Spectroscopic and structural proprieties of LiAr and LiAr<Subscript>2</Subscript> molecules

We determined and tried to understand the spectroscopic and structural properties of small LiAr and LiAr₂ molecules within a simple model considering LiAr as a result of interaction between a valence electron and a LiAr⁺ molecular ion. Potential energy curves, spectroscopic constants, and vibrational levels corresponding to the Li(2s, 2p, 3s, and 3p)+Ar dissociation are reported for the LiAr molecule. The depth of the potential well for the X ²Σ⁺ ground state is found to be 50 cm⁻¹ (the corresponding experimental value is (42.5±1.2) cm⁻1 [1]). R _e is determined to be 9.36 a.u. (the experimental value is 9.24 a.u.). For the first excited state A, R _e = 4.97 a.u. and D _e = 993cm ⁻¹ (the corresponding experimental values are 4.68 a.u. and (925−40) cm⁻¹, respectively [1]). The spacing between the vibrational levels for the ground and first excited states is in very good agreement with the experiment. For the ground state, the difference between our results and the data of the most recent experiment is about 1 cm⁻¹. The model has been extended to study the LiAr₂ molecule in two forms (linear and triangular). We have determined the potential energy surfaces of the states dissociating to Li(2s, 2p)+Ar₂ and thus found the triangular form to be more stable as compared to the linear one. We have also calculated the transition energy between the ground state and first excited states of this molecule. The emission spectrum of the Li(2s)+Ar₂→Li(2p)+Ar₂ transition in both forms redshifts as compared to the Li(2s)→Li(2p) atomic transition.     

Calculation of adiabatic potentials of Li<Subscript>2</Subscript><Superscript>+</Superscript>

We report adiabatic potential energy curves of the Li₂ ⁺ molecule. Our curves are tabulated according to internuclear distance from 2 a₀ to 100 a₀. We compare our theoretical results with the ones calculated by other authors and potential energy curves derived from experiments. For the ground state and 17 excited states we calculate spectroscopic parameters and compare them with parameters obtained by other authors. For the first time we present three new minima for 3²Σ_u ⁺, 4²Σ_u ⁺ and 2²Π_g excited states. In our approach we use the configuration interaction method where only the valence electrons of Li atoms are treated explicitly. The core electrons are represented by pseudopotential. All calculations are performed by means of MOLPRO program package.     

Calculation of potential energy curves for Rb2 including relativistic effects

All-electron relativistic calculations have been performed on the Rb₂ molecule. The molecular orbitals are optimized within a spin-free no-pair Hamiltonian formalism and spin-orbit coupling is treated using quasi-degenerate perturbation theory. Potential curves of the ground state and several excited states are calculated, and the spectroscopic constants T _e, D _e, R _e and ω_e are in good agreement with experimental values. The spin-orbit splittings at the 5p and 6p asymptotic limits are found to be underestimated by about 30%. Large perturbations in the spectra from the 1¹Σ⁺ _u(A) state are predicted due to an avoided crossing with a 1 ³Π_ub state caused by spin-orbit interaction. The predissociation dynamics of the 2 ¹Π_uC and 3 ¹Π_uD states is discussed. The calculations support the observation that a (1) ³ Δ_u state causes the fast predissociation of the ^{3 1}Π_uD state but rule out the (2)³Σ⁺ _u state as causing the slow predissociation at the lower part of the 3 ¹Π_uD potential energy curve.     

