in which M is the number of particles, j a , a = 1 , ⋯ ⋯ M their position, S M is the set of all permutations of the integers 1 , ⋯ ⋯ , M , ( − − 1 ) [ P ] is the parity of the permutation P taking values either positive or negative one, k a is the (quasi-)momentum of the a -th particle, ϕ ϕ is the scattering phase shift function and s g n is the sign function. This form is universal (at least for non-nested systems), with the momentum and scattering functions being model-dependent.