Particle-hole Correlations Research Articles

Hole spectral functions and collective excitations

Proton-hole spectral functions are calculated by solving the Dyson equation for the one-body Green function using a realistic G-matrix interaction. The consequences of replacing non-interacting intermediate states in the second-order self-energy by interacting ones is studied. These interactions are treated in Tamm-Dancoff approximation (TDA) as well as in random-phase approximation (RPA) for particle-hole or particle-particle (hole-hole) correlations. The influence of these correlations is illustrated for the spectral-strength distributions in 48Ca and 90Zr. The influence of a more realistic treatment of the states to which the particles couple is particularly strong at low energy, where such coherence phenomena are most important and where they yield additional fragmentation of single-particle strength. In accord with this observation, an increased depletion of mostly filled shells just below the Fermi energy and an increased occupation of mostly empty shells just above the Fermi energy is obtained. Instabilities found in the RPA treatment, point to the need of a self-consistent approach. Comparison with recent (e,e′p) data yields an estimate of about 10–15% for the amount of strength that is depleted by short-range correlations.

Quasielastic response at large momentum transfer in a relativistic model with Δ baryon

We evaluate the longitudinal and transverse response functions of 56Fe at momentum transfer 1.14 GeV within the relativistic σωϱ model. The result including particle-hole correlations based on a mean-field ground state disagrees with the recent data, while the agreement is much better for a renormalized Hartree ground-state and with additional nucleon-antinucleon correlations. Excitation of the Δ baryon gives the main contribution to the transverse response, and a sizeable contribution to the longitudinal response.

Vacuum Polarization Effects on the Coulomb Sum at Momentum Transfer near 1 GeV

Particle-hole correlations including nucleon-antinucleon excitations reduce the Coulomb sum values of quasielastic scattering models by about 50% at momentum transfer near 1 GeV. This result in a renormalized σ-ω model is consistent with a recent experiment in SLAC

Isoscalar spin response functions in the quasielastic scattering region

The role of particle-hole correlations in isoscalar spin response functions in the quasielastic scattering region is examined within the continuum RPA. Both spin-longitudinal and spin-transverse response functions are appreciably modified from the free response function without correlations, due to the repulsive central force and the exchange term of the tensor force in the particle-hole interaction. The latter force also induces an appreciable difference between the two isoscalar spin response functions. It is shown that the ground-state correlation (the backward-going contribution) due to the tensor force is important in the large momentum transfer region and is not weakened, even at large energy transfer. The experimental ratio between the two spin response functions at q=1.75fm −1 observed in (p, p') reactions is not largely modified around the quasielastic scattering peak by including particle-hole correlations in the spin-isoscalar mode. On the other hand, it is somewhat reduced in the large energy transfer region above the quasielastic scattering peak.

Beyond the born collision term. Inclusion of density fluctuations in one-body dynamics

Closed evolution equations for the single-particle occupation numbers are derived which include particle-hole correlations. They provide for the coupling with density fluctuations in addition to the collisions described by the Boltzmann term.

Effects of the Dirac sea on the Coulomb sum value for electron scattering

Polarization effects of the Dirac sea on the Coulomb sum values for electron scattering are investigated within the framework of the random-phase approximation (RPA) in the relativistic σ-ω model. Divergence due to NN̄ excitations in the correlation functions is renormalized using a method of dimensional regularization. Particle-hole correlations reduce the sum values of the relativistic Hartree approximation by 15≈20%, while effects of the Dirac sea reduce them further by about 10≈20%. The quenching phenomena of the Coulomb sum values observed in medium heavy nuclei are rather well explained in the renormalized relativistic RPA.

Mean field R V B theory: Degeneracy, gauge symmetry and the comparison to exact results

We present a mean field theory for RVB states on a square lattice at and near half-filling, including particle-particle and particle-hole correlations. At half-filling, local SU(2) invariance allows a wavefunction to be expressed variously in fermion operators, which leads to degeneracies in the mean field theory. Away from half-filling the invariance is absent and the lowest energy RVB state is a d-wave superconductor.

