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Pomeron factorisation and the reaction γN → φN
ANNALS
OF PHYSICS
91, 217-218 (1975)
Abstracts Quasi-Classical SATHE.
Scattering
Department
of Papers
to Appear
in Future
Issues
Theory and Bound State Production Processes. E. A. REMLER AND A. P. of Physics, College of William and Mary, Williamsburg, Virginia 23185.
We develop a theoretical approach to collisions involving complex systems with special emphasis to applications involving a short wavelength approximation. Use of the Wigner representation casts the quantum mechanical scattering problem in the form of a stochastic process. Useful analogies to classical transport theory may then be drawn. Monte Carlo calculations of production processes are then discussed in this framework. One immediate result is the derivation of the correct formula for bound state production via the Monte Carlo method. Further development of our general formalism yields a diagrammatic procedure useful for the calculation of various inclusive cross-sections. This is then applied to the problem of fast deuteron production in high energy proton-nucleus collisions. A lowest order calculation is made involving no free parameters. The resulting formulae are physically transparent. Experimental data are reproduced with an accuracy consistent with the first-order, parameter-free nature of the calculation. An Energy
Band
Calculation
of
Linear
Chain
Transition
Metal
Comple.ues.
A.
M.
ABARBANEL.
Department of Physics, Stanford University, Stanford, California 94305. The energy band structure of a class of linear chain compounds is investigated using a modification of the Green’s Function Method. A discussion of the implications of the band structure to the properties of compounds in this class is presented. Thermodynamics. DAVID EIMERL. Department of Physics, University of California, San Diego, La Jolla, California 92037.
On Relativistic
The thermodynamics of moving bodies is developed from first principles. To do this, it is necessary to augment the laws of thermodynamics with a new principle, which asserts the impossibility of thermal equilibrium between bodies in relative motion. Clausius’ theorem is generalized to heat flow between moving systems, and leads naturally to the identification of heat and temperature as Lorentz scalars. The formulation of relativistic statistical mechanics is carried out and the correspondence with classical quantities is made. The quantum distribution laws are generalized to the relativistic case, and are found to differ from their accepted relativistic form. Factorisation and the Reaction yN + #N. G. V. DASS. Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany and Rutherford Laboratory, Chilton, Didcot, Oxon, England AND G. FRAAS. Physikalisches Institut der Universitat Wiirzburg, Germany.
Pomeron
Because of the suitability of yN ---f+N for studying the Pomeron, we systematically investigate the tests for Pomeron factorisation possible in this rather clean reaction, particularly from the more feasible experiment which measures the +-density-matrix, and also an experiment measuring the recoil nucleon polarisation; the complete set of initial polarisation configurations has been considered. For any two-body parity-conserving process, a simple consequence of factorisation is M-purity which asymptotically corresponds to purely natural or purely unnatural parity in the crossed Copyright (3 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
277
278
ABSTRACTS
OF
PAPERS
TO APPEAR
IN
FUTURE
ISSUES
channel. Factorisation tests, therefore, include M-purity tests, but M-purity does not necessarily imply factorisation. For the $-decay density-matrix we give all the possible factorisation tests, and show that our tests are exhaustive. A separate measurement of the recoil nucleon polarisation is shown to complement adequately the information obtained from the +decay density-matrix in the factorising case. For the $-density matrix, some of the M-purity tests refer to dominant amplitudes and persist even if s-channel meson-helicity-conservation (which is experimentally true approximately) holds exactly. These tests should be easy to perform. The tests which invoke factorisation more crucially than only M-purity do not persist in that manner; these refer to the helicity nonconserving amplitudes. However, factorisation for such small amplitudes could be advantageously tested here, because of their being masked by the large amplitudes elsewhere. The factorisation tests for the +-density-matrix can be used to distinguish a pure Regge pole type Pomeron from (a) an M-pure “cut-pole mixture” type Pomeron or an M-impure (hence nonfactorising) “cut-pole mixture” type Pomeron and also (b) a factorising “cut-pole mixture” type Pomeron or a nonfactorising “cut-pole mixture” type Pomeron. Such tests would require polarised photons and/or targets. Present yN +4N data are not adequate enough to allow firm conclusions about Pomeron factorisation, though they do indicate M-purity for the Pomeron, corresponding to pure natural parity. This is consistent with Pomeron factorisation, but M-purity is only a necessary consequence of factorisation. Better and more yN -f+N data are needed to get a more complete picture of Pomeron factorisation. Theory of The Thermal Single-Determinant Approximation. T. A. KAPLAN. Department of Physics, Michigan State University, East Lansing, Michigan 48824 AND P. N. ARGYRES. Department of Physics, Northeastern University, Boston, Massachusetts 02115. An approximation for systems of interacting fermions which goes beyond the standard thermal Hartree-Fock approximation (THFA) is developed on the basis of the variational principle of statistical mechanics. The new approximation consists of choosing the “best” trial Hamiltonian such that all its eigenstates are single determinants whose occupied states are chosen from some (“best”) complete set of orthonormal one-particle states. This thermal single-determinant approximation (TSDA) is a natural extension to nonzero temperature of the Hartree-Fock approximation for the ground state; it is different, and in a well-defined sense better, than thestandard THFA. Various modifications of the TSDA, which are variational, are also defined and the relationship between the TSDA and the THFA is discussed.
