Analytic potential functions for weakly bound molecules

Gou Qing-Dong, Yong Li

The three-body Schrdinger equation is approximately solved in the hyperspherical coordinates and the binding energies of the three-body weakly bound systems are calculated with the purpose to find if He-He-Ba trimers could exist. Using the special feature of the B-spline function like the flexible and highly localized properties, hypersphercial potentials are obtained by modifying the knots distribution of the B-spline basis of different weakly bound three-atom systems. Employing the best empirical interaction potentials between each pair of particles, we obtain that in the ground state binding energies of the weakly bound typical three-atom systems, the bindings of the molecules, 4He-4He-138Ba, 4He-3He-138Ba and 3He-3He-138Ba are possible. The binding energies of these systems are shown in the order of 1 Kelvin, each system could support only one bound state. These weakly bound molecules can exist only in a very cold environment. To get insight into the geometry of the molecules, the features of the channel functions associated with the hyperspherical potential curves of each system are investigated.

Mikhail Lemeshko, Břetislav Friedrich

We show that weakly bound molecules can be probed by "shaking" in a pulsed nonresonant laser field. The field introduces a centrifugal term which expels the highest vibrational level from the potential that binds it. Our numerical simulations applied to the Rb(2) and KRb Feshbach molecules indicate that shaking by feasible laser pulses can be used to accurately recover the square of the vibrational wave function and, by inversion, also the long-range part of the molecular potential.

A. Ronveaux

B B Baizakov, S. M. Al-Marzoug, Usama Al Khawaja +1 more

Abstract Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior in the weakly bound regime, with a small binding energy. Using the variational approach a coupled system of ordinary differential equations for the parameters of a soliton molecule is obtained for the description of their evolution. Predictions of the model are compared with numerical simulations of the governing nonlocal Gross–Pitaevskii equation and good qualitative agreement between them is demonstrated.

Cheng Chin, Paul S. Julienne, Eite Tiesinga