Effect Of Three-body Forces Research Articles

Erratum: Effects of three-body forces on the maximum mass of neutron stars in the lowest-order constrained variational formalism [Phys. Rev. C 91 , 054320 (2015)

Received 5 September 2017DOI:https://doi.org/10.1103/PhysRevC.96.049902©2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEquations of state of nuclear matterNuclear forcesNuclear matter in neutron starsNuclear PhysicsGravitation, Cosmology & Astrophysics

Repulsive three-body force and channel-coupling effects via C12+C12 scattering at 100A MeV

The angular distributions of differential cross sections of $^{12}\mathrm{C}+^{12}\mathrm{C}$ elastic and inelastic scattering populating the ground and excited states in $^{12}\mathrm{C}$ up to 15 MeV excitation energy are precisely measured for the first time at an incident energy of $100A$ MeV to study the effect of repulsive three-body forces. Using the high-resolution spectrometer Grand Raiden at the Research Center for Nuclear Physics (RCNP), Osaka University, we have obtained the differential cross sections for the ground state (${0}_{1}^{+}$) and 4.44 MeV (${2}_{1}^{+}$) excited state, as well as the summed differential cross sections for the states between 4.44 and 15 MeV in the angular range of $1.{0}^{\ensuremath{\circ}}--7.{5}^{\ensuremath{\circ}}$. The results are compared with microscopic coupled-channel calculations. The potential between the colliding nuclei is determined by the double folding method with three different complex $G$-matrix interactions, the ESC, CEG07b, and MPa interactions. The CEG07b and MPa interactions, which include repulsive three-body forces, describe the data well, whereas the ESC interaction, which does not include repulsive three-body forces, fails to reproduce the data. The results provide evidence of repulsive three-body forces in $^{12}\mathrm{C}$ and demonstrate the possible sensitivity of elastic scattering to three-body forces.

Medium effect in high-density nuclear matter probed by a systematic analysis of nucleus-nucleus elastic scattering

We investigate the property of the high-density nuclear matter probed by the nucleus-nucleus elastic scattering in the framework of the double-folding (DF) model with the complex $G$-matrix interaction. The medium effect including three-body-force (TBF) effect is investigated with present two methods based on the frozen density approximation (FDA). The medium effect is clearly seen on the potential and the elastic cross section for the $^{16}$O + $^{16}$O system at $E/A =$ 70 MeV. The crucial role of the medium effect is also confirmed with other effective nucleon-nucleon ($NN$) interactions. In addition, the present methods are applied to other heavy-ion elastic scattering systems. Again, the medium effect is clearly seen in the heavy-ion elastic cross section. The medium effect on the elastic cross section becomes invisible with the increase of the target mass and the incident energy (up to $E/A =$ 200 MeV). However, the medium effect is again important to fix the heavy-ion scattering over $E/A =$ 200 MeV. Finally, we make clear the crucial role of the TBF effect up to $k_F =$ 1.6 fm$^{-1}$ in the nucleus-nucleus elastic scattering.

19aAC-2 殻模型相互作用における有効2体化3体力の効果

19aAC-2 殻模型相互作用における有効2体化3体力の効果

Three-body force effect on the properties of neutron-rich nuclear matter

We review our research work on the single-particle properties and the equation of state (EOS) of isospin asymmetric nuclear matter within the framework of the Brueckner-Hartree-Fock (BHF) approach extended by including a microscopic three-body force (TBF). The TBF is shown to affect significantly the nuclear matter EOS and the density dependence of nuclear symmetry energy at high densities above the normal nuclear matter density, and it is necessary for reproducing the empirical saturation property of symmetric nuclear matter in a nonrelativistic microscopic framework. The TBF-induced rearrangement effect and the ground state (g.s.) correlation effect on the s.p. properties in neutron-rich nuclear matter are investigated. Both effects turn out to be crucial for predicting reliably the s.p. properties within the Brueckner framework. The TBF effect on nucleon superfluidity in neutron star matter and neutron stars has also been discussed.

