Narrow Results

We study the effect of the tensor correlation using a mean-field-type model and a shell model. To treat the tensor correlation in a mean-field-type model, we introduce single-particle states with the parity and charge mixing considering the pseudoscalar and isovector characters of the pion, which mediates the tensor force. We study closed-shell and sub-closed-shell oxygen isotopes and find that a sizable attractive energy from the tensor force is obtained by introducing the parity and charge mixing. We also perform a shell model calculation up to two-particle–two-hole configurations. A large attraction energy is obtained for ¹⁶O when we introduce single-particle wave functions with narrow widths.

Quenched lattice QCD results of nuclear forces are presented. Inter-nucleon potentials are constructed from Bethe-Salpeter wave functions of two nucleon states by using a Schrödinger-type equation. The results of the central force in ¹S₀ channel posses the repulsive core at short distance as well as the attraction at medium distance, both of which are enhanced in the light quark mass region. A preliminary result on the tensor force is also presented with the central force in ³S₁ channel.

We study the effect of the tensor force on nuclear structure with mean-field and beyond-mean-field methods. An important correlation induced by the tensor force is two-particle–two-hole (2p2h) correlation, which cannot be treated with a usual mean-field method. To treat the 2p2h tensor correlation, we develop a new framework (charge- and parity-projected Hartree-Fock (CPPHF) method), which is a beyond-mean-field method. We apply the CPPHF method to oxygen isotopes including neutron-rich ones. The potential energy from the tensor force has the same order of magnitude as that from the LS force and becomes smaller with neutron number, which indicates that excess neutrons do not contribute to the 2p2h tensor correlation significantly. We also study the effect of the tensor force on spin-orbit-splitting (ls-splitting) in a neutron-rich fluorine isotope ²³F. The tensor force reduces the ls-splitting for the proton d-orbits by about 3MeV. This effect is important to reproduce the experimental value.

Gamow–Teller states, possibly with narrow widths, have been searched for by the ⁴He(³He, t) reaction with an energy resolution of 100 keV. The search is motivated by theoretical discussions on the role of pions in nuclear structure and simulation of supernovae explosion. In the preliminary analysis of the spectrum at around 0°, no significant narrow structure is observed.

One of the methods to obtain a precise solution of a few-body equation is to expand the orbital part of the wave function into the correlated Gaussian with double global vectors. In this contribution, we report our recent studies applying this method to light nuclei, (i) excited states of ⁴He and (ii) two-nucleon momentum distribution in ⁶He and ⁶Li, especially focusing on the importance of the tensor force.

β-decay half-lives around ⁷⁸Ni and ¹³²Sn are studied with proton-neutron Quasiparticle Random Phase Approximation on the basis of Skyrme-Hartree-Fock (SHF) method. We take into account tensor force correlation in calculating the ground and excited states and find it improves the half-life of ¹³²Sn. However, the Q value is still underestimated. We also discuss that half-lives do not strongly depend on type of particle-particle interaction in isospin T = 0 channel.

In this work, effects of tensor force on the evaluation of shell structure of Z = 28 and Z = 82 isotopes are investigated in the framework of Hartree–Fock+BCS approach. Skyrme type SLy5 and SIII interactions are used with and without tensor interaction. The effect of tensor force on the gap evaluation, single particle energies and spin-orbit splittings of the selected isotopic chain are presented. Pairing energy results are also discussed. It is shown that tensor force plays a crucial role in the evaluation of the single particle states and changing spin-orbit splittings of Nickel and Lead isotopic chain.

The tensor force effect on the isoscalar giant monopole resonance (ISGMR) of ⁴⁶Ar is investigated in the framework of Hartree–Fock (HF) + random phase approximation (RPA) approach with the Skyrme interactions SLy5, SLy5+T and SLy5+T_w. By using the ISGMR excitation energy, the incompressibility value of ⁴⁶Ar is extracted. It is shown that the incompressibility is enhanced with the SLy5+T interaction compared to the one with the SLy5 interaction. However, the SLy5+T_w interaction makes the incompressibility smaller because of the bubble structure of ⁴⁶Ar.

In many shell model interactions, the tensor force monopole matrix elements often retain systematic trends originating in the bare tensor force. However, in this work, we find that Isospin $T=0$ tensor force monopole matrix elements of widely used p-shell effective interaction CK(8–16) do not share these systematic. We correct these discrepancies by modifying $T=0$ tensor force two-body matrix elements (TBMEs) of CK(8–16) by the analytically calculated tensor force TBMEs. With some additional modification of single-particle energies and TBMEs, the revised effective interaction is named as CKN. The effective interaction CKN has been tested for the calculations of p-shell nuclei of normal parity states from various physics viewpoints such as excitation spectra, electromagnetic moments, and electromagnetic and Gamow–Teller (GT) transitions. The obtained results are found to be satisfactory with respect to the experimental results.

In the present volume, several contributions are devoted to the implementations of the Density Functional Theory (DFT) in atomic nuclei, either in the nonrelativistic or covariant formalism. By restricting ourselves to the nonrelativistic case, in this work we deal with some recent improvement of the theory. We argue that tensor correlations are important to be included in the functionals; in particular, we study the role of the tensor terms of the Skyrme effective interaction on the spin-orbit splittings in the N = 82 isotones and Z = 50 isotopes. We conclude that the experimental isospin dependence of these splittings cannot be described by calculations employing the usual Skyrme parametrizations, but is very well accounted for when the tensor interaction is introduced. The necessity to include other kind of correlations, namely those associated with the particle-vibration coupling, is discussed by using the specific example of ¹³²Sn.

