We present analytic expressions for the zero-order eikonal phase shift and its first-order correction by approximating a distance between two colliding nuclei. This formalism has been applied to elastic scatterings of the 12 C + 40 Ca and the 12 C + 90 Zr systems at E lab = 420 MeV , and the 16 O + 40 Ca and the 16 O + 90 Zr ones at E lab = 1503 MeV . The calculated angular distributions, taking into account up to the analytic first-order eikonal phase shift, are found to be in fairly good agreement with the observed data. The reaction cross-sections obtained from the present model produce very excellent agreements with ones of exact first-order eikonal model calculations. We have found that analytic eikonal phase shift including the first-order correction is one theoretical method to the analysis of heavy-ion elastic scattering.
PIEMAP: Personalized Inverse Eikonal Model from Cardiac Electro-Anatomical Maps
