Fine and hyperfine structure in three low-lying 3Σ+ states of molecular hydrogen

The fine structure constant (electron spin-spin coupling) and the hyperfine structure parameters (electron-nuclear spin coupling, including spin-rotation and electron-nuclear quadrupole coupling) in the low-lying triplet states b³Σ⁺ _u, a³Σ⁺ _g and e³Σ⁺ _u of molecular hydrogen and deuterium are calculated using a recently developed technique with full configuration interaction and multiconfiguration self-consistent field wave functions. The second-order spin-orbit coupling contribution to the ³Σ⁺ states splitting is negligible, and the calculations therefore provide a good estimate of the zero-field splitting based only on the electron spin-spin coupling values. For the bound a³Σ⁺ _g state a negligible zero-field splitting is found, in qualitative agreement with the e-a spectrum. The zero-field splitting parameter is considerable for the repulsive b³Σ⁺ _u state (?1 cm^?1) and of intermediate size for the bound e³Σ⁺ _u state. The isotropic hyperfine coupling constant is very large not only for the valence b³Σ⁺ _u state (1580 MHz) but also for the Rydberg a and e triplet states (?1400 MHz). The quadrupole coupling constants for the deuterium isotopes are negligible (0.04–0.07 MHz) for all studied triplet states. The electric dipole activity of the spin sublevels in the triplet-singlet transitions to the ground state is estimated by means of the quadratic response technique.     

On behaviour of the form factor of decay of the 63-1k63-1k63-1kinto the dalitz pair in a region of small invariant masses

Dependence of the decay form factor \(F_{\pi ^0 \to e^ + e^ - \gamma } (s)\) on the invariant mass squared of the Dalitz pairs=(p ₊+p _?)² at smalls is calculated with the use of bound-state wave functions-solutions of a covariant single-time equation for a system of two spinor quarks. A quasipotential of one-gluon exchange and an oscillator potential are chosen as quasipotential.     

Charmed Deuteron

Possible existence of bound states of a charmed baryon, Λ _c , Σ _c , Σ* _c with a nucleon, N, as well as two charmed baryons, Λ _c Λ _c , etc., are examined in the meson exchange potential approach. The heavy quark spin symmetry induces a strong tensor coupling between Λ _c N, Σ _c N and Σ* _c N states, which causes a bound state of Λ _c N (J = 0⁺ and 1⁺) states. Such a bound state is also seen in the spin-singlet Λ _c Λ _c channel, which resembles the H dibaryon in the strange sector.     

Spectra of charmed and bottom baryons with hyperfine interaction

Up to now,the excited charmed and bottom baryon states have still not been well studied experimentally or theoretically.In this paper,we predict the mass of ?*b,the only L=0 baryon state which has not been observed,to be 6069.2 Me V.The spectra of charmed and bottom baryons with the orbital angular momentum L = 1 are studied in two popular constituent quark models,the Goldstone boson exchange(GBE) model and the one gluon exchange(OGE) hyperfine interaction model.Inserting the latest experimental data from the "Review of Particle Physics",we find that in the GBE model,there exist some multiplets(Σc(b),Ξ c(b)and ?c(b)) in which the total spin of the three quarks in their lowest energy states is 3/2,but in the OGE model there is no such phenomenon.This is the most important difference between the GBE and OGE models.These results can be tested in the near future.We suggest more efforts to study the excited charmed and bottom baryons both theoretically and experimentally,not only for the abundance of baryon spectra,but also for determining which hyperfine interaction model best describes nature.     

Spin–orbit coupling in biradicals. 5. Zero-field splitting in triplet dimethylnitrenium,dimethylphosphenium and dimethylarsenium cations

The spin dipole–spin dipole and spin–orbit coupling contributions to the zero-field splitting parameters D and E of [CH₃–N–CH₃]⁺, [CH₃–P–CH₃]⁺, and [CH₃–As–CH₃]⁺ have been calculated from CASSCF(14,14)/cc-pVTZ wave functions and the Breit–Pauli Hamiltonian at T₁ B3LYP/cc-pVTZ optimized geometries. The spin–orbit coupling contributions represent a minor correction for the dimethylnitrenium cation, which has a triplet ground state. They dominate the spin–spin terms by an order of magnitude in the dimethylphosphenium cation and by more than two orders of magnitude in the dimethylarsenium cation, both of which have a singlet ground state. The properties of all these biradicaloids follow expectations based on the simple algebraic 2-in-2 model of biradical structure.     

