Eur. Phys. J. D 56, 181-188 (2010)
https://doi.org/10.1140/epjd/e2009-00280-8

Dependence of the scattering length for hydrogen atoms on effective mass

¹ Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK
² Department of Chemistry, University of Hong Kong, Hong Kong
³ Centre de Recherche sur les Ions, les Matériaux et la Photonique, UMR CEA-CNRS-ENSICAEN-Université de Caen Basse Normandie 6252, BP 5133, 14070 Caen, France

Corresponding author: mjj@dcs.gla.ac.uk

Received: 8 January 2009
Revised: 21 July 2009
Published online: 6 November 2009

Abstract

The possibility that the non-adiabatic correction to the scattering length of a pair of hydrogen atoms interacting via the ground state molecular potential, X¹Σ_g⁺, of H₂ could be made by replacing the mass of each nucleus by a different effective mass is explored. The Born-Oppenheimer potential with adiabatic, relativistic and radiative corrections is used in calculations of the scattering lengths and the mass-dependent shifts of the rotationless vibrational levels with fixed and varying effective masses. The shifts are compared with established values and it is demonstrated that the semi-classical formula for the scattering length accounts well for the effect of changing the mass. A perturbing potential that is equivalent to a change in mass is derived and it is compared to a published local non-adiabatic potential.