Neutron-proton Pairing Correlations Research Articles

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-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.

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.

Proton-neutron pairing correlations in the self-conjugate nucleus 42Sc

Collinear laser spectroscopy of the N=Z=21 self-conjugate nucleus 42Sc has been performed at the JYFL IGISOL IV facility in order to determine the change in nuclear mean-square charge radius between the Iπ=0+ ground state and the Iπ=7+ isomer via the measurement of the 42g,42mSc isomer shift. New multi-configurational Dirac-Fock calculations for the atomic mass shift and field shift factors have enabled a recalibration of the charge radii of the 42−46Sc isotopes which were measured previously. While consistent with the treatment of proton-neutron, proton-proton and neutron-neutron pairing on an equal footing, the reduction in size for the isomer is observed to be of a significantly larger magnitude than that expected from both shell-model and ab-initio calculations. The measured nuclear magnetic dipole moment and electric quadruple moment, on the other hand, are in good agreement with simple empirical estimates and shell-model calculations.

Bridging the quartet and pair pictures of isovector proton-neutron pairing

The formal implications of a quartet coherent-state ansatz for proton-neutron pairing are analyzed. Its nonlinear annihilation operators, which generalize the BCS linear quasiparticle operators, are computed in the quartetting case. Their structure is found to generate nontrivial relationships between the many-body correlation functions. The intrinsic structure of the quartet coherent state is detailed as it hints to the precise correspondence between the quartetting picture and the symmetry restored pair condensate picture for the proton-neutron pairing correlations.

Exact isovector pairing in a shell-model framework: Role of proton-neutron correlations in isobaric analog states

We utilize a nuclear shell model Hamiltonian with only two adjustable parameters to generate, for the first time, exact solutions for pairing correlations for light to medium-mass nuclei, including the challenging proton-neutron pairs, while also identifying the primary physics involved. In addition to single-particle energy and Coulomb potential terms, the shell model Hamiltonian consists of an isovector $T=1$ pairing interaction and an average proton-neutron isoscalar $T=0$ interaction, where the $T=0$ term describes the average interaction between non-paired protons and neutrons. This Hamiltonian is exactly solvable, where, utilizing 3 to 7 single-particle energy levels, we reproduce experimental data for 0$^+$ state energies for isotopes with mass $A=10$ through $A=62$ exceptionally well including isotopes from He to Ge. Additionally, we isolate effects due to like-particle and proton-neutron pairing, provide estimates for the total and proton-neutron pairing gaps, and reproduce $N$ (neutron) = $Z$ (proton) irregularity. These results provide a further understanding for the key role of proton-neutron pairing correlations in nuclei, which is especially important for waiting-point nuclei on the rp-path of nucleosynthesis.

Isovector and isoscalar proton-neutron pairing in N>Z nuclei

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.

Isovector pairing and particle-number fluctuation effects on the spectroscopic factors of one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei

Expressions of the spectroscopic factors (SFs) corresponding to one-particle transfer reactions have been established using a schematic definition. These expressions have been derived by taking into account the isovector neutron-proton (np) pairing correlations and a particle-number projection in the framework of the generalized Sharp-BCS (SBCS) method. Recently proposed expressions of the projected wave-functions of odd-mass nuclei have been used for this purpose. The formalism has first been tested using the single-particle energies of the schematic picket-fence model. It is shown that the np pairing and particle-number fluctuation effects are far from negligible and they depend on the pairing gap parameter values. Their behavior is not the same when the parent nuclei are even-even or odd. Predictions dealing with the SFs corresponding to one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei have then been established within the framework of the realistic Woods-Saxon model. It is shown that the np pairing effect as well as the particle-number projection effect are important and thus have to be included in future calculations of the SF corresponding to these kinds of reactions.

