The B spline method for calculating the correlation energy of helium atoms is proposed.The result is compared with that by Slater basis functions.The virtue defect and practicability of B spline technique are analysed.It is shown that the B spline technique can be used widely in the calculation of electronic interaction.

Using B-spline method, we take Be3+ in buckyminister fullerence as a n example and have calculated the 2s—3p oscillator strength of the endohedrally confined hydrogen-like system in the confining well with different shapes and l ocations. Resonance enhancement appears as the 2s and 3p states are both bound i n outer well, and a resonance enhancement peak has been found at the “collapse point”. Our results show that resonance enhancement is insensitive to the shape of the confining well, and it is also influenced by confinement ability. The lo cation of the confining well may strongly affect the resonance enhancement.

Based on the B-spline basis method, the properties of the helium atom confined inside an endohedral environment, such as buckminster fullerene, are studied. In our calculations, the endohedral environment is a parabolic potential well. In this situation, the phenomenon of “mirror collapse” is exhibited for energy levels of a confined helium atom. The “giant resonance” of oscillator strength of the dipole transition emerges with the variation of depth of the confining well. The physical mechanisms of these phenomena are analyzed in this paper.

The B-spline basis set method is used to study the properties of helium con ned endohedrally at the geometrical centre of a fullerene. The boundary conditions of the wavefunctions can besimply satis ed with this method. From our results, the phenomenon of \mirror collapse" is found in the case of con ning helium. The interesting be h a viors of con ning helium are also discussed.

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