Department of Physics Papers

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Journal Article

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Physical Review B



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We study the coupled rotation-vibration levels of a hydrogen molecule in a confining potential with cylindrical symmetry. We include the coupling between rotations and translations and show how this interaction is essential to obtain the correct degeneracies of the energy level scheme. We applied our formalism to study the dynamics of H2 molecules inside a “smooth” carbon nanotube as a function of tube radius. The results are obtained both by numerical solution of the (2J+1)-component radial Schrödinger equation and by developing an effective Hamiltonian to describe the splitting of a manifold of states of fixed angular momentum J and number of phonons N. For nanotube radius smaller than ≈3.5Å, the confining potential has a parabolic shape and the results can be understood in terms of a simple toy model. For larger radius, the potential has the “Mexican hat” shape and therefore the H2 molecule is off centered, yielding radial and tangential translational dynamics in addition to rotational dynamics of H2 molecule which we also describe by a simple model. Finally, we make several predictions for the the neutron scattering observation of various transitions between these levels.


At the time of publication, author Taner Yildirim was affiliated with the National Institute of Standards and Technology, Gaithersburg, Maryland. Currently, he is a faculty member in the Materials Science and Engineering Department at the University of Pennsylvania.



Date Posted: 12 August 2015

This document has been peer reviewed.