Low-Lying Isomers of(TiO_(2))_(n)(n=2-8)Clusters

Although there are diverse bond features of Ti and O atoms,so far only several isomers have been reported for each(TiO_(2))n cluster.Instead of the widely used global optimization,in this work,we search for the low-lying isomers of(TiO_(2))_(n)(n=2-8)clusters with up to 10000 random sampling initial structures.These structures were optimized by the PM6 method,followed by density functional theory calculations.With this strategy,we have located many more low-lying isomers than thosereported previously.The number of isomers increases dramatically with the size of the cluster,and about 50 isomers were found for(TiO_(2))_(7) and(TiO_(2))_(8) with the energy within 30 kcal/mol.Furthermore,new lowest isomers have been located for(TiO_(2))_(5) and(TiO_(2))_(8),and isomers with three terminal oxygen atoms,five coordinated oxygen atoms as well as six coordinated titanium atoms have been located.Our work highlights the diverse structural features and a large number of isomers of small TiO_(2) clusters.

AB INITIO STUDY OF LOW-LYING ELECTRONIC STATES OF THE AsH_2 RADICAL

The equilibrium geometries,excitation energies,force constants and vibrational frequencies for the low-ly- ing electronic states X ~2B_1,~2A_1,~2B_2 and ~2A_2 of the AsH_2 radical have been calculated at the MRSDCI level with a 3-21G~* basis set.Our calculated geometries,excitation enegies and vibional frequencies for the X ~2B_1 and ~2A_1 states are in good agreement with available experimental data.The electronic transition dipole mo- ments,oscillator strengths for the ~2A_1→X ~2B_1 and ~2A_2→X ~2B_1 transitions,radiative lifetimes for the ~2A_1 and ~2A_2 states are calculated based on the MRSDC^1 wavefunctions,predicting results in reasonable agreement with available experiment.

Theoretical Investigation on the Low-Lying States of LaP Molecule

The completely unexplored LaP molecule is investigated by ab initio methods. Potential energy curves for the lowlying states of LaP are constructed by means of the diffusion Monte Carlo method combined with three different trial functions. Spectroscopic constants are also numerically derived and the ground state is assigned, looking forward to experimental comparisons. Moreover, variations of the permanent dipole moments as a function of the internuclear separation for the two lowest states of the diatomic LaP are studied and analyzed.

EVAPOTRANSPIRATION OF LOW-LYING PRAIRIE WETLAND IN MIDDLE REACHES OF HEIHE RIVER IN NORTHWEST CHINA

Low-lying prairie wetland, which has characteristics of both grassland and wetland, has irreplaceable ecological functions in inland river basins of Northwest China. Owing to its small-scale distribution, so far, the observation and research on it are rare. The estimation of evapotranspiration is significant to ecological and environmental construction, scientific management of pasture and protection of wetland. For studying the evapotranspiration （ET） of low-lying prairie wetland in the middle reaches of the Heihe River, an inland river, in Northwest China, the automatic weather station in Linze Ecological Experimental Station of Lanzhou University （39°15′ 3″N, 100°03′ 52″ E）, Linze, Gansu Province, was selected as a case study. Based on meteorological data collected, Bowen-Ratio Energy Balance （BREB） method was used to calculate the evapotranspiration （ET） of low-lying prairie wetland. The analysis results showed that in a whole year （September 2003 -August 2004）, the total ET was 611.5mm and mean daily 1.67mm/d. The ET varied with different growing stages. In non-growing stage （NGS）, initial growing stage （IGS）, middle growing stage （MGS） and end growing stage （EGS）, the ET was 0.57, 2.01, 3.82 and 1.49mrrdd, with a percentage of total ET of 18.26%, 9.20%, 61.83% and 10.71% respectively. In March, ET began to increase. But in April, the ET increased most. After that, it increased gradually and got the maximal value in July. From then on, the ET decreased gradually. In September, the ET decreased rapidly. With the ending of growing and the freezing of soil, the ET stopped from the middle of November to February in next year. Hourly ET analysis showed that at 8：00 a.m. （during MGS at 7：00 a.m.）, the evapotranspiration began, at 13：00 p.m. got its maximal value and at 19：00 p.m. （during MGS at 20：00 p.m.）, the evapotranspiration stopped. The intensity of ET in sunny day was much larger than that in cloudy day in the same growing stage.

