Phenomenological Scaling of Rapidity Dependence for Anisotropic Flows in 25 MeV/nucleon Ca＋Ca by Quantum Molecular Dynamics Model

Anisotropic flows （v1, v2, v3 and v4） of light fragments up to the mass number 4 as a function of rapidity are studied for 25 MeV/nucleon ^40Ca ＋ ^40Ca at large impact parameters by a quantum molecular dynamics model. A phenomenological scaling behaviour of rapidity dependent flow parameters vn （n = 1, 2, 3 and 4） is found as a function of mass number plus a constant term, which may arise from the interplay of collective and random motions. In addition, v4/v2^2 keeps to be almost independent of rapidity and remains a rough constant of 1/2 for all light fragments.     

Isospin Effects on Anisotropic Flows in Intermediate Energy Heavy Ion Collisions

Anisotropic flows per nucleon （v1/A, v2/A, v3/A and v4/A） of light fragments up to the mass number 4 as a function of transverse momentum per nucleon are studied for 55 Me V/nucleon 58Fe＋58Fe and 58 Ni＋ 58 Ni at large impact parameters by the isospin-dependent quantum molecular dynamics model. The effects of symmetry energy and nucleon-nucleon cross sections, which are both isospin-dependent on anisotropic flows, are studied in detail. In comparison of the two systems with or without symmetry potential term, the results show that the strength of flows is sensitive to symmetry potential and nucleon-nucleon cross sections, which mainly cause a repulsion effect in this energy region.     

Potential Energy Surfaces of Nitrogen Dioxide for the Ground State

The potential energy function of nitrogen dioxide with the C2v symmetry in the ground state is represented using the simplified Sorbie-Murrell many-body expansion function in terms of the symmetry of NO2. Using the potential energy function, some potential energy surfaces of NO2（C2v, X^-^2A1）, such as the bond stretching contour plot for a fixed equilibrium geometry angle θ and contour for O moving around N-O （R1）, in which R1 is fixed at the equilibrium bond length, are depicted. The potential energy surfaces are analysed. Moreover, the equilibrium parameters for NO2 with the C2v, Cs and Dsn symmetries, such as equilibrium geometry structures and energies, are calculated by the ab initio （CBS-Q） method.     

Potential energy surfaces of ozone in the ground state

Equilibrium parameters of ozone, such as equilibrium geometry structure parameters, force constants and dissociation energy are presented by CBS-Q ab initio calculations. The calculated equilibrium geometry structure parameters and energy are in agreement with the corresponding experimental values. The potential energy function of ozone with a C2v symmetry in the ground state is described by the simplified Sorbie-Murrell many-body expansion potential function according to the ozone molecule symmetry. The contour of bond stretching vibration potential of an O3 in the ground state, with a bond angle （θ） fixed, and the contour of O3 potential for O rotating around O1-O （R1）, with O1-O bond length taken as the one at equilibrium, are plotted. Moreover, the potentials are analysed.     

Potential energy curves and analytical potential energy functions of the metastable states of B2^＋＋

The multi-reference configuration interaction method and aug-cc-pvqz （AVQZ） have been used to calculate potential energy curves （PECs） of the singlet and triplet states of the riu and rig symmetry of B2＋＋. All of the four states （^l∏u, ^1∏g, ^3∏u and ^3∏g） are found to be metastable states, though the potential well of ^3∏u symmetry is very shallow. Based on the PECs, the analytical potential energy functions （APEFs） of these states have been fitted using the least square fitting method and two models of function. The spectroscopic parameters of each state are also calculated, and are compared with other investigations in the literature. The credibility and veracity of the two functions are evaluated. Some ideas to improve the fitting accuracy are presented. Also the vibrational levels for each state are predicted by solving the SchrSdinger equation of nuclear motion.     

Quadratic,Higgs and hilltop potentials in Palatini gravity

In this work, we study the theory of inflation with the non-minimally coupled quadratic, standard model Higgs, and hilltop potentials, through ξφ~2R term in Palatini gravity. We first analyze observational parameters of the Palatini quadratic potential as functions of ξ for the high-N scenario. In addition to this, taking into account that the inflaton field f has a non-zero vacuum expectation value v after inflation, we display observational parameters of well-known symmetry-breaking potentials. The types of potentials considered are the Higgs potential and its generalizations, namely hilltop potentials in the Palatini formalism for the high-N scenario and the low-N scenario. We calculate inflationary parameters for the Palatini Higgs potential as functions of v for different ξ values, where inflaton values are both φv and φv during inflation, as well as calculating observational parameters of the Palatini Higgs potential in the induced gravity limit for high-N scenario. We illustrate differences between the Higgs potential's effect on ξ versus hilltop potentials, which agree with the observations for the inflaton values for φv and ξ, in which v1 for both these high and low N scenarios. For each considered potential, we also display n_s-r values fitted to the current data given by the Keck Array/BICEP2 and Planck collaborations.     

