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Register a new userProton-neutron pairing in N=Z nuclei: quartetting versus pair condensation
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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.
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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.
Previous studies have shown that the ground state of systems of nucleons composed by an equal number of protons and neutrons interacting via proton-neutron pairing forces can be described accurately by a condensate of $alpha$-like quartets. Here we extend these studies to the low-lowing excited states of these systems and show that these states can be accurately described by breaking a quartet from the ground state condensate and replacing it with an excited quartet. This approach, which is analogous to the one-broken-pair approximation employed for like-particle pairing, is analysed for various isovector and isovector-isoscalar pairing
The isovector and isoscalar components of neutron-proton pairing are investigated in the N=Z unstable nuclei of the textit{fp}-shell through the two-nucleon transfer reaction (p,$^3$He) in inverse kinematics. The combination of particle and gamma-ray detection with radioactive beams of $^{56}$Ni and $^{52}$Fe, produced by fragmentation at the GANIL/LISE facility, made it possible to carry out this study for the first time in a closed and an open-shell nucleus in the textit{fp}-shell. The transfer cross-sections for ground-state to ground-state (J=0$^+$,T=1) and to the first (J=1$^+$,T=0) state were extracted for both cases together with the transfer cross-section ratios $sigma$(0$^+$,T=1) /$sigma$(1$^+$,T=0). They are compared with second-order distorted-wave born approximation (DWBA) calculations. The enhancement of the ground-state to ground-state pair transfer cross-section close to mid-shell, in $^{52}$Fe, points towards a superfluid phase in the isovector channel. For the deuteron-like transfer, very low cross-sections to the first (J=1$^+$,T=0) state were observed both for Niphe, and Fephe, and are related to a strong hindrance of this channel due to spin-orbit effect. No evidence for an isoscalar deuteron-like condensate is observed.
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.
We present a new analysis of the pairing vibrations around 56Ni, with emphasis on odd-odd nuclei. This analysis of the experimental excitation energies is based on the subtraction of average properties that include the full symmetry energy together with volume, surface and Coulomb terms. The results clearly indicate a collective behavior of the isovector pairing vibrations and do not support any appreciable collectivity in the isoscalar channel.
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