Quantized TDHF for giant monopole vibrations

The time-dependent Hartree-Fock theory supplemented with the quantum consistency condition for the gauge-invariant component of the wave function is applied to the description of isoscalar giant monopole resonances in 16O, 40Ca and 110Zr. Calculations are performed using the Skyrme SIII effective interaction. Good agreement with experimental data concerning the average resonance energy and the decay width is obtained. This emphasizes an important role of both a finite oscillation amplitude of the mean field and particle-hole correlations beyond RPA.

Pairing correlations: I. The ground-state coupled-cluster formalism as a unifying approach

the general problem of pairing correlations within a many-fermion system of identical particles is discussed at some length. We show in this first work in a series how the ground-state version of the [exp(S) or] coupled-cluster formalism (CCF) of quantum many-body theory may be rather generally applied to this problem, and how it thereby provides a very powerful and unifying approach to it. At the so-called SUB2 level of truncation, which is the lowest natural level of approximation for homogeneous systems, the CCF may be cast as a nonlinear integral equation for a four-point correlation function,S 2, which provides a measure of the two-particle/two-hole component in the true “ground-state” wavefunction. This approximation couples the particle-particle, hole-hole and particle-hole correlations simultaneously, and treats them all on an equal footing. In the present work we concentrate particular attention on particle-particle and hole-hole correlations by focussing on the formulation of generalised ladder approximations within the CCF. These are therefore likely to be physically applicable in the low-density regime. In particular, we show that the well-known Galitskii approximation may be formulated within the CCF as that drastic sub-approximation to the full SUB2 equation which keeps only the so-called complete ladder (CLAD) terms, which we describe. A second paper applies the CCF to the particular case of a general (non-local) separable potential, and obtains exact analytic solutions within the CLAD approximation for the corresponding wavefunctions of the simultaneous particle-particle and hole-hole substructures within the many-fermion system.

The ( 3He,t) reaction at intermediate energies: Spin-isospin transitions to states in 12N and 13N

The ( 3He, t) reaction has been studied at intermediate energies, 600 MeV–2.3 GeV. The reaction is a single-step direct reaction, and the angular distributions are well described by DWIA calculations. At these energies the σρ component of the interaction dominates. The ratio of the isovector strengths ¦J σρ/ ρ¦ derived from the data on 13C appears to remain roughly constant in the energy range 300–700 MeV per nucleon. The triton spectra exhibit a prominent quasi-free peak. The data at momentum transfers q ⪢ 1.7 fm −1 show a shift of the peak towards smaller energy loss than observed in (e, e') experiments at corresponding four-momentum transfers. The shift becomes progressively larger with increasing q and is about 45 MeV at q = 2.5 fm −1. The shift may be caused by particle-hole correlations in the spin-longitudinal channel.

Particle-hole and particle-particle RPA ground state correlations

We show that the expression derived by Kuo et al. to sum the particle-hole ring diagrams yields the quasi-boson correlation energy. This requires correction for double counting in second order. For the particle-particle ring series we give expressions for the correlation energy, wave function, norm and occupation probabilities and show that the quasi-boson approximation is valid. The formulae are illustrated by simple models.

Quasielastic electron scattering in the relativistic σω model

Nuclear response functions for quasielastic electron scattering are investigated in the random phase approximation for the relativistic lagrangian of the σω model. In contrast to the transverse response function, the longitudinal one is strongly affected by particle-hole correlations due to the σ- and ω-meson exchanges. This result is different from the previous understanding in the σω model that the whole effect of the nuclear interactions on the response function would be incorporated into the nucleon effective mass. The Coulomb sum rule is also discussed in the relativistic model.

The role of the tensor force for isoscalar collective spin states

The influence of tensor particle-hole correlations on the motion of isoscalar spin resonances is considered. A simple model for the particle-hole interaction in the spin channels is used in a random-phase description of 1 + states in 208Pb. We discuss changes in the response to inelastic proton scattering for the lowest isoscalar 1 + state.