Consistent Scaling Exponents at the Deconfined Quantum-Critical Point

We report a quantum Monte Carlo study of the phase transition between antiferromagnetic and valence-bond solid ground states in the square-lattice S=1/2 J-Q model.The critical correlation function of the Q terms gives a scaling dimension corresponding to the value v=0.455±0.002 of the correlation-length exponent.This value agrees with previous(less precise) results from conventional methods,e.g.,finite-size scaling of the nearcritical order parameters.We also study the Q-derivatives of the Binder cumulants of the order parameters for L~2 lattices with L up to 448.The slope grows as L~(1/v) with a value of v consistent with the scaling dimension of the Q term.There are no indications of runaway flow to a first-order phase transition.The mutually consistent estimates of v provide compelling support for a continuous deconfined quantum-critical point.     

Sensitive Probe for Symmetry Potential

Based on both very obvious isospin effect of the neutron-proton number ratio of nucleon emissions （n/p）nud on symmetry potential and （n/p）nucl＇s sensitive dependence on symmetry potential in the nuclear reactions induced by halo-neutron projectiles, compared to the same mass stable projectile, probing symmetry potential is investigated within the isospin-dependent quantum molecular dynamics with isospin and momentum-dependent interactions for different symmetry potentials U;ym and U2^sym. It is found that the neutron-halo projectile induces very obvious increase of （n/p）nucl and strengthens the dependence of （n/p） l on the symmetry potential for all the beam energies and impact parameters, compared to the same mass stable projectile under the same incident channel condition. Therefore （n/p）nucl induced by the neutron-halo projectile is a more favourable probe than the normal neutron-rich and neutron-poor projectiles for extracting the symmetry potential.     

Tuning and Validation of the Lundcharm Model with J/ψ Decays

Using J/ψ decays collected with the BES Ⅲ detector, Lundcharm model parameters are optimized with J/ψlight hadron decays. The dependence of the response function on model parameters is approximated up to the quadratic term, and the model parameters are optimized by simultaneously fitting J/ψ inclusive charged track distributions and event shapes. The Monte Carlo simulations show that optimal parameters yield satisfactory MC distributions as compared to both the J/ψ and ψ（2S） data distributions. These optimal values are suggested for the Lundcharm model to produce J/ψ and ψ（2S） decays to light hadrons.     

Assignment of Photoelectron Spectra of MC2 （M= V, Cr, Fe, and Co）

Hybrid density functional theory （DFT） calculations are performed to study MC2 （M= V, Cr, Fe and Co） clusters in the neutral and anionic charge states. We find that the equilibrium geometries of MC2 and their anions are all cyclic structures with C2v symmetry, which agrees well with the previous theoretical studies. The Mulliken charge and spin populations of MC2 clusters and their anions are also calculated, and it is found that the electron charge transformations from anions to neutral molecules mainly take place on the M atoms. Time-dependent DFT is used to calculate the excited states, and a theoretical assignment for the features in the experimental photoelectron spectrum is given, which are in good agreement with the available experimental data.     

Isotopic effect of Cl2+ rovibronic spectra in the A-X system

This paper studies the isotopic effect of Cl2+ rovibronic spectra in the A2Πu(Ω=1/2) X 2Πg(Ω= 1/2) system.Based on the experimental results of the molecular constants of 35 Cl2+,it calculates the vibrational isotope shifts of the(2,7) and(3,7) band between the isotopic species 35 Cl+2,35 Cl 37 Cl+and 37 Cl2+,and estimates the rotational constants of both A 2 Π u and X 2 Π g states for the minor isotopic species 35 Cl 37 Cl+and 37 Cl2+.The experimental results of the spectrum of 35 Cl 37 Cl+(3,7) band proves the above mentioned theoretical calculation.The molecular constants and thus resultant rovibronic spectrum for 37 Cl2+ were predicted,which will be helpful for further experimental investigation.     

