Description of 114 Cd in the E（5） Symmetry

By analysing the known low-lying levels and the E2 transition rates, it is shown that the empirical scheme of 114Cd is in good overall agreement with the predictions of the transitional dynamical symmetry E(5) proposed by Iachello [Phys. Rev. Lett. 85 (2000) 3580]. This suggests that 114Cd may be better described by an E(5) nucleus than a U(5) nucleus as known before.     

Empirical Example of Nucleus with Transitional Dynamical Symmetry X（5）

By analysing the energy spectrum,E2 transition rates and branching ratios,it is shown explicitly that the nucleus ^150Nd provides an empirical example with X(5) symmetry at the critical point of the transition from U(5) to SU(3) symmetry.     

Systematic Study on the Superdeformed Bands of Double Odd Nuclei in A～130 Region

Properties of the superdeformed bands of odd-odd nuclei in A ～ 130 mass region are investigatedsystematically within the supersymmetry scheme including many-body interactions and a perturbation possessing theSO(5) (or SU(5)) symmetry on the rotational symmetry. The obtained γ-ray energies, the dynamical moments ofinertia, and energy differences △Eγ - △Erefγ ef agree with experimental data. It shows that this approach is quite powerfulin describing odd-odd nuclei in 130 mass region.     

Description of the critical point symmetry in ~(124)Te by IBM-2

Based on the neutron and proton degrees of freedom, low-lying energy levels, E2, M1, and E0 transition strengths of nucleus ~(124)Te have been calculated by the neutron-proton interacting boson model. The calculated results are reasonably consistent with the experimental data. By comparing the key observables of the states at the critical point of U_(πv)(5)-O_(πv)(6) transition with the experimental data and calculated results, we show that the ~(124)Te is a possible nucleus at the critical point of the second-order phase transition from vibration to unstable rotation, and such a critical point exhibits slight triaxial rotation. The 0_2~+ state of ~(124)Te can be interpreted as the lowest state of the first-excited family of the intrinsic levels in the critical point symmetry.     

Structure Evolution in the Even-Even (124—134)~Xe with IBM2

We have investigated the structure evolution of the124-134Xe isotopic chain in the framework of the proton-neutron interacting model IBM2. The positive parity spectra of the ground state, quasi-β and quasi-γ bands are reproduced well. The staggering in124-130Xe are almost completely removed and the γ band agree well with the experiment data, even for the high-spin quasi-γ states. The key quantities of the collective structure evolution, including level energies, the B(E2) transition branching ratios, and the M1 excitations to 1+1mixer-symmetry states are analyzed by comparing with the experimental data. The parameters for representation of the Oπν(6) and SU πν(3) features in isotopes are examined. Both experimental data and theoretical results show that the shape phase transition of124 134Xe isotopic chain is from the SU πν(3)(triaxial rotation) to the Uπν(5)(vibration motion) with a considerable constituent of the Oπν(6) symmetry(γ-unstable rotation), where the shape phase transition rapidly takes place between the neutron number N = 76 and N = 78.     

Systematic Study on the Superdeformed Bands of Double Odd Nuclei in A～130 Region

Properties of the superdeformed bands of odd-odd nuclei in A～130 mass region are investigated systematically within the supersymmetry scheme including many-body interactions and a perturbation possessing the SO(5) (or SU(5)) symmetry on the rotational symmetry. The obtained γ-ray energies, the dynamical moments of inertia, and energy differences △Eγ - △Eγ^ref agree wlth experimental data. It shows that this approach is quite powerful in describing odd-odd nuclei in 130 mass region.     

Description of nucleus ^44Ti in new symmetry limit in IBM-3

Analysis of the spectra and E2 transition rates shows that the empirical scheme of {}^{44}Ti is in good agreement with the predictions of the [U_d (5) \otimes U_{T_d} (3)]⊕U_{T_s} (3) symmetry limit.     

Critical behaviour in nuclear structure from spherical to axially symmetric deformed shape in IBM

To compare with the predictions of the transitional dynamical symmetry X(5) proposed by Iachello (2001 Phys. Rev. Lett. 87 052502), the critical behaviours of U(5)--SU(3) are studied in the space of two control parameters in the interacting boson model (IBM). A simple-shaped phased diagram has been presented. It is found that X(5) predictions cannot be exactly reproduced by our calculations and that the best agreement is close to the calculations with boson numbers N = 11 and 12. By comparing with experimental data on X(5)-like nuclei, we find that X(5) predictions and IBM calculations can reproduce the energy ratios and E2 transition ones.     

Relation between the E(5) symmetry and the interacting boson model beyond the mean-field approximation

In a unified algebraic scheme,we investigate the relation between the E(5) symmetry and the interacting boson model beyond the mean-field level.The results indicate that the E(5) symmetry is actually in between the critical point of the U(5)-O(6) transition and the O(6) limit but it is fairly close to the former based on the phase diagram of the interacting boson model at the large boson number limit.In addition,an algebraic Hamiltonian of the E(5)-β2n model is proposed.     

