Terms Of Intrinsic Coordinates Research Articles

Fermionic fields in the d-dimensional anti-de Sitter spacetime

Arbitrary spin free massless fermionic fields corresponding to mixed symmetry representations of the SO ( d −1) compact group and propagating in even d -dimensional anti-de Sitter spacetime are investigated. Free wave equations of motion, subsidiary conditions and the corresponding gauge transformations for such fields are proposed. The lowest eigenvalues of the energy operator for the massless fields and the gauge parameter fields are derived. The results are formulated in SO ( d −1,2) covariant form as well as in terms of intrinsic coordinates.

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.