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The N-quantum approximation in static models
554
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A bootstrap system is sought which satisfies the following conditions: (i) “Consistency” in that all exchanged particles are bound as poles in the appropriate direct channels; (ii) “closure” in that no further low-lying states are bound other than those whose exchange contributes to the forces; and (iii) “completeness ” in that all “low” energy processes involving any of the particles in the spectrum are taken into account. Starting from the O- octet (r, K, 7) and the I- octet (p, R*, $), these consistency considerations lead to the meson supermultiplets listed in Table I. Interesting regularities in the predicted spectrum are noted. In particular one sees that apart from “Regge” recrtrrences, the spect,rum happens to coincide with that contained in the (6*, 6)-(6, 6*) representat,ion of the recently proposed US X US supersymmetry. A tentative assignment, is attempted of known meson states into the scheme. Apart from the K+-r+4 enhancement at 1270 MeV, all reasonably well-established resonances to-date fit, comfortably into the spectrum. Further empirical regularities are noted in the assignment, which include one in the Bronzan-Low quantum number A. Wherever feasible, the dynamical parameters (masses, coupling constants) are computed by requiring numerical “bootstrap” consistency using a method proposed by Zachariasen and Zemach. These values are listed in Table II, where it is seen that qualitative agreement 1s obtained for all parameters so far calculated. Analytical Expressions for Inelastic Scattering Cross Sections. Part II. S. T’ARMA and A. DAR, Department of Nuclear Physics, The Weizmann Institute of Science, Rehovoth, Israel. Closed-form expressions are derived for t,he differential cross section for inelastic scattering via mutual and double collective excitations and under strong absorption conditions. “Blair Phase Rules.” The predictions are comThe expressions result in the generalized pared with experimental data, and good agreement is obtained. The N-Quantum Approximation in Static Models. ANTONIO PAGNAMENT~, Rlltgers, The State University, New Brunswick, New Jersey. The N-quantum approximation (N&A) is a method designed to construct approximate operator solutions to the field equations. It is shown in detail how this method works and can be made compatible with the renormalization program in t,he Lee model and for t,he scalar field interacting with a fixed fermion source. The terminated in-field expansions can still be applied successfully in the presence of bound states, for which one will introduce new in-fields, or if one deals with resonances. This is discussed on the examples of the V-Sbound state and the unstable V-particle. Theory of Alpha Matter. JOHN W. CLARK and TSO-PIN WANG, Depart,ment of Physics, Washington University, St. Louis, Missouri. The usual concept of nuclear matter is discussed, and a generalization of this concept which allows a qualitative understanding of the effects of clustering phenomena is prothe properties of the ground state posed. As an example of “generalized nuclear matter,” of a uniform extended system of structureless OL particles are studied with the method developed by Wu and Feenberg for liquid He4. The Wu-Feenberg method requires the use of (i) a Bijl-Dingle-Jastrow wave function, and (ii) the Kirkwood superposition approximation. The assumed 0l-a interactions fit the S-wave phase shifts up to a c.m. energy of 10 MeV. The results, in comparison with results from theoretical nuclear-matter calculations which entertain no clustering (both expressed in terms of the energy per nucleon as a func-
ABSTRACTS
OF
PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
A bootstrap system is sought which satisfies the following conditions: (i) “Consistency” in that all exchanged particles are bound as poles in the appropriate direct channels; (ii) “closure” in that no further low-lying states are bound other than those whose exchange contributes to the forces; and (iii) “completeness ” in that all “low” energy processes involving any of the particles in the spectrum are taken into account. Starting from the O- octet (r, K, 7) and the I- octet (p, R*, $), these consistency considerations lead to the meson supermultiplets listed in Table I. Interesting regularities in the predicted spectrum are noted. In particular one sees that apart from “Regge” recrtrrences, the spect,rum happens to coincide with that contained in the (6*, 6)-(6, 6*) representat,ion of the recently proposed US X US supersymmetry. A tentative assignment, is attempted of known meson states into the scheme. Apart from the K+-r+4 enhancement at 1270 MeV, all reasonably well-established resonances to-date fit, comfortably into the spectrum. Further empirical regularities are noted in the assignment, which include one in the Bronzan-Low quantum number A. Wherever feasible, the dynamical parameters (masses, coupling constants) are computed by requiring numerical “bootstrap” consistency using a method proposed by Zachariasen and Zemach. These values are listed in Table II, where it is seen that qualitative agreement 1s obtained for all parameters so far calculated. Analytical Expressions for Inelastic Scattering Cross Sections. Part II. S. T’ARMA and A. DAR, Department of Nuclear Physics, The Weizmann Institute of Science, Rehovoth, Israel. Closed-form expressions are derived for t,he differential cross section for inelastic scattering via mutual and double collective excitations and under strong absorption conditions. “Blair Phase Rules.” The predictions are comThe expressions result in the generalized pared with experimental data, and good agreement is obtained. The N-Quantum Approximation in Static Models. ANTONIO PAGNAMENT~, Rlltgers, The State University, New Brunswick, New Jersey. The N-quantum approximation (N&A) is a method designed to construct approximate operator solutions to the field equations. It is shown in detail how this method works and can be made compatible with the renormalization program in t,he Lee model and for t,he scalar field interacting with a fixed fermion source. The terminated in-field expansions can still be applied successfully in the presence of bound states, for which one will introduce new in-fields, or if one deals with resonances. This is discussed on the examples of the V-Sbound state and the unstable V-particle. Theory of Alpha Matter. JOHN W. CLARK and TSO-PIN WANG, Depart,ment of Physics, Washington University, St. Louis, Missouri. The usual concept of nuclear matter is discussed, and a generalization of this concept which allows a qualitative understanding of the effects of clustering phenomena is prothe properties of the ground state posed. As an example of “generalized nuclear matter,” of a uniform extended system of structureless OL particles are studied with the method developed by Wu and Feenberg for liquid He4. The Wu-Feenberg method requires the use of (i) a Bijl-Dingle-Jastrow wave function, and (ii) the Kirkwood superposition approximation. The assumed 0l-a interactions fit the S-wave phase shifts up to a c.m. energy of 10 MeV. The results, in comparison with results from theoretical nuclear-matter calculations which entertain no clustering (both expressed in terms of the energy per nucleon as a func-