Isovector Channel Research Articles

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.

Comparative study on charge radii and their kinks at magic numbers

Isotope dependences of charge radii, i.e., isotope shifts, calculated by the Skyrme Hartree-Fock, the relativistic mean-field, and the relativistic Hartree-Fock calculations are compared against the experimental data of magic and semimagic nuclei. It is found that the tensor interaction plays a role in reproducing the ``kink'' behavior, irregularity of isotope shifts at the neutron magic number, in the relativistic Hartree-Fock approach. With several Skyrme models, it is found that the kink behavior can be reproduced with the spin-orbit interaction having nonzero isovector channel. The single-particle orbitals near the Fermi energy are crucial to determine the kink size. The effects of the symmetry energy and the pairing interaction are also discussed in relation to the kink behavior.

Nucleonic metamodeling in light of multimessenger, PREX-II, and CREX data

The need to reconcile our understanding of the behavior of hadronic matter across a wide range of densities, especially at the time when data from multimessenger observations and novel experimental facilities are flooding in, has provided new challenges to the nuclear models. Particularly, the density dependence of the isovector channel of the nuclear energy functionals seems hard to pin down if experiments like PREX-II (or PREX) and CREX are required to be taken on the same footing. We put to test this anomaly in a semiagnostic modeling technique by performing a full Bayesian analysis of static properties of neutron stars, together with global properties of nuclei as binding energy, charge radii and neutron skin calculated at the semiclassical level. Our results show that the interplay between bulk and surface properties, and the importance of high-order empirical parameters that effectively decouple the subsaturation and the supersaturation density regime, might partially explain the tension between the different measurements and observations. If the surface behaviors, however, are decoupled from the bulk properties, then we found a rather harmonious situation among experimental and observational data.

Spatial correlation of a particle-hole pair with a repulsive isovector interaction

We study the spatial correlation of a particle-hole pair in the isovector channel in $^{56}$Co and $^{40}$K nuclei. To this end, we employ the Hartree-Fock+Tamm-Dancoff approximation with the Skyrme interaction. We find a large concentration of the two-body density at positions where the neutron particle and the proton hole states locate on the opposite side to each other with respect to the core nucleus. This feature originates from a repulsive nature of the isovector residual interaction, which is in stark contrast to the dineutron correlation with an attractive pairing interaction between the valence neutrons discussed e.g., in $^{11}$Li and $^6$He. A possible experimental implication of the repulsive correlation is also discussed.

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.

Symmetry energy effects on the properties of hybrid stars

Symmetry energy is an important part of the equation of state of isospin asymmetry matter. However, the huge uncertainties of symmetry energy remain at suprasaturation densities, where the phase transitions of strongly interacting matter and the quark matter symmetry energy are likely to be taken into account. In this work, we investigate the properties of symmetry energy by using a hybrid star with the hadron-quark phase transition. The interaction among strange quark matter (SQM) in hybrid stars is based on a 3-flavor NJL model with different vector and isovector channels, while the equation of state (EOS) of the nuclear matter is obtained by considering the ImMDI-ST interaction by varying the parameters x, y, and z. Our results indicate that the various parameters and coupling constants of the interactions from the ImMDI-ST and NJL model can lead to widely different trends for the symmetry energy in the hadron-quark mixed phase and the different onsets of the hadron-quark phase transition. In addition, it has been found that the radii and tidal deformabilities of hybrid stars constrain mostly the density dependence of symmetry energy while the observed maximum masses of hybrid stars constrain mostly the EOS of symmetric nuclear and quark matter.

Variational approximations to exact solutions in shell-model valence spaces: Systematic calculations in the sd shell

We study the ability of variational approaches based on self-consistent mean-field and beyond-mean-field methods to reproduce exact energies and electromagnetic properties of the nuclei defined within the $sd$-shell valence space using the non-trivial USD Hamiltonian. In particular, Hartree-Fock-Bogoliubov (HFB), variation after particle-number projection (VAPNP) and projected generator coordinate methods (PGCM) are compared to exact solutions {obtained by} the full diagonalization of the Hamiltonian. We analyze the role played by the proton-neutron ($pn$) mixing as well as the quadrupole and pairing degrees of freedom (including both isoscalar and isovector channels) in the description of the spectra of even-even, even-odd and odd-odd nuclei in the whole $sd$-shell.

Nuclear Equation of State in the Relativistic Point-Coupling Model Constrained by Excitations in Finite Nuclei

Nuclear equation of state is often described in the framework of energy density functional. However, the isovector channel in most functionals has been poorly constrained, mainly due to rather limited available experimental data to probe it. Only recently, the relativistic nuclear energy density functional with an effective point-coupling interaction was constrained by supplementing the ground-state properties of nuclei with the experimental data on dipole polarizability and isoscalar monopole resonance energy in 208Pb, resulting in DD-PCX parameterization. In this work, we pursue a complementary approach by introducing a family of 8 relativistic point-coupling functionals that reproduce the same nuclear ground-state properties, including binding energies and charge radii, but in addition have a constrained value of symmetry energy at saturation density in the range J = 29, 30, …, 36 MeV. In the next step, this family of functionals is employed in studies of excitation properties such as dipole polarizability and magnetic dipole transitions, and the respective experimental data are used to validate the optimal choice of functional as well as to assess reliable values of the symmetry energy and slope of the symmetry energy at saturation.

