Nuclear Correlation Functions Research Articles

Short range correlations and the isospin dependence of nuclear correlation functions

Pair densities and associated correlation functions provide a critical tool for introducing many-body correlations into a wide-range of effective theories. Ab initio calculations show that two-nucleon pair-densities exhibit strong spin and isospin dependence. However, such calculations are not available for all nuclei of current interest. We therefore provide a simple model, which involves combining the short and long separation distance behavior using a single blending function, to accurately describe the two-nucleon correlations inherent in existing ab initio calculations. We show that the salient features of the correlation function arise from the features of the two-body short-range nuclear interaction, and that the suppression of the pp and nn pair-densities caused by the Pauli principle is important. Our procedure for obtaining pair-density functions and correlation functions can be applied to heavy nuclei which lack ab initio calculations.

Nuclear–nuclear correlation function from non-Born–Oppenheimer calculations of diatomic rovibrational states with total angular momentum equal to two (N = 2). Charge asymmetry in HD

ABSTRACTThe HD molecule in rovibrational states where the total angular momentum quantum number is equal to two (N = 2) is characterised with quantum mechanical calculations without assuming the Born–Oppenheimer (BO) approximation. Explicitly correlated all-particle Gaussian functions are used in the calculations. The convergence of the total non-BO energies of the considered states with the basis set size is analysed. The calculations of the averaged interparticle distances demonstrate the asymmetry of the electronic charge distribution. The algorithm to calculate the nuclear–nuclear correlation function for the N = 2 states is derived and implemented. Plots of this function for different rovibrational states provide a visual representation of the molecular structure.

Nuclear correlation functions in lattice QCD

We consider the problem of calculating the large number of Wick contractions necessary to compute states with the quantum numbers of many baryons in lattice QCD. We consider a constructive approach and a determinant-based approach and show that these methods allow the required contractions to be performed in computationally manageable amount of time for certain choices of interpolating operators. Examples of correlation functions computed using these techniques are shown for the quantum numbers of the light nuclei, He, Be, C, O and Si.

High-order harmonic generation from polyatomic molecules including nuclear motion and a nuclear modes analysis

We present a generic approach for treating the effect of nuclear motion in the high-order harmonic generation from polyatomic molecules. Our procedure relies on a separation of nuclear and electron dynamics where we account for the electronic part using the Lewenstein model and nuclear motion enters as a nuclear correlation function. We express the nuclear correlation function in terms of Franck-Condon factors which allows us to decompose nuclear motion into modes and identify the modes that are dominant in the high-order harmonic generation process. We show results for the isotopes CH$_4$ and CD$_4$ and thereby provide direct theoretical support for a recent experiment [Baker {\it et al.}, Science {\bf 312}, 424 (2006)] that uses high-order harmonic generation to probe the ultra-fast structural nuclear rearrangement of ionized methane.

Meson-induced correlations of nucleons in nuclear Compton scattering

The nonresonant (seagull) contribution to the nuclear Compton amplitude at low energies is strongly influenced by nucleon correlations arising from meson exchange. We study this problem in a modified Fermi gas model, where nuclear correlation functions are obtained with the help of perturbation theory. The dependence of the mesonic seagull amplitude on the nuclear radius is investigated and the influence of a realistic nuclear density on this amplitude is discussed. We found that different form factors appear for the static part (proportional to the enhancement constant $\ensuremath{\kappa})$ of the mesonic seagull amplitude and for the parts, which contain the contribution from electromagnetic polarizabilities.

Two-nucleon photoemission and nuclear correlations

The authors study the ( gamma ,np) cross section in light nuclei at medium energies taking into account two-body effects both in the nuclear wavefunction (correlations) and in the electromagnetic operator (meson exchange currents). The Gottfried factorisation is shown to be valid also in the presence of MEC and therefore the total cross section of two-nucleon photoemission is directly related to the Fourier transform of the nuclear correlation function. As an example, they evaluate the total cross section assuming a simplified correlation function and discuss the sensitivity of the results to the theoretical parameters.

Optical-Potential Scattering of Nucleons by Carbon at Medium Energies

The elastic scattering of nucleons by carbon, at incident energies of 142, 210, and 330 MeV, is calculated from an optical potential retaining all terms to second order in the $N\ensuremath{-}N$ amplitudes. The amplitudes are calculated using recent $N\ensuremath{-}N$ phase-parameter sets obtained by the Yale, Livermore, and Michigan State Groups. Nuclear correlation functions of both the Fermi and Brueckner-Gammel types are used to represent nuclear structure. Comparison with experiment is made in order to distinguish among different $N\ensuremath{-}N$ phase-parameter sets, and among different types of nuclear correlation functions.

Forward Scattering Amplitude with Nuclear Correlations and Overlapping Potentials

We have formulated a theory of nuclear scattering for overlapping potentials between the incident particle and each of the target nucleons, without using the impact-parameter approximation of Feshbach. As the nuclear internal Hamiltonian is important for the overlap in the potentials, we include in the energy denominators a term which is dependent on the nuclear internal Hamiltonian, as well as the term which is linear in the momentum transfers. A correction to the Glauber model, due to the overlap in the potentials, is obtained from the principal part of the denominators. The correction reduces both the total cross section and the forward differential cross section by about 15%. We define the "effective solid angle for scattering" to be the total cross section divided by the forward differential cross section. From this quantity we can determine nuclear correlation independently of the correction due to the overlap in the potentials. Range parameters for nuclear correlation functions are obtained from existing data.

Two-Nucleon Phase-Shift-Set Discrimination by Means of the Binary Optical Potential

The scattering of nucleons from light nuclei at energies of 142, 210, and 310 MeV is calculated using the multiple-scattering optical potential obtained by retaining all terms which are binary or less in the two-nucleon amplitudes. The binary potential includes the impulse-approximation correction as well as the double-scattering correction. Nucleon-nucleus scattering observables are computed, using optical potentials calculated with some of the Yale and Livermore phase-parameter sets and the Fermi and Brueckner-Gammel nuclear-correlation functions. The observables are compared with data in an effort to ascertain the differences caused by changing $N\ensuremath{-}N$ scattering phase parameters and/or nuclear-correlation functions and to see whether it is feasible to use such changes in attempts to pin down $N\ensuremath{-}N$ and nuclear parameters.

Nuclear correlation functions and muon capture

Properties of certain nuclear correlation functions which enter into the theory of muon capture in complex nuclei in the closure approximation are examined. The reliability of certain suggested methods for evaluating these correlation functions involving the Fermi gas approximation, and refinements of it, are assessed both from the point of view of internal theoretical self-consistency and by comparison with pertinent empirical information available from photodisintegration data on nuclei.