Nuclear Tensor Forces Research Articles

Relativistic interpretation of the nature of the nuclear tensor force**Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)

The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force.

In search of a pristine signal for (scale-)chiral symmetry in nuclei

I describe the long-standing search for a “smoking-gun” signal for the manifestation of (scale-)chiral symmetry in nuclear interactions. It is prompted by Gerry Brown’s last unpublished note, reproduced verbatim below, on the preeminent role of pions and vector ([Formula: see text]) mesons in providing a simple and elegant description of strongly correlated nuclear interactions. In this note written in tribute to Gerry Brown, I first describe a case of an unambiguous signal in axial-charge transitions in nuclei and then combine his ideas with the more recent development on the role of hidden symmetries in nuclear physics. What transpires is the surprising conclusion that the Landau–Migdal fixed point interaction [Formula: see text], the nuclear tensor forces and Brown–Rho scaling, all encoded in scale-invariant hidden local symmetry, as Gerry put, “run the show and make all forces equal.”

Interplay between tensor force and deformation in even–even nuclei

In this work we study the effect of the nuclear tensor force on properties related with deformation. We focus on isotopes in the Mg, Si, S, Ar, Sr and Zr chains within the Hartree–Fock–Bogoliubov theory using the D1ST2a Gogny interaction. Contributions to the tensor energy in terms of saturated and unsaturated subshells are analyzed. Like–particle and proton–neutron parts of the tensor term are independently examinated. We found that the tensor term may considerably modify the potential energy landscapes and change the ground state shape. We analyze too how the pairing characteristics of the ground state change when the tensor force is included.

Experimental program of the Super-FRS Collaboration at FAIR and developments of related instrumentation

The physics program at the super-conducting fragment separator (Super-FRS) at FAIR, being operated in a multiple-stage, high-resolution spectrometer mode, is discussed. The Super-FRS will produce, separate and transport radioactive beams at high energies up to 1.5 AGeV, and it can be also used as a stand-alone experimental device together with ancillary detectors. Various combinations of the magnetic sections of the Super-FRS can be operated in dispersive, achromatic or dispersion-matched spectrometer ion-optical modes, which allow measurements of momentum distributions of secondary-reaction products with high resolution and precision. A number of unique experiments in atomic, nuclear and hadron physics are suggested with the Super-FRS as a stand-alone device, in particular searches for new isotopes, studies of hypernuclei, delta-resonances in exotic nuclei and spectroscopy of atoms characterized by bound mesons. Rare decay modes like multiple-proton or neutron emission and the nuclear tensor force observed in high-momentum regime can be also addressed. The in-flight radioactivity measurements as well as fusion, transfer and deep-inelastic reaction mechanisms with the slowed-down and energy-bunched fragment beams are proposed for the high-resolution and energy buncher modes at the Super-FRS.

Self-consistent tensor effects on nuclear matter systems within a relativistic Hartree-Fock approach

With the relativistic representation of the nuclear tensor force that is included automatically by the Fock diagrams, we explored the self-consistent tensor effects on the properties of a nuclear matter system. The analysis was performed within the density-dependent relativistic Hartree-Fock (DDRHF) theory. The tensor force is found to notably influence the saturation mechanism, the equation of state, and the symmetry energy of nuclear matter, as well as the neutron star properties. Without introducing any additional free parameters, the DDRHF approach is a natural way to reveal the tensor effects on the nuclear matter system.

A new topological “twist” to BR scaling

When vector mesons are considered on the same footing as pions as suggested by hidden local symmetry, the property of the nuclear tensor forces is strongly controlled by the behavior of the vector mesons in dense medium. This led to BR scaling in 1991. When baryons as skyrmions are put on crystal, there can be a phase transition from skyrmions to half-skyrmions at a density above that of normal nuclear matter. This topology change can induce fundamental changes to the parameters in hidden local symmetric Lagrangian, hence BR scaling, and brings a drastic modification to the structure of nuclear forces, in particular, the tensor forces. This can have far-reaching consequences on the EoS of compact-star matter and the structure of neutron-rich nuclei.

Topology change and tensor forces for the EoS of dense baryonic matter

When skyrmions representing nucleons are put on crystal lattice and compressed to simulate high density, there is a transition above the normal nuclear matter density (n0) from a matter consisting of skyrmions with integer baryon charge to a state of half-skyrmions with half-integer baryon charge. We exploit this observation in an effective field theory framework to access dense baryonic system. We find that the topology change involved in the transition implies changeover from a Fermi liquid structure to a non-Fermi liquid with the chiral condensate in the “melted-off” nucleon. The ∼ 80% of the nucleon mass that remains “unmelted”, invariant under chiral transformation, points to the possible origin of the (bulk of) proton mass that is not encoded in the standard mechanism of spontaneously broken chiral symmetry. The topology change engenders a drastic modification of the nuclear tensor forces, thereby non-trivially affecting the EoS, in particular, the symmetry energy, for compact star matter. It brings in stiffening of the EoS needed to accommodate a neutron star of ∼ 2 solar mass. The strong effect on the EoS in general and in the tensor force structure in particular will also have impact on processes that could be measured at RIB-type accelerators.