In this talk, I will overview recent studies on the evolution of the shell structure in stable and exotic nuclei, and will show results of related shell-model calculations. This shell evolution is primarily due to the tensor force. The robust mechanism and some examples will be presented. Such examples include the disappearance of existing magic numbers and the appearance of new ones. The nuclear magic numbers have been believed, since Mayer and Jensen, to be constants as 2, 8, 20, 28, 50, … This turned out to be changed, once we entered the regime of exotic nuclei. This shell evolution develops at many places on the nuclear chart in various forms. For instance, the Island of Inversion picture has been changed considerably.

The present contribution focuses on three recent experimental achievements obtained at the GANIL facility on the study of the N = 28 shell closure south to the doubly magic nucleus . First, the single particle energies of the neutron fp states in ⁴⁷Ar have been determined by transfer (d,p) reaction using a radioactive beam of . A reduction of the N = 28 gap and of the SO splittings of the f and p states is found. Second, an E0 isomer has been discovered in which is suggestive of a shape mixing. Third, the energy of the first 2⁺ state of has been obtained through in-beam γ-ray emission induced by a 2 protons knock-out reaction. Its low value, 770(19) keV, points to a large deformation there. The gradual change from spherical to deformation in the N = 28 isotones from Z = 20 to Z = 14 is ascribed to specific proton-neutron interactions and to enhanced quadrupole correlations. A global description of all the physics involved at N = 28 is derived along with experimental results.

In the attempt to reach a global view of the effects on single-particle states caused by the tensor interaction, we analyze the evolution of the spin-orbit splittings in the Ca isotopes and in the N = 28 isotones. We also study the isotope shift in the charge radii of the Pb isotopes. Our framework is Hartree-Fock (HF) plus Bardeen-Cooper-Schrieffer (BCS) theory, and we employ a Skyrme interaction complemented by an effective zero-range tensor force, plus a density-dependent interaction in the pairing channel.

In the present volume, several contributions are devoted to the study of the properties of exotic nuclear matter (nuclei at the drip lines or neutron stars) by using implementations of the Density Functional Theory (DFT) in atomic nuclei, either in the nonrelativistic or covariant formalism. In our contribution, we argue that tensor correlations are important to be included in the functionals; the necessity to include other kind of correlations, namely those associated with the particle-vibration coupling, is discussed by using the specific example of ¹³²Sn.

In the attempt to reach a global view of the effects on single-particle states caused by the tensor interaction, we analyze the evolution of the spin-orbit splittings in the Ca isotopes and in the N = 28 isotones.

The proton density distribution of ⁴⁶Ar is calculated in the framework of the Skyrme-Hartree-Fock (SHF) approach with the SLy5, SLy5+T and SLy5+T_w interactions. It is shown that the tensor force in the SLy5+T_w interaction favors its bubble structure due to the inversion between the single-proton states 2s_1/2 and 1d_3/2. However, the SLy5+T interaction can not lead to any 2s_1/2-1d_3/2 inversion, consequently no bubble structure can be found. In addition, a detailed discussion on the competition between tensor force and pairing correlation on the bubble formation is performed within the Skyrme-Hartree-Fock-Bogoliubov (SHFB) approach.

Effects of the tensor force on the Gamow-Teller (GT) and Charge-exchange Spin-Dipole (SD) transitions in ²⁰⁸Pb and ⁹⁰Zr are studied through self-consistent Hartree-Fock plus Random-Phase-Approximation (HF₊RPA) theory based on Skyrme force. It is found that tensor force produce strong effect on the GT and SD transitions. These strong effects can be good candidates to constrain the strength of tensor force or choose Skyrme parameter sets which included the tensor force.

We treat explicitly Δ (1232) isobar degrees of freedom using bare nucleonnucleon interaction, which can be the origin of the three-body forces via the pion exchange. We adopt the Argonne delta model potential (AV28) and study the explicit role of Δ in light nuclei. It is surprising that the additional Δ states generate strong tensor correlations from the transitions between N and Δ states, and change various matrix elements from the results with only the nucleon space.

I present one of the possible paradigm shifts with exotic nuclei. This is the shell evolution due to nuclear forces, such as tensor, central and three-nucleon forces. I shall present major points with the N=34 magic number confirmed in ⁵⁴Ca by RIBF of RIKEN very recently, after the theoretical prediction made in 2001. The shell evolution has been generalized to phenomena caused by massive particle-hole excitations, being referred to as Type II Shell Evolution. This can be found in ^68,70Ni. In particular, the shape coexistence of spherical, oblate and prolate shapes is suggested theoretically. Thus, the perspectives of physics with exotic nuclei is being expanded further from single-particle aspects to shapes/deformation, changing the landscape of nuclear structure.

The superconducting fragment separator (Super-FRS) will be one of the main scientific instruments of the future FAIR facility. This versatile high-resolution spectrometer allows for a variety of exciting experiments in atomic, nuclear and hadron physics. Future directions are presented in this contribution.