Effects of longitudinal short-distance constraints on the hadronic light-by-light contribution to the muon mathbf {g-2}

We present a model-independent method to estimate the effects of short-distance constraints (SDCs) on the hadronic light-by-light contribution to the muon anomalous magnetic moment a_mu ^text {HLbL}. The relevant loop integral is evaluated using multi-parameter families of interpolation functions, which satisfy by construction all constraints derived from general principles and smoothly connect the low-energy region with those where either two or all three independent photon virtualities become large. In agreement with other recent model-based analyses, we find that the SDCs and thus the infinite towers of heavy intermediate states that are responsible for saturating them have a rather small effect on a_mu ^text {HLbL}. Taking as input the known ground-state pseudoscalar pole contributions, we obtain that the longitudinal SDCs increase a_mu ^text {HLbL} by (9.1pm 5.0) times 10^{-11}, where the isovector channel is responsible for (2.6pm 1.5) times 10^{-11}. More precise estimates can be obtained with our method as soon as further accurate, model-independent information about important low-energy contributions from hadronic states with masses up to 1–2 GeV become available.

Erratum: Nucleon form factors and root-mean-square radii on a (10.8 fm)4 lattice at the physical point [Phys. Rev. D 99 , 014510 (2019)

We present the nucleon form factors and root-mean-square (RMS) radii measured on a (10.8 fm$)^4$ lattice at the physical point. We compute the form factors at small momentum transfer region in $q^2\le 0.102$ GeV$^2$ with the standard plateau method choosing four source-sink separation times $t_{\rm sep}$ from 0.84 to 1.35 fm to examine the possible excited state contamination. We obtain the electric and magnetic form factors and their RMS radii for not only the isovector channel but also the proton and neutron ones without the disconnected diagram. We also obtain the axial-vector coupling and the axial radius from the axial-vector form factor. We find that these three form factors do not show large $t_{\rm sep}$ dependence in our lattice setup. On the other hand, the induced pseudoscalar and pseudoscalar form factors show the clear effects of the excited state contamination, which affect the generalized Goldberger-Treiman relation.

Superdeformation in Pb isotopes with large neutron excess

Covariant Density Functional theory (CDFT) is used to investigate superdeformation in Pb isotopes on the neutron rich side of the periodic table. Energy surfaces and deformation parameters in this region are calculated by solving the constrained Relativistic Hartree Bogoliubov (RHB) equations. We use the parameter set DDME2, which has an explicit density dependence as well in the isoscalar as in the isovector channel together with the finite range pairing force DIS of Gogny. With increasing neutron number we find a characteristic pattern for superdeformed minima in these nuclei.

Effects of the isoscalar and isovector interaction on the ground-state magnetic moments of odd-mass 137–145Ce nuclei

A systematic study of the magnetic properties of deformed odd-neutron 137–145Ce isotopes using the microscopic quasiparticle phonon nuclear model (QPNM) has been presented. The QPNM includes residual spin–spin interaction in both isoscalar and isovector channels. The analysis shows that in the isoscalar channel contributions to the magnetic moment coming from the neutron and proton systems practically cancel out each other. On the other hand, in the isovector channel, the coherent contribution coming from the quasiparticle–phonon interactions leads to a spin polarization (core polarization), which is important for determination of the quenched spin gyromagnetic factors (gs). The quenched spin gyromagnetic factors so called [Formula: see text] have been found to range from [Formula: see text] to [Formula: see text] in the odd-mass 137–145Ce isotopic chain, which is similar to its phenomenological value ([Formula: see text] between [Formula: see text] and [Formula: see text]). By taking into consideration the core polarization effects, the available experimental data are satisfactorily reproduced with an accuracy of 0.01μN–0.1μN.

Magnetic properties of K = 1/2 states in deformed odd-mass nuclei

A method for calculation of the ground-state magnetic moment, effective spin gyromagnetic factors and rotational decoupling parameter of the K=1/2 states in deformed odd-mass nuclei has been described by using the concept of the Quasiparticle Phonon Nuclear Model (QPNM). The model includes a Woods-Saxon potential as a mean field with pairing correlations and the residual separable spin-spin force in both isovector and isoscalar channels. The method has been employed to investigate K=1/2 ground-state magnetic properties of 169Er, 167,169Tm, and 171Yb nuclei, as an example. It has been shown that two different quenched spin gyromagnetic factors, i.e., gsz(eff.) and gs+(eff.) have a significant effect on the magnetic properties of K=1/2 states in odd-mass nuclei. Whereas the first one is occurred due to the interaction between the valence nucleon and IπK=1+0 excitations of the core, second one is associated with the coupling of the valence nucleon to IπK=1+1 excitations of the core. The observed magnetic moments and the phenomenological value of gsz(eff.) for considered odd-mass nuclei have been reproduced very well by the calculations. The role of the isoscalar and isovector interactions on the magnetic properties of K=1/2 states in these nuclei has been also discussed.