Calculation of QED Effects in Hydrogen

Atomic mass differences are influenced by QED corrections, and a reliable understanding of these corrections is therefore of importance for the current and next generation of high-precision mass determinations based on Penning traps. We present a numerical evaluation of the self-energy correction, which is the dominant contribution to the Lamb shift, in the region of low nuclear charge. Our calculation is nonperturbative in the binding field and has a numerical uncertainty of 0.8Hz in atomic hydrogen for the ground state and of 1.0Hz for L-shell states (2S_1/2, 2P_1/2, and 2P_3/2). This revised version was published online in July 2006 with corrections to the Cover Date.     

Properties of the absorption spectrum due to the Gamma;1+ → Γ4− transition

We present results for the absorption spectrum due to a localized Γ₁⁺ → Γ₄^? transition that take into account the properties of the linear electron- phonon (e-p) interactions transforming as Γ₁⁺, Γ₃⁺ and Γ₅⁺ in the excited electronic state, in the cases of strong and weak e-p interaction coupling. We show that in the strong e-p interaction coupling limit the asymmetric shape of the structured band is due to the commutation relations of the e-p interaction matrices. Moreover, in the weak coupling limit we present an expression for the spectrum line shape obtained by taking into account the time ordering of the e-p interaction matrices and the phonon propagators at all times. It is shown in the latter case that the densities of phonon states corresponding to the electronic excited state are different from those corresponding to the ground state, and the e-p coupling constants are redefined due to the Jahn-Teller interactions.     

Unitarity bounds in the vector condensate model of electroweak interactions

We replace the standard model scalar doublet by a doublet of vector fields and generate masses by dynamical symmetry breaking. Oblique radiative corrections are small if the new vector bosons (B ⁺,B ⁰) are heavy. In this note it is shown that the model has a low momentum scale and above Λ?2 TeV it does not respect the perturbative unitarity. From tree-graph unitarity the allowed region ofB ⁺ (B ⁰) mass is estimated asm _B ⁺≥333 GeV (m _B ⁰≥373 GeV) at Λ=1 TeV.     

The ion-molecule reaction O+ (4S) + N2(X1Σ+) → NO+ (X1Σ +, v′) + N(4S) and the predissociation of the A2Σ+ and B2Π states of N2O+

The potential energy surfaces (PESs) for several electronic states involved in the reaction O⁺ (⁴S) + N₂(X¹Σ⁺) → NO⁺ (X¹Σ ⁺, v′) + N(⁴S) and the role of the ionic N₂O⁺ intermediate have been investigated by ab initio calculations. The ⁴A″ PES, which correlates with the ground state educts, has a barrier of about 1 eV, and therefore at low collision energies the reaction cannot take place adiabatically on this surface. However, the spin-orbit coupling in the entrance channel allows the system to pass into the Renner-Teller system of the X² Π electronic ground state of the N₂O⁺ intermediate. The reaction then proceeds on these surfaces up to the region in the exit channel where a similar coupling allows it to reach the product quartet asymptote. At collision energies higher than about 1 eV, the reaction proceeds mainly on the adiabatic PES of the ⁴A″ state. The A²Σ⁺ state of N₂O⁺ predissociates via a vibronic coupling with the B²Π state, and in bent structures via a spin-orbit coupling with the ⁴A″ component of the ⁴II state. The electronic structure of the B²Π state is found to be of crucial importance for the understanding of the reactive processes in low lying electronic states of N₂O⁺.     

Hadronic decays of N and Δ resonances in a chiral quark model

π and η decay modes of light baryon resonances are investigated within a chiral quark model whose hyperfine interaction is based on Goldstone-boson exchange. For the decay mechanism a modified version of the ³ P ₀ model is employed. Our primary aim is to provide a further test of the recently proposed Goldstone-boson exchange constituent quark model. We compare the predictions for π and η decay widths with experiment and also with results from a traditional one-gluon exchange constituent quark model. The differences between nonrelativistic and semirelativistic versions of the constituent quark models are outlined. We also discuss the sensitivity of the results on the parameterization of the meson wave function entering the ³ P ₀ model. Received: 11 May 2001 / Accepted: 17 September 2001     

密度泛函方法对SiO分子基态（X 1Σ+）势能函数的研究

利用密度泛函B3P86方法,分别选用STO-3G,D95^**,6-311G,6-311++G,6-311++G^**,cc-PVTZ基组对SiO分子基态(X¹Σ⁺)进行结构优化计算.通过比较得出,cc-PVTZ基组为对SiO分子基态(X¹Σ⁺)进行结构优化最优基组的结论.使用密度泛函B3P86方法,选用cc-PVTZ基组进 关键词： B3P86 SiO 势能函数 光谱常数     

The static Q\bar Q interaction at small distances and OPE violating terms

The nonperturbative contribution to the one-gluon exchange produces a universal linear term in the static potential at small distances ΔV=6N _c α _s σr/2π. Its role in the resolution of long-standing discrepancies in the fine splitting of heavy quarkonia and improving agreement with lattice data for static potentials is examined, and implications for operator product expansion (OPE) violating terms in other processes are discussed. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 7, 471–473 (10 April 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Re-analysis of the baryon mass spectrum using the quark shell model