The Analysis of Four Waters Converting Mechanism in Wet and Low-lying Farmland

Most of China's wetland areas are located in Sanjiang Plain (Three River Basin). It's area has 207×104 hm2 of wet and low-lying farmland, of which 59% is cropped. During 1970s and 1980s, the Chinese government organized intensive scientific research into potential changes to existing natural resources conditions for this farmland. The aim was to make the water resources regime beneficial to crop production. Arterial drainage, field drainage and appropriate sub-soil treatments were suggested. The Four Waters converting mechanism and the estimation of the Four Water converting amount in wet and low-lying farmland were discussed in the paper.

Effect of Electron Correlation and Breit Interaction on Energies, Oscillator Strengths, and Transition Rates for Low-Lying States of Helium

The transition energies, E1 transitional oscillator strengths of the spin-allowed as well as the spin-forbidden and the corresponding transition rates, and complete M1, E2, M2 forbidden transition rates for 1s^(2), 1s2s, and 1s2p states of He I, are investigated using the multi-configuration Dirac–Hartree–Fock method. In the subsequent relativistic configuration interaction computations, the Breit interaction and the QED effect are considered as perturbation, separately. Our transition energies, oscillator strengths, and transition rates are in good agreement with the experimental and other theoretical results. As a result, the QED effect is not important for helium atoms, however, the effect of the Breit interaction plays a significant role in the transition energies, the oscillator strengths and transition rates.

A SCF-SOCI STUDY ON THE LOW-LYING STATES OF H_3^+

The ground state and three low-lying states of the H_3^+ are determined by SOCI(Second Order Configuration Interaction) calculations. The results indicate that the ~3Σ_u^+ state of H_3^+ 3 is a bound state, but ~1A_1 and ~3A_1 states are not stable, each of them will dissociate into H_2^+ and H atom. The SOCI energy -1.1144065au at an equidistant nuclear separation of 1.296A is in good agreement with the lowest value reported so far.

MRSDCI STUDIES OF LOW-LYING ELECTRONIC STATES OF THE N_2F^+ MOLECULE

Ab initio electronic structure calculations are reported for low-lying electronic states,X ~1Σ^+and A ~1Π of the N_2F^+ molecule.Geometric parameters for the ground state X ~1Σ^+ are predicted by means of mul- tireference single and double excitation configuration interaction(MRSDCI)calculations with a double zeta plus polarization(DZ+P)basis set.Vertical excitation energy for these two electronic states is determined using MRSDCI/DZ+P calculations at the ground state equilibrium geometry.The oscillator strength for the X^1Σ+→ A ~1Π transition and the radiative lifetime for the A^1Π state are calculated based on the MRSDCI wavefunc- tions.

2-2 Lifetime Measurements of the Low-lying Excited States in 87 Zr and 87 Nb

Lifetime measurements of low-lying excited states in 87Zr and 87Nb have been performed via and coincidences. The 124 MeV 32S beam was delivered from the Sector-Focusing Cyclotron (SFC) of the Heavy Ion R-esearch Facility in Lanzhou (HIRFL). The parent nuclei 87Nb and 87Mo were produced by the respective reactions 58Ni (32S, 3p) and 58Ni (32S, 2p1n), at a beam energy 100 MeV through the 8 m Al degrader.

