The number of J=0 pairs in {44,46,48}Ti

Abstract

In the single j-shell, the configuration of an even-even Ti isotope consists of 2 protons and n neutrons. The I=0 wave function can be written in terms of D(J,Jv)'s, which are the probability amplitudes for the 2 protons to couple to J and the n neutrons to couple to Jv (where J stands for the angular momentum and v for the seniority quantum number). There are several states with isospin Tmin=|(N-Z)/2|, but only one with Tmax=Tmin+2. By demanding that the Tmax wave function be orthogonal to the Tmin ones, we obtain the following simple expressions for the number of J=0 np pairs in these Ti isotopes: For T=Tmin, number of pairs(J12=0)=2|D(00)|^2/n For T=Tmax, number of pairs(J12=0)=2n|D(00)|^2=2n(2j+1-n)/(2j+1)(n+1) For 44Ti we have also the results for even J12: number of nn pairs=number of pp pairs=number of np pairs=|D(J12,J12)|^2.