96 research outputs found
Spectral properties of non-conservative multichannel SUSY partners of the zero potential
Spectral properties of a coupled potential model obtained with
the help of a single non-conservative supersymmetric (SUSY) transformation
starting from a system of radial Schr\"odinger equations with the zero
potential and finite threshold differences between the channels are studied.
The structure of the system of polynomial equations which determine the zeros
of the Jost-matrix determinant is analyzed. In particular, we show that the
Jost-matrix determinant has zeros which may all correspond to
virtual states. The number of bound states satisfies . The
maximal number of resonances is . A perturbation technique
for a small coupling approximation is developed. A detailed study of the
inverse spectral problem is given for the case.Comment: 17 pages, 4 figure
Darboux transformations for quasi-exactly solvable Hamiltonians
We construct new quasi-exactly solvable one-dimensional potentials through
Darboux transformations. Three directions are investigated:
Reducible and two types of irreducible second-order transformations. The
irreducible transformations of the first type give singular intermediate
potentials and the ones of the second type give complex-valued intermediate
potentials while final potentials are meaningful in all cases.
These developments are illustrated on the so-called radial sextic oscillator.Comment: 11 pages, Late
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
Influence of low energy scattering on loosely bound states
Compact algebraic equations are derived, which connect the binding energy and
the asymptotic normalization constant (ANC) of a subthreshold bound state with
the effective-range expansion of the corresponding partial wave. These
relations are established for positively-charged and neutral particles, using
the analytic continuation of the scattering (S) matrix in the complex
wave-number plane. Their accuracy is checked on simple local potential models
for the 16O+n, 16O+p and 12C+alpha nuclear systems, with exotic nuclei and
nuclear astrophysics applications in mind
Many-body approach to proton emission and the role of spectroscopic factors
The process of proton emission from nuclei is studied by utilizing the
two-potential approach of Gurvitz and Kalbermann in the context of the full
many-body problem. A time-dependent approach is used for calculating the decay
width. Starting from an initial many-body quasi-stationary state, we employ the
Feshbach projection operator approach and reduce the formalism to an effective
one-body problem. We show that the decay width can be expressed in terms of a
one-body matrix element multiplied by a normalization factor. We demonstrate
that the traditional interpretation of this normalization as the square root of
a spectroscopic factor is only valid for one particular choice of projection
operator. This causes no problem for the calculation of the decay width in a
consistent microscopic approach, but it leads to ambiguities in the
interpretation of experimental results. In particular, spectroscopic factors
extracted from a comparison of the measured decay width with a calculated
single-particle width may be affected.Comment: 17 pages, Revte
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
Coherent Backscattering of light in a magnetic field
This paper describes how coherent backscattering is altered by an external
magnetic field. In the theory presented, magneto-optical effects occur inside
Mie scatterers embedded in a non-magnetic medium. Unlike previous theories
based on point-like scatterers, the decrease of coherent backscattering is
obtained in leading order of the magnetic field using rigorous Mie theory. This
decrease is strongly enhanced in the proximity of resonances, which cause the
path length of the wave inside a scatterer to be increased. Also presented is a
novel analysis of the shape of the backscattering cone in a magnetic field.Comment: 27 pages, 5 figures, Revtex, to appear in Phys. Rev.
Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States
We consider the multi-channel inverse scattering problem in one-dimension in
the presence of thresholds and bound states for a potential of finite support.
Utilizing the Levin representation, we derive the general Marchenko integral
equation for N-coupled channels and show that, unlike to the case of the radial
inverse scattering problem, the information on the bound state energies and
asymptotic normalization constants can be inferred from the reflection
coefficient matrix alone. Thus, given this matrix, the Marchenko inverse
scattering procedure can provide us with a unique multi-channel potential. The
relationship to supersymmetric partner potentials as well as possible
applications are discussed. The integral equation has been implemented
numerically and applied to several schematic examples showing the
characteristic features of multi-channel systems. A possible application of the
formalism to technological problems is briefly discussed.Comment: 19 pages, 5 figure
Single- and coupled-channel radial inverse scattering with supersymmetric transformations
The present status of the coupled-channel inverse-scattering method with
supersymmetric transformations is reviewed. We first revisit in a pedagogical
way the single-channel case, where the supersymmetric approach is shown to
provide a complete solution to the inverse-scattering problem. A special
emphasis is put on the differences between conservative and non-conservative
transformations. In particular, we show that for the zero initial potential, a
non-conservative transformation is always equivalent to a pair of conservative
transformations. These single-channel results are illustrated on the inversion
of the neutron-proton triplet eigenphase shifts for the S and D waves. We then
summarize and extend our previous works on the coupled-channel case and stress
remaining difficulties and open questions. We mostly concentrate on two-channel
examples to illustrate general principles while keeping mathematics as simple
as possible. In particular, we discuss the difference between the
equal-threshold and different-threshold problems. For equal thresholds,
conservative transformations can provide non-diagonal Jost and scattering
matrices. Iterations of such transformations are shown to lead to practical
algorithms for inversion. A convenient technique where the mixing parameter is
fitted independently of the eigenphases is developed with iterations of pairs
of conjugate transformations and applied to the neutron-proton triplet S-D
scattering matrix, for which exactly-solvable matrix potential models are
constructed. For different thresholds, conservative transformations do not seem
to be able to provide a non-trivial coupling between channels. In contrast, a
single non-conservative transformation can generate coupled-channel potentials
starting from the zero potential and is a promising first step towards a full
solution to the coupled-channel inverse problem with threshold differences.Comment: Topical review, 84 pages, 7 figures, 93 reference
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