Molecular predissociation resonances below an energy level crossing
We study the resonances of $2\times 2$ systems of one dimensional Schrodinger operators which are related to the mathematical theory of molecular predissociation. We determine the precise positions of the resonances with real parts below the energy where bonding and anti-bonding potentials intersect transversally. In particular, we find that imaginary parts (widths) of the resonances are exponentially small and that the indices are determined by Agmon distances for the minimum of two potentials.
Semiclassical resonance asymptotics for systems with degenerate crossings of classical trajectories
. This paper is concerned with the asymptotics of resonances in the semiclassical limit h → 0 + for 2 × 2 matrix Schr¨odinger operators in one dimension. We study the case where the two underlying classical Hamiltonian trajectories cross tangentially in the phase space. In the setting that one of the classical trajectories is a simple closed curve whereas the other one is non-trapping, we show that the imaginary part of the resonances is of order h ( m 0 +3) / ( m 0 +1) , where m 0 is the maximal contact order of the crossings. This principal order comes from the subprincipal terms of the transfer matrix at crossing points which describe the propagation of microlocal solutions from one trajectory to the other. In addition, we compute explicitly the leading coeﬃcient of the resonance widths in terms of the probability amplitudes associated with all the generalized classical trajectories escaping to inﬁnity from the closed trajectory.
Monte carlo simulation of events with Drell-Yan lepton pairs from antiproton-proton collisions
The complete knowledge of the nucleon spin structure at leading twist requires also addressing the transverse spin distribution of quarks, or transversity, which is yet unexplored because of its chiral-odd nature. Transversity can be best extracted from single-spin asymmetries in fully polarized Drell-Yan processes with antiprotons, where valence contributions are involved anyway. Alternatively, in single-polarized Drell-Yan the transversity happens convoluted with another chiral-odd function, which is likely to be responsible for the well known (and yet unexplained) violation of the Lam-Tung sum rule in the corresponding unpolarized cross section. We present Monte Carlo simulations for the unpolarized and single-polarized Drell-Yan pp{sup ({up_arrow}}{sup )}{yields}{mu}{sup +}{mu}{sup -}X at different center-of-mass energies in both configurations where the antiproton beam hits a fixed proton target or it collides on another proton beam. The goal is to estimate the minimum number of events needed to extract the above chiral-odd distributions from future measurements at the high energy storage ring (HESR) at GSI. It is important to study the feasibility of such experiments at HESR in order to demonstrate that interesting spin physics can be explored already using unpolarized antiprotons.