Detailed numerical comparison of the baryon mass spectrum analysis of Jones, Levi Setti and Lasinski with that of Horgan has led to a deeper understanding of the formulae and techniques used in both analyses. In this light, we have re-analysed the baryon mass spectrum for the (70, 1^?)₁ and (56/70, 2⁺)₂ multiplets updated to include the most recent PDG data and have checked the results for the (70, 1^?)₁ using two independent computer programmes. The predicted spectra obtained are presented and the classification of the states is compared with that of a recent decay analysis by Hey, Litchfield and Cashmore.     

Determination of the ground state energies of the H 2 + , D 2 + and H 2 + molecular ions taking into account relativistic corrections

On the basis of determination of the asymptotic behavior of correlation functions of the corresponding field currents with the corresponding quantum numbers an analytic method for determination of the energy spectrum of three-body Coulomb system is suggested. Our results show that the constituent masses of particles, which we have defined as masses of particles in a bound state, differ from masses of particles in a free-state. The constituent mass to the free state mass relation for the electron is greater than the same mass relation for the proton, deuteron and triton. It was also found that this constituent electron mass has different values in each systems, i.e. in H ₂ ⁺ , D ₂ ⁺ and T ₂ ⁺ hydrogen molecular ions. The contributions of exchange and self-energy diagrams were taken into account in the determination of the energy spectrum of the three-body Coulomb system. Our results show that the self-energy diagram contribution is inversely proportional to the square of the constituent mass of particles. This contribution is sufficient for the electron and is negligible for the proton, deuteron and triton. When defining the energy and the wave function (WF), it is necessary to take into account the contributions of both the exchange and self-energy diagrams.     

Low momentum transfer theorem for two photon exchange in lepton hadron scattering

The two photon exchange contribution to lepton-hadron scattering is considered. Under the assumptions of Lorentz covariance, gauge invariance, unitarity and analyticity, we prove a low momentum transfer theorem for the relevant amplitudes. Fixed energy dispersion relations tell us that their nonanalytic part, in the neighbourhood of t = 0, is given by the contribution of the two photon cut in the t-channel. The t-channel absorptive parts are obtained from unitarity. Their calculation has as input the two amplitudes corresponding to Compton scattering on the hadron with a pole contribution, and the continuum controlled at low t by the electromagnetic polarizabilities. By means of the dispersion integral, one proves the expansion $\text{k}{}_1\text{(s)+k}{}_2\text{(s)}\text{?t}\text{+k}{}_3\text{(s)t}\text{log}\text{(?t)+O(t)}$ for the continuum contribution, where k₁(s) is the only unknown. Explicit expressions are obtained for the pole contribution as M → ∞, where M is the hadron mass, and for the continuum when (?t) <Λ and (?t) < 4m², where m is the muon mass and Λ is a characteristic parameter of the hadron structure.     

The electronic spectrum of AgBr2: Ab initio benchmark vs. DFT calculations on the lowest ligand-field states including spin-orbit effects

The X²Π_g, ²Σ_g⁺ and ²Δ_g states of AgBr₂ have been studied through benchmark ab initio CASSCF + Averaged Coupled Pair Functional (ACPF) and DFT calculations using especially developed valence basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges and spin densities. The spin-orbit (SO) effects were included through the effective hamiltonian formalism using the |ΛSΣ〉 ACPF energies as diagonal elements. At the ACPF level, the ground state is ²Π_g, in contradiction with ligand-field theory and Hartree-Fock results. The ACPF adiabatic excitation energies of the ²Σ_g⁺ and ²Δ_g states are 3825 and 20 152 cm⁻¹, respectively. The inclusion of the SO effects leads to a pure Ω = 3/2 (²Π_g) ground state, a Ω = 1/2 (97% ²Π_g + 3% ²Σ_g⁺) A state, a Ω = 1/2 (3% ²Π_g + 97% ²Σ_g⁺) B state, a Ω = 5/2 (²Δ_g) C state and a Ω = 3/2 (99% ²Δ_g) D state. The B97, B3LYP and PBE0 functionals, which were shown to yield accurate transition energies for CuCl₂, overestimate the X²Π_g-²Σ_g⁺ T_e by around 25% but provide a qualitative energetic ordering in agreement with CASSCF and ACPF results. The nature of the bonding in the X²Π_g ground state is different from that of AgCl₂ since the Mulliken charge on the metal is 0.95 while the spin density is only 0.39. DFT strongly delocalizes the spin density providing even smaller values of around 0.13 on Ag not only for the ground state, but also for the ²Σ_g⁺ state.