Effects of repulsive three-body force in 12C + 12C scattering at 100A MeV

The angular distribution of 12C + 12C scattering at an incident energy of 100A MeV has been measured. The elastic and inelastic scatterings in 12C to the excitation energies of up to ∼45 MeV were measured simultaneously for the first time with the high-resolution Grand Raiden spectrometer at the Research Center for Nuclear Physics (RCNP). The angular distributions of the elastic scattering to the ground state (01+) and inelastic scattering to the 4.44 MeV (21+) excited state were precisely obtained in the angular range of 1.0°–7.5° with a step of 0.1°. Additionally, the angular distribution was obtained for the sum of the cross sections for excitation energies above the 4.44 MeV state up to 11 MeV, which includes the 7.65 MeV (02+), 9.64 MeV (31−), and 10.30 MeV (22+) states, in addition to probably the simultaneous excitation of the 4.44 MeV state in the projectile and the target nuclei. Those combined data provide a means to study the effects of channel coupling on the elastic cross section. The observed angular distributions are compared with theoretical calculations based on three double-folding models with complex G-matrix interactions, the CEG07b, MPa, and ESC models. The importance of three-body repulsive forces included in the CEG07b and MPa models will be discussed.

Mass Spectrum of Baryons in a Relativistic Hypercentral Constituent Quark Model

We have investigated the light and strange baryons as a relativistic three-body bound system. Inspired by lattice QCD calculations, we treated the baryons as a spin-independent three-quark system. For this purpose we introduced a spin independent relativistic description for the SU (6) invariant part of the spectrum by presenting the analytical solution of the three-particle Klein-Gordon equation. We carried out calculations within the constituent quark model based on a hypercentral approach, which takes into account three-body force effects and standard two-body potential contributions. Herewith the average energy values of the nonstrange and strange resonances are reproduced. Then we used the generalized Gursey-Radicati mass formula as a SU (6) breaking interaction to describe the splittings within the SU (6)-multiplets and the hyperfine structure of the baryon. The considered SU (6)-invariant potential is the well-known ＂Coulomb-plus-linear＂ potential. The resulting description of the baryon spectrum is fairly good and comparable with the experimental spectrum.

Proton-three-nucleon nuclei elastic scattering: three-body force effect

Elastic scattering differential cross sections at 0.6 GeV for p-3H and at 0.6, 0.715 and 1 GeV for p-3He are calculated in the framework of the multiple-scattering theory of Glauber. A simple approach for the three-body force effect is used. We have found that the three-body force effect appears in the range of momentum transfer squared $$ q^{2} \ge 0.2\; ( {\text{GeV/c)}}^{ 2} $$ and plays an important role to obtain a good fit with the experimental data at the first minimum region.

Effects of three-body forces on the maximum mass of neutron stars in the lowest-order constrained variational formalism

The equation of state of neutron star matter is calculated within the lowest order constrained variational (LOCV) method using different two-body interactions and an Urbana type three-body force. The core of the neutron star is modelled by $\ensuremath{\beta}$-stable matter. The corresponding neutron star mass-radius relations are presented and the effect of using a three-body interaction on the maximum gravitational mass of the star is also discussed. It is shown that including the three-body force generally increases the maximum gravitational mass.

Effect of three-body forces on response functions in infinite neutron matter

We study the impact of three-body forces on the response functions of cold neutron matter. These response functions are determined in the random phase approximation (RPA) from a residual interaction expressed in terms of Landau parameters. Special attention is paid to the non-central part, including all terms allowed by the relevant symmetries. Using Landau parameters derived from realistic nuclear two- and three-body forces grounded in chiral effective field theory, we find that the three-body term has a strong impact on the excited states of the system and in the static and long-wavelength limit of the response functions for which a new exact formula is established.

Tensor force and delta excitation for the structure of light nuclei

We treat explicitly Δ(1232) isobar degrees of freedom using a bare nucleon-nucleon interaction for few-body systems, where Δ excitations can be the origin of the three-body force via the pion exchange. We adopt the Argonne two-body potential including Δ, named as AV28 potential, and study the role of Δ explicitly in two-body and three-body systems. It was found that the additional Δ states generate strong tensor correlations caused by the transitions between N and Δ states, and change tensor matrix elements largely from the results with only nucleons. We studied the effects of three-body force in the triton and obtained 0.8 MeV attraction due to the intermediate Δ excitation. Due to the lack of the total binding energy for the triton in the delta model, we further studied carefully the effects of the delta excitation in various two body channels and compared with the nucleon only model in the AV14 potential. We modified slightly the AV28 potential in the singlet S channel so that we could reproduce the triton binding energy due to the appropriate amount of the three-body force effects.