Moments of inertia of triaxial nuclei in covariant density functional theory

The covariant density functional theory(CDFT)and five-dimensional collective Hamiltonian(5DCH)are used to analyze the experimental deformation parameters and moments of inertia(MoIs)of 12 triaxial nuclei as extracted by Allmond and Wood[J.M.Allmond and J.L.Wood,Phys.Lett.B 767,226(2017)].We find that the CDFT MoIs are generally smaller than the experimental values but exhibit qualitative consistency with the irrotational flow and experimental data for the relative MoIs,indicating that the intermediate axis exhibites the largest MoI.Additionally,it is found that the pairing interaction collapse could result in nuclei behaving as a rigid-body flow,as exhibited in the^(186-192)Os case.Furthermore,by incorporating enhanced CDFT MoIs(factor of f≈1.55)into the 5DCH,the experimental low-lying energy spectra and deformation parameters are reproduced successfully.Compared with both CDFT and the triaxial rotor model,the 5DCH demonstrates superior agreement with the experimental deformation parameters and low-lying energy spectra,respectively,emphasizing the importance of considering shape fluctuations.

Studies of low-lying states of even-even Xe isotopes within the nucleon pair approximation

We study the relevance of nucleon pairs with higher spins, in addition to spin-zero and spin-two pairs (i.e., S D pairs), in low-lying states of even-even Xe nuclei. By including those higher-spin pairs in our configuration, we recalculate energy level schemes, elec trical quadrupole moments, magnetic moments and electric quadrupole transition rates, for low-lying states of even-even 128-142Xe nuclei. The agreement between our calculated results and the experimental data is substantially improved in comparison with previous studies.

Theoretical study on potential energy curves and spectroscopy properties of ground and low-lying excited electronic states of BrCl^+

The calculations on the potential energy curves and spectroscopic constants of the ground and low-lying excited states of BrCl^+, one of the important molecular ions in environment science, have been performed by using the multireference configuration interaction method at high level of theory in quantum chemistry. Through analyses of the effects of the spin-orbit coupling interaction on the electronic structures and spectroscopic properties, the multiconflguration characteristic of the X^2Π ground state and low-lying excited states was established. The spin-orbit coupling splitting energy of the X^2 Π ground state was calculated to be 1814 cm^(-1), close to the experimental value 2070 cm^(-1). The spin-orbit coupling splitting energy of the ~2Π(II) exited state was predicted to be 766 cm^(-1). The transition dipole moments and Frank-Condon factors of the 3/2(III)-X3/2 and 1/2(III)-1/2(I) transitions were estimated, and the radiative lifetimes of the two transitions were briefly discussed.

Ab initio multi-reference configuration interaction of the low-lying states of the AsP molecule

Nine low-lying electronic states of the AsP molecule, including ∑＋, ∏, and A symmetries with singlet, triplet, and quintet spin multiplicities, are studied using multi-reference configuration interaction method. The potential energy curves and the spectroscopic constants of these nine states are determined, and compared with the experimental observed data as well as other theoretical works available at present. Three quintet states are reported for the first time. Furthermore, the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least sauare fitting method.

Effect of pairing correlation on low-lying quadrupole states in Sn isotopes

We examined the low-lying quadrupole states in Sn isotopes in the framework of fully self-consistent Hartree-Fock+BCS plus QRPA.We focus on the effect of the density-dependence of pairing interaction on the properties of the low-lying quadrupole state.The SLy5 Skyrme interaction with surface,mixed,and volume pairings is employed in the calculations,respectively.We find that the excitation energies and the corresponding reduced electric transition probabilities of the first 2^(+) state are different,given by the three pairing interactions.The properties of the quasiparticle state,two-quasiparticle excitation energy,reduced transition amplitude,and transition densities in ^(112)Sn are analyzed in detail.Two different mechanisms,the static and dynamical effects,of the pairing correlation are also discussed.The results show that the surface,mixed,and volume pairings indeed affect the properties of the first 2^(+) state in the Sn isotopes.

