Study of Density Distributions, Elastic Electron Scattering form factors and reaction cross sections of 9C, 12N and 23Al exotic nuclei

Abstract

The ground state densities of unstable proton-rich 9C, 12N and 23Al exotic nuclei are studied via the framework of the two-frequency shell model (TFSM) and the binary cluster model (BCM). In TFSM, the single particle harmonic oscillator wave functions are used with two different oscillator size parameters βc and βv, where the former is for the core (inner) orbits and the latter is for the valence (halo) orbits. In BCM, the internal densities of the clusters are described by single particle Gaussian wave functions. The long tail performance is clearly noticed in the calculated proton and matter density distributions of these nuclei. The structure of the valence proton in 9C and 12N is a pure (1p1/2) configuration while that for 23Al is mixed configurations with dominant (2s1/2). Elastic electron scattering proton form factors for 9C, 12N and 23Al are studied using the plane wave born approximation (PWBA). It is found that the major difference between the calculated form factors of unstable (exotic) [9C, 12N, 23Al] nuclei and those of stable [12C, 14N, 27Al] nuclei is attributed firstly to the influence of the proton density distributions of the last proton in unstable nuclei and secondly to the difference in the center of mass correction which depends on the mass number and the size parameter β (which is assumed in this case equal to the average of βc and βv). The reaction cross sections for 9C, 12N and 23Al are studied by means of the Glauber model with an optical limit approximation using the ground state densities of the projectile and target, where these densities are described by single Gaussian functions. The calculated reaction cross sections of 9C, 12N and 23Al at high energy are in good agreement with the data. The analysis of the present study supports the halo structure of these nuclei.