Primed
in Belgium
OF PHYSICS
91, 217-218 (1975)
Abstracts Quasi-Classical SATHE.
Scattering
Department
of Papers
to Appear
in Future
Issues
Theory and Bound State Production Processes. E. A. REMLER AND A. P. of Physics, College of William and Mary, Williamsburg, Virginia 23185.
We develop a theoretical approach to collisions involving complex systems with special emphasis to applications involving a short wavelength approximation. Use of the Wigner representation casts the quantum mechanical scattering problem in the form of a stochastic process. Useful analogies to classical transport theory may then be drawn. Monte Carlo calculations of production processes are then discussed in this framework. One immediate result is the derivation of the correct formula for bound state production via the Monte Carlo method. Further development of our general formalism yields a diagrammatic procedure useful for the calculation of various inclusive cross-sections. This is then applied to the problem of fast deuteron production in high energy proton-nucleus collisions. A lowest order calculation is made involving no free parameters. The resulting formulae are physically transparent. Experimental data are reproduced with an accuracy consistent with the first-order, parameter-free nature of the calculation. An Energy
Band
Calculation
of
Linear
Chain
Transition
Metal
Comple.ues.
A.
M.
ABARBANEL.
Department of Physics, Stanford University, Stanford, California 94305. The energy band structure of a class of linear chain compounds is investigated using a modification of the Green’s Function Method. A discussion of the implications of the band structure to the properties of compounds in this class is presented. Thermodynamics. DAVID EIMERL. Department of Physics, University of California, San Diego, La Jolla, California 92037.
On Relativistic
The thermodynamics of moving bodies is developed from first principles. To do this, it is necessary to augment the laws of thermodynamics with a new principle, which asserts the impossibility of thermal equilibrium between bodies in relative motion. Clausius’ theorem is generalized to heat flow between moving systems, and leads naturally to the identification of heat and temperature as Lorentz scalars. The formulation of relativistic statistical mechanics is carried out and the correspondence with classical quantities is made. The quantum distribution laws are generalized to the relativistic case, and are found to differ from their accepted relativistic form. Factorisation and the Reaction yN + #N. G. V. DASS. Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany and Rutherford Laboratory, Chilton, Didcot, Oxon, England AND G. FRAAS. Physikalisches Institut der Universitat Wiirzburg, Germany.
Pomeron
Because of the suitability of yN ---f+N for studying the Pomeron, we systematically investigate the tests for Pomeron factorisation possible in this rather clean reaction, particularly from the more feasible experiment which measures the +-density-matrix, and also an experiment measuring the recoil nucleon polarisation; the complete set of initial polarisation configurations has been considered. For any two-body parity-conserving process, a simple consequence of factorisation is M-purity which asymptotically corresponds to purely natural or purely unnatural parity in the crossed Copyright (3 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
277
278
ABSTRACTS
OF
PAPERS
TO APPEAR
IN
FUTURE
ISSUES
channel. Factorisation tests, therefore, include M-purity tests, but M-purity does not necessarily imply factorisation. For the $-decay density-matrix we give all the possible factorisation tests, and show that our tests are exhaustive. A separate measurement of the recoil nucleon polarisation is shown to complement adequately the information obtained from the +decay density-matrix in the factorising case. For the $-density matrix, some of the M-purity tests refer to dominant amplitudes and persist even if s-channel meson-helicity-conservation (which is experimentally true approximately) holds exactly. These tests should be easy to perform. The tests which invoke factorisation more crucially than only M-purity do not persist in that manner; these refer to the helicity nonconserving amplitudes. However, factorisation for such small amplitudes could be advantageously tested here, because of their being masked by the large amplitudes elsewhere. The factorisation tests for the +-density-matrix can be used to distinguish a pure Regge pole type Pomeron from (a) an M-pure “cut-pole mixture” type Pomeron or an M-impure (hence nonfactorising) “cut-pole mixture” type Pomeron and also (b) a factorising “cut-pole mixture” type Pomeron or a nonfactorising “cut-pole mixture” type Pomeron. Such tests would require polarised photons and/or targets. Present yN +4N data are not adequate enough to allow firm conclusions about Pomeron factorisation, though they do indicate M-purity for the Pomeron, corresponding to pure natural parity. This is consistent with Pomeron factorisation, but M-purity is only a necessary consequence of factorisation. Better and more yN -f+N data are needed to get a more complete picture of Pomeron factorisation. Theory of The Thermal Single-Determinant Approximation. T. A. KAPLAN. Department of Physics, Michigan State University, East Lansing, Michigan 48824 AND P. N. ARGYRES. Department of Physics, Northeastern University, Boston, Massachusetts 02115. An approximation for systems of interacting fermions which goes beyond the standard thermal Hartree-Fock approximation (THFA) is developed on the basis of the variational principle of statistical mechanics. The new approximation consists of choosing the “best” trial Hamiltonian such that all its eigenstates are single determinants whose occupied states are chosen from some (“best”) complete set of orthonormal one-particle states. This thermal single-determinant approximation (TSDA) is a natural extension to nonzero temperature of the Hartree-Fock approximation for the ground state; it is different, and in a well-defined sense better, than thestandard THFA. Various modifications of the TSDA, which are variational, are also defined and the relationship between the TSDA and the THFA is discussed.
Primed
in Belgium