Dissociation energies of molecular hydrogen and the hydrogen molecular ion

We have obtained improved values for the dissociation energies of molecular hydrogen and its ion by using a high-resolution pulse-amplified laser to probe the second dissociation limit. The onset of the vibrational continuum is observed by state-selective detection of the atomic products of dissociation, and several auxiliary measurements link the results to the ground state. The dissociation energies are accurate to 0.010-0.026 cm(-1), improving previous measurements by a factor of 3-7. Agreement with ab initio calculations is good for H2, D2, and their ions, but not for HD and HD+.     

Variational and diffusion Monte Carlo simulations of a hydrogen molecular ion in a spherical box

The variational and diffusion Monte Carlo approaches are used to study the ground-state properties of a hydrogen molecular ion in a spheroidal box. In this work, we successfully treat the zero-point motion of protons in the same formalism with as of electrons and avoid the Born–Oppenheimer approximation in density function theory. The study shows that the total energy increases with the decrease in volume, and that the distance between protons decreases as the pressure increases.Considering the motion of protons, the kinetic energy of the electron is higher than that of the fixed model under the same conditions and increases by 5%. The kinetic energy of the proton is found to be small under high pressure, which is only a fraction of the kinetic energy of the electron.     

Periodic orbits of the hydrogen molecular ion

Based on our previous work [Yiwu Duan, J.M. Yuan, C.G. Bao, Phys. Rev. A 52, 3497 (1995)], we study deeply the periodic orbits of the hydrogen molecular ion within the Born-Oppenheimer approximation (BOA). The Thiele-Burrau's transformation is introduced to regularize the singularities associated with the Coulomb potential terms and to transform the problem into a direct product of a pendulum and an anharmonic oscillator. This facilitates the analysis of the bifurcation properties of the periodic orbits. Some more details are also given about the calculation of the semiclassical density-of-state distribution using the Berry-Tabor formula. Received: 5 February 1999     

Variational calculations on the three-body scattering problem

An extended resonating-group method is used to calculate the elastic scattering amplitudes (up to L = 2 for a system of three identical bosons interacting through local Yukawa potentials. The results are compared to approximate solutions of the Faddeev equations.     

Variational time-dependent Hartree-Fock calculations

A pseudopotential framework is used to develop a simplified version of time-dependent Hartree-Fock theory. Variational solutions of the equations are obtained for the alkali metal hydrides LiH, NaH and KH, and excitation energies, oscillator strengths and other properties are calculated. The results are in good agreement with more elaborate theoretical calculations.     

Structure and stability of the negative hydrogen molecular ion

We present the results of a Coulomb explosion experiment that allows for the imaging of the rovibrational wave function of the metastable H2- ion. Our measurements confirm the predicted large internuclear separation of 6 a.u., and they show that the ion decays by autodetachment rather than by spontaneous dissociation. Imaging of the resulting H2 products reveals a large angular momentum of J = 25 ± 2, quantifying the rotation that leads to the metastability of this most fundamental molecular anion.     

Critical fields for ionization of the hydrogen molecule and the molecular hydrogen ion

We calculate the critical fields for the classical ionization of an ion of the hydrogen molecule and the neutral hydrogen molecule by an electric field. In the case of a molecular ion we examine different internuclear distances and obtain the correct limits for the well-known cases of small and large internuclear distances. Zh. éksp. Teor. Fiz. 112, 828–835 (September 1997)     

Scattering of low-energy positrons by the hydrogen molecular ion

A first application of the Kohn method is made to the calculation of scattering parameters for positron collisions with the hydrogen molecular ion below the positronium formation threshold at 9.45 eV. Phase shifts from the two-centre Coulomb value are obtained for the lowest spheroidal partial wave of _g ⁺ symmetry. For energies as low as 1.2 eV, it is found that a very flexible trial function must be used if accurate results are to be obtained.     

Multiple ionization bursts in laser-driven hydrogen molecular ion

Theoretical study on H2(+) in an intense infrared laser field on the attosecond time scale reveals that the molecular ion shows multiple bursts of ionization within a half-cycle of the laser field oscillation, in contrast to the widely accepted tunnel ionization picture for an atom. These bursts are found to be induced by transient localization of the electron at one of the nuclei, and a relation between the time instants of the localization and the vector potential of the laser light is derived. A scheme is proposed to probe the localization dynamics by an extreme ultraviolet laser pulse.     

Variational aspects of Faddeev calculations

We examine differences between³H binding energies obtained by solving the Faddeev equations using standard partial-wave expansion procedures and results from solving the Schrödinger equation by means of the coupled-rearrangement-channel variational method. Variational bounds generated from Faddeev solutions for several contemporary, realistic potential models are presented as a function of the number of partial waves retained in the potential expansion. We demonstrate that the Faddeev wave function yields an optimal variational bound for the partial-wave truncated potential from which it is generated, but it does not yield optimal bounds for the full Hamiltonian or when the potential is partial-wave truncated at a different level. Finally, qualitative differences between³H solutions for static models such as the AV14 and RSC potentials and for momentum-dependent models such as the Nijmegen soft-core and Paris potentials are explored, and comparison is made with solutions for the RSC/TM two-body-force plus three-body-force model.     

