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On the ground state of an impurity in a dilute fermi gas
ANNALS
OF PHYSICS
78, 297-298 (1973)
Abstracts
of Papers
to
Appear
in Future
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A Class of Exact Solutions for Coupled Electromagnetic and Scalar Fields for Einstein-Rosen Metric. ZZ. A. R. ROY, J. R. RAo, AND R. N. TIWARI. Department of Mathematics, Indian Institute of Technology, Kharagpur - 2 (W.B.), India. This paper is a continuation of the author’s earlier work entitled “A class of exact solutions for coupled electromagnetic and scalar fields for Einstein-Rosen metric. I.” [Ann. Physics 69 (1972), 4731. In this paper we have interpreted some of the solutions from different viewpoints with special reference to singular behavior. It has been observed that the presence of zero mass scalar meson fields does not affect the singular behavior as when the electromagnetic field only is present.
Discussion of the Structure of Nuclear Rotation at High Angular Momenta. J. KRUMLINDE Department of Mathematical Physics, Lund Institute of Technology, Lund, Sweden AND Z. SZYMA~~SKI. Institute for Nuclear Research, Warsaw, Poland. A schematic two-level model is introduced and developed in order to describe the nuclear rotation at high angular momenta. For this problem there exists a symmetry of the Lie algebra belonging to the group R(8). The implications of this symmetry including various subalgebras of R(8) corresponding to different particular cases are studied. It is found that the model is able to describe qualitatively (i) the phase transition from the superfluid to the normal state, (ii) the band structure in the region above the phase transition, and (iii) the retardation of the gamma transitions across the phase transition.
Deep Electroproduction and Deep Electron-Positron Annihilation. R. GARBO. Instituto di Fisica dell’Universit8, Roma, Italy, Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy, P. MENOTTI, Scuola Normale Superiore, Pisa, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Italy I. VENDRAMIN, Istituto di Fisica dell’Universita, Padova, Italy. The problem of continuation of the scaling functions for deep inelastic electron scattering into deep inelastic annihilation is discussed. Dynamical models are produced for which analytic continuation connects the two scaling functions and the general conditions are discussed. The dynamical characterization of those situations for which the analytic continuation rule is invalid is also given. The study also illustrates the structure of the singularities of the scaling functions in the w-plane. Models studied include ladder diagrams and particular diagrams with unstable particles propagated. In the latter case cuts generally appear in the scaling functions in the kinematical region for annihilation.
On the Ground State of an Zmpurity in a DiIute Fermi Gas. R. F. BISHOP. Institute of Theoretical Physics, Department of Physics, Stanford University, Stanford, California 94305. The system under consideration is a large collection of identical fermions (B), forming a background, into which is inserted a relatively small number of distinct impurity (I) particles. The background is considered to be dilute in the sense that R > a, where R is the average separation of the B particles, and a is the range of their interaction potential; and the Z particles Copyright 0 1973 by Academic Press, Inc. All rights of reproduction in any form reserved.
297
298
ABSTRACTS
OF
PAPERS
TO APPEAR
IN
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ISSUES
are so dilute with respect to the B particles that Z - Z interactions can be ignored. The Z particles are then all essentially at rest in their ground state. The BB and BZ interaction potentials are chosen to be hard cores of the same range a. A series expansion is developed for the ground-state energy of the Z particles, and the fist four terms are calculated explicitly using two distinct methods, employing Feynman and Goldstone diagrams respectively. It is shown that each method has distinct advantages over the other, and that a judicious combination of both can be used to considerable benefit.
On the Perturbation Approach to the Particle-Vibration Coupling Model. G. VANDEN BERGHE. Rijksuniversiteit-Gent, Belgium, Instituut voor Nukleaire Wetenschappen and Seminarie voor Wiskundige Natuurkunde, K. HEYDE. Rijksuniversiteit-Utrecht, The Netherlands, Fysisch Laboratorium AND M. WAROQUIER. Rijksuniversiteit-Gent, Belgium, Instituut voor Nukleaire Wetenschappen, F’roeftuinstraat 86, B-9000 Gent, Belgium. The particle-vibration coupling model is treated in a perturbation approach in order to i) obtain simple expressions for the reduced E2 transition probabilities and thus derive approximate selection rules; ii) study the convergence properties of the perturbation series (up to sixth order) by comparing with the exact diagonalization procedure. The results are in both cases compared with diagonalization results and the experimental data available on Ylb and YIb. The perturbation expansion, treated to higher order, can be performed easily in terms of a diagrammatic method based on Goldstone and Jutsis-Bandzaitis-Vizbaraite formalisms. It is shown that the perturbation method gives reliable results if “physical” single-particle energies are used instead of “bare” single-particle energies with the neglect of all self-energy corrections and a renormalized particle-vibration coupling strength. This higher order perturbation expansion is applied to the case of Y3b and l*‘Sb.
