P.A. Deutchman

Pion production via isobar giant resonance formation and decay

A spin, isotopic-spin formalism for the production of pions due to decays of isobar giant resonances formed in peripheral heavy-ion collisions is presented. The projectile nucleus isobar giant resonance state is assumed to coherently form and then incoherently decay to produce the pions. Total spin and isotopic spin for the system are conserved through the concomitant excitation of the target nucleus to an isobaric analog giant resonance state. Comparisons of the predicted total pion cross sections, over a range of energies, are made with heavy-ion pion data.

A particle-hole calculation for pion production in relativistic heavy-ion collisions.

A differential cross section for pi-meson production in peripheral heavy-ion collisions is formulated within the context of a particle-hole model in the Tamm-Dancoff approximation. This is the first attempt at a fully quantum-mechanical particle-hole calculation for pion production in relativistic heavy-ion collisions. The particular reaction studied is an 16O projectile colliding with a 12C target at rest. In the projectile we form a linear combination of isobar-hole states, with the possibility of a coherent isobar giant resonance. The target can be excited to its giant M1 resonance (J pi = 1+, T = 1) at 15.11 MeV, or to its isobar analog neighbours, 12B at 13.4 MeV and 12N at 17.5 MeV. The theory is compared to recent experimental results.

Theoretical contributions to coherent pion production in subthreshold and relativistic heavy-ion collisions

The analytic results from a microscopic calculation for pion production in heavy-ion collisions at intermediate to relativistic energies both above and below pion threshold are presented and the most important terms that contribute to the pion spectrum are determined. The energy dependence and the effects on the pion spectrum due to the various parameters in the theory are examined. The model is applied to coherent pion-production in 16O + 12C collisions.

Isobar giant resonance formation in self-conjugate nuclei

Abstract The production of isobars with concomitant giant resonance excitations due to peripheral collisions of relativistic heavy ions is investigated. The interaction is described by a modified form of the central term in the one-pion-exchange potential (OPEP) where the projectile ordinary spin operator is replaced by a transition spin operator which describes the creation of an isobar from a nucleon. The scattering is analyzed using time-dependent harmonic perturbation theory to determine the reaction total cross sections. The results obtained, which are valid for reactions involving self-conjugate nuclei, are applied to the specific collison of 2.1 GeV nucleon 16O projectiles with 12C targets at rest. Cross sections are investigated using two different models for the nuclear spin states. In the first model, the many-body nuclear spin state is reduced, in the spirit of a particle-hole state, to an equivalent two-body state called a particle-core state. In the second model, the many-body spin states are described by unsymmetrized products of individual particle spins. Properties of the spin giant resonance and isobar giant resonance states are investigated. Finally, isobar decay and isobar/pion absorption effects are discussed.

A local versus non-local t-matrix in the 14N(p, 2p)13C reaction at 46 MeV

Abstract The angular distributions for the 14 N(p, 2p) 13 C reactions at 46 MeV incident proton energy are calculated in the distorted wave t -matrix approximation (DWTA) where approximate optical-model waves are used. A comparison is made between the calculation using a local t -matrix to that of a non-local t -matrix. The (p, 2p) angular distribution is smaller in magnitude where a non-local t -matrix is employed compared to the calculation using a local t -matrix which implies that there is an overall enhancement of absorption associated with the non-local t -matrix. This also implies that differences between the local and non-local off-energy-shell effects can be significant. Parameter studies were undertaken for the distorted waves and bound state wave function and the effects on the angular distributions were similar in the local and non-local cases. The distortion effect due to the final-state focus phase dramatically changes the shape of the angular distribution. The calculations are considered to be a test of the off-energy-shell effects due to non-local interaction. This calculation is also a test of the approximate distorted waves at 46 MeV and the comparison to the 14 N(p, 2p) 13 C data indicates that the distortion is reasonably well described.

A complex T-matrix derivation of a resonance amplitude

A resonant transition amplitude, valid to arbitrary order, is derived through the use of a complex energy T-matrix. A feature of this amplitude is its generality and simplicity making it useful for widespread applications in resonance theory.

The (p, 2p) reaction for slightly deformed nuclei

Abstract A perturbation approach for the calculation of (p, 2p) angular correlations for slightly deformed nuclei is developed using the formalism of the distorted wave t-matrix approximation (DWTA) in the static limit where approximations that incorporate absorption and focussing effects are used for the spin-orbit independent optical-model waves. Using a finite-range off-shell t-matrix that fits p-p scattering at 90° to approximate the p-p interaction inside the nucleus, a zero-order calculation is performed and normalized to 19F(p, 2p)18O angular correlation data at 42.7 MeV. A rms study is undertaken in order to parametrize the bound-state and the sensitivity of the shape of the angular correlation to the rms value is observed. The deformation of the bound-state is introduced using normalized perturbation theory and calculations with various values of the deformation parameter β for prolate and oblate deformations are performed and the results are compared. The shape of the (p, 2p) angular correlation is shown to be highly sensitive to the degree of deformation and is consistent with the shape dependence of the correlation to the rms value of the bound-state wave function.