Short-range Correlation Effects Research Articles

Short-range correlations and neutrinoless double beta decay

Abstract In this work we report on the effects of short-range correlations upon the matrix elements of neutrinoless double beta decay ( 0 ν β β ). We focus on the calculation of the matrix elements of the neutrino-mass mode of 0 ν β β decays of 48 Ca and 76 Ge. The nuclear-structure components of the calculation, that is the participant nuclear wave functions, have been calculated in the shell-model scheme for 48 Ca and in the proton–neutron quasiparticle random-phase approximation (pnQRPA) scheme for 76 Ge. We compare the traditional approach of using the Jastrow correlation function with the more complete scheme of the unitary correlation operator method (UCOM). Our results indicate that the Jastrow method vastly exaggerates the effects of short-range correlations on the 0 ν β β nuclear matrix elements.

A full-configuration interaction “nuclear orbital” method to study doped HeN3 clusters (N⩽4)

An efficient full configuration interaction (FCI) treatment, based on the Jacobi-Davidson algorithm, is developed in order to study small doped (3)He(N) clusters. The state of each He atom in a given cluster is described by a set of wave-functions which by extention of the quantum-chemistry notation are caller here "nuclear orbitals". The FCI treatment is applied to the calculation of binding energies and helium natural orbitals of (3)He(N)...Br(2)(X) complexes. In agreement with our previous calculations using a Hartree-Fock approach [Phys. Rev. Lett. 93, 053401 (2004)], in which the He-He interaction is modified at small distances to account for short-range correlation effects, the lowest-energy states of each multiplet are found to be very close in energy. The natural orbital analysis, in turn, indicates the adequacy of the "nuclear orbital" approach in these systems.

Magnetism and electron correlations

Electron correlation effects on magnetism are discussed from a local point of view on the basis of the dynamical coherent potential approximation (CPA) which completely takes account of the dynamical spin and charge fluctuations within the single-site approximation. The dynamical CPA is equivalent to other single-site theories of strongly correlated electrons: the many-body CPA, the dynamical mean-field theory, and the projection operator method CPA. The method is shown to describe both the dynamical effects on magnetic properties and the many-body band structure on the same footing. The effects of orbital degeneracy and the realistic calculation scheme are discussed with emphasis on Hund's rule coupling. Two types of theories for non-local correlations, the molecular dynamics approach and the self-consistent projection operator approach, are presented. The effects of magnetic short-range order and non-local correlations are discussed with some numerical results.

Low-energy elastic electron scattering by atomic oxygen

The B-spline R-matrix method is employed to investigate the low-energy elastic electron scattering by atomic oxygen. Flexible non-orthogonal sets of radial functions are used to construct the target description and to represent the scattering functions. A detailed investigation regarding the dependence of the predicted partial and total cross sections on the scattering model and the accuracy of the target description is presented. The predicted angle-integrated elastic cross sections are in good agreement with experiment, whereas significant discrepancies are found in the angle-differential elastic cross sections near the forward direction. The near-threshold results are found to strongly depend on the treatment of inner-core short-range correlation effects in the target description, as well as on a proper account of the target polarizability. A sharp increase in the elastic cross sections below 1 eV found in some earlier calculations is judged to be an artefact of an unbalanced description of correlation in the N-electron target structure and the (N + 1)-electron collision problems.

THEORETICAL QUANTUM-INFORMATION PROPERTIES OF NUCLEI AND TRAPPED BOSE GASES

We will study fermionic systems like atomic nuclei and bosonic systems like the correlated atoms in a trap from an information-theoretical point of view. The Shannon and Onicescu information measures are calculated for the above systems by comparing the correlated and uncorrelated cases as functions of the strength of the short range correlations. One-body and two-body density and momentum distributions are employed. Thus, the effect of short-range correlations on the information content is evaluated. The magnitude of distinguishability between the correlated and uncorrelated densities is also discussed employing suitable measures for the distance of states i.e. the well known Kullback–Leibler relative entropy and the recently proposed Jensen–Shannon divergence entropy. We will see that the same information-theoretical properties hold for quantum many-body systems obeying Bose–Einstein and Fermi–Dirac (statistics).

