FHBS calculations are presumably the most accurate if driven to convergence. But the large basis two centered expansions, needed to treat accurately final state interactions with the projectile, are very expensive in computer time. We present a new method, ve&_udi=B6TVT-4MBC4Y1-2&_mathId=mml60&_user=10&_cdi=5543&_rdoc=13&_acct=C000050221&_version=1&_userid=10&md5=0549f3fa81d338afef2f26e70d13ad2b" title="Click to view the MathML source">E-A theory, which is an order of magnitude more efficient.
Differential direct ionization cross sections are generally well described by CTMC and CDW methods. But at 20 keV proton energy, evidence is emerging of the importance of a quantal interference effect wherein the scattered electron diffracts around the projectile and target.