349 research outputs found
Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method I. General Theory
The present paper concerns the derivation of phase-integral quantization
conditions for the two-centre Coulomb problem under the assumption that the two
Coulomb centres are fixed. With this restriction we treat the general
two-centre Coulomb problem according to the phase-integral method, in which one
uses an {\it a priori} unspecified {\it base function}. We consider base
functions containing three unspecified parameters and .
When the absolute value of the magnetic quantum number is not too small, it
is most appropriate to choose . When, on the other hand,
is sufficiently small, it is most appropriate to choose .
Arbitrary-order phase-integral quantization conditions are obtained for these
choices of . The parameters and are determined from the
requirement that the results of the first and the third order of the
phase-integral approximation coincide, which makes the first-order
approximation as good as possible.
In order to make the paper to some extent self-contained, a short review of
the phase-integral method is given in the Appendix.Comment: 23 pages, RevTeX, 4 EPS figures, submitted to J. Math. Phy
Computation of inflationary cosmological perturbations in the power-law inflationary model using the phase-integral method
The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used
for computing cosmological perturbations in the power-law inflationary model.
The phase-integral formulas for the scalar and tensor power spectra are
explicitly obtained up to ninth-order of the phase-integral approximation. We
show that, the phase-integral approximation exactly reproduces the shape of the
power spectra for scalar and tensor perturbations as well as the spectral
indices. We compare the accuracy of the phase-integral approximation with the
results for the power spectrum obtained with the slow-roll and uniform
approximation methods.Comment: 16 pages, Revtex, to appear in Physical Review
Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method
The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used
for computing cosmological perturbations in the quadratic chaotic inflationary
model. The phase-integral formulas for the scalar and tensor power spectra are
explicitly obtained up to fifth order of the phase-integral approximation. We
show that, the phase integral gives a very good approximation for the shape of
the power spectra associated with scalar and tensor perturbations as well as
the spectral indices. We find that the accuracy of the phase-integral
approximation compares favorably with the numerical results and those obtained
using the slow-roll and uniform approximation methods.Comment: 21 pages, RevTex, to appear in Phys. Rev
Classical solution of the wave equation
The classical limit of wave quantum mechanics is analyzed. It is shown that
the general requirements of continuity and finiteness to the solution
, where and
is the reduced classical action of the physical system, result in the
asymptote of the exact solution and general quantization condition for ,
which yields the exact eigenvalues of the system.Comment: 8 Pages, 10 Refs, LaTe
Critical view of WKB decay widths
A detailed comparison of the expressions for the decay widths obtained within
the semiclassical WKB approximation using different approaches to the tunneling
problem is performed. The differences between the available improved formulae
for tunneling near the top and the bottom of the barrier are investigated.
Though the simple WKB method gives the right order of magnitude of the decay
widths, a small number of parameters are often fitted. The need to perform the
fitting procedure remaining consistently within the WKB framework is emphasized
in the context of the fission model based calculations. Calculations for the
decay widths of some recently found super heavy nuclei using microscopic
alpha-nucleus potentials are presented to demonstrate the importance of a
consistent WKB calculation. The half-lives are found to be sensitive to the
density dependence of the nucleon-nucleon interaction and the implementation of
the Bohr-Sommerfeld quantization condition inherent in the WKB approach.Comment: 18 pages, Late
Universal decay law in charged-particle emission and exotic cluster radioactivity
A linear universal decay formula is presented starting from the microscopic
mechanism of the charged-particle emission. It relates the half-lives of
monopole radioactive decays with the -values of the outgoing particles as
well as the masses and charges of the nuclei involved in the decay. This
relation is found to be a generalization of the Geiger-Nuttall law in
radioactivity and explains well all known cluster decays. Predictions on the
most likely emissions of various clusters are presented.Comment: 2 figure
Asymptotic Spectroscopy of Rotating Black Holes
We calculate analytically the transmission and reflection amplitudes for
waves incident on a rotating black hole in d=4, analytically continued to
asymptotically large, nearly imaginary frequency. These amplitudes determine
the asymptotic resonant frequencies of the black hole, including quasinormal
modes, total-transmission modes and total-reflection modes. We identify these
modes with semiclassical bound states of a one-dimensional Schrodinger
equation, localized along contours in the complexified r-plane which connect
turning points of corresponding null geodesics. Each family of modes has a
characteristic temperature and chemical potential. The relations between them
provide hints about the microscopic description of the black hole in this
asymptotic regime.Comment: References adde
Alpha Decay Hindrance Factors: A Probe of Mean Field Wave Functions
A simple model to calculate alpha-decay Hindrance Factors is presented. Using
deformation values obtained from PES calculations as the only input, Hindrance
Factors for the alpha-decay of Rn- and Po-isotopes are calculated. It is found
that the intrinsic structure around the Fermi surface determined by the
deformed mean field plays an important role in determining the hindrance of
alpha-decay. The fair agreement between experimental and theoretical Hindrance
Factors suggest that the wave function obtained from the energy minima of the
PES calculations contains an important part of the correlations that play a
role for the alpha-decay. The calculated HF that emerges from these
calculations render a different interpretation than the commonly assumed
n-particle n-hole picture.Comment: 7 pages, 9 figure
Energy evolution in time-dependent harmonic oscillator
The theory of adiabatic invariants has a long history, and very important
implications and applications in many different branches of physics,
classically and quantally, but is rarely founded on rigorous results. Here we
treat the general time-dependent one-dimensional harmonic oscillator, whose
Newton equation cannot be solved in general. We
follow the time-evolution of an initial ensemble of phase points with sharply
defined energy at time and calculate rigorously the distribution of
energy after time , which is fully (all moments, including the
variance ) determined by the first moment . For example,
, and all
higher even moments are powers of , whilst the odd ones vanish
identically. This distribution function does not depend on any further details
of the function and is in this sense universal. In ideal
adiabaticity , and the variance is
zero, whilst for finite we calculate , and for the
general case using exact WKB-theory to all orders. We prove that if is of class (all derivatives up to and including the order
are continuous) , whilst for class it is known to be exponential .Comment: 26 pages, 5 figure
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