arXiv subjects

M. J. Jamieson

Publications and source records attributed to M. J. Jamieson.

5 recordsLinked to original sources

arXiv2015

Parameters for Cold Collisions of Lithium and Caesium Atoms

We calculate the s-wave scattering length and effective range and the p-wave scattering volume for $^7$Li atoms interacting with $^{133}$Cs atoms via the X$^1Σ^+_g$ molecular potential. The length and volume are found by fitting the log-derivative of the zero energy wave function evaluated at short range to a long range expression that accounts for the leading van der Waals dispersion potential and then incorporating the remaining long range dispersion contributions to first order. The effective range is evaluated from a quadrature formula. The calculated parameters are checked from the zero energy limits of the scattering phase shifts. We comment on ill-conditioning in the calculated s-wave scattering length.

physics.atom-ph↗

arXiv2005

The variable phase method used to calculate and correct scattering lengths

It is shown that the scattering length can be obtained by solving a Riccati equation derived from variable phase theory. Two methods of solving it are presented. The equation is used to predict how long-range interactions influence the scattering length, and upper and lower bounds on the scattering length are determined. The predictions are compared with others and it is shown how they may be obtained from secular perturbation theory.

physics.atom-ph↗

arXiv2005

A note on the calculation of the effective range

The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining the effective range, by fitting a numerical solution of the Schrödinger equation to known asymptotic boundary conditions, can be modified to include the first order contribution of a long range interaction.

physics.atom-ph↗

arXiv2005

Scattering parameters for cold-Li-Rb and Na-Rb collisions derived from variable phase theory

We show how the scattering phase shift, the s-wave scattering length and the p-wave scattering volume can be obtained from Riccati equations derived in variable phase theory. We find general expressions that provide upper and lower bounds for the scattering length and the scattering volume. We show how, in the framework of the variable phase method, Levinson's theorem yields the number of bound states supported by a potential. We report new results from a study of the heteronuclear alkali dimers NaRb and LiRb. We consider $ab$ $initio$ molecular potentials for the X${}^1Σ^+$ and $a{}^3Σ^+$ states of both dimers and compare and discuss results obtained from experimentally based X${}^1Σ^+$ and $a{}^3Σ^+$ potentials of NaRb. We explore the mass dependence of the scattering data by considering all isotopomers and we calculate the numbers of bound states supported by the molecular potentials for each isotopomer.

physics.atom-ph↗

arXiv2004

Theoretical Study of Quantum Scattering Processes for Diatomic Hydrogen $(^{2}S)$ and Oxygen $(^{3}P)$ Complex

We present a quantum mechanical study of the diatomic hydrogen $H(^{2}S)$ and oxygen $O(^{3}P)$ collision and energy transfer for its four molecular symmetry $(X^{2}Π, ^{2}Σ^{-}, ^{4}Π, ^{4}Σ^{-})$, which is important for the investigation of many processes of astrophysical and chemical interests including the one on molecular cooling, trapping or Bose-Einstein condensation. We compute the rovibrational spectra for the $(X^{2}Π)$ state and the resulting bound states are in an excellent agreement with experimental data for the energy range lower than the dissociation threshold. We calculate the phase shifts of its partial-waves, the total cross section, and the differential cross section. They are all well-structured because of the shape of its potential curve. We do the similar studies for the other three dissociative states $(^{2}Σ^{-}, ^{4}Π, ^{4}Σ^{-})$. Finally, we have also decided the thermal rate coefficients for the hydrogen and oxygen collision for its four individual states.

physics.chem-ph↗