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Register a new userNeutron--proton spin--spin correlations in the ground states of N=Z nuclei
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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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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.
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.
The latest experimental data on nuclei at $^{132}$Sn permit us for the first time to determine the spin-orbit splittings of neutrons and protons in identical orbits in this neutron-rich doubly-magic region and compare the case to that of $^{208}$Pb. Using the new results, which are now consistent for the two neutron-rich doubly magic regions, a theoretical analysis defines the isotopic dependence of the mean field spin-orbit potential and leads to a simple explicit expression for the difference between the spin-orbit splittings of neutrons and protons. The isotopic dependence is explained in the framework of different theoretical approaches.
We analyze recent data from high-momentum-transfer $(p,pp)$ and $(p,ppn)$ reactions on Carbon. For this analysis, the two-nucleon short-range correlation (NN-SRC) model for backward nucleon emission is extended to include the motion of the NN-pair in the mean field. The model is found to describe major characteristics of the data. Our analysis demonstrates that the removal of a proton from the nucleus with initial momentum 275-550 MeV/c is $92^{+8}_{-18}%$ of the time accompanied by the emission of a correlated neutron that carries momentum roughly equal and opposite to the initial proton momentum. Within the NN-SRC dominance assumption the data indicate that the probabilities of $pp$ or $nn$ SRCs in the nucleus are at least a factor of six smaller than that of $pn$ SRCs. Our result is the first estimate of the isospin structure of NN-SRCs in nuclei, and may have important implication for modeling the equation of state of asymmetric nuclear matter.
Gamow-Teller (GT) transitions from high-spin isomers are studied using the sum-rule approach and the shell model. The GT transition strengths from the high-spin isomeric states show a stronger collectivity than those from the ground states in two $N=Z$ nuclei, $^{52}$Fe and $^{94}$Ag. It is argued that the spin-up and spin-down Fermi spheres involved in the GT transitions from the high-spin isomeric states play important roles. These Fermi spheres are analogous to the isospin-up and isospin-down Fermi spheres for the GT transitions from the ground states in $N>Z$ nuclei and create a strong collectivity.
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