VARIATIONAL CALCULATIONS FOR THE BOUND-UNBOUND TRANSITION OF THE YUKAWA POTENTIAL

We perform LCAO (linear combination of atomic orbitals) calculations for the ground state of the Yukawa potential V(r) = -(e2/r)e(-qr) as a function of the screening parameter q. We obtain the best variational result so far for the ground-state energy E0 as a function of q. We also obtain the critical exponents of both the probability density at the origin and the ground-state energy as functions of (q-q(c)), where q(c) is the critical q above which V(r) does not have a bound state. The use of the critical exponents permits the so far most precise determination of q(c), q(c) = 1.190 612 27+/-0.000 000 04. We also show that it is possible to use the LCAO calculations as a tool to determine the analytical form of very precise variational wave functions. We obtain, in such a way, the wave function psi=(e(-ar)-e(-br))/r+e(-br)/(r+alpha). This variational wave function has a bound-unbound transition at q(c)=1.190 61074.