Printed
in Belgium
OF PHYSICS
78, 297-298 (1973)
Abstracts
of Papers
to
Appear
in Future
Issues
A Class of Exact Solutions for Coupled Electromagnetic and Scalar Fields for Einstein-Rosen Metric. ZZ. A. R. ROY, J. R. RAo, AND R. N. TIWARI. Department of Mathematics, Indian Institute of Technology, Kharagpur - 2 (W.B.), India. This paper is a continuation of the author’s earlier work entitled “A class of exact solutions for coupled electromagnetic and scalar fields for Einstein-Rosen metric. I.” [Ann. Physics 69 (1972), 4731. In this paper we have interpreted some of the solutions from different viewpoints with special reference to singular behavior. It has been observed that the presence of zero mass scalar meson fields does not affect the singular behavior as when the electromagnetic field only is present.
Discussion of the Structure of Nuclear Rotation at High Angular Momenta. J. KRUMLINDE Department of Mathematical Physics, Lund Institute of Technology, Lund, Sweden AND Z. SZYMA~~SKI. Institute for Nuclear Research, Warsaw, Poland. A schematic two-level model is introduced and developed in order to describe the nuclear rotation at high angular momenta. For this problem there exists a symmetry of the Lie algebra belonging to the group R(8). The implications of this symmetry including various subalgebras of R(8) corresponding to different particular cases are studied. It is found that the model is able to describe qualitatively (i) the phase transition from the superfluid to the normal state, (ii) the band structure in the region above the phase transition, and (iii) the retardation of the gamma transitions across the phase transition.
Deep Electroproduction and Deep Electron-Positron Annihilation. R. GARBO. Instituto di Fisica dell’Universit8, Roma, Italy, Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy, P. MENOTTI, Scuola Normale Superiore, Pisa, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Italy I. VENDRAMIN, Istituto di Fisica dell’Universita, Padova, Italy. The problem of continuation of the scaling functions for deep inelastic electron scattering into deep inelastic annihilation is discussed. Dynamical models are produced for which analytic continuation connects the two scaling functions and the general conditions are discussed. The dynamical characterization of those situations for which the analytic continuation rule is invalid is also given. The study also illustrates the structure of the singularities of the scaling functions in the w-plane. Models studied include ladder diagrams and particular diagrams with unstable particles propagated. In the latter case cuts generally appear in the scaling functions in the kinematical region for annihilation.
On the Ground State of an Zmpurity in a DiIute Fermi Gas. R. F. BISHOP. Institute of Theoretical Physics, Department of Physics, Stanford University, Stanford, California 94305. The system under consideration is a large collection of identical fermions (B), forming a background, into which is inserted a relatively small number of distinct impurity (I) particles. The background is considered to be dilute in the sense that R > a, where R is the average separation of the B particles, and a is the range of their interaction potential; and the Z particles Copyright 0 1973 by Academic Press, Inc. All rights of reproduction in any form reserved.
297
298
ABSTRACTS
OF
PAPERS
TO APPEAR
IN
FUTURE
ISSUES
are so dilute with respect to the B particles that Z - Z interactions can be ignored. The Z particles are then all essentially at rest in their ground state. The BB and BZ interaction potentials are chosen to be hard cores of the same range a. A series expansion is developed for the ground-state energy of the Z particles, and the fist four terms are calculated explicitly using two distinct methods, employing Feynman and Goldstone diagrams respectively. It is shown that each method has distinct advantages over the other, and that a judicious combination of both can be used to considerable benefit.
On the Perturbation Approach to the Particle-Vibration Coupling Model. G. VANDEN BERGHE. Rijksuniversiteit-Gent, Belgium, Instituut voor Nukleaire Wetenschappen and Seminarie voor Wiskundige Natuurkunde, K. HEYDE. Rijksuniversiteit-Utrecht, The Netherlands, Fysisch Laboratorium AND M. WAROQUIER. Rijksuniversiteit-Gent, Belgium, Instituut voor Nukleaire Wetenschappen, F’roeftuinstraat 86, B-9000 Gent, Belgium. The particle-vibration coupling model is treated in a perturbation approach in order to i) obtain simple expressions for the reduced E2 transition probabilities and thus derive approximate selection rules; ii) study the convergence properties of the perturbation series (up to sixth order) by comparing with the exact diagonalization procedure. The results are in both cases compared with diagonalization results and the experimental data available on Ylb and YIb. The perturbation expansion, treated to higher order, can be performed easily in terms of a diagrammatic method based on Goldstone and Jutsis-Bandzaitis-Vizbaraite formalisms. It is shown that the perturbation method gives reliable results if “physical” single-particle energies are used instead of “bare” single-particle energies with the neglect of all self-energy corrections and a renormalized particle-vibration coupling strength. This higher order perturbation expansion is applied to the case of Y3b and l*‘Sb.
Printed
in Belgium