Correlation effects on the nonmesonic weak decay of the Λ hyperon in nuclear matter

The nonmesonic weak decay of a \ensuremath{\Lambda} hyperon is studied in nuclear matter. Special emphasis is placed on a consistent treatment of correlations introduced by the strong interaction on its weak counterpart. The latter is described by the exchange of mesons between the initial $\ensuremath{\Lambda}N$ state and the final NN one. The weak decay is studied in terms of the weak self-energy, which allows a systematic evaluation of short-range and tensor correlation effects that are determined by a realistic hyperon-nucleon interaction. The admixture of $\ensuremath{\Sigma}N$ components through the strong interaction is also included in the calculation of the \ensuremath{\Lambda} decay properties. Calculations for the ratio of the neutron-induced partial width to the corresponding proton-induced one, ${\ensuremath{\Gamma}}_{n}/{\ensuremath{\Gamma}}_{p}$, are discussed in connection with recent experimental results.

DEPENDENCE OF COULOMB SUM RULE ON THE SHORT RANGE CORRELATION BY USING Av18 POTENTIAL

The Coulomb sum rule (CSR) and structure factor are calculated for inelastic electron scattering from nuclear matter at zero and finite temperature in the nonrelativistic limit. The effect of short-range correlation (SRC) is presented by using lowest order constrained variational (LOCV) method and the Argonne Av18 and Δ-Reid soft-core potentials. The effects of different potentials as well as temperature are investigated. It is found that the nonrelativistic version of Bjorken scaling approximately sets in at the momentum transfer of about 1.1 to 1.2 GeV/c and the increase of temperature makes it to decrease. While different potentials do not significantly change CSR, the SRC improves the Coulomb sum rule and we get reasonably close results to both experimental data and others theoretical predictions.

Nuclear Time-Reversal Violation and the Schiff Moment ofRa225

We present a comprehensive mean-field calculation of the Schiff moment of the nucleus 225Ra, the quantity that determines the static electric-dipole moment of the corresponding atom if time-reversal (T) invariance is violated in the nucleus. The calculation breaks all possible intrinsic symmetries of the nuclear mean field and includes, in particular, both exchange and direct terms from the full finite-range T-violating nucleon-nucleon interaction, and the effects of short-range correlations. The resulting Schiff moment, which depends on three unknown T-violating pion-nucleon coupling constants, is much larger than in 199Hg, the isotope with the best current experimental limit on its atomic electric-dipole moment.

QUANTUM-INFORMATION CONTENT OF FRACTIONAL OCCUPATION PROBABILITIES IN NUCLEI

Three measures of the information content of a probability distribution are briefly reviewed. They are applied to fractional occupation probabilities in light nuclei, taking into account short-range correlations. The effect of short-range correlations is to increase the information entropy (or disorder) of nuclei, comparing with the independent particle model. It is also indicated that the information entropy can serve as a sensitive index of order and short-range correlations in nuclei. It is concluded that increasing Z, the information entropy increases, i.e. the disorder of the nucleus increases for all measures of information considered in the present work.

Correlation effects onΛpropagation in nuclear matter

The propagation of a $\ensuremath{\Lambda}$ hyperon in nuclear matter is studied within the Green's function formalism. The probability density for adding a $\ensuremath{\Lambda}$ hyperon with momentum $k$ to the correlated nuclear matter ground state is obtained from the complete energy dependence of the real and imaginary parts of the $\ensuremath{\Lambda}$ self-energy. This self-energy incorporates the effects of short-range correlations induced by the hyperon-nucleon interaction and the strong coupling between $\ensuremath{\Lambda}N$ and $\ensuremath{\Sigma}N$ states which is known to be crucial for a correct determination of the $\ensuremath{\Lambda}$ binding energy. The calculated spectral functions and quasi-particle parameters for the $\ensuremath{\Lambda}$ are found to be qualitatively similar to corresponding results for correlated nucleons. In general, the $\ensuremath{\Lambda}$ is less strongly correlated with the nuclear matter environment at ${k}_{F}=1.36\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ than a nucleon, in agreement with empirical information from finite nuclei.

