Counting pairs in ⁴⁴Ti with various interactions

الأصل · EN

We count the number of pairs in the single j-shell model of ⁴⁴Ti for various interactions. For a state of total angular momentum I, the wave function can be written as Ψ=∑ⱼₚ ⱼₙ D(Jₚ Jₙ) [(j²)ⱼₚ(j²)ⱼₙ]ᵢ, where D(Jₚ Jₙ) is the probability amplitude that the protons couple to Jₚ and the neutrons to Jₙ. For I=0 there are three states with (I=0, T=0) and one with (I=0, T=2). The latter is the double analog of ⁴⁴Ca. In that case (T=2), the magnitude of D(JJ) is the same as that of a corresponding two particle fractional parentage coefficient. In counting the number of pairs with an even angular momentum Jₐ we find a new relationship obtained by diagonalizing a unitary nine-j symbol. We are also able to get results for the 'no-interaction' case for T=0 states, for which it is found that there are less (J=1, T=0) pairs than on the average. Relative to this 'no-interaction case' we find for the most realistic interaction used that there is an enhancement of pairs with angular momentum Jₐ=0,2,1 and 7, and a depletion for the others. Also considered are interactions in which only the (J=0, T=1) pair state is at lower energy, only the (J=1, T=0) pair state is lowered and where both are equally lowered.