Correlated density-dependent chiral forces for infinite-matter calculations within the Green's function approach

The properties of symmetric nuclear and pure neutron matter are investigated within an extended self-consistent Green's function method that includes the effects of three-body forces. We use the ladder approximation for the study of infinite nuclear matter and incorporate the three-body interaction by means of a density-dependent two-body force. This force is obtained via a correlated average over the third particle, with an in-medium propagator consistent with the many-body calculation we perform. We analyze different prescriptions in the construction of the average and conclude that correlations provide small modifications at the level of the density-dependent force. Microscopic as well as bulk properties are studied, focusing on the changes introduced by the density-dependent two-body force. The total energy of the system is obtained by means of a modified Galitskii-Migdal-Koltun sum rule. Our results validate previously used uncorrelated averages and extend the availability of chirally motivated forces to a larger density regime.

Auxiliary-field quantum Monte Carlo simulations of neutron matter in chiral effective field theory.

We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear forces. The ground-state wave function of neutron matter, containing nonperturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10(3) discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of the chiral nuclear force. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of Λ=414 MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction (Entem and Machleidt Λ=414 MeV [L. Coraggio et al., Phys. Rev. C 87, 014322 (2013).

Medium effect in the high-density region probed by nucleus-nucleus elastic scattering

We investigate the sensitivity of the medium effect in the high-density region on nucleus-nucleus elastic scattering in the framework of the double-folding (DF) model with the complex $G$-matrix interaction. The medium effect including the three-body-force (TBF) effect is investigated with two methods. In both methods, the medium effect is clearly seen on the potential and the elastic cross section. Finally, we make clear the crucial role of the TBF effect up to ${k}_{F}=1.6$ ${\mathrm{fm}}^{\ensuremath{-}1}$ in nucleus-nucleus elastic scattering.

Three-body force effect on the properties of nuclear matter under the gap and continuous choices within the BHF approach

We have calculated and compared the three-body force effects on the properties of nuclear matter under the gap and continuous choices for the self-consistent auxiliary potential within the Brueckner-Hartree-Fock approach by adopting the Argonne V18 and the Bonn B two-body potentials plus a microscopic three-body force (TBF). The TBF provides a strong repulsive effect on the equation of state of nuclear matter at high densities for both the gap and continuous choices. The saturation point turns out to be much closer to the empirical value when the continuous choice is adopted. In addition, the dependence of the calculated symmetry energy upon the choice of the self-consistent auxiliary potential is discussed.

Effect of short-range correlation on the density dependence of nuclear symmetry energy at supra-saturation densities

Short-range correlation (SRC) induces a significant high-momentum component in the nucleon momentum distribution n(k) in both finite nuclei and nuclear matter. Recent experiments suggest that the amount of correlation in pure neutron matter (PNM) may be much less than that in symmetric nuclear matter (SNM). In this paper we investigate on a qualitative level how this affects the density dependence of the symmetry energy, especially at supra-saturation densities, in the framework of the well-established MDI energy density functional. In the MDI formalism, SRC affects both the kinetic energy and the potential energy through its effect on n(k). For the n(k) of SNM, we use a formula proposed based on an interesting relation between n(k) at high momentum k (i.e. k > k F ) and the average nucleon density of finite nuclei. For the n(k) of PNM, we use the prediction of a free Fermi gas model. The result is compared to the symmetry energy calculated assuming both the SNM and PNM to be Fermi-gas like. Our study shows that, to have a realistic estimation of the relative contributions to the symmetry energy from the kinetic part and the two-body and three-body potential part, one has to take the SRC effect into account. Furthermore, it is found that the density dependence of the symmetry energy at supra-saturation densities is sensitive to the competition between the SRC effect and the three-body force effect.