Nucleon form factors and root-mean-square radii on a (10.8 fm)4 lattice at the physical point

We present the nucleon form factors and root-mean-square (RMS) radii measured on a ${(10.8\text{ }\text{ }\mathrm{fm})}^{4}$ lattice at the physical point. We compute the form factors at small momentum transfer region in ${q}^{2}\ensuremath{\le}0.102\text{ }\text{ }{\mathrm{GeV}}^{2}$ with the standard plateau method choosing four source-sink separation times ${t}_{\mathrm{sep}}$ from 0.84 to 1.35 fm to examine the possible excited state contamination. We obtain the electric and magnetic form factors and their RMS radii for not only the isovector channel but also the proton and neutron ones without the disconnected diagram. We also obtain the axial-vector coupling and the axial radius from the axial-vector form factor. We find that these three form factors do not show large ${t}_{\mathrm{sep}}$ dependence in our lattice setup, and those RMS radii are consistent with the experimental values. On the other hand, the induced pseudoscalar and pseudoscalar form factors show the clear effects of the excited state contamination, which affect the generalized Goldberger-Treiman relation.

Tensor Fermi liquid parameters in nuclear matter from chiral effective field theory

We compute from chiral two- and three-body forces the complete quasiparticle interaction in symmetric nuclear matter up to twice nuclear matter saturation density. Second-order perturbative contributions that account for Pauli-blocking and medium polarization are included, allowing for an exploration of the full set of central and noncentral operator structures permitted by symmetries and the long-wavelength limit. At the Hartree-Fock level, the next-to-next-to-leading order three-nucleon force contributes to all noncentral interactions, and their strengths grow approximately linearly with the nucleon density up that of saturated nuclear matter. Three-body forces are shown to enhance the already strong proton-neutron effective tensor interaction, while the corresponding like-particle tensor force remains small. We also find a large isovector cross-vector interaction but small center-of-mass tensor interactions in the isoscalar and isovector channels. The convergence of the expansion of the noncentral quasiparticle interaction in Landau parameters and Legendre polynomials is studied in detail.

A lattice calculation of the hadronic vacuum polarization contribution to (g – 2)µ

We present results of calculations of the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment. Specifically, we focus on controlling the infrared regime of the vacuum polarisation function. Our results are corrected for finite-size effects by combining the Gounaris-Sakurai parameterisation of the timelike pion form factor with the Lüscher formalism. The impact of quark-disconnected diagrams and the precision of the scale determination is discussed and included in our final result in two-flavour QCD, which carries an overall uncertainty of 6%. We present preliminary results computed on ensembles with Nf = 2 + 1 dynamical flavours and discuss how the long-distance contribution can be accurately constrained by a dedicated spectrum calculation in the iso-vector channel.

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.

Connected and disconnected contractions in pion–pion scattering

We show that the interplay of chiral effective field theory and lattice QCD can be used in the evaluation of so-called disconnected diagrams, which appear in the study of the isoscalar and isovector channels of pion–pion scattering and have long been a major challenge for the lattice community. By means of partially-quenched chiral perturbation theory, we distinguish and analyze the effects from different types of contraction diagrams to the pion–pion scattering amplitude, including its scattering lengths and the energy-dependence of its imaginary part. Our results may be used to test the current degree of accuracy of lattice calculation in the handling of disconnected diagrams, as well as to set criteria for the future improvement of relevant lattice computational techniques that may play a critical role in the study of other interesting QCD matrix elements.

Dipole response in neutron-rich nuclei with new Skyrme interactions

We investigate the isoscalar and isovector E1 response of neutron-rich nuclei, within a semi-classical transport model employing effective interactions for the nuclear mean-field. In particular, we adopt the recently introduced SAMi-J Skyrme interactions, whose parameters are specifically tuned to improve the description of spin-isospin properties of nuclei. Our analysis evidences a relevant degree of isoscalar/isovector mixing of the collective excitations developing in neutron-rich systems. Focusing on the low-lying strength emerging in the isovector response, we show that this energy region essentially corresponds to the excitation of isoscalar-like modes, which also contribute to the isovector response owing to their mixed character. Considering effective interactions which mostly differ in the isovector channels, we observe that these mixing effects increase with the slope L of the symmetry energy at saturation density, leading to a larger strength in the low-energy region of the isovector response. This result appears connected to the increase, with L, of the neutron/proton asymmetry at the surface of the considered nuclei, i.e., to the extension of the neutron skin.

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.