Neutron-proton Pairing Research Articles

Short-Range Correlations and Urca Process in Neutron Stars.

Recent measurements of high-momentum correlated neutron-proton pairs at JLab suggest that the dense nucleonic component of the compact stars contains a fraction of high-momentum neutron-proton pairs that is not accounted for in the familiar Fermi-liquid theory of the neutron-proton fluid mixture. We compute the rate of the Urca process in compact stars taking into account the non-Fermi liquid contributions to the proton's spectral widths induced by short-range correlations. The Urca rate differs strongly from the Fermi-liquid prediction at low temperatures; in particular, the high threshold on the proton fraction precluding the Urca process in neutron stars is replaced by a smooth increase with the proton fraction. This observation may have a profound impact on the theories of cooling of compact stars.

Exploring Short-Range Correlations in symmetric nuclei: Insights into contacts and entanglement entropy

The Short-Range Correlations between nucleons in nuclei are regarded as a complex system. We investigate the relationship between the orbital entanglement entropy of SRCs Sij in nuclear structures and Tan contact cij, and find that the orbital entanglement entropies and Tan contacts corresponding to proton-proton SRC pairs and neutron-proton SRC pairs in nuclei demonstrate a scaling relation. More specifically, the proportionality of entanglement entropy between proton-proton pairs and neutron-proton pairs is directly related to the ratio of nuclear contacts within the atomic nucleus, demonstrating an approximate ratio of 2.0. Our research suggests that this scaling relationship should hold true for all symmetric nuclei, furthermore, we offer a possible explanation for this phenomenon.

Neutron-proton pairing in the unstable N=Z nuclei of the f-shell through two-nucleon transfer reactions

Pair transfer is a unique tool to study pairing correlations in nuclei. Neutron-proton pairing is investigated in the N=Z nuclei of the f-shell, through the reaction (p,3He) in inverse kinematics, that allows to populate at the same time the lowest J=0+, T=1 (isovector pairing) state and J=1+, T=0 (isoscalar pairing) state. Radioactive beams of 56Ni and 52Fe produced by fragmentation at the GANIL/LISE facility combined with particle and gamma-ray detection make it possible to carry out this study from 48Cr (mid-shell nucleus) to 56Ni (doubly-magic nucleus). The cross-sections were extracted and compared with second-order distorted-wave born approximation (DWBA) calculations performed with neutron-proton amplitudes obtained from shell model calculations with GXPF1 interaction. Very low cross-sections for the J=1+,T=0 state (isoscalar channel) were observed. The cross-section for 56Ni is one of order of magnitude lower than for 40Ca showing a strong reduction of the isoscalar channel in the f-shell as compared to the sd-shell. On the other hand, the increase of the cross-section towards the middle of the shell for the isovector channel points towards a possible superfluid phase.

Proton-neutron pairing, quartet condensation and α− transfer in N=Z nuclei

In the past years various studies have shown that the proton-neutron pairing correlations in N=Z nuclei can be accurately described by a condensate of α-like quartets. It was also shown that the α-like quartets, defined as 4- body collective structures built with two neutrons and two protons, are also able to describe the correlations induced by general two-body interactions of shell-model type. In this paper we summarise the studies mentioned above and then we discuss how the fingerprints of the quartet condensation could be investigated by α-transfer reactions.

Proton and Neutron Pairing Properties within a Mixed Volume-Surface Pairing Type Using the Hartree–Fock–Bogolyubov Theory

This work aims at systematic investigations of the proton and neutron pairing properties and Fermi energies in the region from the proton drip-line to the neutron drip-line. In order to obtain a more accurate mass formula with the Skyrme (SKI3) force, the global descriptive power of the Skyrme–Hartree–Fock–Bogoliubov model for pairing properties is applied. Systematic Skyrme–HFB calculations with a mixed volume-surface pairing are carried out to study the ground-state proton pairing gap, neutron and proton pairing energies, and the neutron and proton Fermi energies for about 2095 even-even nuclei ranging from 2 ≤ Z ≤ 110 to 2 ≤ N ≤ 236 . The calculated values of proton pairing gaps are compared with experimental data, by using the difference-point formulas Δ(3), Δ(4), and Δ(5), and compared with the proton pairing gap in the Lipkin–Nogami model. It is shown that the Skyrme (SKI3) force with the mixed volume-surface pairing can be successfully used for describing the ground-state proton pairing gap, proton and neutron pairing energies, and proton and neutron Fermi properties of the investigated nuclei, in particular, the neutron-rich nuclei and the exotic nuclei near the neutron drip-line. On the other hand, the calculated proton pairing gap shows the acceptable agreement with the available experimental values of the proton pairing gap with the use of the difference-point formulas Δ(3), Δ(4), and Δ(5) and with the data of the Lipkin–Nogami model over the whole nuclear chart.

