Multipole polarizabilities and critical phenomena of hydrogen-like atoms in dense quantum plasmas

Binding energies, oscillator strengths, and polarizabilities of hydrogen-like atoms embedded in dense quantum plasmas are calculated in high precision by employing the generalized pseudospectral method. Benchmark predictions of these quantities are obtained for both the ground and excited states including high-order transitions. The critical behaviour of system eigenenergies, radial mean values, oscillator strengths, and multipole polarizabilities for bound states when they approach to the corresponding continuum limit as increasing the plasma screening strength are investigated in detail. It is shown that near the critical screening parameters the quantities in s -wave states show distinct behaviour from those in non- s states and such phenomenon is attributed to the divergent asymptotic form of wave functions caused by the centrifugal potential of orbital angular momentum. Based on the power laws of energies and radial mean values extracted from numerical calculations and the approximate formulae for dipole polarizabilities, the critical behaviour of the 2 k -pole polarizability of s -wave states is explicitly derived and numerically validated to follow a power law with the exponent −2( k + 1).