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Low density expansion of the nucleon-nucleus optical-model potential
ANNALS
OF PHYSICS:
Abstracts
73, 303-304 (1972)
of Papers
to Appear
in Future
Issues
On The Axial Vector Current and PCAC in The o-Model. R. H. MAURER AND R. S. WILLEY. Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania. An explicit operator construction of the axial vector current in the boson o-model is given in perturbation theory. This current is finite and satisfies the PCAC condition with the renormalized pion field. It also (at least formally) satisfies the SU, x SlJ, equal-time time-component current algebra. Low Density Expansion of the Nucleon-Nucleus Optical-Model Potential. J. H~FNER. Physikalisches Institut der Universitlt, 78 Freiburg, W. Germany AND C. MAHAUX. Institut de Physique, Universite de Liege, Belgium. The optical-model potential for nucleon-nucleus scattering is studied within the framework of the Green function approach to the many-body problem. The optical potential is identified with the self-energy, for which an expansion in terms of irreducible graphs exists. We propose to group the diagrams of this expansion according to the number of independent hole lines and to sum the graphs within each class. This procedure essentially amounts to an expansion in powers of the density and is closely related to the Bethe-Brueckner expansion for the binding energy of nuclear matter. We show that the same convergence parameter appears in both expansions. The one- and two-hole line contributions are studied in detail, numerical estimates are provided and compared with experiment. At low energy, our expansion can be related to the calculation of the optical potential within the framework of nuclear reactions (e.g. using doorway states). At high energy one is lead in a natural way to the expressions derived from multiple scattering theory. Thus the hole-line expansion ties together the low and high energy domains of the optical potential. Hole line expansions for the momentum distribution and the total energy are derived from the expansion of the self energy. The self consistency requirement is discussed. The present study is restricted to nuclear matter but most results apply to finite nuclei as well. Decay of A Perturbation in A Fermi Liquid. G. A. BROOKER. The Clarendon Laboratory, Oxford University, Oxford, England AND J. SYKES. Department of Physics, Duke University, Durham, Uorth Carolina. The behaviour of an arbitrary (but small and homogeneous) disturbance to the distribution function in a degenerate Fermi liquid is investigated. The characteristic decay times, defined after the manner of Uhlenbeck and Ford, are found by solving exactly the linearized kinetic equation. The decay time spectrum consists of a continuum together with discrete decay times; the motion associated with a discrete decay time lasts longer than any associated with the continuum. The discrete decay times are different for each spherical harmonic component of the disturbance, and different for odd and even functions of energy, and for odd and even functions of spin. For each spherical harmonic component and spin dependence, a disturbance symmetric (or antisymmetric) in energy about the Fermi energy can have at most one discrete decay time. A Fermi gas also has discrete decay times, one of which is as much as 44 % larger than any time in the continuum, so the discrete decays are a general feature of relaxation processes and do not rely on strong interactions. By requiring the decay rates for a Fermi liquid all to be positive, we obtain a new derivation of the stability criterion. 303 Copyright All rights
0 1972 by Academic Press, Inc. of reproduction in any form reserved.
OF PHYSICS:
Abstracts
73, 303-304 (1972)
of Papers
to Appear
in Future
Issues
On The Axial Vector Current and PCAC in The o-Model. R. H. MAURER AND R. S. WILLEY. Department of Physics, University of Pittsburgh, Pittsburgh, Pennsylvania. An explicit operator construction of the axial vector current in the boson o-model is given in perturbation theory. This current is finite and satisfies the PCAC condition with the renormalized pion field. It also (at least formally) satisfies the SU, x SlJ, equal-time time-component current algebra. Low Density Expansion of the Nucleon-Nucleus Optical-Model Potential. J. H~FNER. Physikalisches Institut der Universitlt, 78 Freiburg, W. Germany AND C. MAHAUX. Institut de Physique, Universite de Liege, Belgium. The optical-model potential for nucleon-nucleus scattering is studied within the framework of the Green function approach to the many-body problem. The optical potential is identified with the self-energy, for which an expansion in terms of irreducible graphs exists. We propose to group the diagrams of this expansion according to the number of independent hole lines and to sum the graphs within each class. This procedure essentially amounts to an expansion in powers of the density and is closely related to the Bethe-Brueckner expansion for the binding energy of nuclear matter. We show that the same convergence parameter appears in both expansions. The one- and two-hole line contributions are studied in detail, numerical estimates are provided and compared with experiment. At low energy, our expansion can be related to the calculation of the optical potential within the framework of nuclear reactions (e.g. using doorway states). At high energy one is lead in a natural way to the expressions derived from multiple scattering theory. Thus the hole-line expansion ties together the low and high energy domains of the optical potential. Hole line expansions for the momentum distribution and the total energy are derived from the expansion of the self energy. The self consistency requirement is discussed. The present study is restricted to nuclear matter but most results apply to finite nuclei as well. Decay of A Perturbation in A Fermi Liquid. G. A. BROOKER. The Clarendon Laboratory, Oxford University, Oxford, England AND J. SYKES. Department of Physics, Duke University, Durham, Uorth Carolina. The behaviour of an arbitrary (but small and homogeneous) disturbance to the distribution function in a degenerate Fermi liquid is investigated. The characteristic decay times, defined after the manner of Uhlenbeck and Ford, are found by solving exactly the linearized kinetic equation. The decay time spectrum consists of a continuum together with discrete decay times; the motion associated with a discrete decay time lasts longer than any associated with the continuum. The discrete decay times are different for each spherical harmonic component of the disturbance, and different for odd and even functions of energy, and for odd and even functions of spin. For each spherical harmonic component and spin dependence, a disturbance symmetric (or antisymmetric) in energy about the Fermi energy can have at most one discrete decay time. A Fermi gas also has discrete decay times, one of which is as much as 44 % larger than any time in the continuum, so the discrete decays are a general feature of relaxation processes and do not rely on strong interactions. By requiring the decay rates for a Fermi liquid all to be positive, we obtain a new derivation of the stability criterion. 303 Copyright All rights
0 1972 by Academic Press, Inc. of reproduction in any form reserved.