Nuclear properties of Z=114 isotopes and shell structure of ~(298)114

The two-neutron separation energies(S_(2n)) and α-decay energies(Q_α) of the Z=114 isotopes are calculated by the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB) approach with the SLy5,T22,T32 and T43 interactions.It is found that the tensor force effect on the bulk properties is weak and the shell closure at N=184 is seen evidently with these interactions by analyzing the S_(2n) and Q_α evolutions with neutron number N.Meanwhile,the single-particle energy spectra of ~(298)114 are studied using the spherical SHFB approach with these interactions to furthermore examine the shell structure of the magic nucleus ~(298)114.It is shown that the shell structure is almost not changed by the inclusion of the tensor force in the Skyrme interactions.Finally,by examining the energy splitting of the three pairs of pseudospin partners for the protons and neutrons of ~(298)114,it is concluded that the pseudospin symmetry of the neutron states is preserved better than that of the proton states and not all of the pseudospin symmetries of the proton and neutron states are influenced by the tensor force.     

Possible 1d5／2 and 2s1／2 Level Inversion in the Proton—Rich Nucleus ^23Al

The discovered proton halo nucleus of ^23Al is investigated in the nonlinear relativistic mean-field(RMF) model with deformation using the NL075 force parameter,It is shown that there is an energy inversion between the (5/2)^ (202)and (1/2)^ (211)orbitals in the ^23Al nucleus,which may produce a large enhancement of the reaction cross section compared with the neighbouring nuclei.Meanwhile,the NL075 force parameter may be better than the other RMF parameters for the calculation of the large defromed nucleus ^23Al.     

Critical Behavior in Nuclear Structure from Spherical to γ-Soft Deformed Shape in IBM

Comparing with the predictions of the transitional dynamical symmetry E（5） proposed by Iachello [Phys. Rev. Lett. 85 （2000） 3580], the critical behaviors from U（5）-0（6） are studied in the space of two control parameters in the interacting boson model. A simple shape phase diagram has been presented. It is found that E（5） predictions cannot be exactly reproduced by our calculations and that the best agreement is close to the calculations with boson number N = 9. By comparing with experimental data on E（5）-like nuclei, we find that E（5） predictions and IBM calculations can reproduce the energy ratios and E2 transition ones.     

CRE Solvability,Nonlocal Symmetry and Exact Interaction Solutions of the Fifth-Order Modified Korteweg-de Vries Equation

This paper is concerned with the fifth-order modified Korteweg-de Vries(fmKdV) equation. It is proved that the fmKdV equation is consistent Riccati expansion(CRE) solvable. Three special form of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically. Furthermore, based on the consistent tanh expansion(CTE) method, the nonlocal symmetry related to the consistent tanh expansion(CTE) is investigated, we also give the relationship between this kind of nonlocal symmetry and the residual symmetry which can be obtained with the truncated Painlev′e method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlarged system and the corresponding finite transformation group is computed.     

Collectivity under random two-body interactions

In this paper we study collective motion under random two-body interactions in the fermion dynamical symmetry Model (FDSM). It is found that a Hamiltonian with the SO(8) symmetry of the FDSM does not give generic vibration and rotation under random interactions while that with the SP(6) symmetry does.     

Description of the Structural Properties of Low-Lying States in ^102Ru with IBM2

We describe the properties of low-lying states of ^102Ru within the framework of the proton-neutron interacting model IBM2. The theoretical predictions of the ground state, quasi-γ and quasi-β bands, and the ratios of the B（E2） transition strengths are reproduced very well. The structural properties of ^102Ru are identified in the parameters space of the interacting boson model （IBM2）. The characteristic feature of the energy spectrum structure exhibits that ^102Ru is very close to the critical point of Uπv（5）-Oπv（6） transition and towards Uπv（5） symmetry. The key sensitive quantities of the B（E2） branching ratio clearly indicate that ^102Ru is a primary Oπv（6） symmetry, while with a somewhat Uπv（5） symmetry. It is possible that the shape coexistence persists in ^102Ru, whereas the evident fingerprint of the shape coexistence has not been observed.     

