An ab initio investigation of the low-lying electronic states of Bell

Potential energy curves （PECs） for the ground state （X2∑＋） and the four excited electronic states （A2∏, B2∏, C2∑＋, 4∏） of a Bell molecule are calculated using the multi-configuration reference single and double excited configuration interaction （MRCI） approach in combination with the aug-cc-pVTZ basis sets. The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm, and the equilibrium bond length Re and the vertical excited energy Te are determined directly. It is evident that the X2∑＋, A2∏, B2∏, C2∑＋ states are bound and 4∏ is a repulsive excited state. With the potentials, all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero （J = 0） by numerically solving the radial SchrSdinger equation of nuclear motion. Then the spectroscopic data are obtained including the rotation coupling constant w e, the anharmonic constant WeXe, the equilibrium rotation constant Be, and the vibration-rotation coupling constant ae. These values are compared with the theoretical and experimental results currently available, showing that they are in agreement with each other.     

Multi-configuration Dirac-Hartree-Fock (MCDHF) calculations for Zn-like sequence from Z=48 to 54

The 4s4p excitation energies and the 4s2-4s4p E1 transitions for zinc-like ions from Z=48 to 54 are calculated by the multi-configuration Dirac-Hartree-Fock (MCDHF) method in this paper. The results for fine-structure energy levels, wavelengths and lifetimes between Z = 48 (Cd) and Z = 54 (Xe) are presented and compared with other theoretical and experimental results. The calculated values including core-valence correlation are found to be very similar to other theoretical and experimental values. We believe that our calculated values can guide experimentalists in identifying the fine-structure levels in their future work.     

Surface Corrugation in Rotational and Diffractive Scattering of O2 from LiF （001）

A quantum dynamic calculation on a five-dimensional O2/LiF （001） model system is performed using the multi-configuration time-dependent Hartree method. The obtained results show that the mechanism of rotational and diffractive excitation in details： Comparison with the rotational excited state, the initially non-rotational state is seen to favor the inelastic scattering in the rotational excitation process. The surface corrugation can damp the quantum interferences and produce a greater amount of rotational inelastic scattering at the expense of the elastic process in the rotational excitation process. The diffraction process and the average energy transferred into the rotational and diffractive mode are also discussed.     

Systematical Study on Ground-State Ionization Potentials for Boron and Carbon Isoelectronic Sequences with Z =6-42

The multi-configuration Dirac-Fock method is used in this work to calculate ground-state ionization potentials of Boron and Carbon isoelectronic sequences from Z = 6 to Z=42. And the contribution of relativistic corrections, nuclear volume effect, Breit and QED effects to tile results is discussed in the calculation. The results are compared with the scanty existing theoretical and experimental data in the literature and good agreements are achieved. Then analytical expressions of lonization potential along Boron and Carbon isoelectronic sequences are obtained.     

Relativistic Calculations for Be-like Iron

Relativistic configuration interaction calculations for the states of 1s²2s², 1s²2s3l (l=s,p,d) and 1s²2p3l (l=s,p,d) configurations of iron are carried out using relativistic configuration interaction (RCI) and multi-configuration Dirac-Fock (MCDF) method in the active interaction approach. In the present calculation, a large-scale configuration expansion was used in describing the target states. These results are extensively compared with other available calculative and experimental and observed values, the corresponding present results are in good agreement with experimental and observed values, and some differences are found with other available calculative values. Because more relativistic effects are considered than before, the present results should be more accurate and reliable.     

Isotope shift calculations for D lines of stable and short-lived lithium nuclei

The isotope shifts(TSs) for the 2s~2S_(1/2) to 2p~2P_J(J = 1/2,3/2) transitions of the lithium nuclei including the stable and short-lived isotopes are calculated based on the multi-configuration Dirac-Hartree-Fock method and the relativistic configuration interaction approach.The results are in good agreement with the previous theoretical and experimental results within a deviation less than 0.05%.The methods used here could be applied to the IS calculations for other heavier Li-like ions and few-electron systems.     

Theoretical Study of Relativistic Retardation Effects： the Abnormal Fine Structure of OⅡ

Using multi-configuration Dirac-Fock and relativistic configuration interaction methods with high-order corrections, we report our precise calculation results of the fine-structure energy levels of the ground-state configuration of OⅡ（1s^22s^22p^3）. Our calculated fine-structure splittings of ^2D3/2,5/2 and ^2p1/2,3/2 are abnormal We elucidate that the transverse （Breit） interaction, i.e. relativistic retardation effect, plays an important role for the abnormal fine-structure splittings. Our calculation results are in good agreement with experimental measurements.     

