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Bulletin of the Russian Academy of Sciences Physics

Resonance diffusion of beryllium molecule

Pavel M. Krassovitskiy, Ф. М. Пеньков

Published Jul 1, 2015• 1 citation
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Abstract

The probabilities of resonance tunneling through a potential barrier for a rigid molecule and a molecule with excitation are compared. It is shown that the resonance spectrum is mostly determined by the transmission resonance spectrum for a rigid molecule. Analytical expressions for the probability of barrier tunneling by a rigid molecule yield estimates for measured values, including quantum diffusion, averaged over the resonance spectrum.

DOI
10.3103/s1062873815040218

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The probabilities of resonance tunneling through a potential barrier for a rigid molecule and a molecule with excitation are compared. It is shown that the resonance spectrum is mostly determined by the transmission resonance spectrum for a rigid molecule. Analytical expressions for the probability of barrier tunneling by a rigid molecule yield estimates for measured values, including quantum diffusion, averaged over the resonance spectrum.
We study a diatomic homonuclear molecule incident upon a potential barrier. We allow transitions between binding energy states of the molecule during the process of tunneling and consider both single and double barriers. By applying an elegant method to solve this system we show that transmission resonances do occur in both cases and that expressions for the locations of the resonances can be found. Moreover, we find that the addition of binding energy levels tends to decrease the probability of tunneling. We also show that by relaxing rigor and treating the length of the molecule as though it is fixed we can obtain exact analytical expressions for the transmission probability that capture important features of the full solution.
Exact solutions are obtained for the diffusion in single- and square-well potentials, by using the Laplace transform method. We compare transmission of a classical particle through one barrier of given length and through two barriers with a well between them of the same overall length. It turns out that the existence of a well facilitates the transmission of a classical particle for intermediate times, which bears some resemblance to resonances tunneling through quantum barriers. \textcopyright{} 1996 The American Physical Society.
We study a diatomic homonuclear molecule incident upon a potential barrier in three dimensions. We study various initial states for the molecule and allow transitions between rotational states of the molecule during the process of tunneling. By applying an elegant method to solve this problem we show that transmission resonances occur in several cases and that adding more binding energy levels for the molecule can tend to decrease the probability of tunneling. We also find that the probability of transmission can be enhanced by the addition of a second potential barrier. These results are in qualitative agreement with those found for the tunneling of a molecule in a one-dimensional model studied previously.
Some aspects of quantum tunnelling of a composite particle are clarified by a simple model. We calculate the probability that a couple of point particles bound to each other by a square well potential with a hard core tunnel through a rectangular potential barrier. It is shown that resonance structures appear in the transmission spectrum in some cases, which reflects the existence of quasi-bound-states of the centre of mass motion around the potential barrier. It is also shown that an inelastic tunnelling occurs in which the transitions in the relative motion are induced by the tunnelling of the centre of mass.
We summarize our study of a diatomic homonuclear molecule incident upon a potential barrier in one dimension [G.L. Goodvin and M.R.A. Shegelski. Phys. Rev. A, 71, 032719 (2005).]. We study various initial states for the molecule and allow transitions between vibrational states of the molecule during the process of tunneling. By applying an elegant method to solve this problem, we show that transmission resonances occur in several cases and that adding more binding energy levels for the molecule can tend to decrease the probability of tunneling. We also discuss the extension of our results to more realistic three-dimensional and experimental systems.PACS Nos.: 34.20.Cf, 03.65.Xp, 34.20.Gj, 34.50.Pi