Spin-orbit Force Research Articles

Nuclear surface properties in relativistic effective field theory

We perform Hartree calculations of symmetric and asymmetric semi-infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature. In addition to the conventional cubic and quartic scalar self-interactions, the extended models incorporate a quartic vector self-interaction, scalar-vector non-linearities and tensor couplings of the vector mesons. We investigate the implications of these terms on nuclear surface properties such as the surface energy coefficient, surface thickness, surface stiffness coefficient, neutron skin thickness and the spin-orbit force.

POTENTIAL OF NUCLEON INTERACTION WITH ODD NUCLEI IN THE HARTREE-FOCK THEORY

An expression for the real part of the optical potential of nucleon interaction with odd nuclei is derived in the Hartree-Fock approximation with effective density-dependent nucleon-nucleon interaction. It is shown for 13 C nucleus, as an example, that this potential contains the central interaction, as well as two spin-orbit forces connected with the spins of scattered nucleon and nucleus, and quite strong spin-spin and tensor interactions. The simple analytical expressions have been obtained for these potentials. The radial distributions of the interactions obtained and their energy dependences are investigated. It is shown that all potentials differ for neutron and proton scattering while the spin-spin and tensor forces in both cases have opposite signs, complicated radial dependences and are the same by an order of magnitude on the nuclear surface.

Phenomenological spin-orbit three-body force

Phenomenological spin-orbit three-body force

Oxygen isotopes in the hyperspherical functions method

The ground state binding energies and rms radii of the isotopes have been calculated in the minimal approximation of the hyperspherical functions method using different nucleon-nucleon (NN) forces. A reasonable description of the ground state binding energies has been obtained with the Volkov force V1 and the NN potential of Baz' et al (1970 JETP Lett. 12 105) after appropriate choice of the strength of the spin-orbit force. However, the radius is underestimated with V1 and overestimated with the Baz' potential. Both potentials predict that the isotopes are unstable with respect to neutron emission.

Spin-orbit force of instanton-induced interaction in strange and charmed systems

Effects of the spin orbit-force on hadronic systems with strangeness or charm are investigated by a valence quark model with the instanton-induced interaction. By introducing this interaction, the spin-orbit splittings in the negative-parity hyperons becomes 0.14–0.37 times smaller. The flavor-octet baryon mass spectrum and the splittings in the charmed baryons become consistent with the experiments. Although the splitting is also reduced in the flavor-singlet baryons, it still gives two third of the experimental value. The reduction comes from the cancellation between the one-gluon exchange and the instanton-induced interaction, which is channel-specific. In most of the two-baryon channels, the symmetric and antisymmetric spin-orbit force of the YN interaction remains strong after introducing this instanton effect. A few exceptional channels, however, are found where the cancellation affects strongly and the spin-orbit force becomes small.

Inelastic Capture Ratio at Rest and Low-Energy Cross Sections of -p Scattering in the SU6 Quark Model

The inelastic capture ratio at rest, TR, and low-energy total cross sections of E-p scat­ tering are examined in the recent SU6 quark model developed for a unified description of the N Nand Y N interactions. The effect of the small mass difference between E-p and EOn channels is treated approximately and the Coulomb attraction in the E-p channel is properly incorporated in the particle basis. The model FSS predicts TR = 0.461, which is very close to the experimental value. The low-energy cross sections for the charge exchange reaction E-p -+ EOn are improved, although those for E-p -+ An are still too large. Pre­ dictions by another model RGM-H are less favorable, even for the very scarce experimental data presently available. The effect of the Coulomb force is estimated, and the effective range approximation is examined in the low-energy S-matrix. The important roles of the one-pion exchange tensor force and the antisymmetric spin-orbit force in the EN-AN coupling are discussed.

Spin-Orbit Force of NN Interaction Based on Chiral SU(3) Quark Model**The project partly supported by National Natural Science Foundation of China (NNSFC)

Spin-orbit force of the NN interaction is studied in the framework of the chiral SU(3) quark model. Both symmetric and antisymmetric spin-orbit (LS) forces of the one gluon exchange and scalar meson exchanges are taken into account. It is shown that although the inclusions of the LS forces caused by the scalar meson exchanges and the antisymmetric LS terms in this model can notably strengthen the LS couplings in the states of 3PJ of the NN interaction, an additional enhancement factor is still needed in order to describe the experimental data.