Neutron-proton pairing correlations and deformation for N=Z nuclei in the pf shell within the deformed BCS and Hartree-Fock-Bogoliubov approach

We investigated neutron-proton pairing correlations effects on the shell evolution of ground-state energies by the deformation for $N=Z$ nuclei in $pf$ shell, such as $^{44}\mathrm{Ti}$, $^{48}\mathrm{Cr}$, $^{52}\mathrm{Fe}$, $^{64}\mathrm{Ge}$, $^{68}\mathrm{Se}$, $^{72}\mathrm{Kr}$, and $^{76}\mathrm{Sr}$. We started from a simple shell-filling model constructed by a deformed Woods-Saxon potential with ${\ensuremath{\beta}}_{2}$ deformation, and included pairing correlations in the residual interaction, which give rise to smearing of the Fermi surface revealing interesting evolution of the Fermi energy along the shell evolution. In this work, like-pairing and unlike-pairing correlations decomposed as isovector $T=1$ and isoscalar $T=0$ components are explicitly taken into account. Finally, we estimate ground-state energies comprising the mean-field energy, the pairing energy, and the self-energy due to the pairing correlations, in terms of the deformation. The enhanced $T=0$ pairing interaction supports oblate deformations for $^{72}\mathrm{Kr}$ and $^{68}\mathrm{Se}$, whose features are different from other $pf$-shell $N=Z$ nuclei considered in this work.

Neutron--Proton Pairing Correlations in a Single $l$-shell Model

The long standing problem of neutron-proton pairing correlations is revisited by employing the Hartree-Fock-Bogoliubov formalism with neutron-proton mixing in both the particle-hole and particle-hole channels. We compare numerical calculations performed within this method with an exact pairing model based on the $SO(8)$ algebra. The neutron-proton mixing is included in our calculations by performing rotations in the isospin space using the isocranking technique.

Investigating neutron-proton pairing in sd -shell nuclei via (p,He3) and (He3,p) transfer reactions

Neutron-proton pairing correlations are investigated in detail via $np$ transfer reactions in $N=Z\phantom{\rule{4pt}{0ex}}sd$-shell nuclei. In particular, we study the cross-section ratio of the lowest ${0}^{+}$ and ${1}^{+}$ states as an observable to quantify the interplay between $T=0$ (isoscalar) and $T=1$ (isovector) pairing strengths. The experimental results are compared to second-order distorted-wave Born approximation calculations with proton-neutron amplitudes obtained in the shell-model formalism using the universal $sd$-shell interaction B. Our results suggest underestimation of the nonneglible isoscalar pairing strength in the shell-model descriptions at the expense of the isovector channel.

Calculations of the β-decay half-lives of neutron-deficient nuclei**Supported by National Nature Science Foundation of China (11535004, 11375086, 11120101005, 11175085 and 11235001), 973 Nation Major State Basic Research and Development of China (2013CB834400) and Science and Technology Development Fund of Macau (020/2014/A1 and 039/2013/A2)

In this work, β+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation (QRPA), where neutron-neutron, proton-proton and neutron-proton (np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov (HFB) transformation. In addition to the pairing interaction, the Brückner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions. Calculations are performed for even-even proton-rich isotopes ranging from Z=24 to Z=34. It is found that the np pairing interaction plays a significant role in β-decay for some nuclei far from stability. Compared with other theoretical calculations, our calculations show good agreement with the available experimental data. Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference.

Effects of deformation and neutron-proton pairing on the Gamow-Teller transitions forMg24,26in a deformed quasiparticle random-phase approximation

We investigate effects of neutron-proton ($np$) pairing correlations on the Gamow-Teller (GT) transition of $^{24,26}\mathrm{Mg}$ by explicitly taking into account deformation effects. Our calculation is performed by a deformed quasiparticle random phase approximation (DQRPA) which includes the deformation at the Bardeen-Cooper-Schrieffer and RPA stage. In this paper, we include the $np$ pairing as well as neutron-neutron ($nn$) and proton-proton ($pp$) paring correlations to the DQRPA. Our new formalism is applied to the GT transition of well-known deformed Mg isotopes. The $np$ pairing effect is found to affect more or less the GT distribution of $^{24}\mathrm{Mg}$ and $^{26}\mathrm{Mg}$. But the deformation effect turns out to be much larger than the $np$ paring effect because the Fermi surfaces smear more widely by the deformation rather than the $np$ pairing correlations. Correlations between the deformation and the $np$ pairing effects and their ambiguities are also discussed with the comparison to experimental GT strength data by triton and $^{3}\mathrm{He}$ beams.