Multireference configuration interaction study on spectroscopic properties of low-lying electronic states of As2 molecule

The potential energy curves (PECs) of four electronic states (X1Σ+g , e3△u , a 3 Σ-u , and d 3Πg ) of an As 2 molecule are investigated employing the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent aug-cc-pV5Z basis set. The effect on PECs by the relativistic correction is taken into account. The way to consider the relativistic correction is to employ the second-order Douglas-Kroll Hamiltonian approximation. The correction is made at the level of a cc-pV5Z basis set. The PECs of the electronic states involved are extrapolated to the complete basis set limit. With the PECs, the spectroscopic parameters (Te , Re , ωe , ωexe , ωeye , αe , βe , γe , and Be ) of these electronic states are determined and compared in detail with those reported in the literature. Excellent agreement is found between the present results and the experimental data. The first 40 vibrational states are studied for each electronic state when the rotational quantum number J equals zero. In addition, the vibrational levels, inertial rotation and centrifugal distortion constants of d 3Πg electronic state are reported which are in excellent agreement with the available measurements. Comparison with the experimental data shows that the present results are both reliable and accurate.     

Mode control in a high gain relativistic klystron amplifier with 3 GW output power

Higher mode excitation is very serious in the relativistic klystron amplifier, especially for the high gain relativistic amplifier working at tens of kilo-amperes. The mechanism of higher mode excitation is explored in the FIC simulation and it is shown that insufficient separation of adjacent cavities is the main cause of higher mode excitation. So RF lossy material mounted on the drift tube wall is adopted to suppress higher mode excitation. A high gain S-band relativistic klystron amplifier is designed for the beam current of 13 kA and the voltage of 1 MV. PIC simulation shows that the output power is 3.2 GW when the input power is only 2.8 kW.     

Charge Densities of Unstable Nuclei with Electron Scattering

Relativistic mean-field theory and phase-shift analysis are combined together to investigate the elastic Coulomb scattering between electrons and unstable nuclei. Electron scattering at several different energies is studied and compared, in order to see the energy dependence of electron-nucleus scattering. It is shown that electron scattering at 200 MeV or 300 MeV can be used to reveal electron-nucleus scattering information around the first diffraction minimum. Shifts in opposite directions are obtained for the first diffraction minima of the electron scattering off the ground and first excited states of ^17F with ^16O as reference, and similar effects are obtained for ^18Ne. Besides, some neutron-rich N = 8 isotones are also studied. Results show that electron scattering will be very useful and important in studying both proton- and neutron-rich nuclei in the future.     

Octupole deformation for Ba isotopes in a reflection-asymmetric relativistic mean-field approach

The potential energy surfaces of even-even 142-156Ba are investigated in the constrained reflectionasymmetric relativistic mean-field approach with parameter set PK1. It is shown that for the ground states, 142Ba is near spherical,156Ba well quadrupole-deformed, and in between 144-154Ba octupole deformed. In particular, the nuclei 148,150Ba with N=92, 94 have the largest octupole deformations. By including the octupole degree of freedom, energy gaps N = 88, N = 94 and Z = 56 near Fermi surfaces for the singleparticle levels in 148Ba with β2 ～ 0.26 and β3 ～ 0.17 are found. Furthermore, the performance of the octupole deformation driving pairs （ν2f7/2, ν1i13/2） and （π2d5/2, π1h11/2） is demonstrated by analyzing the singleparticle levels near Fermi surfaces in 148Ba.     

Rigorous spectral representation of relativistic random phase approximation for finite nuclei

By using the rigorous spectral representation of relativistic random phase approximation, the low-lying excitation of finite nuclei and its longitudinal response function for quasielastic electron scattering are calculated in the σ-ω model of quantum hadrodynamics. It is shown that the reproduction of the correct order of the 1- and 3- excitation states of 16O is due to the contribution of the exchange vertex. There is no significant influence of the retardation effect on the low-lying excitation states. In contrast, the retardation effect plays an important role in the electron scattering process of nuclei. The theoretical longitudinal responses of 12C and 40Ca, including the contributions of the exchange vertex and the retardation effect, are suppressed and reproduce the experimental data better than the results excluding them.     

Theoretical Study on N = 126 Shell Evolution

The nuclei around magic number N = 126 are investigated in the deformed relativistic mean field （RMF） model with effective interactions TMA. We focus investigations on the N = 126 isotonic chain. The N = 126 shell evolution is studied by analyzing the variations of two-neutron （proton） separation energies, quadruple deformations, single particle levels etc. The good agreement of two-neutron separation energies between experimental data and calculated values is reached. The RMF theory predicts that the sizes of N = 126 shell become smaller and smaller with the increasing of proton number Z. However, the N = 126 shell exists in our calculated region all along. According to the calculated two-proton separation energies, the RMF theory suggests ^220Pu is a two-proton drip-line nucleus in the N = 126 isotonic chain.     