Nuclear Tensor Force and Effective Pions in the Relativistic Hartree-Fock Formalism

In the framework of nonlinear nuclear models based on the relativistic Hartree-Fock approximation, we have isolated the contribution of the tensor force of pions in the effective NN interaction, by means of two different approximate methods, recently developed by us, in order to dilucidate its role in a variety of nuclear properties. Results show that a reduction of the contribution of this tensor force considerably influences the spin-orbit splittings and magic gaps in the spin-unsaturated midweight 56Ni nucleus as well as the behaviour of the total binding energies with A in heavy nuclei. Both methods give similar results. We also study the evolution of the splitting of the proton 1d spin-orbit doublet in the chain Z=14, from N=20 to N=28, and the neutron 2p − 1f shell in the chain N=28, from the 48Ca nucleus to the 42Si nucleus. Whereas, in the first case, the pion tensor force (PTF) plays an important role and its reduction is needed to reproduce the corresponding experimental results; in the second case, the quenching of the neutron 2p3/2 − 1f7/2 gap in the mentioned isotonic chain N=28 is hardly affected by the PTF.

Half-Skyrmions and the equation of state for compact-star matter

The half-skyrmions that appear in dense baryonic matter when skyrmions are put on crystals modify drastically hadron properties in dense medium and affect strongly the nuclear tensor forces, thereby influencing the equation of state (EoS) of dense nuclear and asymmetric nuclear matter. The matter comprised of half skyrmions has vanishing quark condensate but non-vanishing pion decay constant and could be interpreted as a hadronic dual of strong-coupled quark matter. We infer from this observation combined with certain predictions of hidden local symmetry in low-energy hadronic interactionsa a set of new scaling laws -- called "new-BR" -- for the parameters in nuclear effective field theory controlled by renormalization-group flow. They are subjected to the EoS of symmetric and asymmetric nuclear matter, and are then applied to nuclear symmetry energies and properties of compact stars. The changeover from the skyrmion matter to a half-skyrmion matter that takes place after the cross-over density $n_{1/2}$ provides a simple and natural field theoretic explanation for the change of the EoS from soft to stiff at a density above that of nuclear matter required for compact stars as massive as $\sim 2.4M_\odot$. Cross-over density in the range $1.5n_0 \lsim n_{1/2} \lsim 2.0 n_0$ has been employed, and the possible skyrmion half-skyrmion coexistence {or cross-over} near $n_{1/2}$ is discussed. The novel structure of {the tensor forces and} the EoS obtained with the new-BR scaling is relevant for neutron-rich nuclei and compact star matter and could be studied in RIB (rare isotope beam) machines.

FLAVOR SYMMETRY AND TOPOLOGY CHANGE IN NUCLEAR SYMMETRY ENERGY FOR COMPACT STARS

The nuclear symmetry energy figures crucially in the structure of asymmetric nuclei and, more importantly, in the equation of state (EoS) of compact stars. At present it is almost totally unknown, both experimentally and theoretically, in the density regime appropriate for the interior of neutron stars. Basing on a strong-coupled structure of dense baryonic matter encoded in the skyrmion crystal approach with a topology change and resorting to the notion of generalized hidden local symmetry in hadronic interactions, we address a variety of hitherto unexplored issues of nuclear interactions associated with the symmetry energy, i.e., kaon condensation and hyperons, possible topology change in dense matter, nuclear tensor forces, conformal symmetry, chiral symmetry, etc., in the EoS of dense compact-star matter. One of the surprising results coming from HLS structure that is distinct from what is given by standard phenomenological approaches is that at high density, baryonic matter is driven by renormalization group flow to the "dilaton-limit fixed point" constrained by "mended symmetries". We further propose how to formulate kaon condensation and hyperons in compact-star matter in a framework anchored on a single effective Lagrangian by treating hyperons as the Callan–Klebanov kaon-skyrmion bound states simulated on crystal lattice. This formulation suggests that hyperons can figure in the stellar matter — if at all — when or after kaons condense, in contrast to the standard phenomenological approaches where the hyperons appear as the first strangeness degree of freedom in matter, thereby suppressing or delaying kaon condensation. In our simplified description of the stellar structure in terms of symmetry energies, which is compatible with that of the 1.97 solar mass star, kaon condensation plays a role of "doorway state" to strange quark matter.

