclei of the p- and the sd-shell. In this model the uncorrelated many-particle state is given as a Slaterdeterminant of Gaussian wave-packets with spin and isospin degrees of freedom which allows a consistent description of spherically symmetric, intrinsically deformed and clustered nuclei.
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.