High-order harmonic generation in a two-color strong laser field with Bohmian trajectory theory

We theoretically study the high-order harmonic generation(HHG) in a two-color laser field using the Bohmian mechanics. Our results show that, for the case of a weak second-color laser field, the simulation of the HHG with only one central Bohmian trajectory is in a good agreement with the ab initio time-dependent Schr o¨dinger equation(TDSE) results.In contrast, with the increase of the amplitude of the second-color laser field, the HHG spectra from the single central Bohmian trajectory deviate from the TDSE results more and more significantly. By analyzing the Bohmian trajectories,we find that the significant deviation is due to the fact that the central Bohmian trajectory leaves the core quickly in the two-color laser field with the breaking of inversion symmetry. Interestingly, we find that another Bohmian trajectory with different initial position, which keeps oscillating around the core, could qualitatively well reproduce the TDSE results. Furthermore, we study the HHG spectrum in a two-color laser field with inversion symmetry and find that the HHG spectrum in TDSE can be still well simulated with the central Bohmian trajectory. These results indicate that, similar to the case of one color laser field, the HHG spectra in a two-color laser field can be also reproduced with a single Bohmian trajectory,although the initial position of the trajectory is dependent on the symmetry of the laser field. Our work thus demonstrates that Bohmian trajectory theory can be used as a promising tool in investigating the HHG process in a two-color laser field.     

Two-dimensional Langevin modeling of fission dynamics of the excited compound nuclei ~(188)Pt,~(227)Pa and ~(251)Es

A stochastic approach based on one-and two-dimensional Langevin equations is applied to calculate the pre-scission neutron multiplicity,fission probability,anisotropy of fission fragment angular distribution,fission cross section and the evaporation cross section for the compound nuclei ~(188)Pt,~(227)Pa and ~(251)Es in an intermediate range of excitation energies.The chaos weighted wall and window friction formula are used in the Langevin equations.The elongation parameter,c,is used as the first dimension and projection of the total spin of the compound nucleus onto the symmetry axis,K,considered as the second dimension in Langevin dynamical calculations.A constant dissipation coefficient of K,γk=0.077(MeV zs)~(-1/2),is used in two-dimensional calculations to reproduce the above mentioned experimental data.Comparison of the theoretical results of the pre-scission neutron multiplicity,fission probability,fission cross section and the evaporation cross section with the experimental data shows that the results of two-dimensional calculations are in better agreement with the experimental data.Furthermore,it is shown that the two-dimensional Langevin equations together with a dissipation coefficient of K,γk=0.077(MeV zs)~(-1/2),can satisfactorily reproduce the anisotropy of fission fragment angular distribution for the heavy compound nucleus(251)~Es.However,a larger value of γk=0.250(MeV zs)~(-1/2)is needed to reproduce the anisotropy of fission fragment angular distribution for the lighter compound nucleus(227)Pa.     

Spin Symmetry for Anti-Lambda Spectrum in Atomic Nucleus

The spin symmetry of the anti-Lambda spectrum in nucleus 16O is studied in the relativistic mean field theory. The spin-orbit splittings of spin doublets are found to be around 0.03-0.07MeV and the dominant components of the Dirac spinor for the anti-Lambda spin doublets are found to be near identical. It is indicated that there is an even better spin symmetry in the anti-Lambda spectrum than that in the anti-nucleon spectrum.     

Symmetry energy at subsaturation densities and the neutron skin thickness of ~(208)Pb

The mass-dependent symmetry energy coefficients asym(A) has been extracted by analysing the heavy nuclear mass differences reducing the uncertainties as far as possible in our previous work.Taking advantage of the obtained symmetry energy coefficient asym(A) and the density profiles obtained by switching off the Coulomb interaction in208 Pb,we calculated the slope parameter L0.11 of the symmetry energy at the density of 0.11 fm-3.The calculated L0.11 ranges from 40.5 Me V to 60.3 Me V.The slope parameter L0.11 of the symmetry energy at the density of 0.11 fm-3is also calculated directly with Skyrme interactions for nuclear matter and is found to have a fine linear relation with the neutron skin thickness of208 Pb,which is the difference of the neutron and proton rms radii of the nucleus.With the linear relation the neutron skin thickness Rn pof208 Pb is predicted to be 0.15–0.21 fm.     

Molecular Dynamics Simulation of Xe Behavior in U-Mo Alloys Fuel

Classical molecular dynamics simulations are used to investigate the fission gas Xe behavior in a U-Mo alloy fuel matrix. The embedded atom method potential proposed by Smirnova et al. is used to describe the U-Mo-Xe system. The results show that the initial configuration of interstitial Xe atoms in U-Mo alloys is very instable and has a strong tendency to get together and to form a Xe bubble by ejecting the adjacent U atoms and Mo atoms from their former normal lattice sites. The pressure in Xe bubbles is initially quite high and then drops with increasing Xe concentration obviously. The matrix swelling of U-Mo alloys associated with the Xe bubble growth follows approximately a linear relationship with the ratio of Xe to U at low Xe concentration while the rate of swelling increases rapidly at high Xe concentration. The simulation results are in good agreement with the experimental data. The recovery of the damaged structure in the U-Mo alloys matrix is also investigated. It is shown that a damaged structure cannot be recovered completely after a system is relaxed for a long time while still having lots of defects.