304 research outputs found
Coherent-Path Model for Nuclear Resonant Scattering of Gamma Radiation From Nuclei Excited by Synchrotron Radiation
Previous theoretical descriptions of nuclear resonant scattering of synchrotron radiation have been based on the semiclassical optical model or on several quantum mechanical models. These models are fine but do not give a clear physical picture of all the processes. The theory presented here gives a clear physical picture of all the relevant aspects of nuclear resonant scattering. The model treats the nuclear resonant sample as a one-dimensional chain of effective nuclei. However, the model is deceptive. It only appears to be one dimensional. It actually treats the sample as a series of effective planes. The analysis uses the time-dependent quantum mechanical techniques due to Heitler. A closed form solution, for the time-dependent forward scattered intensity, is found. The only parameter in the theory is N the number of effective nuclei (planes) in the model. It is shown that the prominent experimental features, the speed-up and dynamical beat effects, are primarily due to a π phase change of reemitted radiation. compared to the incident radiation, that occurs when radiation is absorbed and reemitted without recoil by a single \u27\u27effective nucleus (plane). The model also predicts results for the incoherent processes
On the feasibility of a nuclear exciton laser
Nuclear excitons known from M\"ossbauer spectroscopy describe coherent
excitations of a large number of nuclei -- analogous to Dicke states (or Dicke
super-radiance) in quantum optics. In this paper, we study the possibility of
constructing a laser based on these coherent excitations. In contrast to the
free electron laser (in its usual design), such a device would be based on
stimulated emission and thus might offer certain advantages, e.g., regarding
energy-momentum accuracy. Unfortunately, inserting realistic parameters, the
window of operability is probably not open (yet) to present-day technology --
but our design should be feasible in the UV regime, for example.Comment: 7 pages RevTeX, 4 figure
The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum Mechanics and its Exact Solutions
The analytic solutions of the one-dimensional Schroedinger equation for the
trigonometric Rosen-Morse potential reported in the literature rely upon the
Jacobi polynomials with complex indices and complex arguments. We first draw
attention to the fact that the complex Jacobi polynomials have non-trivial
orthogonality properties which make them uncomfortable for physics
applications. Instead we here solve above equation in terms of real orthogonal
polynomials. The new solutions are used in the construction of the
quantum-mechanic superpotential.Comment: 16 pages 7 figures 1 tabl
M\"ossbauer Antineutrinos: Recoilless Resonant Emission and Absorption of Electron Antineutrinos
Basic questions concerning phononless resonant capture of monoenergetic
electron antineutrinos (M\"ossbauer antineutrinos) emitted in bound-state
beta-decay in the 3H - 3He system are discussed. It is shown that lattice
expansion and contraction after the transformation of the nucleus will
drastically reduce the probability of phononless transitions and that various
solid-state effects will cause large line broadening. As a possible
alternative, the rare-earth system 163Ho - 163Dy is favoured.
M\"ossbauer-antineutrino experiments could be used to gain new and deep
insights into several basic problems in neutrino physics
Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
We study a model of non-intersecting squared Bessel processes in the
confluent case: all paths start at time at the same positive value , remain positive, and are conditioned to end at time at . In
the limit , after appropriate rescaling, the paths fill out a
region in the -plane that we describe explicitly. In particular, the paths
initially stay away from the hard edge at , but at a certain critical
time the smallest paths hit the hard edge and from then on are stuck to
it. For we obtain the usual scaling limits from random matrix
theory, namely the sine, Airy, and Bessel kernels. A key fact is that the
positions of the paths at any time constitute a multiple orthogonal
polynomial ensemble, corresponding to a system of two modified Bessel-type
weights. As a consequence, there is a matrix valued
Riemann-Hilbert problem characterizing this model, that we analyze in the large
limit using the Deift-Zhou steepest descent method. There are some novel
ingredients in the Riemann-Hilbert analysis that are of independent interest.Comment: 59 pages, 11 figure
Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials
We introduce a spectral transform for the finite relativistic Toda lattice
(RTL) in generalized form. In the nonrelativistic case, Moser constructed a
spectral transform from the spectral theory of symmetric Jacobi matrices. Here
we use a non-symmetric generalized eigenvalue problem for a pair of bidiagonal
matrices (L,M) to define the spectral transform for the RTL. The inverse
spectral transform is described in terms of a terminating T-fraction. The
generalized eigenvalues are constants of motion and the auxiliary spectral data
have explicit time evolution. Using the connection with the theory of Laurent
orthogonal polynomials, we study the long-time behaviour of the RTL. As in the
case of the Toda lattice the matrix entries have asymptotic limits. We show
that L tends to an upper Hessenberg matrix with the generalized eigenvalues
sorted on the diagonal, while M tends to the identity matrix.Comment: 24 pages, 9 figure
Cavity-induced coherence effects in spontaneous emission from pre-Selection of polarization
Spontaneous emission can create coherences in a multilevel atom having close
lying levels, subject to the condition that the atomic dipole matrix elements
are non-orthogonal. This condition is rarely met in atomic systems. We report
the possibility of bypassing this condition and thereby creating coherences by
letting the atom with orthogonal dipoles to interact with the vacuum of a
pre-selected polarized cavity mode rather than the free space vacuum. We derive
a master equation for the reduced density operator of a model four level atomic
system, and obtain its analytical solution to describe the interference
effects. We report the quantum beat structure in the populations.Comment: 6 pages in REVTEX multicolumn format, 5 figures, new references
added, journal reference adde
Level-Crossing Resonance of r-Ray Anisotropy for the 398-keV 9/22 State of 69Ge in Zn Single Crystal
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