The splitting of low-lying states for hydroxyl molecule under spin orbit coupling

The splitting of potential energy curves for the states X^2Ⅱ3/2, ^2Ⅱ1/2 and A^2∑＋ of hydroxyl OH under spin-orbit coupling （SOC） has been calculated by using the SO multi-configuration quasi-degenerate perturbation theory （SO- MCQDPT）. Their Murrell Sorbic （M-S） potential functions have been derived, then, the spectroscopic constants for X^2Ⅱ3/2, ^2Ⅱ1/2 and A^2∑＋ have been derived from the M-S function. The calculated dissociation energies for the three states are Do[OH（X^2Ⅱ3/2）]=34966,632cm^-1, Do[OH（^2Ⅱ1/2）]=34922.802cm^-1, and Do[OH（A^2∑ ）]=17469.794cm^-1, respectively. The vertical excitation energy u[^2Ⅱ1/2（v = 0） → X^2Ⅱ3/2（v = 0）] = 139.6cm^-1. All the spectroscopic data for the X^2Ⅱ3/2 and ^2Ⅱ1/2 are given for the first time except the dissociation energy of X^2Ⅱ3/2.     

Electron tunnelling phase time and dwell time through an associated delta potential barrier

The electron tunnelling phase time τP and dwell time τD through an associated delta potential barrier U(x) = ξδ(x) are calculated and both are in the order of 10^-17～10^-16s. The results show that the dependence of the phase time on the delta barrier parameter ξ can be described by the characteristic length lc = h^2/meξ and the characteristic energy Ec=meξ^2/h^2 of the delta barrier, where me is the electron mass, lc and Ec are assumed to be the effective width and height of the delta barrier with lcEc=ξ, respectively. It is found that TD reaches its maximum and τD = τp as the energy of the tunnelling electron is equal to Ec/2, i.e. as lc =λDB, λDB is de Broglie wave length of the electron.     

A possible experimental observable for the determination of neutron skin thickness

The dependence between neutron skin thickness and neutron abrasion cross section （σnabr） for neutron-rich nuclei is investigated within the framework of the statistical abrasion ablation model. Assuming that the density distributions for proton and neutron are of Fermi-type, and adjusting the diffuseness parameter of neutron density distribution in the droplet model, we find out the good linear correlation between the neutron skin thickness and the abrasion cross section σnabr for neutron-rich nuclei. The uncertainty of neutron skin thickness determined from σnabr is very small. It is suggested that σnabr can be used as a new experimental observable to extract the neutron skin thickness for neutronrich nucleus. The scaling behaviours between neutron skin thickness and σnabr, separately, for isotopes of ^26-35Na, ^44-56Ar, ^48-60Ca, ^67-78Ni are also investigated.     

Theoretical calculation of the quadratic Zeeman shift coefficient of the 3P0o clock state for strontium optical lattice clock

In the weak-magnetic-field approximation, we derived an expression of quadratic Zeeman shift coefficient of $^3P^{\rm o}_0$ clock state for $^{88}$Sr and $^{87}$Sr atoms. By using this formula and the multi-configuration Dirac-Hartree-Fock theory, the quadratic Zeeman shift coefficients were calculated. The calculated values $C_2$ = $-23.38(5)$ MHz/T$^2$ for $^{88}$Sr and the $^3P^{\rm o}_0$, $F = 9/2$, $M_F = \pm9/2$ clock states for $^{87}$Sr agree well with the other available theoretical and experimental values, especially the most accurate measurement recently. In addition, the calculated values of the $^3P^{\rm o}_0$, $F = 9/2$, $M_F = \pm9/2$ clock states were also determined in our $^{87}$Sr optical lattice clock. The consistency with measurements verifies the validation of our calculation model. Our theory is also useful to evaluate the second-order Zeeman shift of the clock transition, for example, the new proposed $^1S_0$, $F = 9/2$, $M_F = \pm5/2$-${}^3P^{\rm o}_0$, $F = 9/2$, $M_F = \pm3/2$ transitions.     

SF_6分子最高占据轨道对称性的判断

量化计算是理论研究分子的重要手段,对于具有高对称群的分子,采用子群计算是常用的方法.分子的电子态或分子轨道等的对称性在子群的表示中会出现重迭,从而不能从子群的结果直接给出电子态或分子轨道对称性的归属.本文以如何判断SF6基态1 A_(1g)的电子组态中最高占据轨道的对称性为例来解决这个问题.针对某些文献中的SF6基态1 A1g的电子组态中,最高占据轨道对称性是T_(1g)却写成T_(2g)的问题,采用Molpro量化计算软件,对SF6基态的平衡结构,进行了HF/6-311G*计算,得到了能量三重简并的最高占据轨道的函数表达式,进而运用O_h群的对称操作作用在三个轨道函数上,得到各操作的矩阵表示,于是得到特征标,最后确定了最高占据轨道为T_(1g)对称性.     

