Dresden 2011 – scientific programme

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MO: Fachverband Molekülphysik

MO 3: Cold Molecules I

MO 3.9: Talk

Monday, March 14, 2011, 12:30–12:45, BAR Schön

Near-threshold vibrational bound states in long-range molecules — •Tim-Oliver Müller and Harald Friedrich — Physik Department, TU München, Germany

Interatomic potentials with attractive tails asymptotically vanishing as −1/r^α (with α > 2) support at most a finite number of vibrational bound states, and their energies E_v are related to their quantum numbers v via a quantization rule v_D − v = F(E_v), where v_D is the – not necessarily integer – threshold quantum number. At near-threshold energies the quantization function F(E) is predominantly determined by a contribution F_tail(E) stemming from the potential’s tail, which is a universal function depending only on the power α. Quantum effects are important near the dissociation threshold and F(E) differs significantly from the widely used semiclassical expression derived by LeRoy and Bernstein [1]. Explicit analytical expressions for F_tail have been presented for to the van der Waals interaction between two neutral polarizable atoms or molecules (α=6) [2] as well as for the dispersion energy occuring in certain diatomic molecular ions (α=4) [3] and recently also for the power α=3 [4], which corresponds to the resonant dipole-dipole interaction between two identical atoms in a homonuclear dimer. Applications to sodium dimers show the importance of correctly including quantum effects near threshold.

[1] R. J. LeRoy and R. B. Bernstein, J. Chem. Phys 52, 3869 (1970).

[2] P. Raab and H. Friedrich, Phys. Rev. A 78, 022707 (2008).

[3] P. Raab and H. Friedrich, Phys. Rev. A 80, 052705 (2009).

[4] T.-O. Müller and H. Friedrich, submitted to Phys. Rev. A.