Spin-orbit field and extrapolated properties of exotic nuclei

Using the extended Thomas-Fermi plus Strutinsky integral approximation to the Skyrme-Hartree-Fock method we show that provided the nuclear mass data are well fitted extrapolations to neutron-rich and superheavy nuclei are quite insensitive to generalizations intended to simulate the main effects of relativistic mean-field theory. In particular, as far as energy-related quantities are concerned, it is sufficient to use the conventional spin-orbit force.

Spin-orbit force of hyperon-nucleon interaction in the chiral SU(3) quark model

The spin-orbit (LS) force of the hyperon-nucleon interaction is studied in the chiral SU(3) quark model. The symmetric LS terms from the one gluon exchange (OGE) and the scalar nonet exchange (OSE) are taken into account. It is shown that two different treatments (the LS coupling from either OGE or OSE being artificially enhanced in order to reproduce the 3 P J phase shifts of the nucleon-nucleon scattering) lead to very similar LS couplings in the ΣN(I = 3 2 ) channel but give quite different results in the ΛN - ΣN(I = 1 2 ) coupled-channel system. A prominent resonance occurs in the 1 P 1 state of the ΛN channel mainly due to the stronger LS (−) couplings in the ΛN - ΣN(I = 1 2 ) coupled-channel system in the OGE enhanced case. Comparatively, the ΛN 1 P 1phase shift curve exhibits a rather smooth behaviour in the OSE enhanced case. Comparing our theoretical results with the experimental data available, and considering the requirement of the baryon spectrum, one can deduce that a stronger color-independent LS coupling is preferred in the chiral quark model.

Pairing-plus-quadrupole model and nuclear deformation: A look at the spin-orbit interaction

The pairing-plus-quadrupole model, realized in the framework of the Elliott SU(3) scheme, is used to study the combined effects of the quadrupole-quadrupole, pairing, and spin-orbit interactions on ground state shapes of nuclear systems. Relevant measures for nuclear deformation are reviewed. Representation mixing induced by the symmetry-breaking pairing and spin-orbit forces is shown to soften the deformation. The angular momentum dependence of the results is discussed.

The nuclear spin-orbit force in chiral effective field theories

A compelling feature of relativistic mean-field phenomenology has been the reproduction of spin-orbit splittings in finite nuclei after fitting only to equilibrium properties of infinite nuclear matter. This successful result occurs when the velocity dependence of the equivalent central potential that leads to saturation arises primarily because of a reduced nucleon effective mass. The spin-orbit interaction is then also specified when one works in a four-component Dirac framework. Here the nature of the spin-orbit force in more general chiral effective field theories of nuclei is examined, with an emphasis on the role of the tensor coupling of the isoscalar vector meson (ω) to the nucleon.

Roles of quark degrees of freedom in hypernuclei

The quark model description of the hyperon nucleon forces, especially the antisymmetric spin-orbit forces, is studied from the spin-flavor SU(6) and the flavor SU(3) symmetry point of view. It is pointed out that the quark exchange interaction predicts strong antisymmetric spin-orbit force between the hyperon and nucleon.

Self-consistent description of Λ hypernuclei in the quark-meson coupling model

The quark-meson coupling (QMC) model, which has been successfully used to describe the properties of both finite nuclei and infinite nuclear matter, is applied to a study of $\Lambda$ hypernuclei. With the assumption that the (self-consistent) exchanged scalar, and vector, mesons couple only to the u and d quarks, a very weak spin-orbit force in the $\Lambda$-nucleus interaction is achieved automatically. This is a direct consequence of the SU(6) quark model wave function of the $\Lambda$ used in the QMC model. Possible implications and extensions of the present investigation are also discussed.

Nucleon-nucleon potential in the 1/Nc expansion

The nucleon-nucleon potential is analyzed using the 1/N{sub c} expansion of QCD. The NN potential is shown to have an expansion in 1/N{sub c}{sup 2}, and the strengths of the leading order central, spin-orbit, tensor, and quadratic spin-orbit forces (including isospin dependence) are determined. Comparison with a successful phenomenological potential (Nijmegen) shows that the large-N{sub c} analysis explains many of the qualitative features observed in the nucleon-nucleon interaction. The 1/N{sub c} expansion implies an effective Wigner supermultiplet symmetry for light nuclei. Results for baryons containing strange quarks are presented in an appendix. {copyright} {ital 1997} {ital The American Physical Society}