Structural, Spectroscopic and Vibrational Properties for Low-Lying Electronic States of LiCl

A multireference configuration interaction （MRCI） study has been carried out on the LiCl molecule. The potential energy has been calculated over a wide range of internuclear separation for the 21 low-lying electronic states of the LiCl molecule dissociating into Li （^2S, ^2p, ^3S）＋Cl （^2p）. The （4）^1∑^＋, （3）∏, 1-3^3∑^＋, 1-3^3∏, 1,3Δ, ^1,3∑^-, （5）^1∑^＋,（4）^3∑^＋, （4）^3∏, （4）^3∏ excited states are studied for the first time in theory. Molecular spectroscopic constants .（Re, De,ωe, ωeΧe,Be and αe） have been derived for the 9 bound states （X^1∑^＋, （3）^1∑^＋, （2）^3∑^＋, ^1,3Δ, ^1,3∑^-, （4）^∏, （4）^3∏） with a regular shape, and the spectroscopic constants of ground states X^1 ∑^＋ are in good agreement with available experimental and theoretical values. The relative differences between experimental values and our values for Re, De, ωe, ωeΧe, Be and α3 are 1.02%, 0.60%, 1.72%, 9.46%, 2.0%, and 0.75%, respectively. Moreover, vibrational levels of 9 bound states, which have not been investigated experimentally, are computed.

Low-lying states of ^(184)W and ^(184)Os nuclei

The energy levels, transition energy, B （E2） values,intrinsic quadrupole moment Q_0 and potential energy surface for even-even ^（184）W and ^（184）Os nuclei were calculated using IBM-1. The predicted energy levels, transition energy, B（E2） values and intrinsic quadrupole moment Q_0 results are reasonably consistent with the experimental data. A contour plot of the potential energy surfaces shows that two interesting nuclei are deformed and have rotational characters.

The complex momentum representation approach and its application to low‑lying resonances in 17 O and^(29,31)F

Approaches for predicting low-lying resonances,uniformly treating bound,and resonant levels have been a long-standing goal in nuclear theory.Accordingly,we explored the viability of the complex momentum representation(CMR)approach coupled with new potentials.We focus on predicting the energy of the low-lying 2p_(3∕2)resonance in 17 O,which is critical for s-process nucleosynthesis and missing in previous theoretical research.Using a Woods-Saxon potential based on the Koning-Delaroche optical model and constrained by the experimental one-neutron separation energy,we successfully predicted the resonant energy of this level for the first time.Our predictions of the bound levels and 1d_(3∕2)resonance agree well with the measurement results.Additionally,we utilize this approach to study the near-threshold resonances that play a role when forming a two-neutron halo in^(29,31)F.We found that the CMR-based predictions of the bound-level energies and unbound 1f7∕2 level agree well with the results obtained using the scattering phase shift method.Subsequently,we successfully found a solution for the 2p_(3∕2)resonance with energy just above the threshold,which is decisive for halo formation.

Shell Model Description of Neutron-Deficient Sn Isotopes

The shell model calculations in the sdgh major shell for the neutron-deficient ^106,107,108,109Sn isotopes have been carried out by using CD-Bonn and Nijmegenl two-body effective nucleon-nucleon interactions. The singleshell states and the corresponding matrix elements needed for describing Sn isotopes are reconstructed to calculate the coefficient of fractional parantage by reducing the calculation requirements. This reconstruction allows us to do the shell model calculations of the neutron deficient Sn isotopes in very reasonable time. The results are compared to the recent high-resolution experimental data and found to be in good agreement with experiments.

Iterative solutions for low lying excited states of a class of SchrSdinger equation

The convergent iterative procedure for solving the groundstate Schrodinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.

Floquet Theory in Electron-Helium Scattering in a Nd:YAG Laser Field

The dynamics of laser-assisted elastic collisions in helium is studied. The formalism which will be developed to describe such laser-assisted collisions, treats the laser-projectile interaction to all orders, while the electron-helium interaction is treated within the first Born-approximation. Detailed calculations are performed for the elastic scattering of 50 eV electrons by helium accompanied by the transfer of photons. The numerical results show that the good physical interpretation of relevant processes needs to consider the maximum of atomic states.