Attractive Two-Body Interactions in Partially Ionized Plasmas

It has recently been shown that in a classical plasma a shielded Coulomb (Yukawa) potential describes the effective two-particle interactions through chains of intermediate particles. It therefore seemed reasonable to use this potential to approximate two-particle quantum interactions in a sea of charged particles, such as a hydrogen plasma. Consequently, an approximate solution of the Schrödinger equation was obtained for a hydrogen atom in a shielded Coulomb potential. With this potential, the number of H-atom bound states is finite and the energy eigenvalues are a function of the density and temperature. A variational calculation was performed using hydrogen-like single electron functions as a basis set and the effective nuclear charge as a variational parameter. Bound-state energies were obtained for 45 states of hydrogen in a gird of values for the screening constant. As the screening increases, the bound-state energy increases. For each state there is a maximum shielding above which the state is free, i.e., for which $E>\mathrm{}0\mathrm{}$. According to the present calculation, the energy of the ground state becomes zero at a screening of 1.15 atomic units. Above this value then, no bound states can exist.