APPLICATION OF A VARIATIONAL PRINCIPLE FOR THE SCATTERING LENGTH FOR THE TARGET WAVE-FUNCTION IMPRECISELY KNOWN

In the past, variational calculations of the scattering length for scattering by a target system whose ground-state wave function is imprecisely known have suffered from numerical instabilities which severely limit their utility. The problem has recently been analyzed and the difficulty removed by the introduction of a minimum principle, not for the true scattering length, but for that of a closely connected problem. Here we report on numerical tests of this new calculational procedure. We have studied the scattering of positrons and electrons by atomic hydrogen with a trial hydrogenic ground-state wave function which is allowed to differ from the correct function. As predicted, no instability difficulties whatsoever are encountered as the trial scattering wave function and the trial target wave function are improved; apart from at most one jump for each composite bound state, the estimate of the scattering length converges monotonically. © 1979 The American Physical Society.