Correlated nucleons in configuration space

Several recent studies have dealt with the effects of short range correlations on the momentum distribution of nucleons in nuclei. Here we investigate the correlation effects on the density and spectral distribution in coordinate space. A combination of experimental data and spectral functions calculated from realistic N-N interactions allows us to resolve a recently uncovered discrepancy with occupation of quasi-particle states derived from (e,e'p) data.

Self consistent and covariant propagation of pions, nucleon and isobar resonances in cold nuclear matter

We evaluate the in-medium spectral functions for pions, nucleon and isobar resonances in a self consistent and covariant manner. The calculations are based on a recently developed formulation which leads to predictions in terms of the pion–nucleon scattering phase shifts and a set of Migdal parameters describing important short range correlation effects. We do not observe significant softening of pion modes if we insist on reasonable isobar resonance properties but predict a considerable broadening of the N ( 1440 ) and N ( 1520 ) resonances in nuclear matter. Contrasted results are obtained for the s-wave N ( 1535 ) and N ( 1650 ) resonances which are affected by a nuclear environment very little. The properties of slowly moving isobar's in nuclear matter are found to depend very sensitively on a soft form factor in the π N N vertex, which is not controlled by the πN scattering data.

One-neutron knockout reactions on proton-rich nuclei withN=16

One-neutron knockout reactions from the deeply bound $N=16$ isotones with $Z=16,17,$ and 18 have been studied in inverse kinematics with intermediate-energy beams. $\ensuremath{\gamma}$-ray spectroscopy in coincidence with the detection of knockout residues allowed for an investigation of the one-neutron removal leading to individual excited states. Spectroscopic factors are deduced in the framework of the sudden and eikonal approximations and are compared to USD shell-model predictions. The momentum distributions observed in the experiment are used to identify the angular momentum $l$ carried by the knockedout neutron by comparing with calculations based on a black-disk reaction model. The systematics of reduced single-particle occupancies attributed to the effect of short-range correlations, observed so far for stable and near-magic nuclei in $(e,{e}^{\ensuremath{'}}p)$ and $(d,^{\mathrm{3}}\mathrm{He})$ reactions and in one-nucleon knockout on light deeply bound systems, are extended in this work.

ON THE TWO-BODY MOMENTUM DISTRIBUTION IN FINITE NUCLEI

We present compact analytic expressions for the two-body momentum distribution η2(p1, p2) in Z=N closed-shell nuclei derived within the context of the independent particle shell model. Results are derived for the nucleus 16 O . The effect of dynamical short-range correlations is estimated using Jastrow-type correlation functions in the case of the nucleus 4 He .

Dynamical correlations in Coulomb drag effect

Motivated by recent Coulomb drag experiments in pairs of low-density two-dimensional (2D) electron gases, we investigate the influence of correlation effects on the interlayer drag rate as a function of temperature. We use the self-consistent field method to calculate the intra and interlayer local-field factors G ij ( q, T) which embody the short-range correlation effects. We calculate the transresistivity using the screened effective interlayer interactions that result from incorporating these local-field factors within various approximation schemes. Our results suggest that dynamic (frequency dependent) correlations play an important role in enhancing the Coulomb drag rate.

