Zero-Mode Contribution in Nucleon-Delta Transition

We investigate the transition form factors between nucleon and $\Delta$(1232) particles by using a covariant quark-spectator-diquark field theory model in (3+1) dimensions. Performing a light-front calculation in parallel with the manifestly covariant calculation in light-front helicity basis, we examine the light-front zero-mode contribution to the helicity components of light-front good ("+") current matrix elements. Choosing the light-front gauge ($\epsilon^+_{h=\pm}=0$) with circular polarization in Drell-Yan-West frame, we find that only the helicity components $({1\over 2}, {1\over 2})$ and $({1\over 2},-{1\over 2})$ of the good current receive the zero-mode contribution. Taking into account the zero-mode, we find the prescription independence in obtaining the light-front solution of form factors from any three helicity matrix elements with smeared light-front wavefunctions. The angular condition, which guarantees the full covariance of different schemes, is recovered.Comment: 16 latex pages, 7 figures, to appear in PR

Neutron Density Distributions of Neutron-Rich Nuclei Studied with the Isobaric Yield Ratio Difference

The isobaric yield ratio difference (IBD) between two reactions of similar experimental setups is found to be sensitive to nuclear density differences between projectiles. In this article, the IBD probe is used to study the density variation in neutron-rich $^{48}$Ca. By adjusting diffuseness in the neutron density distribution, three different neutron density distributions of $^{48}$Ca are obtained. The yields of fragments in the 80$A$ MeV $^{40, 48}$Ca + $^{12}$C reactions are calculated by using a modified statistical abrasion-ablation model. It is found that the IBD results obtained from the prefragments are sensitive to the density distribution of the projectile, while the IBD results from the final fragments are less sensitive to the density distribution of the projectile.Comment: 3 figure