The critical endpoint (CEP) and the phase structure are studied in the Polyakov-loop extended Nambu-Jona-Lasinio model in which the scalar type eight-quark (σ 4 ) interaction and the vector type four-quark interaction are newly added. The σ 4 interaction largely shifts the CEP toward higher temperature and lower chemical potential, while the vector type interaction does oppositely.At zero chemical potential, the σ 4 interaction moves the pseudo-critical temperature of the chiral phase transition to the vicinity of that of the deconfinement phase transition.

The chiral phase transition and color superconductivity in an extended NJL model with eight-quark interactions are studied. The scalar-type nonlinear term hastens the chiral phase transition, the scalar-vector mixing term suppresses effects of the vector-type linear term and the scalar-diquark mixing term makes the coexisting phase wider.Quantum Chromodynamics (QCD) has non-perturbative properties. First-principle lattice QCD simulations are useful to study thermal systems at zero or small density [1,2]. At high density, however, lattice QCD is still not feasible due to the sign problem. Therefore, effective models are used in finite density region. One of the models is the Nambu-Jona-This model has the mechanism of spontaneous chiral symmetry breaking, but it has not the confinement mechanism. However, this model has been widely used [4,5] with the mean field approximation (MFA), for example, for analyses of the critical endpoint of chiral phase transition [6,7,8,9,10,11].As for the NJL model, only a few studies were done so far on roles of higher-order multiquark interactions [12,13], except for the case of the six-quark interaction coming from the

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The three moments of inertia associated with the wobbling mode built on the superdeformed states in 163 Lu are investigated by means of the cranked shell model plus random phase approximation to the configuration with an aligned quasiparticle. The result indicates that it is crucial to take into account the direct contribution to the moments of inertia from the aligned quasiparticle so as to realize J x > J y in positive-gamma shapes. Quenching of the pairing gap cooperates with the alignment effect. The peculiarity of the recently observed 163 Lu data is discussed by calculating not only the electromagnetic properties but also the excitation spectra.PACS numbers: 21.10. Re, 21.60.Jz, 23.20.Lv Rotation is one of the specific collective motions in finite many-body systems. Most of the nuclear rotational spectra can be understood as the outcome of one-dimensional (1D) rotations of axially symmetric nuclei. Two representative models -the moment of inertia of the irrotational fluid, J irr , and that of the rigid rotor, J rig , both specified by an appropriate axially-symmetric deformation parameter β -could not reproduce the experimental ones,From a microscopic viewpoint, the moment of inertia can be calculated as the response of the many-body system to an externally forced rotation -the cranking model [1]. This reproduces J exp well by taking into account the pairing correlation. Triaxial nuclei can rotate about their three principal axes and the corresponding three moments of inertia depend on their shapes in general. In spite of a lot of theoretical studies, their shape (in particular the triaxiality parameter γ) dependence has not been understood well because of the lack of decisive experimental data. Recently some evidences of three-dimensional (3D) rotations have been observed, such as the shears bands and the so-called chiral-twin bands [2]. In addition to these fully 3D motions, from the general argument of symmetry breaking, there must be a low-lying collective mode associated with the symmetry reduction from a 1D rotating axially symmetric mean field to a 3D rotating triaxial one. This is called the wobbling mode. Notice that the collective mode associated with the "phase transition" from an axially symmetric to a triaxial mean field in the nonrotating case is the well known gamma vibration. Therefore the wobbling mode can be said to be produced by an interplay of triaxiality and rotation. The wobbling mode is described as a small amplitude fluctuation of the rotational axis away from the principal axis with the largest moment of inertia. Bohr and Mottelson first discussed this mode [3].Mikhailov and Janssen [4] and Marshalek [5] described this mode in terms of the random phase approximation (RPA) in the rotating frame. In these works it was shown that at γ = 0 this mode turns into the odd-spin members of the gamma-vibrational band while at γ = 60 • or −120 • it becomes the precession mode built on top of the high-K isomeric states [6]. Here we note that, according to the direction of the rotational axis ...

The nuclear wobbling motion is studied from a microscopic viewpoint. It is shown that the expressions not only of the excitation energy but also of the electromagnetic transition rate in the microscopic RPA framework can be cast into the corresponding forms of the macroscopic rotor model. Criteria to identify the rotational band associated with the wobbling motion are given, based on which examples of realistic calculations are investigated and some theoretical predictions are presented.

The wobbling motion excited on triaxial superdeformed nuclei is studied in terms of the cranked shell model plus random phase approximation. Firstly, by calculating at a low rotational frequency the γ-dependence of the three moments of inertia associated with the wobbling motion, the mechanism of the appearance of the wobbling motion in positive-γ nuclei is clarified theoretically -the rotational alignment of the πi 13/2 quasiparticle(s) is the essential condition. This indicates that the wobbling motion is a collective motion that is sensitive to the single-particle alignment. Secondly, we prove that the observed unexpected rotational-frequency dependence of the wobbling frequency is an outcome of the rotational-frequency dependent dynamical moments of inertia.

High-spin states in138 Nd were investigated using the reaction 94 Zr( 48 Ca,4n), detecting coincident γ-rays with the gasp spectrometer. A rich level scheme was constructed including 4 bands of negative parity at low spins, 8 bands of dipole transitions and 8 bands of quadrupole transitions at medium spins. The Cranked Shell Model and the Tilted Axis Cranking model are used to assign configurations to the observed bands, where zero pairing is assumed. For selected configurations the case of finite pairing is also considered. A consistent notation for configuration assignment is introduced, which applies both for zero and finite pairing. The observed bands are interpreted as rotation around the short and long principal axes (quadrupole bands), as well as around a tilted axis (dipole bands). The dipole bands have an intermediate character, between magnetic and collective electric rotation. A pair of dipole bands are candidates for chiral partners, the first case this property has been identified in an even-even nucleus. The possible existence of the wobbling mode at low deformation and medium spins is discussed. The consistent interpretation of the multitude of observed bands strongly supports the existence of stable triaxial deformation at medium spins in 138 Nd.

There are various different definitions for the triaxial deformation parameter "γ ". It is pointed out that the parameter conventionally used in the Nilsson (or Woods-Saxon) potential, γ (pot:Nils) [or γ (pot:WS)], is not appropriate for representing the triaxiality γ defined in terms of the intrinsic quadrupole moments. The difference between the two can be as large as a factor two in the case of the triaxial superdeformed bands recently observed in Hf and Lu nuclei, i.e., γ (pot:Nils) ≈ 20 • corresponds to γ ≈ 10 • . In our previous work, we studied the wobbling excitations in Lu nuclei using the microscopic framework of the cranked Nilsson mean-field and the random phase approximation. The most serious problem was that the calculated B(E2) value is about factor two too small. It is shown that the origin of this underestimate can mainly be attributed to the small triaxial deformation parameter γ ≈ 10 • that corresponds to γ (pot:Nils) ≈ 20 • . If the same triaxial deformation parameter is used as in the analysis of the particle-rotor model, γ ≈ 20 • , the calculated B(E2) gives correct magnitude of the experimental data.