Long-range and short-range Coulomb correlation effects as simulated by Hartree-Fock, local density approximation, and generalized gradient approximation exchange functionals

Exchange functionals used in density functional theory (DFT) are generally considered to simulate long-range electron correlation effects. It is shown that these effects can be traced back to the self-interaction error (SIE) of approximate exchange functionals. An analysis of the SIE with the help of the exchange hole reveals that both short-range (dynamic) and long-range (nondynamic) electron correlation effects are simulated by DFT exchange where the local density approximation (LDA) accounts for stronger effects than the generalized gradient expansion (GGA). This is a result of the fact that the GGA exchange hole describes the exact exchange hole close to the reference electron more accurately than the LDA hole does. The LDA hole is more diffuse, thus leading to an underestimation of exchange and stronger SIE effects, where the magnitude of the SIE energy is primarily due to the contribution of the core orbitals. The GGA exchange hole is more compact, which leads to an exaggeration of exchange in the bond and the nonbonding region and negative SIE contributions. Partitioning of the SIE into intra-/interelectronic and individual orbital contributions makes it possible to test the performance of a given exchange functional in different regions of the molecule. It is shown that Hartree–Fock exchange always covers some long-range effects via interelectronic exchange while self-interaction-corrected DFT is lacking these effects.

Metal surface energy: Persistent cancellation of short-range correlation effects beyond the random phase approximation

The role that nonlocal short-range correlation plays at metal surfaces is investigated by analyzing the correlation surface-energy into contributions from dynamical density fluctuations of various two-dimensional wave vectors. Although short-range correlation is known to yield considerable correction to the ground-state energy of both uniform and nonuniform systems, short-range correlation effects on intermediate and short-wavelength contributions to the surface formation energy are found to compensate one another. As a result, our calculated surface energies, which are based on a nonlocal exchange-correlation kernel that provides accurate total energies of a uniform electron gas, are found to be very close to those obtained in the random-phase approximation, and support the conclusion that the error introduced by the local-density approximation is small.

Description of metals based on localized electrons

We study dielectric properties of metallic systems using a modified Pariser-Parr-Pople model in the single determinant approximation. Our model does not invoke extra screening; it describes long-range coulomb interaction exactly and approximates and neglects only the short-range exchange and correlation effects. We show that in metallic systems this long-range coulomb interaction leads to spatial localization of electronic orbitals over several atoms, different from orbital localization on single atoms in Mott insulators. We speculate that such localization is also important for the description of metallic transport properties based on Hartree–Fock or Kohn–Sham density functional theory formalisms.

Short-Range Correlations and Meson Exchange Currents in Photonucleon Emission

One-nucleon emission processes induced by photon absorption are studied by considering short-range correlation effects. At energies above the giant resonance region the validity of the direct knock-out model has been tested by comparison with continuum random phase approximation results. Nucleon re-scattering effects have been considered by using an optical potential. The role of the electromagnetic convection, magnetization, and meson exchange currents has been investigated as a function of both excitation energy and momentum transfer. The short-range correlation effects have been studied by using various correlation functions. We found that the nucleon photo-emission cross section is rather sensitive to the presence of short-range correlations at large values of nucleon emission angle. In this region, however, the effects of meson exchange currents are even larger than those produced by short-range correlations.

Effects of short-range correlations in(e,e′p)reactions and nuclear overlap functions

A study of the effects of short-range correlations over the ${(e,e}^{\ensuremath{'}}p)$ reaction for low missing energy in closed-shell nuclei is presented. We use correlated quasihole overlap functions extracted from the asymptotic behavior of the one-body density matrix, containing central correlations of Jastrow type, up to first order in a cluster expansion, and computed in the very high asymptotic region, up to 100 fm. The method to extract the overlap functions is checked in a simple shell model, where the exact results are known. We find that the single-particle wave functions of the valence shells are shifted to the right due to the short-range repulsion by the nuclear core. The corresponding spectroscopic factors are reduced by only a few percent with respect to the shell model. However, the ${(e,e}^{\ensuremath{'}}p)$ response functions and cross sections are enhanced in the region of the maximum of the missing momentum distribution due to short-range correlations.