Impossibility of distinguishing between identical particles in quantum collision processes

Abstract

The very successful convergent close-coupling (CCC) method [I. Bray and D. V. Fursa, Phys. Rev. A $54,$ 2991 (1996)] for calculating cross sections for the ionization of atoms by electron impact is examined for the case of hydrogen ionization. The theory is recast in an operator theoretic form, allowing explicit formulas to be given for the solutions of the truncated CCC equations. The limit to which these solutions tend as ever more terms are included in the truncation is shown to be the exact transition operator for the system. This analytical result is not consistent with the numerical CCC results, which yield amplitudes that violate the symmetrization principle of quantum mechanics and which depend for success on treating the electrons as classically, rather than quantally, indistinguishable particles. This new result is also inconsistent with the ``step function hypothesis'' [I. Bray, Phys. Rev. Lett. $78,$ 4721 (1997)] that was introduced to restore the consistency of the CCC calculations with the symmetrization postulate. In addition, the CCC method does not include long-range effects of the Coulomb interaction that are expected to be important in certain kinematic configurations at low energies. Consequently, it is not justified yet to interpret the numerical successes of the CCC method as confirmation of a fundamental dynamical understanding of electron-induced atomic ionization.