Electronic states of CsLi and CsLi<Superscript>+</Superscript> molecules

Configuration interaction calculations have been carried out on electronic states of the CsLi molecule and the CsLi⁺ cation. Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels are presented for the lowest states of ^1,3Σ⁺, ^1,3Π, and ^1,3Δ symmetries of the alkali dimer CsLi molecule dissociating into Cs (6s, 6p, 5d, 7s, and 7p) + Li (2s, 2p, 3s, 3p, and 3d) as well as for the lowest ²Σ⁺, ²Π, and ²Δ electronic states of the CsLi⁺ cation dissociating into Li (2s, 2p, 3s, 3p, and 3d) + Cs⁺ and Li⁺ + Cs (6s, 6p, 5d, 7s, and 7p). The results of the present many-electron configuration interaction calculations on the cation support the previous core-polarization effective potential calculations. The present calculations on the CsLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously. We have used an ab initio approach involving a nonempirical pseudopotential for the Li (1s²) and Cs cores and a core-valence correlation correction. A very good agreement of data from spectroscopic constants for some of the lowest states of the CsLi and CsLi⁺ molecules with those available in recent theoretical works has been obtained. The existence of numerous avoided crossings between electronic states of ²Σ⁺ and ²Π symmetries is related to a charge transfer process between the two ionic CsLi⁺ and LiCs⁺ systems.     

Graviton resonances in e<Superscript>+</Superscript>e<Superscript>-</Superscript>→μ<Superscript>+</Superscript>μ<Superscript>-</Superscript> at linear colliders with beamstrahlung and ISR effects

The electromagnetic radiation emitted by colliding beams is expected to play an important role at the next generation of high energy e⁺e^- linear colliders. Focussing on the simplest process, e⁺e^-→μ⁺μ^-, we show that, for suitable machine parameters and luminosity, radiative effects like initial state radiation (ISR) and beamstrahlung can be used to search for resonant graviton modes of the Randall–Sundrum model in an efficient manner.     

Theoretical study of the MgAr molecule and its ion Mg<Superscript>+</Superscript>Ar: potential energy curves and spectroscopic constants

The adiabatic potential energy curves of the low-lying electronic states of the MgAr molecule dissociating into Mg (3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p)+Ar have been investigated. The electronic structure of the Mg-Ar molecule is calculated using [Mg²⁺] and [Ar] core pseudopotentials complemented by the core polarization operators for both atoms, considering the molecule to be a two-electron system. The derived spectroscopic constants of the ground state and lower excited states are in good agreement with available experimental and theoretical work. In addition, for the purpose of checking the pseudopotential accuracy on a simpler related system, low lying potential energy curves of the single active electron Mg⁺Ar ion are also reported and the corresponding molecular constants are compared with those in the existing literature.     

Accurate spectroscopic properties of 10 Λ-S states and 25 Ω states of BS<Superscript>+</Superscript> cation including the electronic transition properties

The potential energy curves of 10 Λ–S states of BS⁺ yielded from the first four dissociation limits are calculated by the internally contracted multireference configuration interaction approach with the Davidson correction. The core-valence correlation and scalar relativistic corrections are included. Basis on the calculated potential energy curves, the spectroscopic parameters are evaluated. All the PECs are extrapolated to the complete basis set limit. The spin-orbit coupling are taken into account by the state interaction method with the Breit-Pauli Hamiltonian. Finally, the transition dipole moments, Franck-Condon Factors and radiative lifetimes of transitions from the 2³Π_0-, 2³Π₀₊, 2³Σ₀ ^- and 2³Σ₁ ^- states to ground state 1³Π₂ are predicted for future experiment.     

Theoretical investigation of the molecular structure and transition dipole moments of the NaK low lying electronic states

The electronic structure and the spectroscopic constants of the low lying electronic states of the NaK⁺ ionic molecule have been determined through using an ab initio approach involving a non-empirical pseudopotential for the Na and K cores and core valence correlation correction. The potential energy of nearly 26 electronic states of ²Σ⁺, ²Π, and ²Δ symmetries has been calculated up to their dissociation limit Na(4d) + K⁺ and Na⁺ + K(6s). Their spectroscopic constants (R_e, D_e, T_e, ω_e, ω_eχ_e, and B_e) are derived and compared with the few available theoretical studies. A good agreement has been found for the ground state and few excited states with previous works. New potential energy curves were presented, for the first time, for the higher excited states. Numerous avoided crossing between electronic states of ²Σ⁺, ²Π symmetries have been localized and analyzed. Their existences are related to the charge transfer between the two ionic molecules Na⁺K and NaK⁺. Furthermore, we have determined the transition dipole moments for several states and analyzed the avoided crossings related to charge transfer between alkaline atoms.     

