27 research outputs found
Zero range potential for particles interacting via Coulomb potential: application to electron positron annihilation
The zero range potential is constructed for a system of two particles
interacting via the Coulomb potential. The singular part of the asymptote of
the wave function at the origin which is caused by the common effect of the
zero range potential singularity and of the Coulomb potential is explicitly
calculated by using the Lippmann-Schwinger type integral equation. The singular
pseudo potential is constructed from the requirement that it enforces the
solution to the Coulomb Schr\"odinger equation to possess the calculated
asymptotic behavior at the origin. This pseudo potential is then used for
constructing a model of the imaginary absorbing potential which allows to treat
the annihilation process in positron electron collisions on the basis of the
non relativistic Schr\"odinger equation. The functional form of the pseudo
potential constructed in this paper is analogous to the well known
Fermi-Breit-Huang pseudo potential. The generalization of the optical theorem
on the case of the imaginary absorbing potential in presence of the Coulomb
force is given in terms of the partial wave series
Underthreshold resonances in three-particle molecular systems
To determine the lifetimes of Efimov states of negative two-atomic ions, the
problem of resonance scattering of a light particle on a pair of identical
particles has been considered. An analytic expression has been obtained for
resonance widths in the limit of forces of zero radius and low binding energies
in pairs. Calculations are compared with the numerical solution of the Faddeev
integral equations in a wide region of masses of the light particle. It is
shown that the widths of underthreshold resonances in the scattering amplitude
obtained from the integral equations with the Yamaguchi potential are well
described by the analytic expression, which allows this expression to be used
in the mass region inaccessible for numerical calculations. It has been
concluded that the lifetime of highly excited negative molecular ions with a
binding energy close to the threshold of disintegration is practically
unlimited.Comment: Latex, 15 page
A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields
Let R be a regular local ring, containing an infinite field. Let G be a
reductive group scheme over R. We prove that a principal G-bundle over R is
trivial, if it is trivial over the fraction field of R.Comment: Section "Formal loops and affine Grassmannians" is removed as this is
now covered in arXiv:1308.3078. Exposition is improved and slightly
restructured. Some minor correction