Physical Review A

Tunneling of a diatomic molecule with many bound states

Jeff Hnybida, Mark R. A. Shegelski

Published Sep 30, 2008• 16 citations

Abstract

We study the effects of multiple bound states on the probability of tunneling of a homonuclear diatomic molecule incident upon a potential barrier in one dimension. We obtain additional bound states by several means: by varying individual features of the binding potential as well as increasing the mass of the two atoms. We find that the tunneling behavior of a molecule with a large number of bound states $(\ensuremath{\sim}30)$ is drastically different from that for a molecule with a small number of states $(\ensuremath{\lesssim}5)$. Further, we find that the effect of multiple bound states on the proabability of tunneling is largely dependent upon the separation between the bound-state energies. It is also found that intermediary transitions between many bound states results in significantly larger reductions in the probability of tunneling. Finally, we investigate molecules of different masses and observe common qualitative features. We focus on molecules incident upon a $\ensuremath{\delta}$ barrier but we also consider Gaussian barriers.

DOI: 10.1103/physreva.78.032711

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Physical Review A

Tunneling of a diatomic molecule with many bound states

Jeff Hnybida, Mark R. A. Shegelski

Published Sep 30, 2008• 16 citations

Publisher

Abstract

(\ensuremath{\sim}30)

is drastically different from that for a molecule with a small number of states

(\ensuremath{\lesssim}5)

. Further, we find that the effect of multiple bound states on the proabability of tunneling is largely dependent upon the separation between the bound-state energies. It is also found that intermediary transitions between many bound states results in significantly larger reductions in the probability of tunneling. Finally, we investigate molecules of different masses and observe common qualitative features. We focus on molecules incident upon a

\ensuremath{\delta}

barrier but we also consider Gaussian barriers.

DOI: 10.1103/physreva.78.032711

Related papers

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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.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.

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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.PiWe 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

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(\ensuremath{\sim}30)

is drastically different from that for a molecule with a small number of states

(\ensuremath{\lesssim}5)

\ensuremath{\delta}

barrier but we also consider Gaussian barriers.

{e}_{0}

approaches zero and the step potential

{V}_{0}

goes to infinity, the molecule cannot remain in a bound state if the center of mass gets closer to the step than an arbitrarily large distance

{x}_{0}

which increases as the magnitude of

{e}_{0}

decreases, as

{V}_{0}

increases, or both. We also show that, for ${e}_{0}\ensuremath{\rightarrow}{0}^{\ensuremath{-}}$ and ${V}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$, if the molecule is incident in the bound state, it is reflected in the bound state with probability equal to unity, when the center of mass reaches the reflection distance

{x}_{0}

. We verify that the unbound states exhibit the expected physical behavior. We discuss some surprising results. Connections between our results and investigations done in cold atoms, excitons, Cooper pairs, and Rydberg atoms are discussed.