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Register a new userThree-body model for an isoscalar spin-triplet neutron-proton pair in $^{102}{rm Sb}$
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We discuss the isoscalar $T=0, S=1$ pairing correlation in the low-lying states of $^{102}{rm Sb}={}^{100}{rm Sn}+p+n$ nucleus. To this end, we employ ${rm core}+p+n$ three-body model with the model space constructed by self-consistent mean-field calculations. The model is developed with both non-relativistic and relativistic effective interactions, the latter of which are found to be more realistic for the present case due to the pseudo-spin symmetry. It turns out that the $(L,S,T)=(0,1,0)$ pairing scheme is strongly hindered in $^{102}$Sb with the relativistic model because of the near degeneracy of the $g_{7/2}$ and $d_{5/2}$ orbitals in the valence space. This pair-breaking effect is clearly seen in the charge-exchange Gamow-Teller-type transitions rather than in the binding energies of $T=0$ and $T=1$ states.
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Background: Spin-triplet ($S=1$) proton-neutron (pn) pairing in nuclei has been under debate. It is well known that the dynamical pairing affects the nuclear matrix element of the Gamow-Teller (GT) transition and the double beta decay. Purpose: We investigate the effect of the pn-pair interaction in the $T=0, S=1$ channel on the low-lying spin-dipole (SD) transition. We then aim at clarifying the distinction of the role in between the SD and GT transitions. Method: We perform a three-body model calculation for the transition ${}^{80}mathrm{Ni}to{}^{80}mathrm{Cu}$, where ${}^{78}mathrm{Ni}$ is taken as a core. The strength of the pair interaction is varied to see the effect on the SD transition-strength distribution. To fortify the finding obtained by the three-body model, we employ the nuclear energy-density functional method for the SD transitions in several nuclei, where one can expect a strong effect. Results: The effect of the $S=1$ pn-pair interaction depends on the spatial overlap of the pn pair and the angular momentum of the valence nucleons; the higher the angular momentum of the orbitals, the more significant the effect. Conclusions: The dynamical $S=1$ pairing is effective even for SD states although the spatial overlap of the pn pair can be smaller than GT states. The SD transition involving high-$ell$ orbitals with the same principal quantum number is strongly affected by the dynamical $S=1$ pairing.
The isoscalar $pn$ pair is expected to emerge in nuclei having the similar proton and neutron numbers but there is no clear experimental evidence for it. We aim to clarify the correspondence between the $pn$ pairing strength in many-body calculation and the triple differential cross section (TDX) of proton-induced deuteron knockout ($p,pd$) reaction on $^{16}$O. The radial wave function of the isoscalar $pn$ pair with respect to the center of $^{16}$O is calculated with the energy density functional (EDF) approach and is implemented in the distorted wave impulse approximation (DWIA) framework. The $pn$ pairing strength $V_0$ in the EDF calculation is varied and the corresponding change in the TDX is investigated. A clear $V_0$ dependence of the TDX is found for the $^{16}$O($p,pd$)$^{14}$N($1_2^+$) at $101.3$ MeV. The nuclear distortion is found to make the $V_0$ dependence stronger. Because of the clear $V_0$-TDX correspondence, the ($p,pd$) reaction will be a promising probe for the isoscalar $pn$ pair in nuclei. For quantitative discussion, further modification of the description of the reaction process will be necessary.
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.
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.
We introduce the concept of neutron-proton two-particle units ($np$-Weisskopf units) to be used in the analysis of the ($^3$He,$p)$ and $(p,^3$He) added{reactions on nuclei} along the N=Z line. These are presented for the conditions relevant to the $(n,j,ell$) orbits expected from $^{16}$O to $^{100}$Sn. As is the case of the Weisskopf units for electromagnetic transitions, the $np$-WUs will provide a simple, yet robust, measure of isoscalar and isovector $np$ pairing collective effects.
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