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Glauber Model Analysis of Reaction Cross Section for C+C System in the Energy Range 300-700 MeV/A

The availability of radioactive ion beams has made it possible to investigate the properties of nuclei lying in the close proximity of neutron and proton drip lines. The pioneering experiments performed by I. Tanihata and collaborators using beams of highly neutron rich nuclei have confirmed the existence of a novel halo structure among some of these isotopes [1]. Subsequently many more neutron and proton halo nuclei have been identified through experiments measuring the reaction cross sections or breakup cross sections differential in longitudinal component of momentum of the fragments produced in the breakup process. Since more than one carbon isotopes have been found to have neutron halo structure, the carbon isotopic chain has attracted special attention. Very recently reaction cross section of C on C target has been measured at an energy 307 MeV/A [2]. Since reaction cross section is a very sensitive probe in determining the size and hence in deciding the halo character of a nuclear isotope, here we have analyzed it through Glauber model by employing two different single particle wave functions. Within the Glauber model, the projectile target total reaction cross section is given by [3] σR = ∫ db (1 − |< φ0|e CTcNTC|φ0 >| ) where all the symbols have their usual meanings as given in Ref. [3]. It is pertinent to mention here that the projectile is assumed to has a core plus one nucleon structure. The core-target and nucleon-target phase shifts that is χCT and χNT need the profile functions and nuclear densities for their determination. The profile function is usually parametrized as [3] Γ(b) = 1−iα 4πβ σNNe −b2/2β The values of parameters σNN, cross section for nucleon-nucleon collision, and α, the ratio of real to imaginary part of nucleon-nucleon scattering amplitudes, are obtained by using the recent prescription of Ref. [4]. While those of β, slope parameter of the nucleon-nucleon elastic differential cross section, are taken as an appropriate average of the values quoted in Ref. [5]. The core and target densities are considered to be described by sum of two Gaussians with four free parameters. The parameters of density distributions are determined to fulfill the following four conditions. (i) The density at the center of the nucleus is constant with a value of 0.1382 fm. (ii) The integration of the density is normalized to the total number of nucleons. (iii) The integration of density multiplied by r is normalized to mean square radius of the nucleus and (iv) at a distance of 1.07 A fm from the center the density becomes half of that at center. Another key factor in the determination of reaction cross section is the ground state single particle wave function of the projectile which is obtained by solving the following radial Schrodinger equation d2R(r) dr2 + 2μ ħ2 [E − U(r) − l(l+1)ħ2 2μr2 ] R(r) = 0. The potential U(r) consists of nuclear, spin-orbit and Coulomb parts and is written as U(r) = −V0f(r) + Vls(l. s)r0 2 1 r d dr f(r) + VCoul. In the present work two different kinds of approaches are adopted for nuclear and spin-orbit parts of the potential while the Coulomb part is zero for n+C system. One of the most frequently used potential is the usual Woods-Saxon (WS) potential with the following form factor