Chun Wa Wong

Vector bracket and transformed wave function of a few-body state

Abstract Explicit expressions and symmetry properties are obtained for the vector bracket r a lr b L , λ | r 1 l 1 r 2 l 2 , λ > and for the corresponding transformed wave function of a two-body state. The equivalence between these results and certain expressions appearing in the angularmomentum decomposition of few-body problems is discussed. The rather fundamental role of these brackets and wave functions in few-body problems is pointed out. Further examples are given of their usefulness. In the Brueekner-Hartree-Fock problem they permit the dynamical equations in coordinate or momentum space to be written in forms suitable for numerical calculation. They also make possible the use of arbitrary single-particle wave functions in nuclearstructure calculations, as illustrated in a numerical study of the single-particle spin-orbit splitting in 16 O.

Quark model of nucleon-nucleon spin-orbit potentials

Abstract The lowest-order spin-orbit potentials between two nucleons are calculated by using nonrelativistic two-quark spin-orbit interactions obtained from meson masses. The resulting scattering matrices (calculated in the Born approximation) are compared with those from phenomenological nuclear forces. They are found to have the correct signs and roughly the correct strengths in both the T = 1 and T = 0 channels. The many uncertainties and difficulties inherent in the quark picture of nucleon-nucleon spin-orbit forces are briefly discussed.

GENERALIZED HARMONIC OSCILLATOR SHELL MODEL AND GENERALIZED OSCILLATOR TRANSFORMATION BRACKETS.

Abstract The motivation for using a generalized harmonic oscillator shell model with any number (≦ A ) of different oscillator lengths and of separated centers of well is discussed. Formulas, including recursion formulas and expansion theorems, are obtained by means of generating functions for the calculation of matrix elements of many-body operators. Most of the generating functions in the model have a simple form, for which recursion formulas can be classified, enumerated, and given in simple standard forms. The simplicity of the generating functions also enables explicit expressions for the matrix elements to be written down in a number of equivalent ways. Of particular interest are the generalized two-body transformation brackets to the relative and c.m. representation, with which matrix elements of a general two-body potential and of the Brueckner-Bethe reaction matrix can be calculated. A significant result is that the formulas in this generalized oscillator shell model are very similar to those in the usual oscillator shell model with unseparated centers of well. This means that relatively minor modifications of available computer codes will make possible calculations in the generalized oscillator shell model. The generalized oscillator wave functions can be used as quantum mechanical cluster wave functions and, more generally and also more satisfactorily, as generator-coordinate wave functions. It is hoped that these wave functions will be useful in problems of nuclear reactions as well as in those of nuclear structure.

Strangeness vibrations and the strangeness content of the nucleon

Abstract A schematic model of strangeness vibrations is used to show the importance of continuum contributions to strangeness correlations in both S =−1 and S =1 baryon channels. The strangeness content of the nucleon due to vibrational correlations of the skyrmion is found to be convergent in the sum over vibrational eigenmodes, but the associated correlation energy and the number of strange mesons in the nucleon both diverge. The divergence comes from an angular momentum transmutation potential caused by the “cowlick” of the hedgehog pion field located at the origin. The model dependence and other problems of the calculated vibrational contributions to the strangeness content of the nucleon are discussed.

Baryon-nucleon spin-orbit forces from symmetric quark-quark spin-orbit interactions

Abstract Baryon-nucleon spin-orbit forces generated from symmetric quark-quark spin-orbit interactions are studied. Under certain conditions, the results for both hyperon-nucleon and nucleon-nucleon channels are found to be roughly the same whether the quark-quark interactions arise from one-gluon exchange or one-boson exchanges. Both are in rough agreement with the Nijmegen one-boson-exchange potential models. The reasons for these similarities are discussed.

The Deuteron matter radius

Abstract The deuteron matter radius r m calculated for most realistic nucleon-nucleon potentials fitting the experimental triplet scattering length is about 1% larger than the experimental value, or 0.6% larger than a “shape-independent” value in the effective-range expansion. However, it is 2.6% larger than experiment for the full Bonn potential. We find that this is caused by the energy dependence of the full Bonn potential induced by the 3.8% admixture of abnormal components involving higher-mass states. A correction to r m of about −1.8% is found to be necessary to allow for the smaller sizes of these abnormal components, thus bringing the Bonn result in line with the other realistic potentials. The explicit appearance of the D-state in realistic potential models of the deuteron is shown to increase r m by 0.8%. Reductions of r m made with the help of phase-equivalent unitary scale transformations show significant redistributions of the matter density inside a two-nucleon separation of 3 fm. Such redistributions will reduce the size of the neutron electric form factor deduced from e-D scattering.

Charge asymmetry and neutron-neutron scattering

Abstract The uncertainty in the subtraction of electromagnetic effects from S-wave proton-proton scattering potentials is studied in two models using unitarily transformed potentials. Restrictions on these models caused by theoretical, off-shell and deuteron constraints are imposed. The probable uncertainty of physical interest is found to be small. It is typically only a few parts per thousand of the one-pion exchange potential. It has relatively little effect on Coulomb displacement energies. Phenomenological charge-symmetry-breaking potentials are constructed which both fit the experimental neutron-neutron (nn) scattering length (−16.4 fm). and give roughly the needed Coulomb displacement energies. These phenomenological potentials are found to contain a short-range repulsion and a strong long-range attraction for a neutron pair. The need for experimental information on the shape and state dependence of the nn force is emphasized. These can probably be obtained from precise nn scattering measurements.

Diagrammatic expansions for isobaric analog states and the Coulomb displacement energy

Abstract Certain aspects of diagrammatic expansions for isobaric analog states are discussed. The effect of the charge-distortion potential of Auerbach, Kahana and Weneser on the Coulomb displacement energy is estimated to be about 6% by relating it to the average isotope shift of the core charge distribution.

Nucleon core size and nucleon-nucleon spin-orbit forces

Abstract Information on the rms radius of quarks in nucleons is deduced from the nucleon-nucleon spin-orbit forces when the latter are derived from a simple quark model of nucleons in (ls) 3 spatial configurations with one-gluon-exchange and/or one-meson-exchange quark-quark interactions. Values of 0.3–0.5 fm appear to be favored. Some of the uncertainties and limitations of these estimates are briefly discussed.

Relativistic center-of-mass motion of quarks in bags

Abstract Simple expressions are obtained for center-of-mass (c.m.) corrections on masses of hadrons made up of relativistic quarks in given shell-model configurations. They are applicable to quarks in bags even when the quark wave functions are discontinuous at the bag surface. Analogous c.m. corrections on magnetic moments are shown to be due to the artificial confinement of the hadron in the bag. They can be separated into a Halprin-Kerman magneton correction and a new point-moment correction. These results are illustrated by using four bag models fitted to hadron masses. The magnetic-moment corrections are found to account for about half of the discrepancies of the simple bag moments from the experimental values. The implications for the magnetic moments of composite leptons are also discussed.