47 research outputs found
Modified effective-range theory for low energy e-N2 scattering
We analyze the low-energy e-N2 collisions within the framework of the
Modified-Effective Range Theory (MERT) for the long-range potentials, developed
by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. In
comparison to the traditional MERT we do not expand the total cross-section in
the series of the incident momentum \hbar k, but instead we apply the exact
analytical solutions of the Schroedinger equation for the long-range
polarization potential, as proposed in the original formulation of O'Malley et
al. This extends the applicability of MERT up to few eV regime, as we confirm
using some simplified model potential of the electron-molecule interaction. The
parameters of the effective-range expansion (i.e. the scattering length and the
effective range) are determined from experimental, integral elastic cross
sections in the 0.1 - 1.0 eV energy range by fitting procedure. Surprisingly,
our treatment predicts a shape resonance that appears slightly higher than
experimentally well known resonance in the total cross section. Agreement with
the experimentally observed shape-resonance can be improved by assuming the
position of the resonance in a given partial wave. Influence of the quadrupole
potential on resonances is also discussed: we show that it can be disregarded
for N2. In conclusion, the modified-effective range formalism treating the
long-range part of the potential in an exact way, reproduces well both the very
low-energy behavior of the integral cross section as well as the presence of
resonances in the few eV range.Comment: 9 pages, LaTex, 4 eps figures, EPJ style; extended and upgraded
version of arXiv:0708.2991, now considering only e-N2 scatterin
Universal rate constants for reactive collisions of ultracold molecules
A simple quantum defect model gives analytic expressions for the complex
scattering length and threshold collision rates of ultracold molecules. If the
probability of reaction in the short-range part of the collision is high, the
model gives universal rate constants for s- and p-wave collisions that are
independent of short-range dynamics. This model explains the magnitudes of the
recently measured rate constants for collisions of two ultracold 40K87Rb
molecules, or an ultracold 40K atom with the 40K87Rb molecule [Ospelkaus et
al., Science 327, 853 (2010)].Comment: 4 pages, 2 figures; v2: final version, accepted for publication in
Physical Review Letter
Quantum reactive scattering in the long-range ion-dipole potential
An ion and a polar molecule interact by an anisotropic ion-dipole potential
scaling as at large distances. Due to its
long-range character, it modifies the properties of angular wave functions,
which are no longer given by spherical harmonics. In addition, an effective
centrifugal potential in the radial equation can become attractive for low
angular momenta. In this paper, we develop a general framework for an
ion-dipole reactive scattering, focusing on the regime of large . We
introduce modified spherical harmonics as solutions of the angular part of the
Schr\"odinger equation and derive several useful approximations in the limit of
large . We present a formula for the scattering amplitude expressed in
terms of the modified spherical harmonics and we derive expressions for the
elastic and reactive collision rates. The solutions of the radial equation are
given by Bessel functions, and we analyse their behaviour in two distinct
regimes corresponding, basically, to attractive and repulsive long-range
centrifugal potentials. Finally, we study reactive collisions in the universal
regime, where the short-range probability of loss or reaction is equal to
unity.Comment: 19 pages, 11 figures, 5 appendice