A highly accurate study of a helium atom under pressure

Basis sets incorporating the interelectronic distance r 12 are employed in variational calculations of the non-relativistic ground-state energies and pressures of a helium atom confined at the centre of an impenetrable spherical cavity and results are presented for a series of cavity radii R c . The calculated values asymptotically approach the correct values in the limits R c → 0 and R c → ∞, and a simple analytical expression is obtained which makes accurate predictions for small cavities. The same method is also used to study two penetrable cavities modelled by Gaussian and harmonic potential wells. It is concluded that the present results are the most accurate currently available for a confined helium atom. The calculation method employs Gaussian quadrature to evaluate integrals and can very easily be adapted to any spherical confining potential.