Role of short-range and tensor correlations in nuclei

The present theoretical understanding of the role of short-range correlations in nuclei near stability is reviewed. Two effects are identified in particular: first, the depletion of mean-field single-particle strength that is no longer available to participate in low-lying excitations. Second, the admixture of high-momentum nucleons in the ground state that is implied by the vanishing relative wave functions of pairs in the medium. The role of the tensor force will be further clarified by discussing isospin-polarized matter. It is demonstrated that the depletion of the proton and neutron Fermi seas depends strongly on the nuclear tensor force and appears to be determined by nucleon-nucleon scattering data. The increased role of short-range and tensor correlations for the minority species makes the case for further experimental scrutiny of nuclei with large neutron excess. Appropriate data of single- and two-nucleon knockout experiments are employed to illustrate the role of short-range and tensor correlations.

Half-Skyrmions, tensor forces, and symmetry energy in cold dense matter

In a previous article, the 4D half-skyrmion (or 5D dyonic salt) structure of dense baryonic matter described in crystalline configuration in the large $N_c$ limit was shown to impact nontrivially on how anti-kaons behave in compressed nuclear matter with a possible implication on an "ice-9" phenomenon of deeply bound kaonic matter and condensed kaons in compact stars. We extend the analysis to make a further prediction on the scaling properties of hadrons that have a surprising effect on the nuclear tensor forces, the symmetry energy and hence on the phase structure at high density. We treat this problem relying on certain topological structure of chiral solitons. Combined with what can be deduced from hidden local symmetry for hadrons in dense medium and the "soft" dilatonic degree of freedom associated with the trace anomaly of QCD, we uncover a novel structure of chiral symmetry in the "supersoft" symmetry energy that can influence the structure of neutron stars.

Bonn potential and sd-shell nuclei.

Using a G-matrix folded diagram method and the Bonn nucleon-nucleon potential, the s-d shell effective interaction is derived and applied to evaluate the spectra of some light sd-shell nuclei. Due to the relatively weak tensor-force characteristic for the Bonn potential, the effective interaction matrix elements, particularly those with isospin T=0, come out generally more attractive than in earlier derivations in which local, strong tensor-force potentials were used. As a consequence of this, our results for the effective interaction and the spectra are in considerably better agreement with empirical determinations and experimental data. The sensitivity of the above nuclear structure calculations to the strength of the nuclear tensor force is demonstrated systematically and the dependence of the s-d shell matrix elements on the nuclear mass number is studied.

Uncertainties in the two-nucleon potential and nuclear matter predictions.

The effects of uncertainties in the two-nucleon potential on the saturation properties of nuclear matter are studied. The nuclear matter energy is calculated by a recently developed ring-diagram method. The largest variations in the energy are due to ambiguities in the (off-shell) strength of the nuclear tensor force. For the six different realistic potential models considered, the total uncertainty is about 3 MeV for the saturation energy and 0.2 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ for the saturation Fermi momentum. This variation is substantially smaller than the corresponding one obtained in standard lowest-order Brueckner calculations (6 MeV, 0.3 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$). The relevance of the tensor force for ring-diagram contributions is investigated systematically.

Evidence for a Nuclear Tensor Force from Mass-14 Beta- and Gamma-Ray Data

The role of beta- and gamma-ray matrix elements in the determination of wave functions for the ${s}^{4}{p}^{10}$ states of mass 14 is examined. The data considered include the Gamow-Teller (beta) matrix elements of $^{14}\mathrm{C}$ and $^{14}\mathrm{O}$ and the $M1$ and $E2$ matrix elements connecting the lowest four ${s}^{4}{p}^{10}$ states of $^{14}\mathrm{N}$. The magnetic moment of $^{14}\mathrm{N}$ is also discussed. The shell-model wave functions considered arise mainly from the ${s}^{4}{p}^{10}$ configuration but include admixtures of the ${s}^{4}{p}^{8}$ ($2s, 1d$) configuration. It is found that the data, considered as a whole, cannot be explained if the ${s}^{4}{p}^{10}$ components of the wave functions are derived from a central plus spin-orbit interaction only, but that quite satisfactory agreement is obtained if the nuclear force includes a tensor part. The bulk of the cancellation of the $^{14}\mathrm{C}$ beta decay matrix element takes place within the ${s}^{4}{p}^{10}$ configuration. In general, configuration mixing is of secondary importance; its most noticeable effect is on the $M1$ decay of the first-excited state of $^{14}\mathrm{N}$.