Coherent Compton scattering on light nuclei in theΔ-resonance region

Abstract

Coherent Compton scattering on light nuclei in the ⌬-resonance region is studied in the impulse approximation and is shown to be a sensitive probe of the in-medium properties of the ⌬ resonance. The elementary amplitude on a single nucleon is calculated from the unitary K-matrix approach developed previously. Modifications of the properties of the ⌬ resonance due to the nuclear medium are accounted for through the self-energy operator of the ⌬, calculated from the one-pion loop. The dominant medium effects such as the Pauli blocking, mean-field modification of the nucleon and ⌬ masses, and particle-hole excitations in the pion propagator are consistently included in nuclear matter.The properties of the ⌬ in the nuclear medium are calculated in a relativistic framework for symmetrical nuclear matter, along the lines of Refs. ͓14 -16͔. The medium modifications, which are expressed through the dressing of the ⌬ propagator, are investigated using different levels of approximation. The imaginary part of the ⌬ self-energy ͑or the ⌬ decay width͒ is calculated in different models for the nuclear medium. Dispersion relations are used to determine the real part ͑mass modification͒ of the ⌬ self-energy.

Covariant propagator of the Rarita-Schwinger field in the nuclear medium

“…(15) with a p / + b 1 1 (on the left or the right) to get the complete expression for the propagator (as done in Refs. [8,9]), only the positive-energy and negative-energy content will change, while the coefficients giving the helicity-1/2 and helicity-3/2 components necessarily remain the same. In this way the splitting between different helicity states of the spin-3/2 sector is neglected in the approach mentioned, which is in this respect reminiscent of the non-relativistic treatment (however, keeping both positive-energy and negative-energy contributions).…”

“…[8,9], where the assumption is made that the in-medium isobar propagator is proportional to the spin-3/2 projector. The latter can be written through the terms of our basis introduced in Eqs.…”

“…To our knowledge a complete calculation involving all these terms has not been carried out and either a nonrelativistic approach (for example as in Ref. [6]), a description based on combining off-shell and on-shell behavior [7], or a treatment based on the assumption that the isobar propagator is proportional to the spin-3/2 projector [8,9] was used. The implications of this latter approach we discuss in some detail in the subsection II B.…”