Variational calculations with unbounded operators

In a constrained variational calculation, the minimum of the expectation value of an operator H, subject to the constraint that the expectation value of an operator A have a definite value, is sought. Fonte and Schiffrer have recently noted that the Lagrange multiplier method of of determining the solution to this problem fails when the operator A is unbounded. We show that in this case, the expectation value of H can be made arbitrarily close to the unconstrained minimum, for any constrained value of 〈A〉. This result casts doubt on the validity of the results of calculations, in which an unbounded operator (such as the quadrupole moment of a nucleus) is constrained, even if these calculations are carried out using a finite-dimensional basis in which the restricted operator is bounded. Various alternatives to these calculations are discussed.     

双原子分子离子SiC~-激发态A~2∏的势能函数的变分研究

根据能量变分的思想,将双原子分子离子XY 的新解析势能函数ECMI势和关于离子XY 的能量自洽法(Energy-consistent-method for ion,ECMI)推广到双原子分子离子XY-的势能函数研究之中,具体研究了双原子分子离子SiC-激发态A2∏的势能函数,并与将中性双原子分子的势能函数如Morse势和Huxley-Murrrell-Sorbie(HMS)势直接用于双原子分子离子XY-的结果和ab initio计算结果进行了比较.结果表明,ECMI势和ECMI方法对双原子分子离子XY-的势能函数研究同样是成功的,在重要的渐近区和离解区优于中性势能函数,与精确的ab initio结果一致.     

Variational calculations on the energy levels of graphene quantum antidots

The critical properties of the two-dimensional Ising and Blume-Capel model on directedsmall-world lattices with quenched connectivity disorder are investigated. The disordered system is simulated by applying the Monte Carlo method with heat bath update algorithm and histogram re-weighting techniques. The critical temperature, as well as the critical exponents are obtained. For both models the critical parameters have been obtained for several values of the rewiring probability p. It is found that these disorder systems do not belong to the same universality class as two-dimensional ferromagnetic model on regular lattices. In particular, the Blume-Capel model, with zero crystal field interaction, on a directedsmall-world lattice presents a second-order phase transition for p < p _c , and a first-order phase transition for p > p _c , where p _c  ≈ 0.25. The critical exponents for p < p _c are different from those of the same model on a regular lattice, but are identical to the exponents of the Ising model on directedsmall-world lattice.     

LCAO truncated crystal calculations on some electronic properties of compressed molecular hydrogen crystal

The truncated crystal method is used to describe the band gap, work function, repulsive ground state crystal potential, Davydov excitons and defect states due to H and N₂ impurities, in molecular Pa3 hydrogen crystal, utilizing a simplified minimal basis set and semiempirical quantum chemical methods. Favorable results are achieved regarding experimental optical data.     

双原子分子离子SiC-激发态A2Ⅱ的势能函数的变分研究

根据能量变分的思想,将双原子分子离子XY 的新解析势能函数ECMI势和关于离子XY 的能量自洽法(Energy-consistent-method for ion, ECMI)推广到双原子分子离子XY-的势能函数研究之中,具体研究了双原子分子离子SiC-激发态A2∏的势能函数,并与将中性双原子分子的势能函数如Morse势和Huxley-Murrrell-Sorbie (HMS)势直接用于双原子分子离子XY-的结果和ab initio计算结果进行了比较.结果表明,ECMI势和ECMI方法对双原子分子离子XY-的势能函数研究同样是成功的,在重要的渐近区和离解区优于中性势能函数,与精确的ab initio结果一致.     

Variational calculations of asymmetric nuclear matter

We report on variational calculations of the energy E(ρ, β) of asymmetric nuclear matter having ? = ?_n + ?_p = 0.05 to 0.35 fm^?3, and β = (?_n ? ?_p/g9 = 0 to 1. The nuclear h used in this work consists of a realistic two-nucleon interaction, called v₁₄, that fits the available nucleon-nucleon scattering data up to 425 MeV, and a phenomenological three nucleon interaction adjusted to reproduce the empirical properties of symmetric nuclear matter. The variational many-body theory of symmetric nuclear matter is extended to treat matter with neutron excess. Numerical and analytic studies of the β-dependence of various contributions to the nuclear matter energy show that at ? < 0.35 fm^?3 the β⁴ terms are very small, and that the interaction energy EI(ρ, β) defined as E(ρ, β) ? T_F(ρ, β), where T_F is the Fermi-gas energy, is well approximated by EI₀(?) + β²EI₂(ρ). The calculated symmetry energy at equilibrium density is 30 MeV and it increases from 15 to 38 MeV as ? increases from 0.05 to 0.35 fm^?3.