The compressed helium atom variationally treated via a correlated Hylleraas wave function

We calculate ground state energy, critical cage and ionization radius for the confined helium atom centered in a spherical impenetrable box. Total and ionization energies, pressure on the confining boundary and the expectation value are obtained as a function of the box radii. Three nonlinear parameters and N (=1,5 and 10) linear coefficients are variationally optimized within wave functions expressed in a generalized Hylleraas basis set that explicitly incorporates the interelectronic distance r12, both, via a Slater type exponent and through polynomial terms entering the expansion. The wave function includes a cut-off factor to ensure correct fulfillment of the boundary condition (vanishing wave function at the box edge). With the 10-term basis set we obtain energy values very close (within millihartrees) to the nearly exact results of Joslin and Goldman [J. Phys. B 25 (1992) 1965] obtained by means of a Quantum Monte Carlo method which, computationally, is a great deal more demanding than our variational approach