Correlations between neutrinoless double- β , double Gamow-Teller, and double-magnetic decays in the proton-neutron quasiparticle random-phase approximation framework

We explore the relation between the nuclear matrix elements of neutrinoless double-beta ($0\nu\beta\beta$) decay and two other processes: double Gamow-Teller (DGT) and double-magnetic dipole (M1M1) transitions, with focus on medium-mass to heavy nuclei studied with the proton-neutron quasiparticle random-phase approximation (pnQRPA) framework. We explore a wide span of isoscalar proton-neutron pairing strengths covering the typical range of values that describe well $\beta$- and two-neutrino $\beta\beta$-decay data. Our results indicate good linear correlations between $0\nu\beta\beta$ and both DGT and M1M1 matrix elements. Together with future measurements of DGT and M1M1 transitions, these correlations could help constrain the values of the $0\nu\beta\beta$-decay nuclear matrix elements.

Neutrinoless ββ -decay nuclear matrix elements from two-neutrino ββ -decay data

We study two-neutrino ($2\nu\beta\beta$) and neutrinoless double-$\beta$ ($0\nu\beta\beta$) decays in the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) frameworks. Calculating the decay half-life of several dozens of nuclei ranging from calcium to xenon with the shell model, and of $\beta\beta$ emitters with a wide range of proton-neutron pairing strengths in the pnQRPA, we observe good linear correlations between $2\nu\beta\beta$- and $0\nu\beta\beta$-decay nuclear matrix elements for both methods. We then combine the correlations with measured $2\nu\beta\beta$-decay half-lives to predict $0\nu\beta\beta$-decay matrix elements with theoretical uncertainties based on our systematic calculations. Our results include two-body currents and the short-range $0\nu\beta\beta$-decay operator.

Proton-neutron pairing, α-like quarteting and ground/excited states of N=Z nuclei

Various studies have shown that the proton-neutron (pn) pairing correlations can be accurately described not by a condensate of Cooper pairs, as considered in the majority of mean-field calculations, but by a condensate of α-like quartets. After a short review of the quartet condensate model (QCM), it is discussed the effect of the pn pairing on the ground states of N = Z nuclei, analysed recently in the framework of Skyrme-HF+QCM calculations. An interesting aspect pointed out by these calculations is the strong interdependence between all types of pairing correlations. In particular, when the isoscalar pn pairing channel is switched on, the pairing correlations are redistributed among all the pairing channels without changing significantly the total pairing energy. Due to this reason, for the majority of N = Z nuclei, the binding energy is not affected much when the isoscalar pairing channel is switched on. Yet, in all calculations which include both the isovector and the isoscalar pairing forces, the isoscalar pairing correlations contribute significantly to the binding energies and coexist always with the isovector pn pairing. Finally it is presented a recent extension of the QCM approach to the excited stated of pn pairing Hamiltonians. It will be shown that the low-lying excited states of these Hamiltonians can be described by breaking a quartet from the ground state condensate and replacing it with an “excited” quartet, an approach which is analogous to the one-broken-pair approximation which is commonly used for like-particle systems.

Observation of the proton emitter {}_{,57}^{116}La59

The quantum tunneling and emission of a single constituent nucleon provide a beautifully simple and unique window into the complex properties of atomic nuclei at the extreme edge of nuclear existence. In particular, for odd-odd proton emitting nuclides, the associated decay energy and partial half-life can be used to probe the correlations between the valence neutrons and protons which have been theoretically predicted to favour a new type of nuclear superfluidity, isoscalar neutron-proton pairing, for which the experimental “smoking gun" remains elusive. In the present work, proton emission from the lanthanum isotope {}_{,57}^{116}La59, 23 neutrons away from the only stable isotope {}_{,57}^{139}La82, is reported. 116La nuclei were synthesised in the fusion-evaporation reaction 58Ni(64Zn, p5n)116La and identified via their proton radioactivity using the mass spectrometer MARA (Mass Analysing Recoil Apparatus) and the silicon detectors placed at its focal plane. Comparisons of the measured proton energy (Ep = 718 ± 9 keV) and half-life (T1/2 = 50 ± 22 ms) with values calculated using the Universal Decay Law approach indicate that the proton is emitted with an orbital angular momentum l = 2 and that its emission probability is enhanced relative to its closest, less exotic, odd-even lanthanum isotope ({}_{,57}^{117}La60) while the proton-emission Q-value is lower. We propose this to be a possible signature for the presence of strong neutron-proton pair correlations in this exotic, neutron deficient system. The observations of γ decays from isomeric states in 116La and 117La are also reported.

