Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions

Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions. The first series applies single Beta functions as expansion functions, while the second one involves a combination of two Beta functions. The coefficients of expansions obey four- and five-term recurrence relations, respectively. It is shown that the proposed technique is potent to produce series solutions in terms of other special functions. Two examples of such expansions in terms of the incomplete Gamma functions are presente

Rotational and rotationless states of weakly-bound molecules

By making use of the quantization rule of Raab and Friedrich [P. Raab and H. Friedrich, Phys. Rev. A 78, 022707 (2008)], we derive simple and accurate formulae for the number of rotational states supported by a weakly-bound vibrational level of a diatomic molecule and the rotational constants of any such levels up to the threshold, and provide a criterion for determining whether a given weakly-bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential and are applicable to halo molecules.Comment: slightly corrected version, 4 pages, 1 figure, 3 table

Stimulated Raman Adiabatic Passage via bright state in Lambda medium of unequal oscillator strengths

We consider the population transfer process in a Lambda-type atomic medium of unequal oscillator strengths by stimulated Raman adiabatic passage via bright-state (b-STIRAP) taking into account propagation effects. Using both analytic and numerical methods we show that the population transfer efficiency is sensitive to the ratio q_p/q_s of the transition oscillator strengths. We find that the case q_p>q_s is more detrimental for population transfer process as compared to the case where $q_p \leq q_s$. For this case it is possible to increase medium dimensions while permitting efficient population transfer. A criterion determining the interaction adiabaticity in the course of propagation process is found. We also show that the mixing parameter characterizing the population transfer propagates superluminally