Proton-neutron versusα-like correlations aboveSn100

It is known that the $\ensuremath{\alpha}$ particle reduced width has the largest values in the region above $^{100}\mathrm{Sn}$, and this behavior is usually attributed to the proton-neutron correlations. To reproduce the reduced $\ensuremath{\alpha}$-decay width we use an additional pocket-like surface potential in the single-particle mean field that simulates four-body correlations. We show that the strength of this interaction has a universal linear dependence on the experimental reduced width above the double magic nuclei $^{100}\mathrm{Sn}$ and $^{208}\mathrm{Pb}$. Moreover, we demonstrate that proton-neutron pairing correlations have a small influence on this dependence and therefore cannot explain the larger reduced decay widths above $^{100}\mathrm{Sn}$. We give an indication of the possibility of detecting $\mathrm{Sn}+n\ensuremath{\alpha}$ structures as dipole Pigmy-like resonances.

Isoscalar-isovector proton-neutron pairing and quartet condensation inN=Znuclei

We show that the correlations generated in the ground state of $N=Z$ nuclei by the isovector and isoscalar pairing forces can be treated with high precision as a condensate of alpha-like quartets. To treat these correlations, the quartet condensation model (QCM) is extended to the treatment of spherically symmetric isovector $(T=1,J=0)$ and isoscalar $(T=0,J=1)$ pairing forces . Within QCM we discuss the competition between $T=1$ and $T=0$ pairing correlations in the case of a two-level model and for $N=Z$ nuclei with nucleons moving in the open shells above $^{16}$O, $^{40}$Ca and $^{100}$Sn. We show that in $N=Z$ systems isovector and isoscalar proton-neutron pairing correlations always coexist.

Interplay between proton-neutron pairing and deformation in self-conjugated medium mass nuclei

We employ a model combining self-consistent mean-field and shell model techniques to study the competition between particle-like and proton-neutron pairing correlations in fp-shell even-even self-conjugate nuclei. Deformation effects are realistically and microscopically described. The resulting approach can give a precise description of pairing correlations and eventually treat the coexistence of different condensate formed of pairs with different total spin/ isospin. The standard BCS calculations are systematically compared with approaches including correlation effects beyond the independent quasi-particle picture. The competition between proton-neutron correlations in the isoscalar and isovector channels is also analyzed, as well as their dependence on the deformation properties.

Proton–neutron pairing in N = Z nuclei: Quartetting versus pair condensation

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 100Sn. We find that in these nuclei the isovector pairing prevail over the isoscalar pairing, especially for heavier nuclei.

Effects of deformation on the coexistence between neutron-proton and particle-like pairing inN=Zmedium-mass nuclei

A model combining self-consistent mean-field and shell-model techniques is used to study the competition between particle like and proton-neutron pairing correlations in fp-shell even-even self-conjugate nuclei. Results obtained using constant two-body pairing interactions as well as more sophisticated interactions are presented and discussed. The standard BCS calculations are systematically compared with more refined approaches including correlation effects beyond the independent quasi-particle approach. The competition between proton-neutron correlations in the isoscalar and isovector channels is also analyzed, as well as their dependence on the deformation properties. Besides the expected role of the spin-orbit interaction and particle number conservation, it is shown that deformation leads to a reduction of the pairing correlations. This reduction originates from the change of the single-particle spectrum and from a quenching of the residual pairing matrix elements. The competition between isoscalar and isovector pairing in the deuteron transfer is finally addressed. Although a strong dependence the isovector pairing correlations with respect to nuclear deformation is observed, they always dominate over the isoscalar ones.

β-decay half-lives including first-forbidden contributions for neutron-rich Zn isotopes in the extended QRPA with neutron-proton pairing

The β decays of neutron-rich Zn isotopes are investigated within the extended quasiparticle random-phase approximation, where neutron-neutron, proton-proton, and neutron-proton pairing correlations are considered in the similar manner. The Brückner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions in addition to the pairing interactions. Contributions from both allowed Gamow-Teller and first-forbidden transitions are considered, and β-decay half-lives together with β-delayed neutron emission probabilities are calculated. The calculated results are found to agree well with the available experimental data.

Proton-neutron pairing correlations in the nuclear shell model

Systematic shell-model calculations in 2p1f shell nuclei are reported, to assess the relative importance of isoscalar and isovector pairing in the presence of nuclear deformation and spin-orbit effects. Results are presented for three N = Z nuclei, 44Ti, 46V and 48Cr.