skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space

Abstract

We propose a method for solving exactly the nuclear eigenvalue problem within a multiphonon space constructed out of Tamm-Dancoff phonons. The method consists in deriving, within a given n-phonon subspace, a set of equations, of simple structure for any n, which are solved iteratively, starting from the particle-hole vacuum, to yield a set of states covering a multiphonon space up to an arbitrary number of phonons. The intrinsic redundancy of the set so generated is removed completely and exactly by a simple and efficient prescription. Such a multiphonon basis reduces the Hamiltonian into diagonal blocks plus residual off-diagonal terms of simple form. Its diagonalization becomes straightforward and yields exact eigensolutions. {sup 16}O is adopted as numerical test ground.

Authors:
; ;  [1]; ;  [2]
  1. Dipartimento di Scienze Fisiche, Universita di Napoli Federico II and Istituto Nazionale di Fisica Nucleare, Monte S. Angelo, via Cintia, I-80126 Naples (Italy)
  2. Institute of Particle and Nuclear Physics, Charles University, V Holesovickach 2, CZ-18000 Prague 8 (Czech Republic)
Publication Date:
OSTI Identifier:
20995205
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevC.75.044312; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; HAMILTONIANS; MATHEMATICAL SOLUTIONS; OXYGEN 16; PARTICLES; PHONONS; REDUNDANCY

Citation Formats

Andreozzi, F., Iudice, N. Lo, Porrino, A., Knapp, F., and Kvasil, J. Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.044312.
Andreozzi, F., Iudice, N. Lo, Porrino, A., Knapp, F., & Kvasil, J. Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space. United States. doi:10.1103/PHYSREVC.75.044312.
Andreozzi, F., Iudice, N. Lo, Porrino, A., Knapp, F., and Kvasil, J. Sun . "Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space". United States. doi:10.1103/PHYSREVC.75.044312.
@article{osti_20995205,
title = {Exact formulation and solution of the nuclear eigenvalue problem in a microscopic multiphonon space},
author = {Andreozzi, F. and Iudice, N. Lo and Porrino, A. and Knapp, F. and Kvasil, J.},
abstractNote = {We propose a method for solving exactly the nuclear eigenvalue problem within a multiphonon space constructed out of Tamm-Dancoff phonons. The method consists in deriving, within a given n-phonon subspace, a set of equations, of simple structure for any n, which are solved iteratively, starting from the particle-hole vacuum, to yield a set of states covering a multiphonon space up to an arbitrary number of phonons. The intrinsic redundancy of the set so generated is removed completely and exactly by a simple and efficient prescription. Such a multiphonon basis reduces the Hamiltonian into diagonal blocks plus residual off-diagonal terms of simple form. Its diagonalization becomes straightforward and yields exact eigensolutions. {sup 16}O is adopted as numerical test ground.},
doi = {10.1103/PHYSREVC.75.044312},
journal = {Physical Review. C, Nuclear Physics},
number = 4,
volume = 75,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
  • The electromagnetic response in {sup 16}O is studied within a recently developed approach that generates iteratively a microscopic multiphonon basis well suited for reformulating and solving exactly the nuclear eigenvalue problem within spaces of large dimensions spanned by complex configurations. These multiphonon configurations are seen to modify appreciably, dramatically in some cases, the mean field response. This is shown to be increasingly affected by the center-of-mass motion as the number of phonons increases. The method for removing such a spurious motion is briefly outlined and the effects discussed.
  • A closed-form solution for a terminal cost problem is obtained for synthesizing suboptimal control of nuclear reactors with spatially distributed parameters by using the Sylvester theorem. The inverse of the neutron velocity is regarded as a small sngular parameter, and the model, adopted for simplicity, is a cylindrically symmetrical reactor. The Helmholtz mode expansion is used for the application of the optimal theory for lumped parameter systems to the spatially distributed parameter systems. The explicitly obtained control is particularly convenient for machine calculation to any degree of precision.
  • In this paper we show that it is possible to separate the Dirac equation exactly into particle and antiparticle parts for the hydrogen-atom problem. A careful analysis uncovers two additional terms. These two terms are small in the P states, but diverge in the S states. Use of appropriate cutoffs determine by electric and magnetic properties of the proton interaction gives a direct account of the hyperfine splitting in the 1S state and a value of 1057.841 MHz for the shift of the 2S state relative to the 2P state. This approach may be viewed as a mirror image ofmore » the standard theory in that all problems are physically attributable to ambiguities in the field structure of the proton at small distances.« less