Response functions of hot and dense matter in the Nambu-Jona-Lasino model

We investigate current-current correlation functions,or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density.The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach.The response functions can be obtained by expanding the generational functional in powers of the external sources.We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics,namely mean-field theory and a beyond-mean-field theory,taking into account mesonic contributions.Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation.We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation,showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons,respectively.Noting that the mesonic contributions are not taken into account in the random phase approximation,we also derive the response functions parallel to the beyond-mean-field theory.We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions:the Aslamazov-Lakin contribution,the self-energy or density-of-state contribution,and the Maki-Thompson contribution.Unlike the equilibrium case,in evaluating the fluctuation contributions,we need to carefully treat the linear terms in external sources and the induced perturbations.In the chiral symmetry breaking phase,we find an additional chiral order parameter induced contribution,which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities.These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover,where the mesonic degrees of freedom are still important.

Description of mixed symmetry states in 96Ru using IBM-2

We have investigated the properties of low-tyiag states iu 96Ru within the framework of the neutron-proton interacting boson model （IBM-2）, with special attention paid to the characteristics of the mixed symmetry states. By considering the relative energy of d proton boson to be different from that of neutron boson, the level energies and M1, E2 transition strengths have been calculated. The IBM-2 calculation is consistent with the experimental data of 96Ru both quantitatively and qualitatively. Particularly, the strong M1 transition between the 42^＋ and 41^＋ states has been reproduced nicely. The calculated results show that the M1 transition strength of B（M1,42^＋ → 41^＋） in 96Ru carl be described successfully by the IBM-2.

Nuclear structure of ^(76)Ge from proton-neutron interacting boson model calculations

The properties of low-lying states in 76Ge, especially the characteristics of the mixed-symmetry states, have been investigated within the neutron-proton interacting boson model （IBM-2）. By considering the relative energy of d proton boson to be different from that of neutron boson, the low-lying positive parity levels and M1, E2 transition strengths have been calculated. The IBM-2 calculated results are in good agreement with the experimental data. Particularly, the mixed-symmetry states have been reproduced quite well. The calculation and systematic analysis demonstrated that the collective character of 76Ge lies closest to the SUπv^＊（3）, with some possible Oπv（6） dynamic symmetry in IBM-2 viewpoint.

Description of spectrum and electromagnetic transitions in ^(94)Mo through the proton-neutron interacting boson model

We investigated the properties of low-lying states in ^(94)Mo within the framework of the proton-neutron interacting boson model(IBM-2), with special focus on the characteristics of mixed-symmetry states. We calculated level energies and M1 and E2 transition strengths. The IBM-2 results agree with the available quantitative and qualitative experimental data on ^(94)Mo. The properties of mixed-symmetry states can be well described by IBM-2 given that the energy of the d proton boson is different from that of the neutron boson, especially for the transition of B(M1, 4_2^+→ 4_1^+).

Description of the shape coexistence in neutron-deficient ^(74,76)Kr with IBM2

The shape deformation and shape coexistence in ^(74,76) Kr isotopes are investigated within the framework of the proton-neutron interacting boson model(IBM2). By considering the relative energy of the d proton boson to be different from that of the neutron boson, the low-lying energy spectrum is in good agreement with experimental results both qualitatively and quantitatively. In particular, the low-lying 0_2^+ states associated with the shape-coexistence phenomenon are reproduced quite well. The calculated key sensitive quantities of B(E2) transition branch ratios are fairly consistent with the experimental data except for R_4. The predicated deformation parameter is very similar for the ground states in ^(74)Kr and ^(76)Kr, showing good agreement with the experimental result,and the calculated deformation parameter for the second 0^+ state in ^(74)Kr is close to the experimental data. The calculated results of the triaxiality parameter indicated an almost purely prolate shape for the ground state of ^(76)Kr and a mostly prolate shape with a little triaxiality for the ground state of ^(74)Kr. The calculations also show an oblate triaxial shape for the second 0^+ state in ^(76)Kr and maximum triaxiality for the second 0^+ state in ^(74)Kr. These results confirm the importance of the triaxial deformation for the description of such shape coexistence.