Gound State Properties of Nuclei in ^295118 α-Decay Chain

The properties of nuclei belonging to the α-decay chain of superheavy element ^295118 have been studied in the framework of axially deformed relativistic mean field （RMF） theory with the parameter set of NL-Z2 in the blocked BCS approximation. Some ground state properties such as binding energies, deformations, and α-decay energies Qα have been obtained and agree well with those from finite-range droplet model （FRDM）. The single-particle spectra of nuclei in ^295118 α-decay chain show that the shell gaps present obviously nucleon number dependence. The root-mean-square （rms） radii of proton, neutron and matter distributions change slowly from ^283112 to ^295118 but dramatically from ^279110 to ^283112, which may be due to the subshell closure at Z = 110 in ^279110. The α-decay half-lives in 295118 decay chain are evaluated by employing the cluster model and the generalized liquid drop model （GLDM）, and the overall agreement is found when they are compared with the known experimental data. The α-decay lifetimes obtained from the cluster model are slightly larger than those of GLDM ones. Finally, we predict the α-decay half-lives of Z=118, 116, 114, 112 isotopes using the cluster model and GLDM, which also indicate these two models can corroborate each other in studies on superheavy nuclei. The results from GLDM are always lower than those obtained from the cluster model.     

Deexcitation Energy of Superdeformed Secondary Minima as a Probe to Density Dependence of Symmetry Energy

Deexcitation energies of superdeformed secondary minima of odd-odd A u and T1 isotopes are investigated with the relativistic mean field （RMF） model where the isoscalar-isovector coupling is included to change the symmetry energy. It is verified by the theoretical analysis and numerical results that the deexcitation energies of superdeformed secondary minima relative to the ground states in these heavy nuclei are sensitive to differences in the symmetry energy. In particular, the linear correlation between the deexeitation energies of odd-odd Au and T1 isotopes and the neutron skin thickness in 208Pb is established. Moreover, explorations are extended to superdeformed candidates of other mass regions. It is found that the linear correlation can even be established between the deexcitation energies and the symmetry pressure at subsaturation density. These indicate that deexcitation energies can serve as a probe to the density dependence of the symmetry energy.     

System size dependence in backward relativistic hadron production in pA and AA collisions

Abstract： In this comprehensive study the multiplicity characteristics of the backward emitted relativistic hadron （shower particle） through hadron-nucleus and nucleus-nucleus are overviewed in three dimensions. These dimensions are the projectile size, target size, and energy. To confirm the universality in this production system, wide ranges of system size and energy （Elab～2.1 A up to 200 A GeV） are used. The multiplicity characteristics of this hadron imply a limiting behavior with respect to the projectile size and energy. The target size is the main effective parameter in this production system. The exponential decay shapes is a characteristic feature of the backward shower particle multiplicity distributions. The decay constant changes with the target size to be nearly 2.02, 1.41, and 1.12 for the interactions with CNO, Era, and AgBr nuclei, respectively, irrespective of the projectile size and energy. While the backward production probability and average multiplicity are constants at different projectile sizes and energies, they can be correlated with the target size in power law relations.     

Adomian Decomposition Method and Pade Approximants for Nonlinear Differential-Difference Equations

Combining Adomian decomposition method （ADM） with Pade approximants, we solve two differentiaidifference equations （DDEs）： the relativistic Toda lattice equation and the modified Volterra lattice equation. With the help of symbolic computation Maple, the results obtained by ADM-Pade technique are compared with those obtained by using ADM alone. The numerical results demonstrate that ADM-Pade technique give the approximate solution with faster convergence rate and higher accuracy and relative in larger domain of convergence than using ADM.     

Nuclear structure around 80Zr

Recent years have witnessed intense activity concerning the study of nuclei with equal numbers of neutrons and protons （N = Z）. Exotic properties have been exhibited in the N = Z nuclei, especially in those with atomic masses around 80. In the present paper, the projected shell model（PSM）together with a relativistic Hartree-Bogoliubov （RHB） theory is used to study the nuclear structure near the N = Z line in the mass A ≈ 80 region. For three Zr isotopes 80,82,84Zr, the projected potential energy surfaces and ground state bands are calculated. It is shown that shape coexistence occurs in all of these nuclei. Moreover, we find that the residual neutron-proton interaction strongly affects the ground state band of 80Zr; however, it slightly modifies those of 82Zr and 84Zr.     

Influence of Hyperon-Hyperon Interaction on Properties of Hadronic Star

The influences of hyperon-hyperon interaction on the overall properties of hadronic star are investigated in the framework of relativistic mean field （RMF） theory. For certain hyperon coupling, the weaker hyperon-hyperon interaction can lead to the heavier hadronic star, which accords with the observation of heavy neutron star in X-ray binaries. We find that the threshold densities of the hyperons with larger masses are brought to a lower values with the increase of the hyperon-hyperon interaction. The possibility of the existence of hyperon star is checked with the consideration of hyperon-hyperon interaction.     

前身中子星转动惯量的研究

The influences of σ^＊ and Ф mesons, temperature and coupling constants of nucleons on the moment of inertia of the proto neutron star （PNS） are examined in the framework of relativistic mean field theory for the baryon octet {n, p, A, ∑^-, ∑^,∑^＋,^-, ^0} system. It is found that, compared with that without considering σ^＊ and Ф mesons, the moment of inertia decreases. It is also found that the higher the temperature, the larger the incompressibility and symmetry energy coefficient, and the larger the moment of inertia of a PNS. The influence of temperature and coupling constants of the nucleons on the moment of inertia of a PNS is larger than that of the σ^＊ and Ф mesons.