Theory for Relative Strengths of Trapping of He+ Ions in Solid, Liquid and Gaseous Hydrogen

R. H. Scheicher(1), A. N. U. Roy(1), T. P. Das(1), K. Ishida(2), T. Matsuzaki(2), S. N. Nakamura(2), N. Kawamura(2), K. Nagamine(2,3)
(1) Department of Physics, State University of New York at Albany, Albany, NY 12222, USA
(2) Muon Science Laboratory, RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan
(3) Meson Science Laboratory, High Energy Accelerator Research Organization, Oho 1-1, Tsukuba, Ibaraki 305-0801, Japan

The trapping of He+ ion in solid hydrogen has been studied because of its basic importance both as a solid state problem as well as in the field of muon catalyzed fusion (µCF) as a trap for µ- [1], interrupting the chain aspect of the catalytic role of µ- in producing fusion of deuteron and triton and of triton and triton in solid hydrogen composed of 2H-3H and 3H-3H molecules. Using the Hartree-Fock procedure, combined with procedures for including many-body effects, as well as relaxation effects associated with the He+-H distances and the adjustment of the H-H separation, the trapping of He+ in gaseous and solid state environments has been studied. For the former, the environment of He+ is simulated by a single-hydrogen molecule and for the solid by clusters appropriately chosen to represent the hexagonal close-packed structure. Our results for the gaseous state indicates that the trapping is rather strong with a binding energy of 8.5 eV, with almost equal binding energy in the linear and perpendicular configurations with respect to the H-H direction. For the solid, both the likely sites for He+ trapping, namely the
tetrahedral and octahedral interstitial sites, are also found to provide deep traps (8.6 eV) of almost equal strength, independent of the orientations of the neighboring molecules, showing that the trapping is not influenced by the orientational disorder in the surrounding hydrogen molecules. Lastly, the influence of next nearest neighbor hydrogen molecules is found to enhance the trapping energy for He+ substantially, by 0.6 eV, with the incorporation of the third nearest neighbors having a much smaller added influence, demonstrating the convergence of our results with respect to the size of the cluster chosen to simulate the solid. The substantial added influence of the neighbors beyond the nearest ones provide an explanation of the greater accumulation of He gas, in the solid state of hydrogen as compared to the liquid state, in µCF experiments.

[1] K. Nagamine and M. Kamimura, Advances in Nuclear Physics, Vol. 24, edited by J. W. Negele and E. W. Vogt, Plenum
Press, New York (1998)

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