Trajectory modifications in the Glauber model for heavy ions

Abstract

Expressions are presented for the modification due to the nuclear potential apart from the Coulomb potential both for the eikonal and the noneikonal trajectories. Calculations for heavy ion total reaction cross sections are performed using these expressions. Results are given for several systems. It is found that the expression used by Cha leads to unrealistic values for the distance of closest approach at small impact parameters at low energies and therefore lead to inaccurate values of the total reaction cross section. The exactly calculated distance of closest approach leads to improved results both for the eikonal and the noneikonal trajectories. PACS number(s): 25.70.Bc, 24. 10.Ht

Glauber model and the heavy ion reaction cross section

“…By replacing b by r cn , CNMGM is obtained. The non eikonal trajectory [9] around r c in the presence of the Coulomb field is represented by r 2 = r 2 c + (C + 1)z 2 , where the quantity C is given by…”

“…The CMGM [7,8] consists of replacing the eikonal trajectory at an impact parameter b with the eikonal trajectory at the corresponding distance r c of closest approach. The distance of closest approach r cn in the presence of both the Coulomb and nuclear potential [9] is obtained by solving Eq. (15) numerically, where V N (r) has been derived from Eq.…”

“…There have been various prescriptions [13,14] to modify the NN cross sections due to nuclear density. Most of the work reported earlier [7,8,10,9,13,14] has been done using Gaussian densities. The reaction cross section is sensitive to surface density of the colliding nuclei.…”

“…The Coulomb modified Glauber model (CMGM) [7,8] consists of replacing the eikonal trajectory at an impact parameter b, with the eikonal trajectory at the corresponding distance r c of closest approach in the presence of the Coulomb field. Later the non eikonal nature of the trajectory around r c , has also been taken into account [9]. Replacing r c by the distance r cn of closest approach in the presence of both the Coulomb and the nuclear field gives the Coulomb plus Nuclear modified Glauber model (CNMGM) [9,10].…”

“…Later the non eikonal nature of the trajectory around r c , has also been taken into account [9]. Replacing r c by the distance r cn of closest approach in the presence of both the Coulomb and the nuclear field gives the Coulomb plus Nuclear modified Glauber model (CNMGM) [9,10]. This model (CMGM/CNMGM) has been widely used in recent literature [11][12][13][14].…”