From the ansatz of our wave function eq. (2.36) we see that the calculation of the necessary matrix elements can be performed in several steps, after decomposing the antisymmetrizer into a sum over all permutations acting on spatial and spin-isospin coordinates: Since the potential terms in the Hamiltonian can be written as a product of operators acting in coordinate space and spin-isospin space separately

^ = ^^(-1)q w° (k> — q)wiijT (k, q) (3Л)

i<j i<j kq

we can also calculate the respective matrix elements of each operator sepa­rately. The rank of the interaction is denoted by k, e. g. k = 1 for the spin orbit force. Since the multi-dimensional integration in coordinate space is usually by far the most elaborate part of the calculation, we first describe the essential parts of this calculation.