The effects of finite range of the NN force and in-medium NN cross-section on the proton–nucleus total reaction cross-section
Introduction
Recently, the total reaction cross-section, for proton–nucleus and nucleus–nucleus collisions has attracted great attention experimentally [1], [2], [3], [4] and theoretically [5], [6], [7], [8], [9], [10], [11], [12], [13] for studies, as it is one of the most important physical quantities characterizing nuclear reaction [14], [15]. The total reaction cross-section is useful for extracting information about nuclear sizes, and the Glauber models have been very successful in getting the measured total reaction cross-section at intermediate and high energies with invoking different nuclear medium effects [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. The optical limit approximation works reasonably well down to energies of about 30 MeV/nucleon provide that it is suitably modified to account for the deviation of the projectile trajectory due to the Coulomb potential [27]. This is known as the Coulomb modified Glauber model (CMGM) [28], [29]. CMGM consists of replacing the eikonal path at an impact parameter with the eikonal path at the compatible distance of closest approach in the presence of the Coulomb field.
Distribution of the nucleon density and the nucleon–nucleon (NN) cross-section are two main components of the Glauber model. The in-medium (NN) total cross-section provides an immediate connection with the nucleon mean free path, , one of the most fundamental quantities characterizing the propagation of nucleons through nuclear matter. In turn, enters the calculation of the nuclear transparency function where the later is related to the total reaction cross-section of the nucleus.
Rui et al. [30], used the zero range approximation and different density-dependent models for in-medium NN cross section. However, they used these models with constant density and they found that the phenomenological model [31] with very small constant density fm−3 could describe the data for light symmetric nuclei. For asymmetry heavier target nuclei, the results of the total reaction cross-section data have been found to depend significantly on the nuclear density distribution at large radius, especially in the low energy region.
In the present work, the finite range of the NN force and in-medium effects are employed to calculate the total reaction cross-section of proton on near symmetric, 12C, 16O, 27Al, 28Si, 40Ca, 56Fe, 90Zr and asymmetric Sn and 208Pb targets in a wide energy range 10–1000 MeV. Comparison with the zero-range approximation as well as Rui et al. are considered.
Section snippets
Mathematical model
The total reaction cross-section can be written in the CMGM as [31], [32], [33], where is an impact parameter and denotes the influence of the Coulomb force. In the optical limit approximation, the scattering matrix can be expressed in terms of the phase shift as, where, is the phase shift function, which can be written in momentum space as [29] where, is the relative wave number. and
Results and discussion
The density functions for target nuclei are obtained directly from 2pF, 3pF and 3pG density distributions whose parameters are determined from electron scattering experiments [44], The parameters for the proton densities are listed in Table 1. The parameters for the neutron densities are taken as the same as the proton ones except for the neutron radius and diffuseness which are increased by the neutron excess
Conclusion
The total reaction cross section of nucleon scattering from different nuclei are calculated using the CMGM. Finite range and in-medium effects of the NN total reaction cross section are investigated. The reaction cross section strongly increased at low and intermediate energies when using finite range NN force. Medium effects reduced the reaction cross section especially at low and intermediate energies. Both effects are found to be important to well describe the data. At high energy
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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