1,296 research outputs found
Self-consistent theory of large amplitude collective motion: Applications to approximate quantization of non-separable systems and to nuclear physics
The goal of the present account is to review our efforts to obtain and apply
a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic
degrees of freedom, starting from a Hamiltonian system with more or many more
degrees of freedom. The approach is based on an analysis of the classical limit
of quantum-mechanical problems. Initially, we study the classical problem
within the framework of Hamiltonian dynamics and derive a fully self-consistent
theory of large amplitude collective motion with small velocities. We derive a
measure for the quality of decoupling of the collective degree of freedom. We
show for several simple examples, where the classical limit is obvious, that
when decoupling is good, a quantization of the collective Hamiltonian leads to
accurate descriptions of the low energy properties of the systems studied. In
nuclear physics problems we construct the classical Hamiltonian by means of
time-dependent mean-field theory, and we transcribe our formalism to this case.
We report studies of a model for monopole vibrations, of Si with a
realistic interaction, several qualitative models of heavier nuclei, and
preliminary results for a more realistic approach to heavy nuclei. Other topics
included are a nuclear Born-Oppenheimer approximation for an {\em ab initio}
quantum theory and a theory of the transfer of energy between collective and
non-collective degrees of freedom when the decoupling is not exact. The
explicit account is based on the work of the authors, but a thorough survey of
other work is included.Comment: 203 pages, many figure
Relativistic Coulomb Sum Rules for
A Coulomb sum rule is derived for the response of nuclei to
scattering with large three-momentum transfers. Unlike the nonrelativistic
formulation, the relativistic Coulomb sum is restricted to spacelike
four-momenta for the most direct connection with experiments; an immediate
consequence is that excitations involving antinucleons, e.g., pair
production, are approximately eliminated from the sum rule. Relativistic recoil
and Fermi motion of target nucleons are correctly incorporated. The sum rule
decomposes into one- and two-body parts, with correlation information in the
second. The one-body part requires information on the nucleon momentum
distribution function, which is incorporated by a moment expansion method. The
sum rule given through the second moment (RCSR-II) is tested in the Fermi gas
model, and is shown to be sufficiently accurate for applications to data.Comment: 32 pages (LaTeX), 4 postscript figures available from the author
Derivation and assessment of strong coupling core-particle model from the Kerman-Klein-D\"onau-Frauendorf theory
We review briefly the fundamental equations of a semi-microscopic
core-particle coupling method that makes no reference to an intrinsic system of
coordinates. We then demonstrate how an intrinsic system can be introduced in
the strong coupling limit so as to yield a completely equivalent formulation.
It is emphasized that the conventional core-particle coupling calculation
introduces a further approximation that avoids what has hitherto been the most
time-consuming feature of the full theory, and that this approximation can be
introduced either in the intrinsic system, the usual case, or in the laboratory
system, our preference. A new algorithm is described for the full theory that
largely removes the difference in complexity between the two types of
calculation. Comparison of the full and approximate theories for some
representative cases provides a basis for the assessment of the accuracy of the
traditional approach. We find that for well-deformed nuclei, e.g. 157Gd and
157Tb, the core-coupling method and the full theory give similar results.Comment: revtex, 3 figures(postscript), submitted to Phys.Rev.
