Complete Glauber calculations of reaction and interaction cross sections for light-ion collisions
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EMENTARY PARTICLES AND FIELDS Theory
Complete Glauber Calculations of Reaction and Interaction Cross Sections for Light-Ion Collisions I. S. Novikov1)* and Yu. M. Shabelski2)** Received December 8, 2014; in final form, April 7, 2015
Abstract—The differences of the interaction and reaction cross sections for collisions between relativistic light ions of mass number in the range of A < 40 are calculated on the basis of Glauber theory. In the optical approximation of Glauber theory, these differences are about 1% of the interaction cross sections. Upon taking into account all diagrams in Glauber theory, these differences reach 3 to 4% of the interaction cross section. DOI: 10.1134/S106377881507011X
1. INTRODUCTION Various targets are used to measure interaction cross sections for stable and unstable light nuclear isotopes [1, 2]. The parameters of nuclear-density distributions are determined on the basis of data obtained in this way, Glauber theory being frequently used for this purpose [3–5]. The reaction cross sec(R) tions σAB are calculated within Glauber theory, and the results are compared with experimental data on (I) the interaction cross sections σAB . The values obtained for the parameters of nuclear-density distributions can be found in [6–8]. The estimates presented in [1, 2, 9] reveal that the differences between the reaction and interaction cross sections are negligible. In [10, 11], the difference of (I) (R) σAB and σAB was estimated at a value below a few percent. In [12], the differences between the reaction and interaction cross sections for A < 80 nuclei were analyzed on the basis of the black-sphere model and under the assumption of a uniform nuclear-density distribution. As a result, it was shown that the differences of these cross sections are not greater than (R) 60 mb or 4% to 6% of the reaction cross section σAB .
basis of complete Glauber theory and in its optical approximation. 2. ELASTIC AND INELASTIC NUCLEUS–NUCLEUS SCATTERING IN GLAUBER THEORY In this section, we present the expressions for (R) the reaction cross sections σAB and the interaction (I)
cross sections σAB , as well as for their difference, in Glauber theory. A detailed derivation of these expressions can be found in [13].
2.1. Reaction Cross Section (R) for Light-Ion Collisions, σAB Within Glauber theory, reaction cross sections can be obtained from elastic-scattering amplitudes. As a result, we have (R) tot el σAB = σAB − σAB = d2 b[1 − |SAB (b)|2 ]. (1) where (2) SAB (b) ⎫ ⎧ ⎬ ⎨ [1 − ΓN N (b + ui − sj )] |B|A. = A|B| ⎭ ⎩
However, the black-sphere model is not quite appropriate for calculating the cross-section difference in question. For this reason, we calculate here the (I) (R) difference of the cross sections σAB and σAB on the 1)
Department of Physics and Astronomy, Western Kentucky University, 1906 College Heights Bvld., 11077, Bowling Green, KY 42101-1077, USA. 2) Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute, Gatchina, 188300 Russia. * E-mail: [email protected] ** E-mail: sha
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