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On some singularities in the dielectric properties of an electron gas in a uniform magnetic field
300
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A Theory of Intermediate Structure, Overlapping Resonances and Photonuclear Reactions in Light Nuclei. M. G. MUSTAFA. Physics Division, Oak Ridge National Laboratory, P. 0. Box X, Oak Ridge, Tennessee 37830 and F. BARY MALIK. Institut de Physique, Universite de Neuchatel, Neuchltel, Switzerland. Starting from a many body Hamiltonian a general theory involving intermediate structures and overlapping resonances in nuclear reaction has been worked out. This treatment, based on Trefftz’s work on dielectronic recombination in atomic physics, avoids explicit use of projection operators and all relevant quantities like decay widths and energy shifts are explicitly expressed in terms of two body matrix elements. In particular, attention has been focus& on the interaction of bound states among themselves and then on the coupling of the continuum with these interacting bound states. For the case of overlapping resonances, it is shown that in general one cannot take a simple energy average of the resonant amplitudes, and explicit equations for this case have been obtained. This microscopic theory also provides a justification of the model of Duke, Malik, and Firk in explaining the intermediate structure in giant dipole resonance region of IsO and %i. However, the formalism is a general one and is suitable for the study of intermediate structure involving isolated and overlapping resonances for many types of reactions. Symmetric Distributions of Fermi Quarks in Mesons. KURT JUST. Department of Physics, University of Arizona, Tucson, Arizona 85721. A bound state of fermions can be described by a totally symmetric distribution S as well as by its Bethe-Salpeter amplitude T. Since it vanishes by spin and statistics in the spacelike region, estimating S is easier than solving the Rethe-Salpeter equation for T. These previous findings are here confirmed by a relativistic model for mesons composed of massless quarks interacting by vector gluons. Asymptotic Behavior of the Pion Electromagnetic Form Factors in Bethe-Salpeter Model. S. N. BISWAS, SANT~KH SINGH, AND THAKUR VIDHANI. Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India. Asymptotic behavior of the pion form factors has been discussed treating pion as a bound state of the elementary nucleon and antinucleon system. The matrix-element of the electromagnetic current is written in terms of the Bethe-Salpeter amplitude for the nucleon-antinucleon bound system. Using suitable approximations the Bethe-Salpeter equation for nucleon-antinucleon hound state with nucleons as Dirac spinors has been solved and the corresponding off-shell pion form factors are determined. The form factors are strongly interaction dependent. For coupling 92/16r* = 15/4 the form factors vanish asymptotically like t-l and for 14/4 < 92/l&* < 15/4 the form factors still vanish but less rapidly than t-l. On Some Singularities in the Dielectric Properties of an Electron Gas in a Uniform Magnetic Field. H. P. GAIL AND J. SCHMID-BURGK. Lehrstuhl fiir Theoretische Astrophysik, University of Heidelberg, Heidelberg, Germany. The effects of a magnetic field on the self-shielding of an electron gas against small electrostatic perturbations Pare studied by use of Bloch wave functions and by the random phase approximation. V is taken to be periodic along the field lines. It is demonstrated that in the weak field limit, p,,B/eV + 0, magnetic effects become negligible. For p,,B > eV such effects may be important only under limited physical conditions. Singularities discussed by Glasser and Kaplan are replaced by peaks of finite amplitude and width, appearing with the frequency of neck orbit oscillations. Peak profiles and the Lindhard singularity are investigated for the case V # 0.
ABSTRACTS
OF
PAPERS
TO APPEAR
IN
FUTURE
ISSUES
A Theory of Intermediate Structure, Overlapping Resonances and Photonuclear Reactions in Light Nuclei. M. G. MUSTAFA. Physics Division, Oak Ridge National Laboratory, P. 0. Box X, Oak Ridge, Tennessee 37830 and F. BARY MALIK. Institut de Physique, Universite de Neuchatel, Neuchltel, Switzerland. Starting from a many body Hamiltonian a general theory involving intermediate structures and overlapping resonances in nuclear reaction has been worked out. This treatment, based on Trefftz’s work on dielectronic recombination in atomic physics, avoids explicit use of projection operators and all relevant quantities like decay widths and energy shifts are explicitly expressed in terms of two body matrix elements. In particular, attention has been focus& on the interaction of bound states among themselves and then on the coupling of the continuum with these interacting bound states. For the case of overlapping resonances, it is shown that in general one cannot take a simple energy average of the resonant amplitudes, and explicit equations for this case have been obtained. This microscopic theory also provides a justification of the model of Duke, Malik, and Firk in explaining the intermediate structure in giant dipole resonance region of IsO and %i. However, the formalism is a general one and is suitable for the study of intermediate structure involving isolated and overlapping resonances for many types of reactions. Symmetric Distributions of Fermi Quarks in Mesons. KURT JUST. Department of Physics, University of Arizona, Tucson, Arizona 85721. A bound state of fermions can be described by a totally symmetric distribution S as well as by its Bethe-Salpeter amplitude T. Since it vanishes by spin and statistics in the spacelike region, estimating S is easier than solving the Rethe-Salpeter equation for T. These previous findings are here confirmed by a relativistic model for mesons composed of massless quarks interacting by vector gluons. Asymptotic Behavior of the Pion Electromagnetic Form Factors in Bethe-Salpeter Model. S. N. BISWAS, SANT~KH SINGH, AND THAKUR VIDHANI. Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India. Asymptotic behavior of the pion form factors has been discussed treating pion as a bound state of the elementary nucleon and antinucleon system. The matrix-element of the electromagnetic current is written in terms of the Bethe-Salpeter amplitude for the nucleon-antinucleon bound system. Using suitable approximations the Bethe-Salpeter equation for nucleon-antinucleon hound state with nucleons as Dirac spinors has been solved and the corresponding off-shell pion form factors are determined. The form factors are strongly interaction dependent. For coupling 92/16r* = 15/4 the form factors vanish asymptotically like t-l and for 14/4 < 92/l&* < 15/4 the form factors still vanish but less rapidly than t-l. On Some Singularities in the Dielectric Properties of an Electron Gas in a Uniform Magnetic Field. H. P. GAIL AND J. SCHMID-BURGK. Lehrstuhl fiir Theoretische Astrophysik, University of Heidelberg, Heidelberg, Germany. The effects of a magnetic field on the self-shielding of an electron gas against small electrostatic perturbations Pare studied by use of Bloch wave functions and by the random phase approximation. V is taken to be periodic along the field lines. It is demonstrated that in the weak field limit, p,,B/eV + 0, magnetic effects become negligible. For p,,B > eV such effects may be important only under limited physical conditions. Singularities discussed by Glasser and Kaplan are replaced by peaks of finite amplitude and width, appearing with the frequency of neck orbit oscillations. Peak profiles and the Lindhard singularity are investigated for the case V # 0.