Equilibrium configuration of (H2O)n, for n = 1–3

The equilibrium configurations of water molecule (H2O)n=1, its dimer (H2O)n=2 and trimer (H2O)n=3 have been studied in this paper. The ionic character of the OHO hydrogen bond, formed between the electronegative oxygen atoms, in (H2O)n=2, appears as a change in bond lengths in one of the water molecules while the bond lengths in the other molecule remain same as in (H2O)n=1. The increased hydrogen bond strength, caused by the cooperative effect of three-body forces (H2O)n=3, as compared to (H2O)n=2, results in the equilibrium structure of the water trimer to be much more rigid than that of the dimer. An attempt has been made, from the energy standpoint, to understand the controversy on chemical formula of water as H2O or H1·5O by studying the equilibrium configuration of (H2O) OH, which corresponds to 2H1·5O. The ground-state energy of (H2O) OH is found to be lower than the sum of the ground-state energies of OH and H2O at infinite separation. Calculations also show the ground-state energy of (H2O) OH to be lower than the sum of the energies of the constituent atoms at infinite separation. This shows that the binding energy of (H2O) OH is positive, which indicates that (H2O) OH is relatively stable.

Three-body force effect on the neutron and proton spectral functions in asymmetric nuclear matter

We investigate the effect of microscopic three-body forces (TBFs) on the off-shell behavior of the neutron and proton mass operators ${M}^{\ensuremath{\tau}}(k,\ensuremath{\omega})={V}^{\ensuremath{\tau}}(k,\ensuremath{\omega})+i{W}^{\ensuremath{\tau}}(k,\ensuremath{\omega})$ in asymmetric nuclear matter within the framework of the extended Brueckner-Hartree-Fock approach. We adopt the Argonne ${V}_{18}$ two-body potential supplemented with a microscopic TBF as the realistic nucleon-nucleon interaction. At high densities well above the normal nuclear matter density, the TBF turns out to affect significantly the off-shell behavior of both the proton and neutron mass operators. The neutron and proton spectral functions in asymmetric nuclear matter are calculated and discussed. At low densities around and below the normal density, the TBF effect on the spectral functions turns out to be negligibly weak. At high densities well above the saturation density, the TBF is shown to affect noticeably the neutron and proton spectral functions.

Auxiliary-field quantum Monte Carlo simulations of neutron matter in chiral effective field theory

We present variational Monte Carlo calculations of the neutron matter equation of state using chiral nuclear interactions. The ground-state wavefunction of neutron matter, containing nonperturbative many-body correlations, is obtained from auxiliary-field quantum Monte Carlo simulations of up to about 340 neutrons interacting on a 10 discretized lattice. The evolution Hamiltonian is chosen to be attractive and spin-independent in order to avoid the fermion sign problem and is constructed to best reproduce broad features of chiral nuclear forces. This is facilitated by choosing a lattice spacing of 1.5 fm, corresponding to a momentum-space cutoff of 414 MeV/c, a resolution scale at which strongly repulsive features of nuclear two-body forces are suppressed. Differences between the evolution potential and the full chiral nuclear interaction are then treated perturbatively. Our results for the equation of state are compared to previous quantum Monte Carlo simulations which employed chiral two-body forces at next-to-next-to-leading order (N2LO). In addition we include the effects of three-body forces at N2LO, which provide important repulsion at densities higher than 0.02 fm, as well as two-body forces at N3LO.

Three-body force effect on nuclear symmetry energy and single-particle properties of asymmetric nuclear matter

We present an upgraded review of our microscopic investigation on the single-particle properties and the EOS of isospin asymmetric nuclear matter within the framework of the Brueckner theory extended to include a microscopic three-body force. We pay special attention to the discussion of the three-body force effect and the comparison of our results with the predictions by other ab initio approaches. Three-body force is shown to be necessary for reproducing the empirical saturation properties of symmetric nuclear matter within nonrelativistic microscopic frameworks, and also for extending the hole-line expansion to a wide density range. The three-body force effect on nuclear symmetry energy is repulsive, and it leads to a significant stiffening of the density dependence of symmetry energy at supra-saturation densities. Within the Brueckner approach, the three-body force affects the nucleon s.p. potentials primarily via its rearrangement contribution which is strongly repulsive and momentum-dependent at high densities and high momenta. Both the rearrangement contribution induced by the three-body force and the effect of ground-state correlations are crucial for predicting reliably the single-particle properties within the Brueckner framework.