Unwanted States Research Articles

Potential energy curves using unrestricted Mo/ller–Plesset perturbation theory with spin annihilation

Unrestricted Hartree–Fock and unrestricted Mo/ller–Plesset perturbation theory are convenient methods to compute potential energy curves for bond dissociation, since these methods approach the correct dissociation limit. Unfortunately, a spin unrestricted wave function can contain large contributions from unwanted spin states that can distort the potential energy surface significantly. The spin contamination can be removed by projection or annihilation operators. As is well known, the spin project unrestricted Hartree–Fock bond dissociation curves have a large kink at the onset of the UHF/RHF instability, and a spurious minimum just beyond. However, the spurious minimum disappears and the kink is very much less pronounced at the unrestricted Mo/ller–Plesset level with spin projection. Bond dissociation potentials for LiH and CH4 were computed at the fourth order Mo/ller–Plesset level plus spin projection,4 and good agreement was found with full CI and MR-CISD calculations.

Gauge invariance and fermion doubling on the lattice

(1) We consider a possible chiral invariant solution of the lattice fermion doubling problem. This makes the unwanted states decouple in the continuum limit, at least in the non-interacting theory. The introduction of gauge interactions restores doubling. We examine how local gauge invariance makes all the species in a doubled spectrum act alike. (2) We generalise earlier results to show how gauge invariance forces a doubled spectrum on us even when other considerations do not.

State selection of [formula omitted] hyperfine levels of hydrogen in zero magnetic field

We describe a method of hyperfine level selection using rf quenching of a metastable (2S) hydrogen beam in zero magnetic field. The method provides excellent suppression of unwanted states with acceptable transmission of desired states. The technique has been used to study a very weakly induced hyperfine transition.

Spin dependent properties of perturbed wave functions: An analytic comparison of the exact, UHF, and spin-projected UHF states

A generally applicable diagrammatic representation for spin-annihilated wave functions is developed; the diagrammatic approach avoids the complex algebra usually associated with the application of spin-annihilation operators. The diagrammatic formulation is first applied to the perturbation expansion for the exact wave function to elucidate the diagrammatic origin of the (correct) spin eigenfunction properties of the exact perturbed state. Employing a previously derived perturbation expansion for the unrestricted Hartree–Fock (UHF) wave function, the diagrammatic spin-annihilation formalism is then used to analyze the effect of projecting unwanted spin states from the UHF wave function. Results obtained for the projected UHF state are compared to those appropriate to both the exact perturbed wave function and the unprojected UHF wave function. It is shown that results obtained by annihilating only the lowest unwanted spin multiplicity are expected, in a perturbation theory sense, to be very similar to those obtained by annihilating all unwanted spin states. However, it is further shown that additional terms are introduced into the UHF wave function by the spin projection procedure and that these terms are in general unrelated to the exact perturbative corrections to the UHF state. In particular, the wave function, energy, one and two-electron density matrices, and spin densities obtained for the projected state are all shown to be in error in the lowest order of perturbation theory; in contrast, the UHF state leads to the correct one-electron density matrix and spin densities in lowest order.

Three-lens heavy ion beam transport system for terminals of two-stage (tandem) electrostatic accelerators

A beam transport system for heavy ions in a terminal of an electrostatic accelerator is described. The system consists of three electrostatic quadropole lenses and four apertures in series. The first two lenses act as the charge selector and the third lens acts as a matching lens for the high energy tube. Most of the unwanted charge states are filtered down to a background level at least one order of magnitude below the selected charge state level. With ±60 kV supplies the system can be used for ions with energy-to-charge ratio of 2.5 MeV per electronic charge. Whenever less filtering is tolerated, its use may be extended up to about 4 MeV per electronic charge.

Generalized Veneziano model with isospin

A generalization of the Veneziano model to the N-point function was proposed which was crossing symmetric and bootstrap consistent in treating all particles as bound states of others. However, the model was so far limited to only neutral mesons. Here we propose a very simple general method for incorporating isospin into the model which preserves all the desirable properties and gives no unwanted states of high isospin. Previously known results for the four and five point functions appear as special cases of our solution.

Interacting Rarita-Schwinger Field

To avoid the mutual inconsistency between interaction, quantization, and subsidiary conditions of the Rarita-Schwinger spin-$\frac{3}{2}$ field, an additional subsidiary field is introduced in the spirit of the St\uckelberg formalism. Relativity is violated in the time development of the subsidiary field, but no observable consequences seem to follow. The unwanted states are removed invariantly from the asymptotic states through a Gupta-Bleuler kind of subsidiary condition. Energy has a positive-definite expectation value in the physical states.