Calculation of a complete set of spin observables for proton elastic scattering from stable and unstable nuclei

Abstract

A microscopic study of proton elastic scattering from unstable nuclei at intermediate energies using a relativistic formalism is presented. We have employed both the original relativistic impulse approximation (IA1) and the generalised impulse approximation (IA2) formalisms to calculate the relativistic optical potentials, with target densities derived from relativistic mean field (RMF) theory using the NL3 and FSUGold parameter sets. Comparisons between the optical potentials computed using both IA1 and IA2 formalisms, and the different RMF Lagrangians are presented for both stable and unstable targets. The comparisons are required to study the effect of using IA1 versus IA2 optical potentials, with different RMF parameter sets, on elastic scattering observables for unstable targets at intermediate energies. We also study the effect of full-folding versus the factorized form of the optical potentials on elastic scattering observables. As with the case for stable nuclei, we found that the use of the full-folding optical potential improves the scattering observables (especially spin observables) at low intermediate energy (e.g. 200MeV). No discernible difference is found at a projectile incident energy of 500 MeV. To check the validity of using localized optical potential, we calculate the scattering observables using non-local potentials by solving the momentum space Dirac equation. The Dirac equation is transformed to two coupled Lippmann-Schwinger equations, which are then numerically solved to obtain elastic scattering observables. The results are discussed and compared to calculations involving local coordinate-space optical potentials.

Energy-independent optical $^{1}S_{0}NN$ potential from Marchenko equation

“…(1-6) and our algebraic form of the Marchenko equation Eqs. (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) to reconstruct local, and energy-independent OP from an absorbing S-matrix and corresponding bound states' characteristics. We present an absorptive single partial channel S-matrix on the q-axis as…”

“…The concept of optical potential (OP) is a useful tool in many branches of nuclear physics. There are a number of microscopically derived [8][9][10][11][12][13][14][15][16][17][18][19][20][21] as well as phenomenological [12,19,[23][24][25][26][27][28][29][30] optical potentials used for description of nuclei and nuclear reactions. Nucleon-nucleon potentials are used as an input for (semi)microscopic descriptions of nuclei and nuclear reactions [8,9,12,17,19,21,26].…”

Model of multiple Dirac eikonal scattering of protons by nuclei

“…In the MDST, which was first proposed by Glauber in [1] and further developed in a great number of works (see, e.g., [2][3][4][5][6][7][8][9][10][11] and references therein), the amplitude of the p − A interaction is expressed in terms of the elementary nucleonnucleon (N N ) scattering amplitudes and the target-nucleus wave function (primarily the nucleon distribution densities) within the eikonal approximation. The RIA approach (see [12][13][14][15][16][17][18][19][20][21] and references therein) is based on solving the Dirac equation with a relativistic microscopic optical potential, which is also constructed from the N N -amplitudes and the target-nucleus nucleon densities, normally the relativistic ones.…”

“…As for the RIA model, it has clearly shown its advantages over the nonrelativistic impulse approximation (see, for example, [16,17,19]) and turned out to be successful in describing the experimental data on cross sections and spin observables for the proton scattering by various stable nuclei in the energy range from lower values about 200 MeV up to higher energies where the Glauber MDST is usually applied, for which a number of precise measurements are available in the literature. Besides the consideration of stable target nuclei, recently, the interest has been rising to employing the RIA approach to the theoretical studies of proton scattering by various unstable nuclei (see, [19][20][21] and references therein), owing to the expected future experimental possibilities in this area basing on using radioactive beams.…”