Skyrme representation of a relativistic spin-orbit field

We find that a spin-orbit force with the conventional Skyrme form reproduces satisfactorily the isospin dependence of the spin-orbit field generated in relativistic Hartree calculations on semi-infinite nuclear matter with different neutron excesses. We also examine a generalization of the Skyrme-type energy-density functional that leads to still better agreement with the relativistic Hartree calculations. {copyright} {ital 1997} {ital The American Physical Society}

Skyrme-Hartree-Fock treatment ofΛandΛΛhypernuclei withG-matrix motivated interactions

Skyrme-like hyperon-nucleon potentials are derived from $G$-matrix calculations and shown to reproduce well the $\ensuremath{\Lambda}$ single-particle spectra of hypernuclei measured at BNL and KEK. Previously known potentials are reexamined systematically. The fit of the spectra can restrict the radii of $\ensuremath{\Lambda}$ orbits in hypernuclear ground states, $\ensuremath{\Lambda}$ well depth and effective mass in nuclear matter, and polarization of nuclear cores caused by hyperon rather tightly. The implications of the $\ensuremath{\Lambda}N$ spin-orbit force to the spectra are considered. Hartree-Fock calculations of binding energies of ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{13}$B with density-dependent $G$-matrix $\ensuremath{\Lambda}\ensuremath{\Lambda}$ potentials are presented, taking note of the core-rearrangement effects induced by $\ensuremath{\Lambda}N$ interactions.

Isoscalar NN spin-orbit potential from a Skyrme model with scalar mesons

As a first step toward circumventing the difficulty to obtain an attractive isospin-independent NN spin-orbit force from Skyrme-type models involving only pions, we investigate an improved Skyrme Lagrangian that incorporates the scalar-isoscalar meson \epsilon which can be viewed as the cause behind the enhancement of the $\pi \pi S$-wave. We find that at large distances, the main contribution to the spin-orbit potential comes from the scalar Lagrangian and it is found to be attractive. We briefly discuss how to pursue this work to finally obtain a medium-range attractive interaction.

Spin-isospin symmetry in nuclear physics

The article is a review of the development of Wigner’sSU(4) description of different nuclear phenomena. It includes descriptions of the collective isospin, spin and spin-isospin states and charge exchange reactions in terms of Wigner’s symmetry. By using microscopic schemes we demonstrate that one can useSU(4) terms both in the deformed and spherical nuclei for special types of collective states: Analogue and Gamow-Teller Resonances, in the charged excitation branch, independently of whether the basic coupling schemes of the nucleons are ofjj orLS type. However the situation in the neutral excitation branch is quite different. For the deformed nuclei one can useSU(4) terms for the description ofM1-transitions in terms of the perturbation effect of spin-orbital forces. For the spherical onesM1-collective states should be described in terms of a brokenSU(4) symmetry as a consequence of great spin-orbit forces and non-saturation of the spin degree of freedom at the line of nuclear stability, even in “magic” nuclei. Simple examples of the use ofSU(4) symmetry for nuclear charge exchange reactions with phenomenological theories are also demonstrated.

Magnetic moments of C isotopes studied with antisymmetrized molecular dynamics.

We studied the magnetic dipole moments $\ensuremath{\mu}$ of even-odd C isotopes, ranging from proton-rich to neutron-rich nuclei, with antisymmetrized molecular dynamics (AMD). The results are in good agreement with the experimental data. In the $^{9}\mathrm{C}$ ground state the total intrinsic spin of the protons is found to be nonzero (${S}_{p}\ensuremath{\ne}0$), which is unusual in even-odd nuclei. The interesting point is that the spin-orbit force breaks slightly the coupling off of intrinsic spins of the even nucleon group in isospin $T=\frac{3}{2}$ nuclei. This result is consistent with the newly measured $\ensuremath{\mu}$ data that, when combined with $^{9}\mathrm{Li}$ data, indicate an unusual $〈\ensuremath{\sigma}〉$ value larger than unity. A $\ensuremath{\mu}$ moment $\ensuremath{-}1.05{\ensuremath{\mu}}_{N}$ of $^{17}\mathrm{C}$ is theoretically predicted. We also show a good reproduction of $E2$ transition data.

Further Discussion of Effective Quark–Quark Interaction Created by Quark–Antiquark Pair Excitation11The project supported by NSFC, the fundamental research project of SSTC and the graduate study fund of SEDC

The fourth-order quark–quark potentials in perturbative QCD are derived with special emphasis on the colour-independent spin-orbit terms, and these terms may be useful in understanding the suppression of the spin-orbit forces in baryons.