Short-range Dynamical Correlations Research Articles

Quantum Theory of the Equation of State for Solid Hydrogen

A variational calculation of the ground-state energy of molecular crystalline hydrogen has been carried out, including the effect of correlation between the motions of the particles. The principal purpose was to obtain the equation of state for solid hydrogen at absolute-zero temperature over a wide range of densities. We are concerned with energies on a scale appropriate to high-pressure phenomena, and therefore approximated the molecular rotational behavior, so that the very low-temperature phase transitions are not describable in the present model. The variational form of the energy was obtained by truncating the cluster expansion of the ground-state energy. The effect of short-range dynamic correlation is taken into consideration through a Jastrow-type pair-correlation function in the trial wave function. To facilitate the fast convergence of the cluster expansion, a model correlation function with an explicit hard-core exclusion effect was employed. With this pair-correlation function, the truncation approximation was extended into the high-density region where previous functional forms for pair correlation had not been satisfactory. Numerical computations were done for a Lennard-Jones potential, a Buckingham exp-6-type potential, and a nonspherical molecular interaction due to Wang Chang. The results compare favorably with experiment, although there is a systematic difference at high density; either all of the assumed potentials are inadequate or the experimental data are in error.

Angular distributions of high energy photoprotons from 6Li(γ, p)

(γ, p) angular distributions have been studied for photon energies E γ ⩾ 100 MeV on the basis of a shell model modified by short-range dynamical correlations (SRC's)between the nucleons. It is shown that short-range correlations affect the magnitude as well as the shape of the proton angular distributions. It turns out that the shell model underestimates the experimental data appreciably, whereas the inclusion of SRC's tends to reproduce the measured angular distribution.

On high-energy scattering by nuclei—II

A coupled equation description of the scattering of fast particles is formulated. For elastic scattering two coupled channels are employed. One wavefunction describes the elastic channel. The other is an “average” wavefunction which takes into account the collisions which remove the incident particles from the elastic channel. Explicit formulas are given for the coupling and diagonal potentials as obtained from the Kerman, McManus, and Thaler multiple scattering theory which includes the effects of single and double scattering in their nonlocal optical potential. The properties of the target nucleus involved are its density and pair correlation function. These are described in terms of intrinsic coordinates, the relation to model wavefunctions being briefly discussed. Three kinds of correlations are considered; the center-of-mass correlation required of the target nucleons in order that the target recoil as a unit, the exclusion principle or Pauli correlation and the short-range dynamical correlations. The coupling potential is directly related to correlation function vanishing if the correlation funciton vanishes. Numerical calculations are performed for protons of 1.69 Gev/c momentum incident on 4He and 16O. It is found that the Pauli correlation has little effect, that the center-of-mass correlation is the dominant correlation effect for the 4He target but not important for 16O. The effect of the short-range correlation is measured by the parameter ( r cR )/[1 + 2 r v 2r c 2 ] where r c is the correlation length, R the nuclear radius, r v the nuclear “force range.” In the heavier nuclei, the effect of short-range correlations is proportional to this parameter; in 4He, because of interference with the center-of-mass correlation terms, the effect is proportional to its square root. Short-range correlations are thus more difficult to observe for heavier nuclei and when their range is small compared to the ranges of nuclear forces. Absence of required nucleon-nucleon data prevents a definitive statement with respect to the presence of short range correlations. However the present nucleon-nucleon and proton- 4He data are not inconsistent with the presence of a repulsive short-range correlation.

Dispersive effects in high-energy elastic electron-nucleus scattering and nuclear correlations

The effects of virtual nuclear excitations in high-energy elastic electron-nucleus scattering are analyzed in a self-consistent manner. We describe the scattering by an infinite system of coupled equations which we solve in the semiclassical approximation. The resulting scattering amplitude is explicity expressed in terms of the one- and two-body densities. The dispersion corrections are then directly related to the nucleon-nucleon correlations. To investigate the above ideas we study the elastic scattering of 420 MeV and 840 Mev electrons by 16O and 208Pb. The dispersive effects are most pronounced in the diffraction minima and small elsewhere, slightly energy and momentum-transfer dependent, and unlikely to be reproduceable by changes in the charge density. Even if dispersion corrections were experimentally measureable, it would still be extremely difficult to extract from them information about dynamical short-range correlations because the short-range correlations are entangled with the Pauli correlations, self-correlations, and the differences in excited states. We also show that the elastic scattering may be obtained by solving a pair of coupled equations or a simple Dirac equation with an effective optical potential and we critically compare the above approaches.

On the investigation of nucleon-nucleon correlations by means of high-energy scattering

The possible effects of short-range dynamical nucleon-nucleon correlations on high-energy hadron scattering on 4He are examined. The Glauber theory of multiple scattering is used as the basis for the computations. The conclusion is that very small effects are to be expected for elastic and sum total inelastic scattering of commonly available projectiles.