Application of the Kerman-Klein method to the solution of a spherical shell model for a deformed rare-earth nucleus
Core-particle coupling models are made viable by assuming that core
properties such as matrix elements of multipole and pairing operators and
excitation spectra are known independently. From the completeness relation, it
is seen, however, that these quantities are themselves algebraic functions of
the calculated core-particle amplitudes. For the deformed rare-earth nucleus
158Gd, we find that these sum rules are well-satisfied for the ground state
band, implying that we have found a self-consistent solution of the non-linear
Kerman-Klein equations.Comment: revtex and postscript, including 1 figure(postscript), submitted to
Phys.Rev.Let
Foundations of self-consistent particle-rotor models and of self-consistent cranking models
The Kerman-Klein formulation of the equations of motion for a nuclear shell
model and its associated variational principle are reviewed briefly. It is then
applied to the derivation of the self-consistent particle-rotor model and of
the self-consistent cranking model, for both axially symmetric and triaxial
nuclei. Two derivations of the particle-rotor model are given. One of these is
of a form that lends itself to an expansion of the result in powers of the
ratio of single-particle angular momentum to collective angular momentum, that
is essentual to reach the cranking limit. The derivation also requires a
distinct, angular-momentum violating, step. The structure of the result implies
the possibility of tilted-axis cranking for the axial case and full
three-dimensional cranking for the triaxial one. The final equations remain
number conserving. In an appendix, the Kerman-Klein method is developed in more
detail, and the outlines of several algorithms for obtaining solutions of the
associated non-linear formalism are suggested.Comment: 29 page
Quantum theory of large amplitude collective motion and the Born-Oppenheimer method
We study the quantum foundations of a theory of large amplitude collective
motion for a Hamiltonian expressed in terms of canonical variables. In previous
work the separation into slow and fast (collective and non-collective)
variables was carried out without the explicit intervention of the Born
Oppenheimer approach. The addition of the Born Oppenheimer assumption not only
provides support for the results found previously in leading approximation, but
also facilitates an extension of the theory to include an approximate
description of the fast variables and their interaction with the slow ones.
Among other corrections, one encounters the Berry vector and scalar potential.
The formalism is illustrated with the aid of some simple examples, where the
potentials in question are actually evaluated and where the accuracy of the
Born Oppenheimer approximation is tested. Variational formulations of both
Hamiltonian and Lagrangian type are described for the equations of motion for
the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf
styl
Nuclear pairing: new perspectives
Nuclear pairing correlations are known to play an important role in various
single-particle and collective aspects of nuclear structure. After the first
idea by A. Bohr, B. Mottelson and D. Pines on similarity of nuclear pairing to
electron superconductivity, S.T. Belyaev gave a thorough analysis of the
manifestations of pairing in complex nuclei. The current revival of interest in
nuclear pairing is connected to the shift of modern nuclear physics towards
nuclei far from stability; many loosely bound nuclei are particle-stable only
due to the pairing. The theoretical methods borrowed from macroscopic
superconductivity turn out to be insufficient for finite systems as nuclei, in
particular for the cases of weak pairing and proximity of continuum states. We
suggest a simple numerical procedure of exact solution of the nuclear pairing
problem and discuss the physical features of this complete solution. We show
also how the continuum states can be naturally included in the consideration
bridging the gap between the structure and reactions. The path from coherent
pairing to chaos and thermalization and perspectives of new theoretical
approaches based on the full solution of pairing are discussed.Comment: 47 pages, 11 figure
Dynamics of a Simple Quantum System in a Complex Environment
We present a theory for the dynamical evolution of a quantum system coupled
to a complex many-body intrinsic system/environment. By modelling the intrinsic
many-body system with parametric random matrices, we study the types of
effective stochastic models which emerge from random matrix theory. Using the
Feynman-Vernon path integral formalism, we derive the influence functional and
obtain either analytical or numerical solutions for the time evolution of the
entire quantum system. We discuss thoroughly the structure of the solutions for
some representative cases and make connections to well known limiting results,
particularly to Brownian motion, Kramers classical limit and the
Caldeira-Leggett approach.Comment: 41 pages and 12 figures in revte
Inelastic nucleon contributions in nuclear response functions
We estimate the contribution of inelastic nucleon excitations to the
inclusive cross section in the CEBAF kinematic range.
Calculations are based upon parameterizations of the nucleon structure
functions measured at SLAC. Nuclear binding effects are included in a
vector-scalar field theory, and are assumed have a minimal effect on the
nucleon excitation spectrum. We find that for q\lsim 1 GeV the elastic and
inelastic nucleon contributions to the nuclear response functions are
comparable, and can be separated, but with roughly a factor of two uncertainty
in the latter from the extrapolation from data. In contrast, for q\rsim 2 GeV
this uncertainty is greatly reduced but the elastic nucleon contribution is
heavily dominated by the inelastic nucleon background.Comment: 20 pages, 7 figures available from the authors at Department of
Physics and Astronomy, University of Rochester, Rochester NY 1462
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