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Register a new userIsovector and isoscalar proton-neutron pairing in $N>Z$ nuclei
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We propose a particle number conserving formalism for the treatment of isovector-isoscalar pairing in nuclei with $N>Z$. The ground state of the pairing Hamiltonian is described by a quartet condensate to which is appended a pair condensate formed by the neutrons in excess. The quartets are built by two isovector pairs coupled to the total isospin $T=0$ and two collective isoscalar proton-neutron pairs. To probe this ansatz for the ground state we performed calculations for $N>Z$ nuclei with the valence nucleons moving above the cores $^{16}$O, $^{40}$Ca and $^{100}$Sn. The calculations are done with two pairing interactions, one state-independent and the other of zero range, which are supposed to scatter pairs in time-revered orbits. It is proven that the ground state correlation energies calculated within this approach are very close to the exact results provided by the diagonalization of the pairing Hamiltonian. Based on this formalism we have shown that moving away of N=Z line, both the isoscalar and the isovector proton-neutron pairing correlations remain significant and that they cannot be treated accurately by models based on a proton-neutron pair condensate.
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Neutron-proton (np-) pairing is expected to play an important role in the N Z nuclei. In general, it can have isovector and isoscalar character. The existence of isovector np-pairing is well established. On the contrary, it is still debated whether there is an isoscalar np-pairing. The review of the situation with these two types of pairing with special emphasis on the isoscalar one is presented. It is concluded that there are no substantial evidences for the existence of isoscalar np-pairing.
The quartet condensation model (QCM) is extended for the treatment of isovector and isoscalar pairing in odd-odd N=Z nuclei. In the extended QCM approach the lowest states of isospin T=1 and T=0 in odd-odd nuclei are described variationally by trial functions composed by a proton-neutron pair appended to a condensate of 4-body operators. The latter are taken as a linear superposition of an isovector quartet, built by two isovector pairs coupled to the total isospin T=0, and two collective isoscalar pairs. In all pairs the nucleons are distributed in time-reversed single-particle states of axial symmetry. The accuracy of the trial functions is tested for realistic pairing Hamiltonians and odd-odd N=Z nuclei with the valence nucleons moving above the cores $^{16}$O, $^{40}$Ca and $^{100}$Sn. It is shown that the extended QCM approach is able to predict with high accuracy the energies of the lowest T=0 and T=1 states. The present calculations indicate that in these states the isovector and the isoscalar pairing correlations coexist together, with the former playing a dominant role.
The isoscalar proton-neutron pairing and isovector pairing, including both isovector proton-neutron pairing and like-particle pairing, are treated in a formalism which conserves exactly the particle number and the isospin. The formalism is designed for self-conjugate (N=Z) systems of nucleons moving in axially deformed mean fields and interacting through the most general isovector and isoscalar pairing interactions. The ground state of these systems is described by a superposition of two types of condensates, i.e., condensates of isovector quartets, built by two isovector pairs coupled to the total isospin T=0, and condensates of isoscalar proton-neutron pairs. The comparison with the exact solutions of realistic isovector-isoscalar pairing Hamiltonians shows that this ansatz for the ground state is able to describe with high precision the pairing correlation energies. It is also shown that, at variance with the majority of Hartree-Fock-Bogoliubov calculations, in the present formalism the isovector and isoscalar pairing correlations coexist for any pairing interactions. The competition between the isovector and isoscalar proton-neutron pairing correlations is studied for N=Z nuclei with the valence nucleons moving in the $sd$ and $pf$ shells and in the major shell above $^{100}$Sn. We find that in these nuclei the isovector pairing prevail over the isoscalar pairing, especially for heavier nuclei. However, the isoscalar proton-neutron correlations are significant in all nuclei and they always coexist with the isovector pairing correlations.
We present recent investigations on dipole and quadrupole excitations in spherical skin nuclei, particular exploring their connection to the thickness of the neutron skin. Our theoretical method relies on density functional theory, which provides us with a proper link between nuclear many-body theory of the nuclear ground state and its phenomenological description. For the calculation of the nuclear excited states we apply QPM theory. A new quadrupole mode related to pygmy quadrupole resonance (PQR) in tin isotopes is suggested.
We present expressions for the matrix elements of the spin--spin operator $vec S_{rm n}cdotvec S_{rm p}$ in a variety of coupling schemes. These results are then applied to calculate the expectation value $langlevec S_{rm n}cdotvec S_{rm p}rangle$ in eigenstates of a schematic Hamiltonian describing neutrons and protons interacting in a single-$l$ shell through a Surface Delta Interaction. The model allows us to trace $langlevec S_{rm n}cdotvec S_{rm p}rangle$ as a function of the competition between the isovector and isoscalar interaction strengths and the spin--orbit splitting of the $j=lpm frac{1}{2}$ shells. We find negative $langlevec S_{rm n}cdotvec S_{rm p}rangle$ values in the ground state of all even--even $N=Z$ nuclei, contrary to what has been observed in hadronic inelastic scattering at medium energies. We discuss the possible origin of this discrepancy and indicate directions for future theoretical and experimental studies related to neutron--proton spin--spin correlations.
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