Lowest Angular Momentum States Research Articles

GROUND STATE CHARGE OF O(3) NONLINEAR σ MODEL SOLITONS IN 2+1 DIMENSIONS

The ground state charge of (2+1)-dimensional nonlinear σ model solitons is calculated by a combination of adiabatic method and spectral flow analysis. Induced charge is calculated by evolving adiabatically the fields from a vacuum having a background field which has spectral symmetry. The spectral flow is calculated by analyzing the bound state spectrum. It is shown that the ground state charge gets contribution only from the lowest angular momentum states and is discontinuous at the fermion mass. It is also shown that the ground state charge is independent of the way in which the final configuration is obtained.

GROUND STATE CHARGE OF FERMION SOLITON SYSTEM IN 1+1 AND 3+1 DIMENSIONS

Ground state charge of some fermion soliton system without C-invariance is calculated in 1+1 and 3+1 dimensions by a combination of adiabatic method and spectral flow analysis. Induced charge is calculated by evolving adiabatically the fields from a vacuum having a background field which has a zero energy state and spectral symmetry. The spectral flow is calculated by an analysis of the bound state spectrum. In 1+1 dimension our calculations are in agreement with the results already found in the literature. In 3+1 dimension we study the interaction of fermions with monopoles and dyons. In the case of monopoles, even though there is spectral asymmetry, ground state charge is found to be ±1/2. It is shown that ground state charge gets contribution only from the lowest angular momentum states and is discontinuous at the fermion mass.

Unimolecular reaction rate measurements for molecules with excited overtone vibrations

Unimolecular reaction rate constant measurements on systems with well known total energy contents permit detailed comparison with the predictions of statistical theories. Vibrational overtone excitation is a preparation technique that adds a precise energy increment to the reacting molecules and, when applied to a sample cooled in a free jet expansion, produces an ensemble with a known total energy content. Combining this preparation scheme with time resolved product detection yields the unimolecular reaction rate constant for a large molecule, tetramethyldioxetane. These free jet data serve to fix the parameters in an RRKM calculation, which is then averaged over a thermal distribution of initial vibrational energy for comparison to extensive room temperature measurements on the vibrational overtone initiated reaction. Applying this excitation scheme to a small molecule, hydrogen peroxide, in a free jet expansion permits the spectroscopic inference of its fast unimolecular reaction rate. Observation of the width of individual features in the well resolved vibrational overtone excitation spectrum establishes an upper limit to the unimolecular reaction rate constant for these molecules in their few lowest angular momentum states.

Dynamical supersymmetry of the magnetic monopole and the 1/r 2-potential

We examine the recently discovered dynamical OSp(1, 1) supersymmetry of the Pauli Hamiltonian for a spin 1/2 particle with gyromagnetic ratio 2, in the presence of a Dirac magnetic monopole. Using this symmetry and algebraic methods only, we construct the spectrum and obtain the wave functions. At all but the lowest angular momenta, the states transform under a single irreducible representation of OSp(1, 1). On the lowest angular momentum states, it is impossible to define self-adjoint supercharges, and the states transform under an irreducible representation of SO(2, 1) only. The Hamiltonian is not self-adjoint in thes-wave sector, but admits a one parameter family of self-adjoint extensions. The full SO(2, 1) algebra can be realized only for two specific values of the parameter.

Spin-zero photoproduction parity experiments beyond the threshold region

It is suggested that parity determining experiments can often be greatly simplified if one can assume that only the few lowest angular momentum states are important. The assumptions made here are not as restrictive as those made for the conventional threshold experiments, and hence the applicability of the schemes is much wider. In particular, a parity experiment is suggested in the photoproduction of spin-zero bosons which does not require polarized photons at all, and which is well within present day experimental techniques. It involves two measurements at the same energy and angle, one measuring the recoil polarization of the fermion, and the other the differential cross section from a polarized target.

Characteristic Exponent for the Radial Wave Equation with a Maxwellian Potential

The radial Schrödinger equation with a repulsive R—4 potential energy is equivalent to a Mathieu equation, and the associated characteristic exponent is an important parameter in determining the properties of the solution. The characteristic exponent has been tabulated for the six lowest angular momentum states and for a range of energies of interest in molecular dynamics.