Short-range dynamical correlations from elastic and quasi-elastic scattering of high-energy electrons

Short-range dynamical correlations from elastic and quasi-elastic scattering of high-energy electrons

Self-consistent reaction matrix calculation of the pion capture rate in finite nuclei

Abstract The Hartree-Fock (HF) wave functions calculated from a realistic nucleon-nucleon interaction are used to study the two-nucleon emission process following π − capture in complex nuclei. In particular, we study the π(su−) absorption in the 12 C nucleus. The calculated angular distributions of the absorption rate and the branching ratios are compared with available experimental and theoretical results. In some cases, the agreement of our results with experiment is found to be much better than the results obtained by various other approaches which have been used to introduce the effect of short-range correlations in the wave function of the pion-capturing pair of nucleons. Calculations are also made with harmonic oscillator wave functions. In this case we study the corrections to the absorption rate due to various effects, in particular those arising from (i) short-range dynamical correlations, (ii) final state nucleon-nucleus scattering and (iii) final state nucleon-nucleon scattering. It is found that the pure harmonic oscillator model gives reasonably good results after including the contribution from low-lying excited states of the residual nucleus. The correction due to the first effect increases the absorption rate whereas the corrections due to the last two effects suppress the absorption for back-to-back emission of the nucleon pair. Further, it is noticed that the second correction is more important than the third one. The effect of these corrections on the branching ratio R = W (pn → nn)/ W (pp → pn) is studied in detail. Finally, it is pointed out that the Jastrow method of introducing short-range correlations is inadequate in explaining the angular distributions and branching ratio data simultaneously.

Information on Short-Range Nucleon-Nucleon Correlations and Woods-Saxon Nuclear Potential from High-Energy Elastic Electron Scattering

A method has been developed which allows the effect of the short-range dynamical correlations on the nuclear-charge form factors generated in arbitrary potential wells to be taken into account. Recent highenergy experimental data on elastic electron scattering by $^{6}\mathrm{Li}$, $^{12}\mathrm{C}$, and $^{16}\mathrm{O}$ have been analyzed with this method. The single-particle radial wave functions have been generated in a state-dependent Woods-Saxon well whose parameters have been chosen to fit the eigenenergies to the proton separation energies, as obtained from ($p, 2p$) reactions. It is shown that only by the inclusion of correlations is it possible to reproduce theoretically the experimental charge form factor of $^{6}\mathrm{Li}$ and $^{16}\mathrm{O}$ nuclei. It is also pointed out that the inclusion of correlations leads to the use of potential wells which are deeper and narrower than usually assumed. The radial wave functions of the harmonic oscillator have also been used. It is shown that these wave functions also give a good reproduction of the experimental data, provided that correlations are taken into account. The effect of the center-of-mass motion on the form factors calculated in the finite well is also considered.

Hartree-fock charge distribution and the form factor of4He

Recently, the Hartrec-Foek (HF) theory along with an effective interaction which is obtained as a result of uni tary transformation, has provided satisfactory results for a large number of nuclei (1-3). The calculations based on this approach are further extended for fight nuclei (A < 16) after including the corrections due to Coulomb effects and centre-of-mass motion in a self-consistent manner (4). The binding energies so obtained are in fairly good agreement with experiments. On the other hand, as a test of the wave functions the calculated charge densities are compared (3) with the electron scattering data for a few light nuclei such as 4He, 3Be, lzC, l°0. The recent experimental results of FROSCH et al. (6) at large momentum transfers have shown the failure of the Gaussian model for ~He. In order to explain these results, there have been several attempts (~) by modifying the oscillator charge distribution (3) for short-range dynamical correlations. These various attempts differ either in the choice of the correlation function or in the inclusion of the antisymmetrization in the wave function of the alpha-particle. The form of the charge distribution used by CHOU (6) consists of the difference of two Gaussiau shapes with different parameters. JAIN (lo)has compared the charge density obtained from the Irving wave functions with these experiments. From these analyses, it seems that the electronscattering results for large momentum transfers provide an effective tool to test the theories dealing with nucleon-nucleon correlations. The purpose of this note is to c o m -

Short-range dynamical correlations in the12C nucleus from elastic electron scattering

In a recent paper (~) it was shown that there were difficulties in interpreting in a unified way the elastic (2) and quasi-free (a) electron scattering data from carbon by using the phenomenological spherical shell model (*). In fact, i t was impossible to obtain a set of single-particle wave function parameters which fitted both the elastic and quasifree scattering data. In paper (~) it was suggested that this result could probably be changed by considering the possible distortion of the single-particle wave functions by the short-range dynamical correlations arising from repulsive cores. One expects these correlations to have their grea%est effect on the high-momentum components of the single-particle wave functions, and consequently it is reasonable to assume that the elastic form factor, where one measures high-momentum components, will be very sensitive to these correlations. The recent results on 4He (4), and the consequent a t tempts to explain them (5), seem to confirm this hypothesis. The introduction of correlations has proved to be useful also in computing the electron elastic form factor of the eLi nucleus (5~). First results are presented in this note which show tha t if one computes the elast ic form factor with correlated wave functions, one obtains oscillator parameters similar to those given by the (o, e'p) reaction, that is sensibly state-dependent. The correlations were treated in the usual Jastrow method (6), so that the nuclear