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Nucleon-nucleon boundary condition methods for nuclear matter
512
ABSTRACTS
curvature, i.e., the gage fields. The step from local to integral conservation laws is considered with care, casting some doubt on the conventional procedure and indicating an apparent possibility for geometric breaking of conservation laws. The concept of holonomy groups has been used freely; one of the remaining questions concerns the asymptotic behavior of internal holonomy groups at large distances from a physical system. Part of the dynamics is proposed to be carried by a postulate linking event space with internal space, and defining a map among the holonomy groups for these spaces. Several candidates for such a postulate have group theoretical implications similar to higher symmetry schemes. The translation group is absent here however, since the energy-momentum vector is constructed from the Einstein tensor in Riemannian event space. Spin angular momentum has been tentatively identified with a geometric construct as well. Nucleon-Nucleon Boundary Condition Methods for Nuclear Matter. M. M. HOENIG AND E. L. LOMON, Department of Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts. It is shown that, as a consequence of the energy independence of the boundary condition f on the radial Schroedinger wave function u at r0 , u = 0 for r < ro ; and that the boundary condition is equivalent to replacing vu, in the equation for u in T < r0 , by an expression linear in U(TO + e) and u’(ro + l ). The Bethe-Goldstone wave function uN is determined by the same replacement in its integral equation. But u N # 0 in r < rg , so that UN depends on an extra parameter b, the boundary condition at ro - E. Pseudo-potentials at r0 that give the boundary condition exactly are presented. The self-consistent single particle potential energy in nuclear matter is investigated with a simple S state boundary condition, without a potential tail. The effective mass approximation is found inadequate. For the same interaction, the effect of summing the hole-hole contributions is found to be important for the two-body correlations, and small but significant for the saturation and binding energy. A calculation is made with a more realistic model with a potential tail. A modified Moszkowski-Scott type expansion, separated at r0 , is used. Convergence is poor and binding is not obtained. More recent nucleon-nucleon boundary condition models may give convergence and binding. Bounds for the Correction to the Born Term and Applications to p-p Scattering for a Generalized Dispersion Model. JUDITH BINSTOCK, Lawrence Radiation Laboratory, University of California, Berkeley, California. The unitarizing corrections to the Born term, as given by the Chew-Arndt, MacGregorArndt 0’0 even), and Scotti-Wong models, are shown to be bounded above and below. The bounds follow from the mathematical forms of the models, to all of which forms a theorem (proved in this paper) applies. The correction bounds are given for several p-p amplitudes for the range 0 to 300 MeV. The results are shown to explain why the apparently different models mentioned above give similar Born terms after subtraction of the correction from the experimentally determined (p-p) amplitude. A generalization of these models for the unitarizing correction is proposed, which has properties leading to partial-wave dispersion relations, and which has a specified relationship between the asymptotic behavior and the fluctuation of the sign of the left-hand discontinuity. Upper and lower bounds are found for the correction term prescribed by this generalized model (which is not restricted, in its application, to nucleon-nucleon scattering).
ABSTRACTS
curvature, i.e., the gage fields. The step from local to integral conservation laws is considered with care, casting some doubt on the conventional procedure and indicating an apparent possibility for geometric breaking of conservation laws. The concept of holonomy groups has been used freely; one of the remaining questions concerns the asymptotic behavior of internal holonomy groups at large distances from a physical system. Part of the dynamics is proposed to be carried by a postulate linking event space with internal space, and defining a map among the holonomy groups for these spaces. Several candidates for such a postulate have group theoretical implications similar to higher symmetry schemes. The translation group is absent here however, since the energy-momentum vector is constructed from the Einstein tensor in Riemannian event space. Spin angular momentum has been tentatively identified with a geometric construct as well. Nucleon-Nucleon Boundary Condition Methods for Nuclear Matter. M. M. HOENIG AND E. L. LOMON, Department of Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, Massachusetts. It is shown that, as a consequence of the energy independence of the boundary condition f on the radial Schroedinger wave function u at r0 , u = 0 for r < ro ; and that the boundary condition is equivalent to replacing vu, in the equation for u in T < r0 , by an expression linear in U(TO + e) and u’(ro + l ). The Bethe-Goldstone wave function uN is determined by the same replacement in its integral equation. But u N # 0 in r < rg , so that UN depends on an extra parameter b, the boundary condition at ro - E. Pseudo-potentials at r0 that give the boundary condition exactly are presented. The self-consistent single particle potential energy in nuclear matter is investigated with a simple S state boundary condition, without a potential tail. The effective mass approximation is found inadequate. For the same interaction, the effect of summing the hole-hole contributions is found to be important for the two-body correlations, and small but significant for the saturation and binding energy. A calculation is made with a more realistic model with a potential tail. A modified Moszkowski-Scott type expansion, separated at r0 , is used. Convergence is poor and binding is not obtained. More recent nucleon-nucleon boundary condition models may give convergence and binding. Bounds for the Correction to the Born Term and Applications to p-p Scattering for a Generalized Dispersion Model. JUDITH BINSTOCK, Lawrence Radiation Laboratory, University of California, Berkeley, California. The unitarizing corrections to the Born term, as given by the Chew-Arndt, MacGregorArndt 0’0 even), and Scotti-Wong models, are shown to be bounded above and below. The bounds follow from the mathematical forms of the models, to all of which forms a theorem (proved in this paper) applies. The correction bounds are given for several p-p amplitudes for the range 0 to 300 MeV. The results are shown to explain why the apparently different models mentioned above give similar Born terms after subtraction of the correction from the experimentally determined (p-p) amplitude. A generalization of these models for the unitarizing correction is proposed, which has properties leading to partial-wave dispersion relations, and which has a specified relationship between the asymptotic behavior and the fluctuation of the sign of the left-hand discontinuity. Upper and lower bounds are found for the correction term prescribed by this generalized model (which is not restricted, in its application, to nucleon-nucleon scattering).