Abstract
A diagonalization scheme for the shell model mean-field plus isovector pairing Hamiltonian in the O(5) tensor product basis of the quasi-spin SUΛ(2) ⊗ SUI(2) chain is proposed. The advantage of the diagonalization scheme lies in the fact that not only can the isospin-conserved, charge-independent isovector pairing interaction be analyzed, but also the isospin symmetry breaking cases. More importantly, the number operator of the np-pairs can be realized in this neutron and proton quasi-spin basis, with which the np-pair occupation number and its fluctuation at the J = 0+ ground state of the model can be evaluated. As examples of the application, binding energies and low-lying J = 0+ excited states of the even–even and odd–odd N∼Z ds-shell nuclei are fit in the model with the charge-independent approximation, from which the neutron–proton pairing contribution to the binding energy in the ds-shell nuclei is estimated. It is observed that the decrease in the double binding-energy difference for the odd–odd nuclei is mainly due to the symmetry energy and Wigner energy contribution to the binding energy that alter the pairing staggering patten. The np-pair amplitudes in the np-pair stripping or picking-up process of these N = Z nuclei are also calculated.
Highlights
It is evident from both theoretical and experimental analysis of available data that, besides neutron–neutron and proton–proton pairing, neutron–proton pairing is of importance in N∼Z nuclei [1,2,3,4,5,6,7,8,9]
A diagonalization scheme for the shell model mean-field plus isovector pairing Hamiltonian in the O(5) tensor product basis is adapted to accommocate quasispin, which means the scheme is equivalent to a MT-scheme realized in the O(5) ⊃ SUΛ(2) ⊗ SUI (2) ⊃ UΛ(1) ⊗ UI (1) basis
The scheme conserves a chargeindependent isovector pairing interaction while accommodating isospin symmetry breaking and provides for a number operator that counts the effective number of np-pairs that can be realized in a neutron–proton quasi-spin basis
Summary
It is evident from both theoretical and experimental analysis of available data that, besides neutron–neutron (nn) and proton–proton (pp) pairing, neutron–proton (np) pairing is of importance in N∼Z nuclei [1,2,3,4,5,6,7,8,9]. For the O(5) seniority zero case corresponding to v = t = 0 and J = 0 discussed in this work, the quantum numbers of Sp(2j + 1) and SUJ(2) are neglected In this case, for a given number of valence nucleons nj, the basis vectors (8) can be constructed by using nj (J = 0, T = 1) pair creation operators A+μ (j) coupled to isospin T as shown in [48]. + 1), where Dim(O(5), (v1, v2)) is the dimension of the O(5) irrep (v1, v2) with v1 ≥ v2 ≥ 0
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