Spin polarization effect for Os2 molecule

Density functional Theory （DFT） （B3p86） of Gaussian03 has been used to optimize the structure of Os2 molecule. The result shows that the ground state for Os2 molecule is 9-multiple state and its electronic configuration is ^9∑^＋g, which shows spin polarization effect of Os2 molecule of transition metal elements for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions with higher energy states. So, the fact that the ground state for Os2 molecule is a 9-multiple state is indicative of spin polarization effect of Os2 molecule of transition metal elements. That is, there exist 8 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Os2 molecule is minimized. It can be concluded that the effect of parallel spin of Os2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell-Sorbie potential functions with the parameters for the ground state ^9∑^＋g and other states of Os2 molecule are derived. Dissociation energy De for the ground state of Os2 molecule is 3.3971eV, equilibrium bond length Re is 0.2403nm, vibration frequency ωe is 235.32cm^-1. Its force constants f2, f3, and f4 are 3.1032×10^2aJ·nm^-2, -14.3425×10^3aJ·nm^-3 and 50.5792×10^4aJ·nm^-4 respectively. The other spectroscopic data for the ground state of Os2 molecule ωexe, Be and ae are 0.4277cm^- 1, 0.0307cm^- 1 and 0.6491 × 10^-4cm^-1 respectively.     

Elastic collisions between Si and D atoms at low temperatures and accurate analytic potential energy function and molecular constants of the SiD（χ^2П） radical

Interaction potential of the SiD(X2Π) radical is constructed by using the CCSD(T) theory in combination with the largest correlation-consistent quintuple basis set augmented with the diffuse functions in the valence range. Using the interaction potential, the spectroscopic parameters are accurately determined. The present D0, De, Re, ωe, αe and Be values are of 3.0956 eV, 3.1863 eV, 0.15223 nm, 1472.894 cm-1, 0.07799 cm-1 and 3.8717 cm-1, respectively, which are in excellent agreement with the measurements. A total of 26 vibrational states is predicted when J=0 by solving the radial Schro¨dinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J=0 are reported for the first time, which are in good accord with the available experiments. The total and various partial-wave cross sections are calculated for the elastic collisions between Si and D atoms in their ground states at 1.0×10-11–1.0×10-3 a.u. when the two atoms approach each other along the SiD(X2Π) potential energy curve. Four shape resonances are found in the total elastic cross sections, and their resonant energies are of 1.73×10-5, 4.0×10-5, 6.45×10-5 and 5.5×10-4 a.u., respectively. Each shape resonance in the total elastic cross sections is carefully investigated. The results show that the shape of the total elastic cross sections is mainly dominated by the s partial wave at very low temperatures. Because of the weakness of the shape resonances coming from the higher partial waves, most of them are passed into oblivion by the strong s partial-wave elastic cross sections.     

Observational constraints on the accelerating universe in the framework of a 5D bounce cosmological model

In the framework of a five-dimensional (5D) bounce cosmological model, a useful function f (z) is obtained by giving a concrete expression of deceleration parameter q(z) = q1 + q2/1 +ln(1+ z) . Then using the obtained Hubble parameter H(z) according to the function f (z), we constrain the accelerating universe from recent cosmic observations: the 192 ESSENCE SNe Ia and the 9 observational H(z) data. The best fitting values of transition redshift zT and current deceleration parameter q0 are given as zT = 0.65-0.12 +0.25 and q0 = 0.76 -0.15+0.15(1σ). Furthermore, in the 5D bounce model it can be seen that the evolution of equation of state (EOS) for dark energy wde can cross over -1 at about z = 0.23 and the current value w0de =-1.15 <-1. On the other hand, by giving a concrete expression of model-independent EOS of dark energy wde, in the 5D bounce model we obtain the best fitting values zT = 0.66 -0.08+0.11 and q0 = 0.69-0.10+ 0.10(1σ) from the recently observed data: the 192 ESSENCE SNe Ia, the observational H(z) data, the 3-year Wilkinson Microwave Anisotropy Probe (WMAP), the Sloan Digital Sky Survey (SDSS) baryon acoustic peak and the x-ray gas mass fraction in clusters.