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

Abstract

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${}^1{\Sigma }^{+}$ and $a{}^3{\Sigma }^{+}$ states of both dimers and compare and discuss results obtained from experimentally based X${}^1{\Sigma }^{+}$ and $a{}^3{\Sigma }^{+}$ 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.

7 pages in two-column format, including 3 figures

References in corpus (9)

• A quasi-pure Bose-Einstein condensate immersed in a Fermi sea
• Two-species mixture of quantum degenerate Bose and Fermi gases
• A two atomic species superfluid
• Fermi-Bose quantum degenerate ^40 K - ^87 Rb mixture with attractive interaction
• High-precision calculations of van der Waals coefficients for heteronuclear alkali-metal dimers
• Accurate relativistic many-body calculations of van der Waals coefficients C_8 and C_10 for alkali-metal dimers
• The potential of the ground state of NaRb
• Calculation of the interspecies s-wave scattering length in an ultracold Na-Rb vapor
• The variable phase method used to calculate and correct scattering lengths

Cited by in corpus (7)

• Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases
• Ultracold Thermalization of ${}^7$Li and ${}^{87}$Rb
• S-wave and p-wave scattering in a cold gas of Na and Rb atoms
• Sympathetic cooling route to Bose-Einstein condensate and Fermi-liquid mixtures
• p-wave phase shift and scattering length of ${}^6$Li
• Geometrically Frustrated Coarsening Dynamics in Spinor Bose-Fermi Mixtures
• Scattering states of coupled valence-band holes in point defect potential derived from variable phase theory