A mathematically rigorous formulation of the pseudopotential method

The Huang–Yang multipolar pseudopotential (see [K. Huang, Statistical Mechanics, Wiley, New York, 1963; K. Huang, C.N. Yang, Quantum-mechanical many-body problem with hard-sphere interaction, Phys. Rev. 105 (1957) 767–775]) is derived in a mathematically correct way using distribution theory. Up to recently, due to wrong numerical factors, only the first approximation term (the s-wave contribution) furnished correct results, and the conceptual validity of the higher approximations was in doubt, cf. [A. Derevianko, Revised Huang–Yang multipolar pseudopotential, Phys. Rev. A 72 (2005) 044701].