30 research outputs found
Perturbative Effective Theory in an Oscillator Basis?
The effective interaction/operator problem in nuclear physics is believed to
be highly nonperturbative, requiring extended high-momentum spaces for accurate
solution. We trace this to difficulties that arise at both short and long
distances when the included space is defined in terms of a basis of harmonic
oscillator Slater determinants. We show, in the simplest case of the deuteron,
that both difficulties can be circumvented, yielding highly perturbative
results in the potential even for modest (~6hw) included spaces.Comment: 10 pages, 4 figure
Comparison of the Effective Interaction to Various Orders in Different Mass Regions
The convergence of the perturbation expansion for the effective interaction
to be used in shell-model calculations is investigated as function of the mass
number , from to . As the mass number increases, there are more
intermediate states to sum over in each higher-order diagram which contributes
to the effective interaction. Together with the fact that the energy
denominators in each diagram are smaller for larger mass numbers, these two
effects could largely enhance higher-order contributions to the effective
interaction, thereby deteriorating the order-by-order convergence of the
effective interaction. This effect is counterbalanced by the short range of the
nucleon-nucleon interaction, which implies that its matrix elements are weaker
for valence single-particle states in ``large'' nuclei with large mass number
as compared to those in light nuclei. These effects are examined by comparing
various mean values of the matrix elements. It turns out that the contributions
from higher-order terms remain fairly stable as the mass number increases from
to . The implications for nuclear structure calculations are
discussed.Comment: Revtex, 20 pages, 1 figure not include
Renormalisation and fixed points in Hilbert Space
The energies of low-lying bound states of a microscopic quantum many-body
system of particles can be worked out in a reduced Hilbert space. We present
here and test a specific non-perturbative truncation procedure. We also show
that real exceptional points which may be present in the spectrum can be
identified as fixed points of coupling constants in the truncation procedure.Comment: 4 pages, 1 tabl
Comparison of techniques for computing shell-model effective operators
Different techniques for calculating effective operators within the framework
of the shell model using the same effective interaction and the same excitation
spaces are presented. Starting with the large-basis no-core approach, we
compare the time-honored perturbation-expansion approach and a model-space
truncation approach. Results for the electric quadrupole and magnetic dipole
operators are presented for Li. The convergence trends and dependence of
the effective operators on differing excitation spaces and Pauli Q-operators is
studied. In addition, the dependence of the electric-quadrupole effective
charge on the harmonic-oscillator frequency and the mass number, for A=5,6, is
investigated in the model-space truncation approach.Comment: 18 pages. REVTEX. 4 PostScript figure
Moyal products -- a new perspective on quasi-hermitian quantum mechanics
The rationale for introducing non-hermitian Hamiltonians and other
observables is reviewed and open issues identified. We present a new approach
based on Moyal products to compute the metric for quasi-hermitian systems. This
approach is not only an efficient method of computation, but also suggests a
new perspective on quasi-hermitian quantum mechanics which invites further
exploration. In particular, we present some first results which link the Berry
connection and curvature to non-perturbative properties and the metric.Comment: 14 pages. Submitted to J Phys A special issue on The Physics of
Non-Hermitian Operator