Pairing tendencies of nuclei

Supplementing the experimental data of excited states of nuclei with those of the canonical assemble, we determine the temperature-dependent specific heat formula, with finite system corrections, in the mass range of 22<A<206. Phase transition structures in shapes of peaks in the specific heat diagram have been identified as distinct pairing processes and are used in comparison to the pairing energy correction term (Gilbert and Cameron, 1965). Through mass dependent pairing gap equations the addition of the proton–neutron pairing procedure and finally the distinction of the pairing tendency, of each nuclei, was made possible.

Improved measurement of the 02+→01+E0 transition strength for Se72 using the SPICE spectrometer

The selenium isotopes lie at the heart of a tumultuous region of the nuclear chart where shape coexistence effects grapple with neutron-proton pairing correlations, triaxiality, and the impending proton drip line. In this work, a study of $^{72}\mathrm{Se}$ by internal conversion electron and $\ensuremath{\gamma}$-ray spectroscopy was undertaken with the SPICE and TIGRESS arrays. New measurements of the branching ratio and lifetime of the ${0}_{2}{}^{+}$ state were performed, yielding a determination of ${\ensuremath{\rho}}^{2}(E0;{0}_{2}{}^{+}\ensuremath{\rightarrow}{0}_{1}{}^{+})=29(3)$ milliunits. Two-state mixing calculations were performed that highlighted the importance of interpretation of such $E0$ strength values in the context of shape coexistence.

Symmetry breaking of Gamow-Teller and magnetic-dipole transitions and its restoration in calcium isotopes

Nuclear magnetic-dipole (M1) and Gamow-Teller (GT) transitions provide insight into the spin-isospin properties of atomic nuclei. By considering them as unified spin-isospin transitions, the M1/GT transition strengths and excitation energies are subject to isospin symmetry. The excitation properties associated to the M1/GT symmetry need to be clarified within consistent theoretical approach. In this work, the relationship between the M1 and GT transitions in Ca isotopes is investigated in a unified framework based on the relativistic energy-density functional (REDF) with point-coupling interactions, using the relativistic quasi-particle random-phase approximation (RQRPA). It is shown that the isovector-pseudovector (IV-PV) residual interaction affects both transitions, and the symmetry of M1 and giant-GT transitions is disrupted by this interaction in closed-shell nuclei. In open-shell Ca isotopes, the proton-neutron pairing in the residual RQRPA interaction also plays a role in GT transitions. Due to the interplay between these interactions, the M1/GT symmetry can be restored especially in the $^{42}$Ca nucleus, i.e., the giant-GT strength can become comparable to that of the M1 mode in terms of the unified spin-isospin transitions by adjusting the PN-pairing strength to reproduce the experimental low-lying GT-excitation energies. The mirror symmetry of both M1 and GT transitions is also demonstrated for open-shell mirror partners, $^{42}$Ca and $^{42}$Ti. Further improvements are required to achieve simultaneous reproduction of M1 and GT-transition energies in the REDF framework.

A Hartree-Fock-Bogoliubov Study on the Pairing Correlations of the Isotopes of Cobalt

Background: The phenomena of nucleon pairing could be outlined from the Bethe-Weizäcker semi-empirical formula, from which the nuclear properties, viz. the binding energy, stability, shape etc. could be clearly sketched. Though the pairing correlation seems to be a small correction to the binding energy term, it plays a determinative role in defining the structure of nuclear systems. The addition to the binding energy in turn affects the position of the isotope on the dripline and hence increases the stability.&#x0D; Purpose: To study the effects of pairing on the ground state properties of the isotopes of Cobalt.&#x0D; Methods: We use Hartree-Fock-Bogoliubov (HFB) theory for the study. The general wave functions for the HFB approach are determined from variational principle. The eigen functions for the Hamiltonian are connected with the particle operators through the Bogoliubov transformations. The Hartree-Fock energy is obtained through the minimization of the variational parameter and the HFB equation is solved by iterative diagonalization by restoring the particle number symmetry.&#x0D; Results: The HFB analysis substantiates the effect of pairing correlation on binding energies, neutron and proton pairing energies, neutron and proton pairing gaps and one- and two-neutron separation energies of the Cobalt isotopes. The binding energies and one and two-neutron separation energies match with the experimental values and for pairing energies and pairing gaps, the regions where pairing is significant and the effects of shell closure at the vicinity of magic configuration of neutrons could be recognized.&#x0D; Conclusion: The Hartree-Fock-Bogoliubov calculations of the effects of pairing could be used as an efficient tool to study the nuclear structure. It can be ascertained that pairing plays an important role in determining the ground state properties of atomic nuclei.

