Mathematically rigorous formulation of the Fermi pseudopotential for higher-partial-wave scattering in arbitrary dimension

The Huang-Yang multipolar pseudopotential [see Huang and Yang, Phys. Rev. 105, 767 (1957); later revised by Huang, Statistical Mechanics (Wiley, New York, 1963)] is derived in a mathematically rigorous way using distribution theory in arbitrary dimension. For higher partial waves (i.e., all except s waves), the original pseudopotential contained wrong numerical factors in dimension 3, which were corrected only recently [see Derevianko, Phys. Rev. A 72, 044701 (2005); Stampfer and Wagner, J. Math. Anal. Appl. 342, 202 (2008)]. Here, we generalize the expression for the pseudopotential, in particular to even dimension, enabling the study of scattering processes in a large class of systems, especially in dimension 2.