29,450 research outputs found
Collisional deexcitation of exotic hydrogen atoms in highly excited states. II. Cascade calculations
The atomic cascades in mu-p and pbar-p atoms have been studied in detail
using new results for the cross-sections of the scattering of highly excited
exotic atoms from molecular hydrogen. The cascade calculations have been done
with an updated version of the extended standard cascade model that computes
the evolution in the kinetic energy from the beginning of the cascade. The
resulting X-ray yields, kinetic energy distributions, and cascade times are
compared with the experimental data.Comment: 13 pages, 23 figure
Collisional deexcitation of exotic hydrogen atoms in highly excited states. I. Cross-sections
The deexcitation of exotic hydrogen atoms in highly excited states in
collisions with hydrogen molecules has been studied using the
classical-trajectory Monte Carlo method. The Coulomb transitions with large
change of principal quantum number n have been found to be the dominant
collisional deexcitation mechanism at high n. The molecular structure of the
hydrogen target is shown to be essential for the dominance of transitions with
large \Delta n. The external Auger effect has been studied in the eikonal
approximation. The resulting partial wave cross-sections are consistent with
unitarity and provide a more reliable input for cascade calculations than the
previously used Born approximation.Comment: 10 pages, 20 figure
Nontrivial Sha in the Jacobian of an Infinite Family of Curves of Genus 2.
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit model of an associated family of surfaces which violate the Hasse principle
Square-well solution to the three-body problem
The angular part of the Faddeev equations is solved analytically for s-states
for two-body square-well potentials. The results are, still analytically,
generalized to arbitrary short-range potentials for both small and large
distances. We consider systems with three identical bosons, three non-identical
particles and two identical spin-1/2 fermions plus a third particle with
arbitrary spin. The angular wave functions are in general linear combinations
of trigonometric and exponential functions. The Efimov conditions are obtained
at large distances. General properties and applications to arbitrary potentials
are discussed. Gaussian potentials are used for illustrations. The results are
useful for numerical calculations, where for example large distances can be
treated analytically and matched to the numerical solutions at smaller
distances. The saving is substantial.Comment: 34 pages, LaTeX file, 9 postscript figures included using epsf.st
Efimov effect in nuclear three-body resonance decays
We investigate the effects of the nearly fulfilled Efimov conditions on the
properties of three-body resonances. Using the hyper-spheric adiabatic
expansion method we compute energy distributions of fragments in a three-body
decay of a nuclear resonance. As a realistic example we investigate the 1-
state in the halo nucleus 11Li within a three-body 9Li+n+n model.
Characteristic features appear as sharp peaks in the energy distributions.
Their origin, as in the Efimov effect, is in the large two-body s-wave
scattering lengths between the pairs of fragments
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