- Email: [email protected]
Ground state of an interacting boson system
532
ABSTRACTS
OF
PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
An extensive use of the quasispin formalism is made. In some particular cases, analytical formulae, some of which are new, are derived for the centroids and widths. Numerical calculations are performed in the nickel and tin isotopes. They show that although the admixtures with , do = 4 should in many cases be relatively small, those with AC 1 = 2 should be very large, owing to the important contribution of the single-particle potential. Representation of Density Operators for Optical Fields Having Gaussian Quasiprobability Functions. HARI PRAKASH, NARESH CHANDRA, AND VACHASPATI. Department of Physics, University of Allahabad, Allahabad, India. For radiation having Gaussian quasiprobability functions, a general method of representation of density operators in terms of outer products of coherent states with nonsingular weight function and only two real variables of integration for every mode is given. It is shown that the representation simplifies, if minimum uncertainty states are used. Ground State of an Interacting Boson System. EUGENEFEENBERG.Department of Physics, Washington University, St. Louis, Missouri 63130. The ground state wave function for a system of interacting bosons is written in the form & = exp 4 [ 2 U(v,,) + 1 U&j, i 4:j i
k) + ...I
Assuming the existence of Fourier coefficients for the potential v(ri,) and the correlation functions U, , the Schroedinger equation transforms into a set of coupled nonlinear differentialintegral equations for the correlation functions. A basic separation property of multidimensional Fourier series is involved in the derivation of the coupled equations. Leading terms in the formula for the energy resemble the corresponding Bogoliubov formula with a partial replacement of the interaction potential by an effective (or renormalized) potential. For a weak interaction the energy is given correctly through third order terms. The same leading terms give a useful approximation under realistic conditions. The analysis is useful in giving connections within a wide range of methods and over a wide range of physical conditions. Formalism for the T(d, ?I) “He and 3He(d, pJ4He Reactions. P. W. KEATON, JR., JOHN L. GAMMEL, AND GERALD G. OHLSEN. Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87544. The formalism required to describe the T(d, n)4He or 3He(d, p)4He reaction when all particles may be polarized is discussed. The relation among the various sets of spin-l tensors is stated explicitly, so that the formulas applying to a particular experiment may be written easily in terms of any desired system. On a cal An two-
One-Dimensional Four-Body Scattering System. J. WOLFES. International Centre for TheoretiPhysics, Trieste, Italy. exact solution is given to a four-body equal-mass linear scattering system interacting via and/or four-body potential.
ABSTRACTS
OF
PAPERS
TO
APPEAR
IN
FUTURE
ISSUES
An extensive use of the quasispin formalism is made. In some particular cases, analytical formulae, some of which are new, are derived for the centroids and widths. Numerical calculations are performed in the nickel and tin isotopes. They show that although the admixtures with , do = 4 should in many cases be relatively small, those with AC 1 = 2 should be very large, owing to the important contribution of the single-particle potential. Representation of Density Operators for Optical Fields Having Gaussian Quasiprobability Functions. HARI PRAKASH, NARESH CHANDRA, AND VACHASPATI. Department of Physics, University of Allahabad, Allahabad, India. For radiation having Gaussian quasiprobability functions, a general method of representation of density operators in terms of outer products of coherent states with nonsingular weight function and only two real variables of integration for every mode is given. It is shown that the representation simplifies, if minimum uncertainty states are used. Ground State of an Interacting Boson System. EUGENEFEENBERG.Department of Physics, Washington University, St. Louis, Missouri 63130. The ground state wave function for a system of interacting bosons is written in the form & = exp 4 [ 2 U(v,,) + 1 U&j, i 4:j i
k) + ...I
Assuming the existence of Fourier coefficients for the potential v(ri,) and the correlation functions U, , the Schroedinger equation transforms into a set of coupled nonlinear differentialintegral equations for the correlation functions. A basic separation property of multidimensional Fourier series is involved in the derivation of the coupled equations. Leading terms in the formula for the energy resemble the corresponding Bogoliubov formula with a partial replacement of the interaction potential by an effective (or renormalized) potential. For a weak interaction the energy is given correctly through third order terms. The same leading terms give a useful approximation under realistic conditions. The analysis is useful in giving connections within a wide range of methods and over a wide range of physical conditions. Formalism for the T(d, ?I) “He and 3He(d, pJ4He Reactions. P. W. KEATON, JR., JOHN L. GAMMEL, AND GERALD G. OHLSEN. Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87544. The formalism required to describe the T(d, n)4He or 3He(d, p)4He reaction when all particles may be polarized is discussed. The relation among the various sets of spin-l tensors is stated explicitly, so that the formulas applying to a particular experiment may be written easily in terms of any desired system. On a cal An two-
One-Dimensional Four-Body Scattering System. J. WOLFES. International Centre for TheoretiPhysics, Trieste, Italy. exact solution is given to a four-body equal-mass linear scattering system interacting via and/or four-body potential.