Many-body field theoretic framework for inelastic pion-nucleus scattering

We consider inelastic scattering of pions from nuclei using many-body quantum field theory methods. We find that, in an inelastic amplitude for small energy transfer, one can separate out effects of particle-hole correlations in the final nuclear state. The ratio of π + and π − inelastic cross sections can differ substantially from the analogous ratio for free πN scattering.

Alpha-particle strengths from the 16O(6Li, d)20Ne reaction

Abstract The 16 O( 6 Li, d) 20 Ne reaction has been studied at bombarding energies of 20, 32 and 38 MeV. The α-particle spectroscopic strengths have been extracted for levels up to 12.15 MeV in excitation. Nondirect processes appear to contribute significantly to all levels at 20 MeV and to high spin levels (6 + and 8 + ) at 32 MeV. Strengths extracted for members of the ground state band assuming (sd) 4 transfer are unequal at both 32 and 38 MeV, in marked contrast to theoretical predictions. To explain this, particle-hole correlations in 16 O(g.s.), inelastic channel coupling in the reaction and perhaps other effects as well, have to be considered. Strengths extracted for members of excited bands and α-decay reduced widths compare poorly with each other and with simple SU(3) predictions.

Two-particle one-hole multiple-scattering contribution to 17O energies using an energy-dependent reaction matrix

The role of 2p1h correlations in 17O is studied within a multiple-scattering formalism. An accurate, energy-dependent reaction matrix with orthogonalized plane-wave intermediate states is used to assess the relative importance of particle-particle and particle-hole correlations in the 17O energies. The effect of energy dependence of the reaction matrix is closely examined.

Two-Particle-Two-Hole J =0+ States of 40Ca: Interplay between Particle-Particle (Hole-Hole) Correlations and Particle-Hole Correlations

Two-Particle-Two-Hole J =0+ States of 40Ca: Interplay between Particle-Particle (Hole-Hole) Correlations and Particle-Hole Correlations

Particle-hole and particle-particle RPA ground state correlations and the Green function formalism

Green function techniques are used to derive the two-particle and particle-hole RPA correlations in the ground state of a closed shell nucleus. The correlation energy and density are calculated with the Tabakin interaction for 16O and 40Ca and compared to the second order perturbation theory contributions. The correlation energies are respectively − 12.80 and − 18.78 MeV for 16O and 40Ca.

A study of photoproduction of charged pions from 16O

Photoproduction of π + from 16O leading to the four bound states in 16N has been studied using different dynamical amplitudes and considering particle-hole correlations in the nuclear wave functions. It is shown that the total cross section is strongly affected by the choice of dynamical amplitudes whereas the effect of 3p - 3h correlations in 16N is small.

Damping of nuclear dipole states: Carl B. Dover and R. H. Lemmer. Institut de Physique Nucléaire, Division de Physique Théorique, 91—Orsay—France and F.J.W. Hahne. National Physical Research Laboratory, C.S.I.R., Pretoria, South Africa

Proton-hole spectral functions are calculated by solving the Dyson equation for the one-body Green function using a realistic G-matrix interaction. The consequences of replacing non-interacting intermediate states in the second-order self-energy by interacting ones is studied. These interactions are treated in Tamm-Dancoff approximation (TDA) as well as in random-phase approximation (RPA) for particle-hole or particle-particle (hole-hole) correlations. The influence of these correlations is illustrated for the spectral-strength distributions in 48Ca and 90Zr. The influence of a more realistic treatment of the states to which the particles couple is particularly strong at low energy, where such coherence phenomena are most important and where they yield additional fragmentation of single-particle strength. In accord with this observation, an increased depletion of mostly filled shells just below the Fermi energy and an increased occupation of mostly empty shells just above the Fermi energy is obtained. Instabilities found in the RPA treatment, point to the need of a self-consistent approach. Comparison with recent (e,e′p) data yields an estimate of about 10–15% for the amount of strength that is depleted by short-range correlations.