575 research outputs found
Eigenphase preserving two-channel SUSY transformations
We propose a new kind of supersymmetric (SUSY) transformation in the case of
the two-channel scattering problem with equal thresholds, for partial waves of
the same parity. This two-fold transformation is based on two imaginary
factorization energies with opposite signs and with mutually conjugated
factorization solutions. We call it an eigenphase preserving SUSY
transformation as it relates two Hamiltonians, the scattering matrices of which
have identical eigenphase shifts. In contrast to known phase-equivalent
transformations, the mixing parameter is modified by the eigenphase preserving
transformation.Comment: 16 pages, 1 figur
Canonical-basis solution of the Hartree-Fock-Bogoliubov equation on three-dimensional Cartesian mesh
A method is presented to obtain the canonical-form solutions of the HFB
equation for atomic nuclei with zero-range interactions like the Skyrme force.
It is appropriate to describe pairing correlations in the continuum in
coordinate-space representations. An improved gradient method is used for
faster convergences under constraint of orthogonality between orbitals. To
prevent high-lying orbitals to shrink into a spatial point, a repulsive
momentum dependent force is introduced, which turns out to unveil the nature of
high-lying canonical-basis orbitals. The asymptotic properties at large radius
and the relation with quasiparticle states are discussed for the obtained
canonical basis.Comment: 23 pages including 17 figures, REVTeX4, revised version, scheduled to
appear in Phys. Rev. C, Vol.69, No.
Microscopic description of the beta delayed deuteron emission from \bbox{^6}He
The beta delayed deuteron emission from He is studied in a dynamical
microscopic cluster model. This model gives a reasonably good description for
all the subsystems of He and Li in a coherent way, without any free
parameter. The beta decay transition probability to the Li ground state is
underestimated by a few percents. The theoretical beta delayed deuteron
spectrum is close to experiment but it is also underestimated by about a factor
1.7. We argue that, in spite of their different magnitudes, both
underestimations might have a common origin. The model confirms that the
neutron halo part of the He wave function plays a crucial role in quenching
the beta decay toward the + d channel.Comment: LATEX with REVTEX, Submitted to Phys. Rev. C, 11 pages, 3 figures
(not included) are available upon request. ATOMKI-93/
Vortex line in a neutral finite-temperature superfluid Fermi gas
The structure of an isolated vortex in a dilute two-component neutral
superfluid Fermi gas is studied within the context of self-consistent
Bogoliubov-de Gennes theory. Various thermodynamic properties are calculated
and the shift in the critical temperature due to the presence of the vortex is
analyzed. The gapless excitations inside the vortex core are studied and a
scheme to detect these states and thus the presence of the vortex is examined.
The numerical results are compared with various analytical expressions when
appropriate.Comment: 8 pages, 6 embedded figure
Clarification of the relationship between bound and scattering states in quantum mechanics: Application to 12C + alpha
Using phase-equivalent supersymmetric partner potentials, a general result
from the inverse problem in quantum scattering theory is illustrated, i.e.,
that bound-state properties cannot be extracted from the phase shifts of a
single partial wave, as a matter of principle. In particular, recent R-matrix
analyses of the 12C + alpha system, extracting the asymptotic normalization
constant of the 2+ subthreshold state, C12, from the l=2 elastic-scattering
phase shifts and bound-state energy, are shown to be unreliable. In contrast,
this important constant in nuclear astrophysics can be deduced from the
simultaneous analysis of the l=0, 2, 4, 6 partial waves in a simplified
potential model. A new supersymmetric inversion potential and existing models
give C12=144500+-8500 fm-1/2.Comment: Expanded version (50% larger); three errors corrected (conversion of
published reduced widths to ANCs); nine references added, one remove
Breakup reaction models for two- and three-cluster projectiles
Breakup reactions are one of the main tools for the study of exotic nuclei,
and in particular of their continuum. In order to get valuable information from
measurements, a precise reaction model coupled to a fair description of the
projectile is needed. We assume that the projectile initially possesses a
cluster structure, which is revealed by the dissociation process. This
structure is described by a few-body Hamiltonian involving effective forces
between the clusters. Within this assumption, we review various reaction
models. In semiclassical models, the projectile-target relative motion is
described by a classical trajectory and the reaction properties are deduced by
solving a time-dependent Schroedinger equation. We then describe the principle
and variants of the eikonal approximation: the dynamical eikonal approximation,
the standard eikonal approximation, and a corrected version avoiding Coulomb
divergence. Finally, we present the continuum-discretized coupled-channel
method (CDCC), in which the Schroedinger equation is solved with the projectile
continuum approximated by square-integrable states. These models are first
illustrated by applications to two-cluster projectiles for studies of nuclei
far from stability and of reactions useful in astrophysics. Recent extensions
to three-cluster projectiles, like two-neutron halo nuclei, are then presented
and discussed. We end this review with some views of the future in
breakup-reaction theory.Comment: Will constitute a chapter of "Clusters in Nuclei - Vol.2." to be
published as a volume of "Lecture Notes in Physics" (Springer
Multi-channel phase-equivalent transformation and supersymmetry
Phase-equivalent transformation of local interaction is generalized to the
multi-channel case. Generally, the transformation does not change the number of
the bound states in the system and their energies. However, with a special
choice of the parameters, the transformation removes one of the bound states
and is equivalent to the multi-channel supersymmetry transformation recently
suggested by Sparenberg and Baye. Using the transformation, it is also possible
to add a bound state to the discrete spectrum of the system at a given energy
if the angular momentum at least in one of the coupled channels .Comment: 9 pages, revtex; to be published in Phys. At. Nucl. (Oct. 2000
On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms
The energy spectra of two different quantum systems are paired through
supersymmetric algorithms. One of the systems is Hermitian and the other is
characterized by a complex-valued potential, both of them with only real
eigenvalues in their spectrum. The superpotential that links these systems is
complex-valued, parameterized by the solutions of the Ermakov equation, and may
be expressed either in nonlinear form or as the logarithmic derivative of a
properly chosen complex-valued function. The non-Hermitian systems can be
constructed to be either parity-time-symmetric or non-parity-time-symmetric.Comment: 9 pages, 2 figures (affiliation institution corrected
Refined Factorizations of Solvable Potentials
A generalization of the factorization technique is shown to be a powerful
algebraic tool to discover further properties of a class of integrable systems
in Quantum Mechanics. The method is applied in the study of radial oscillator,
Morse and Coulomb potentials to obtain a wide set of raising and lowering
operators, and to show clearly the connection that link these systems.Comment: 11 pages, LaTeX file, no figure
Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case
While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions
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