从头计算研究BCl+基态和激发态的势能曲线和光谱性质

基于相关一致极化4zeta(aug-cc-pVQZ)基组, 应用量子化学从头计算中高水平的多参考组态相互作用方法计算了BCl⁺ 两个离解极限B⁺(¹S_g)+Cl(²P_u)和B (²P_u)+Cl⁺ (³P_g)的14个Λ-S态势能曲线. 在计算中考虑了Davidson修正(+Q)和标量相对论效应, 并首次在计算中考虑了BCl⁺ 的旋轨耦合效应, 获得了由能量最低的4个Λ-S态分裂出的7个Ω 态. 计算结果表明相同对称性的Ω 态的势能曲线存在着非常明显的避免交叉. 通过分析Λ-S态的电子结构, 得到了各态的电子跃迁特性, 并确认了电子态的多组态性质. 使用LEVEL程序通过求解径向的Schrödinger方程得到了束缚Λ-S 和Ω态的光谱参数D_e, R_e, T_e, ω_e, ω_eχ_e和B_e. 通过和已有的Λ-S态X²∑⁺ 的实验数据进行对比发现, 本文所得的计算结果与实验结果非常一致. 而文中其他电子态的光谱参数均为首次报道. 关键词： 势能曲线 光谱参数 多参考组态相互作用方法 旋轨耦合     

BF自由基X1∑+和a3∏态光谱常数和分子常数研究

采用内收缩多参考组态相互作用方法和相关一致基aug-cc-pV6Z, 对BF自由基X¹∑⁺和a³∏ 态的势能曲线进行了研究. 计算是在0.095---1.33 nm的核间距内进行的. 为获得更准确的结果, 计算中还考虑了Davidson修正、相对论修正及核价相关修正对势能曲线的影响. 相对论修正采用的方法是二阶DouglasKroll哈密顿近似, 修正计算是在cc-pV5Z基组水平上进行的. 核价相关修正使用的是cc-pCV5Z基组. 利用得到的势能曲线, 拟合出了各种修正下BF自由基X¹∑⁺和a³∏ 态的光谱常数D_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e和α_e、并与实验结果进行了比较. 结果表明: 考虑Davidson修正、相对论修正和核价相关修正后得到的光谱常数最接近实验结果. 利用修正后的势能曲线, 通过求解径向振转Schrödinger方程, 找到了转动量子数J = 0时这两个电子态的全部振动态, 并计算了每一电子态前20个振动态的振动能级、惯性转动常数和离心畸变常数, 其值与已有的实验结果较为一致. 本文得到的光谱常数和分子常数达到了很高的精度, 能为进一步的光谱实验提供可靠的参考.     

Tests of the final-state radiation model at DAFNE near <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>-</Superscript> threshold

Effects due to the non-pointlike behaviour of pions in the process e ⁺ e ^-→π ⁺ π ^- γ can arise for hard photons in the final state. By means of a Monte Carlo event generator, which also includes the contribution of the direct decay φ→π ⁺ π ^- γ, we estimate these effects in the framework of the resonance perturbation theory. We consider angular cuts used in the KLOE analysis of the pion form factor at threshold. A method to reveal the effects of the non-pointlike behaviour of pions in a model-independent way is proposed.     

Study of the isobar configurations in the <Superscript>12</Superscript>C and <Superscript>16</Superscript>O ground states

Experimental research on positive-pion photoproduction on the oxygen nucleus in the ¹⁶O(γ, π⁺p) reaction at high recoil momenta of the residual nuclear system was performed. The yield for the ¹⁶O(γ, π⁺p) reaction was analyzed using a model that takes Δ-isobar configurations in nuclei ground states into account, together with the earlier-measured yield of the¹²C(γ, π⁺p) reaction. The estimated number of isobars per nucleon N _Δ = 0.012 ± 0.005 was obtained for the ¹²C nucleus, and ¹⁶O N _Δ = 0.018 ± 0.004 was obtained for the ¹⁶O nucleus.     