Characterization of the inner edge of the neutron star crust

The poorly known crustal equation of state plays a critical role in many observational phenomena associated with a neutron star. Using semi-classical Monte Carlo simulations, we explore the possible configurations of the inner edge of the neutron-star crust for a variety of baryon densities and proton fractions. Applying the Kirkwood--Buff theory to these two-component systems, we observe how the isothermal compressibility reaches a maximum when isolated non-symmetric clusters are formed in an extremely dilute neutron gas. To determine the neutron fraction, we suggest a geometrical model based on the behavior of the proton-neutron pair correlation function. Accordingly, the equation of state of the inner crust is calculated, illustrating that the nuclear energy in beta-equilibrium follows a power-law behavior with baryon density. As a possible astrophysical outcome of this study, our results could help refine the mass-radius relation. Finally, our results pave the way towards further investigations of the impact of the proton-neutron pair correlation function on transport properties within the neutron-star crust.

Neutron-proton pairing in the N=Z radioactive fp-shell nuclei 56Ni and 52Fe probed by pair transfer

The isovector and isoscalar components of neutron-proton pairing are investigated in the N=Z unstable nuclei of the fp-shell through the two-nucleon transfer reaction (p,3He) in inverse kinematics. The combination of particle and gamma-ray detection with radioactive beams of 56Ni and 52Fe, 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 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 σ(0+,T=1)/σ(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 52Fe, 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 56Ni(p,3He) and 52Fe(p,3He) 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.

Proton-neutron pairing and binding energies of nuclei close to the N=Z line

We analyze the contribution of isovector and isoscalar proton-neutron pairing to the binding energies of even-even nuclei with $N\ensuremath{-}Z=0, 2, 4$ and atomic mass $20&lt;A&lt;100$. The binding energies are calculated in the mean-field approach by coupling a Skyrme-type functional to an isovector-isoscalar pairing force of zero range. The latter is treated in the framework of quartet condensation model (QCM), which conserves exactly the particle number and the isospin. The interdependence of pairing and deformation is taken into account by performing self-consistent Skyrme-HF $+$ QCM calculations in the intrinsic system. It is shown that the binding energies are not changing much when the isoscalar pairing is switched on. This fact is related to the off-diagonal matrix elements of the pairing force, which are less attractive for the isoscalar force, and to the competition between the isoscalar and isovector pairing channels.

Neutron-proton pair transfer reactions and corresponding Weisskopf-type units

We introduce the concept of neutron-proton two-particle units (np-Weisskopf units) to be used in the analysis of the (3He,p) and (p,3He) reactions on nuclei along the N=Z line. These are presented for the conditions relevant to the (n,j,ℓ) orbits expected from 16O to 100Sn. As is the case of the Weisskopf units for electromagnetic transitions, the np-WU's will provide a simple, yet robust, measure of isoscalar and isovector np pairing collective effects.

Isoscalar pairing correlations by the tensor force in the ground states of C12, O16, Ne20 , and S32 nuclei

We investigate roles of the tensor force (TF) on the pairing correlations in the ground-state structure of $^{12}\mathrm{C}, ^{16}\mathrm{O}, ^{20}\mathrm{Ne}$, and $^{32}\mathrm{S}$ nuclei within a deformed BCS model. For pairing matrix elements, we exploit the Brueckner $G$ matrix derived from the charge-dependent Bonn potential. In particular, the isoscalar (IS) neutron-proton ($np$) pairing is studied in detail in relation to spin-triplet even TF in the nucleon-nucleon interaction. Detailed analyses of the $np$ pairing and possible enhancement of the IS channel are performed by focusing on roles of attractive spin-triplet even and repulsive spin-triplet odd channels in the TF for the ground states of the nuclei with some deformation. It is also shown that the TF may play a crucial role of properly interpreting the experimental data of a two-nucleon knockout reaction from $^{12}\mathrm{C}$.

Axial shape and pairing evolution of 82−106Zr, 86−112Mo, 90−116Ru and 94−122Pd isotopic chains in the framework of the deformed BCS approach

The Deformed Bardeen–Cooper–Schrieffer (DBCS) approach is used to study the axial shape evolution of even–even [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] isotopic chains. Regarding the residual interaction, both like-particle pairing and unlike-particle pairing are considered in this study. It is found that, in general, the proton–neutron pairing does not affect the ground state shapes of nuclei except for few nuclei, where the inclusion of proton–neutron pairing predicts spherical shape in the ground state rather than a deformed one in case of considering only like-particle pairing. Pairing gaps, energies and strengths of both like- and unlike-pairing modes are discussed. One can conclude that the contribution of proton–neutron pairing to the total pairing energy is not negligible, even if the neutron excess number is high.

Np-Pair Correlations in the Isovector Pairing Model

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.