Nuclear transparency to intermediate-energy protons

Abstract

Nuclear transparency in the (e, e ′ p) reaction for 135 ≤ T p ≤ 800 MeV is investigated using the distorted wave approximation. Calculations using densitydependent effective interactions, both empirical and theoretical, are compared with phenomenological optical potentials. We find that nuclear transparency is well correlated with proton absorption and neutron total cross sections and that calculations using density-dependent effective interactions provide the best agreement with data. Nuclear transparency calculations are compared with recent electron scattering data for Q 2 < 2 (GeV/c) 2 . For T p < ∼ 200 MeV we find that there is considerable sensitivity to the choice of optical model and that the empirical effective interaction provides the best agreement with the data, but remains 5-10% low. For T p > ∼ 300 MeV we find that there is much less difference between these models, but that the calculations significantly underpredict transparency data and that the discrepancy increases with A. The differences between Glauber and optical model calculations are related to their respective definitions of the semi-inclusive cross section. By using a more inclusive summation over final states the Glauber model emphasizes nucleonnucleon inelasticity, whereas with a more restrictive summation the optical model emphasizes nucleon-nucleus inelasticity; experimental definitions of the semi-inclusive cross section lie between these extremes.

Quasifree(e,e′p)Reactions and Proton Propagation in Nuclei

“…These features of the N-N interaction would be expected to be reflected in the energy dependence of attenuation of protons as they pass through the nucleus but many body effects, including Pauli blocking, nonlocality, and correlations in the nuclear wave functions, can play an essential role in modifying this expectation (See Refs. [4][5][6], and references therein). The quasifree region is roughly defined by proton kinetic energies T p ϳ Q 2 ͞2M p and outgoing proton momenta, p 0 , close to q 1 p i where q is the electron three momentum transfer, Q 2 is the absolute value of the electron four momentum transfer squared, M p is the proton mass, and p i is a typical three momentum of the initial struck nucleon with j p i j less than the Fermi momentum.…”

“…Little evidence of momentum transfer or final-state proton energy dependence can be seen above Q 2 of 1.8 GeV 2 . The dashed curves from 0.3 , Q 2 , 1.3 GeV 2 are distorted wave impulse approximation calculations of Kelly [4] using a density dependent empirical effective interaction, of Ref. [4], fit to inelastic scattering data that successfully describe proton-nucleus absorption cross sections up to T p 700 MeV.…”

“…The dashed curves from 0.3 , Q 2 , 1.3 GeV 2 are distorted wave impulse approximation calculations of Kelly [4] using a density dependent empirical effective interaction, of Ref. [4], fit to inelastic scattering data that successfully describe proton-nucleus absorption cross sections up to T p 700 MeV. These calculations provide a good description of the carbon results but underpredict the transparency on the heavier nuclei.…”

“…The errors from the present work, 63.2%, and the NE-18 errors shown here do not include model dependent systematic errors on the simulations. The dashed curves from 0.3 , Q 2 , 1.3 GeV 2 are DWIA calculations [4] and the solid curves from 0.2 , Q 2 , 8 GeV 2 are Glauber calculations [5].…”

Nuclear transparency from quasielasticC12(e,e'p

“…In general the yield obtained in perpendicular kinematics exceeds the one measured in parallel kinematics due to additional reaction mechanisms present in perpendicular kinematics [33]. In the single-particle region (below the Fermi momentum) a difference of 6 % is expected [34,35].…”