Theoretical study of the electronic structure of LiNa and LiNa<Superscript>+</Superscript> molecules

Adiabatic potential energy, spectroscopic constants, dipole moments, and vibrational levels of the lowest electronic states of the alkali dimer LiNa molecule dissociating into Na (3s, 3p, 4s, 3d, and 4p) + Li (2s, 2p, 3s, and 3p) in ^1,3Σ, ^1,3Π, and ^1,3Δ symmetries are presented. Adiabatic results are also reported for ²Σ, ²Π, and ²Δ electronic states of the molecular ion LiNa⁺ dissociating into Li (2s, 2p, 3s, and 3p) + Na⁺ and Li⁺  + Na(3s, 3p, 4s, 3d, and 4p). We use an ab initio approach involving a non-empirical pseudopotential for the Li (1s²) and Na (1s²2s²2p⁶) cores and core valence correlation correction. A very good agreement is obtained for some lowest states of the LiNa and LiNa⁺ molecules for spectroscopic constants with the available theoretical works. The existence of numerous avoided crossings between electronic states of ²Σ and ²Π symmetries is related to the charge transfer process between the two ionic systems Li⁺Na and LiNa⁺.     

Nuclear quadrupole moments of 5/2<Superscript>-</Superscript> and 9/2<Superscript>-</Superscript> states in <Superscript>169</Superscript>Ta

The nuclear spectroscopic quadrupole moments for the πh_9/25/2^-, 1/2^-[541] and the πh_11/29/2^-, 9/2^-[514] isomeric states in ¹⁶⁹Ta have been measured employing the time differential perturbed angular-distribution technique following the nuclear reaction ¹⁵⁹Tb(¹⁶O, 6nγ)¹⁶⁹Ta at beam energy 104 MeV. The ratio of the intrinsic quadrupole moments has been derived as 1.87(13) from the measured quadrupole precession frequencies of the corresponding states. The model-independent analysis of the equilibrium deformation indicates strong prolate- and oblate-driving nature of the 1/2^-[541] and 9/2^-[514] orbitals in ^169,171Ta isotopes, respectively.     

Investigation of negative ion states in HCl and HF by configuration interaction methods

Multi-reference configuration interaction calculations are employed for the study of Born-Oppenheimer potential energy curves in HF/HF^- and HCl/HCl^-. Large gaussian basis sets including negative ion functions as well as diffuse s, p and d AOs are employed thereby. In HCl^- a repulsive 2Σ⁺ state emerges from the calculations approximately 4·2 eV above the HCl X ¹Σ⁺ ground state; no such entity could be observed in HF^- in the energy range treated. All other CI roots which produce potential curves parallel to and above the X ¹Σ⁺ curve are found to possess quite diffuse charge distributions in the basis set variations undertaken and can therefore not be considered resonant states but rather as discrete representations of free-electron species in the HX + e^- continuum. For large internuclear distances the HF^- and HCl^- curves lie below those of the neutral species, whereby the crossing between the X ²Σ⁺ ionic and X ¹Σ⁺ curves are calculated to occur at 3·2 a ₀ in HCl/HCl^- and 2·6 a ₀ in HF/HF^-. Finally it is argued that non-adiabatic effects involving the low energy HX^- continuum states in the Born-Oppenheimer approximation and the bound HX^- species at large internuclear separations (with continuation inside the HX potential well) are ultimately responsible for observed electron scattering resonances, in accordance with recent work of Domcke and Cederbaum and of Nesbet.     

