The study of spatial confinement of quantum systems is of great interest these decades especially with the advent of modern techniques for the synthesis of nanostructured materials in order to allow molecular insertion and storage. The behavior of electronic and structural properties of a confined atom or molecule is studied in comparison to their free counterparts. The typical confining potentials are spherically symmetric, cylindrical or spheroidal. Confined hydrogen in its neutral, ionic and molecular forms has been the subject of several studies using different theoretical methods [1]. These studies are limited to low excited states for the atomic hydrogen and molecular ion  and to the ground state in equilibrium bond length for molecular hydrogen beyond the Born-Oppenheimer approximation. We are interested in the effect of spatial confinement in a hard prolate spheroidal box on potential energies and electric dipole transition moments of hydrogenic systems  and . To realize this study, we used an ab initio variational R matrix method which enables ground and excited states of diatomic systems to be calculated for fixed nuclei on the foci of the spheroidal box [2]. In this contribution, potential energies and electric dipole moments are evaluated within the Born-Oppenheimer approximation for internuclear distances  and for different spheroidal box sizes. To validate our theoretical approach, potential energies and electronic dipole transition moments are calculated first in a very large cavity to simulate the situation of the free case for  and . The results are then compared to the best available ones [3]. An overall agreement is obtained.

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[2] M. Telmini and Ch. Jungen, Phys. Rev. A , 2003,  68, 062704 ; S. Bezzaouia, M.Telmini and Ch. Jungen Phys. Rev. A , 2004,  70, 012713.
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