Physicochemical properties of the confined hydrogen atom under dense semiclassical hydrogen plasma

Some fundamental quantities governing the physicochemical properties of the spherically confined (contained in a spherical box) hydrogen atom embedded in dense semiclassical hydrogen plasma have been investigated. These quantities specifically include the energy levels, wavefunctions, 2(k)-pole oscillator strength, 2(k)-pole polarizability, hyperfine spitting, effective pressure on the boundary of the confining surface. The effect of plasma is described by a pseudopotential which takes care of the collective effect and the quantum mechanical effects at short distances of the plasma particles by means of two adjustable parameters, namely, the screening parameter and the de Broglie wavelength. Energy eigenvalues of the atom for various box sizes and for different values of the plasma parameters are computed accurately within a variational framework by employing a large wavefunction which automatically takes care of the requisite boundary conditions. Convergence of the computed results is corroborated by increasing the number of terms in the wavefunction. Particular attention is paid on determining the critical size box for which all the bound states of the atom cease to exist. Based on the computed energies and the corresponding eigenfunctions, mean values of various powers of the radial coordinate, oscillator strengths, polarizability of various order, hyperfine splitting, and the effective pressure on the boundary have been evaluated. A comprehensive study is made on the changes of those quantities for varying box size and plasma parameters. Efforts are made to distinguish the changes arising out of the spatial confinement and the plasma confinement.