QED radiative corrections to the decay π<Superscript>0</Superscript>→e<Superscript>+</Superscript>e<Superscript>-</Superscript>

We reconsider QED radiative corrections (RC) to the π⁰→e⁺e^- decay width. One kind of RC investigated earlier has a renormalization group origin and can be associated with the final state interaction of electron and positron. It determines the distribution of lepton pair invariant masses in the whole kinematic region. The other type of RC has a double-logarithmic character and is related to almost on-mass-shell behavior of the lepton form factors. The total effect of RC for π⁰→e⁺e^- decay is estimated to be 3.2%, and for η→e⁺e^- decay it is 4.3%. PACS  13.25.Cq; 12.38.Lg; 12.38.-t     

The ground state and doubly-excited <Superscript>1,3</Superscript>P° states of hot-dense plasma-embedded Li<Superscript>+</Superscript> ions

We have investigated the ground state and the doubly excited ^1,3P^○ resonance states of plasma-embedded Li⁺ ion. The plasma effect is taken care of by using a screened Coulomb potential obtained from the Debye model. A correlated wave function has been used to represent the correlation effect between the charged particles. The ground state of Li⁺ in plasmas for different screening parameters has been estimated in the framework of Rayleigh-Ritz variational principle. In addition, a total of 18 resonances (9 each for ¹P^○ and ³P^○ states) below the n=2 Li⁺ thresholds has been estimated by calculating the density of states using the stabilization method. For each spin state, this includes four members in the 2snp₊ (2≤n ≤5) series, three members in the 2snp_- (3≤n ≤5) series, and two members in the 2pnd (n=3, 4) series. The resonance energies and widths for various Debye parameters ranging from infinity to a small value for these ^1,3P^○ resonance states along with the ground state energies of Li⁺ and the Li²⁺ (1S), Li²⁺ (2S) threshold energies are reported. Furthermore, the wavelengths for the photo-absorption of lithium ion from its ground state to such ¹P^○ resonance states for different Debye lengths are also reported.     

A relativistic quark model for mesons with an instanton-induced interaction

We present new results of a relativistic quark model based on the Bethe-Salpeter equation in its instantaneous approximation. Assuming a linearly rising confinement potential with an appropriate spinorial structure in Dirac space and adopting a residual interaction based on instanton effects, we can compute masses of the light mesons up to highest observed angular momenta with a natural solution of the U _A(1) problem. The calculated ground states masses and the radial excitations describe the experimental results well. In this paper, we will also discuss our results concerning numerous meson decay properties. For processes like π⁺/K ⁺↦e ⁺υ_eγ and 0^-↦γγ at various photon virtualities, we find a good agreement with experimental data. We will also comment on the form factors of the K _?3 decay and on the decay constants of the π, K and η mesons. For the sake of completeness, we will furthermore present the electromagnetic form factors of the charged π and K mesons as well as a comparison of the radiative meson decay widths with the most recent experimental data. Received: 28 August 2000 / Accepted: 12 September 2000     

Ab initio calculations on the ground and excited states of InI

Potential energy curves (PECs) of the ground and the low-lying excited states of the InI molecule are computed using the internally contracted multireference singles and doubles configuration interaction with the Davidson correction (ic-MR-CISD + Q) method based on the relativistic effective core potentials (RECPs). The spectroscopic constants are obtained, including the excitation energy (T _e), the equilibrium bond distance (R _e), the dipole moment (μ_e) and the vibrational constants (ω_e and ω_e). Finally, we predict the transition dipole moments, the radiative lifetimes, and the Franc-Condon factors for the transitions of A³Π₀+ ? X¹Σ₀ ⁺ and B³Π^l ? X¹Σ₀ ⁺,. The results reveal that A³Π₀+ and B³Π_l are long-lived states with the lifetimes being of the order of microseconds.     

Pair production of the heavy leptons in future high energy linear e<Superscript>+</Superscript>e<Superscript>-</Superscript> colliders

The littlest Higgs model with T-parity predicts the existence of the T-odd particles, which can only be produced in pairs. We consider pair production of the T-odd leptons in a future high energy linear e⁺e^- collider (ILC). Our numerical results show that, as long as the T-odd leptons are not too heavy, they can be copiously produced and their possible signals might be detected via the processes e⁺e^-→L̄_iL_j in future ILC experiments.