Ro-vibrational states of H+2. Variational calculations

The non-relativistic variational calculation of a complete set of ro-vibrational states in the H⁺₂ molecular ion supported by the ground 1sσ adiabatic potential is presented. It includes both bound states and resonances located above the n = 1 threshold. In the latter case we also evaluate a predissociation width of a state wherever it is significant. Relativistic and radiative corrections are discussed and effective adiabatic potentials of these corrections are included as supplementary files.     

Variational calculations of vibrational energy levels for XY4 molecules 1. Stretching states

A variational method for calculating excited stretching states of symmetric tetrahedral pentaatomic molecules is presented based on the use of Radau coordinates and Morse oscillator-like basis functions. Symmetry is used both to reduce the size of the secular matrix to be diag-onalized and to calculate the potential energy matrix elements over a reduced grid of quadrature points. Test results are presented for methane, silane and germane. For CH₄, stretch-bend coupling is found to be significant, whereas it is less important for the more strongly local mode SiH₄ and GeH₄ molecules. Converged results are obtained for stretching states significantly higher than considered in previous calculations. These states will be used to represent stretching motions in a fully coupled stretch-bend calculation.     

Ab initio calculations of lower resonant states of two-electron systems

The complex scaling and the stabilization methods are applied to calculating the parameters of the lowest resonance states of He and Li⁺. The results obtained by both methods are in a good agreement with the published data. It is shown that the wave functions constructed using the restricted configuration interaction approximation provide fairly accurate estimates of the resonance parameters. The possibility of using the stabilization method for calculating the phase shift function is also discussed.     

Variational calculations of vibrational energy levels for XY4 molecules: 2. Bending states of methane

A variational method for calculating excited bending states of symmetric tetrahedral pentaatomic molecules is presented based on the use of Radau coordinates and Jacobi polynomials as the basis functions. Symmetry is used both to reduce the size of secular matrix to be diagonalized and to calculate potential energy matrix elements over a reduced grid of quadrature points. Methods of treating the redundant coordinate are investigated and fitting is found to be more effective than the use of Taylor expansions. Test results are presented for methane, for which stretch-bend coupling and the contribution due to the redundant coordinate are found to be significant. Converged results are obtained for bending states significantly higher than considered in previous calculations. These states will be used as a basis for bending motions in a fully coupled stretch-bend calculation.     

Three-nucleon bound states: Detailed calculations of3H and3He

The works of the Sendai group on investigations of the properties of the trinucleon bound states³H and³He are reviewed in detail. For these mirror nuclei, results are summarized that have been obtained from rigorous solutions of the (Coulomb-modified) Faddeev equations for various realistic nucleon-nucleon potentials with inclusion of three-nucleon forces as well as chargeindependence-and charge-symmetry-breaking forces. It becomes evident that for most trinucleon bound-state observables quite reasonable results have been achieved.     

Coupling effects of resonant and discretized non-resonant continuum states in4He +6Li scattering at 10 MeV/A

Alpha- particle scattering from the resonant (3 ₁ ⁺ ) and non-resonant continuum states of⁶Li is studied at incident energy 10 MeV/A. Theα+d breakup continuum part within the excitation energyE _ex=1.475–2.475 MeV is discretized in two energy bins. Unlike the results at higher incident energies, here the coupled-channel calculations show significant breakup continuum coupling effects on the elastic and inelastic scattering. It is shown that even when the continuum-continuum coupling effects are strong, the experimental data of the ground state and the resonant as well as discretized non-resonant continuum states impose stringent constraint on the coupling strengths of the non-resonant continuum states.     

Coupling effects of resonant and discretized non-resonant continuum states in 4He + 6Li scattering at 10 MeV/A

Alpha-particle scattering from the resonant (3 ₁ ⁺ ) and non-resonant continuum states of ⁶Li is studied at incident energy 10 MeV/A. The α + d breakup continuum part within the excitation energy E _ex = 1.475–2.475 MeV is discretized in two energy bins. Unlike the results at higher incident energies, here the coupled-channel calculations show significant breakup continuum coupling effects on the elastic and inelastic scattering. It is shown that even when the continuum-continuum coupling effects are strong, the experimental data of the ground state and the resonant as well as discretized non-resonant continuum states impose stringent constraint on the coupling strengths of the non-resonant continuum states.     

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.     

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.     

Path integral Monte Carlo calculations of4He and6Li

We have performed Monte Carlo calculations to estimate the exact energies of model problems for⁴He and theL=0,1, and 2 states of⁶Li. Using a Feynman path-integral expression for the imaginary-time evolution operator, we recast the ground state energy as a sum over histories, which are then sampled stochastically. Use of a trial wave function dramatically improves the efficiency of the Monte Carlo method. For a state-independent Malfliet-Tjon potential, together with the Coulomb interaction, we find a ground state energy of ?28.00+0.20 MeV for⁴He, and a degeneracy of theL=0,1, and 2 states in⁶Li at about ?59.65+-0.50 MeV. Density distributions for these nuclei are also calculated.     

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.