S. M. Blinder

Electron photodetachment from a Dirac bubble potential. A model for the fullerene negative ion CC60

Abstract A model for the fullerene anion C 60 − is proposed in which the outer electron moves in an attractive deltafunction potential in the shape of a spherical bubble. Exact solutions for this “Dirac bubble potential” were previously worked out. On the basis of this model, the photodetachment cross-section and its angular distribution are computed as functions of photoelectron energy, for the electron in both S-like and P-like bound states. Secondary maxima and minima in the cross section appear at higher energy values, somewhat analogous to the scattering of radiation from a conducting sphere.

Schrödinger equation for a dirac bubble potential

Abstract The quantum-mechanical problem of a particle moving in a “Dirac bubble potential” U ( r ) = (λ/ r o )δ( r - r o ) is solved exactly for both bound and continuum states by making use of partial wave Greens functions G l ( r , r 0 , k ). Phase shifts are expressed in a compact form related to those for an impenetrable sphere.

Delta function model for the helium trimer: origin of three-body forces

The Dirac bubble potential, previously used to model the helium dimer, is applied to the trimer. It is shown that the quantum mechanical kinetic energy operator for a three-body system contains terms over and above the analogues of classical pairwise contributions. The additional terms, the ‘Borromean couplings’, are responsible for a dramatic increase in the binding energy of the trimer. For example, 4He3 is bounded by two orders of magnitude more strongly than 4He2, 279 mK versus 1.31 mK, respectively, according to our calculations. Moreover, the trimer is considerably more compact than the dimer, with (r12) decreasing to 9.01 Å from 51.9 Å.

Atom-pair formulation of the rotational and vibrational motions of molecules

We have expressed the angular momentum and the internal kinetic energy of a molecule (a system of point masses) in terms of atom-pair contributions, paralleling the use of pairwise additive potential energy functions. The partitioning of the internal kinetic energy into rotational and vibrational contributions is then made following the analysis of Jellinek, J., and Li, D. H., 1989, 98, Phys. Rev. Lett., 62, 241. The resulting expressions contain pair position and velocity variables whose redundancy may be removed by transformation to Jacobi vector coordinates. These expressions should prove especially useful for describing the internal motions of clusters of like atoms.

Time-dependent WKB expansion for the non-relativistic coulomb propagator

Abstract An approximation to the non-relativistic Coulomb propagator, correct to second order in ħ, is derived. The result is expressed in terms of the auxiliary variables introduced in the solution of the corresponding Hamilton-Jacobi equation. Higher-order contributions can be computed as required, but no explicit summation of the expansion has yet been found.

Time-dependent WKB expansions for a class of propagators

A time-dependent variant of the WKB method is developed for propagators which do not have the simple Feynman structure K = jexp(iS/h) with j = j( t). The method is applied to radial propagators for N-dimensional isotropic oscillators. An expansion in ascending powers of h results in an asymptotic series, which sums to a simple form involving a Bessel function. Alternatively, a convergent series for the propagator is obtained by expansion in inverse powers of tr. Semiclassical approximations to propagators are extensively applied in spectroscopy, scattering theory, molecular dynamics, irreversible thermodynamics and elementary-particle theory [ 11. Terms in the WKB expansion involving higher powers of ti are less often considered. In this paper, we develop a time-dependent formulation of the WKB method which can be systematically extended to arbitrary powers of fi. The method is applied to the radial components of the Feymnan propagators for N-dimensional isotropic harmonic oscillators. Consider accordingly anN-dimensional Euclidean space (x1, x2 . . .xN) with the generalized radial variable

Calculations on the helium isoelectronic sequence using Coulomb Green's function variables

Abstract Calculations on the ground states of the helium isoelectronic series are carried out using variational wavefunctions of the form ψ ( x , y ), in which x and y are the combinations r 1 + r 2 ± r 12 occurring in the Coulomb Greens function. The results for helium are the most accurate to date using a two-variable wavefunction accounting for 71.5% of the correlation energy.

Relativistic corrections in a series of helium excited states

Abstract Relativistic corrections to order (υ/ c ) 2 are applied to the helium excited states 2 1,3 P, 3 1,3 D,…, 8 1,3 K. Simple correlated open-shell wavefunctions are employed and the Breit operators H 1 through H 5 treated as perturbations. Account is also taken of mass polarization and lowest-order one electron Lamb shift. The energies thus calculated agree with experiment to within 2.2 cm −1 or better.