Proton-nucleus Reaction Cross Sections Research Articles

Deformation and orientation effects on reaction cross-sections at intermediate and high energies

The effects of deformation and orientation on the nucleus–nucleus and proton–nucleus reaction cross-sections are investigated at intermediate and high energies, in the framework of the Coulomb modified Glauber model. The matter density of the projectile is treated by a deformed Fermi shape with quadrupole and hexadecapole deformations. In-medium effects are included through a local density- and an energy-dependent effective nucleon–nucleon total cross-section. Calculations are performed for the deformed projectiles [Formula: see text] colliding by [Formula: see text] and by protons. It is found that the average of reaction cross-section over all directions of the symmetry axis of the deformed projectile differs by about 2[Formula: see text] compared with that calculated for a spherical projectile with the same rms matter radius as the deformed one. The difference between the cross-sections calculated with and without medium effects is of the order 2[Formula: see text] for both deformed and spherical cases. The integrated reaction cross-sections over all orientation angles provide a consistent explanation of the experimental data. The orientation of the heavy projectile can produce a difference in the calculated cross-section about 35[Formula: see text] for nucleus–nucleus and about 45[Formula: see text] for proton–nucleus. This study is also useful for experiments of polarized beams that have created opportunities to study oriented collisions of deformed nuclei. The method is applied to extract the rms radius of [Formula: see text] and it is found to be about 3.56 and 3.45[Formula: see text]fm when using deformation with and without in-medium effects.

Proton-nucleus inelastic cross section at ultra high energy

Energy dependence of proton-nucleus reaction cross section at very high energy is discussed. It is stressed that depending on the gluon distribution near the nuclear surface, proton-nucleous total cross section increases much more rapidly compared to the usual Glauber independent nucleon estimate. The recent observation of smaller X max than the expected value at UHECR domain can be an indication for such a mechanism.

Formula for Proton–Nucleus Reaction Cross Section at Intermediate Energies and Its Application

We construct a formula for proton–nucleus total reaction cross section as a function of the mass and neutron excess of the target nucleus and the proton incident energy. We deduce the dependence of the cross section on the mass number and the proton incident energy from a simple argument involving the proton optical depth within the framework of a black sphere approximation of nuclei, while we describe the neutron excess dependence by introducing the density derivative of the symmetry energy, L , on the basis of a radius formula constructed from macroscopic nuclear models. We find that the cross section formula can reproduce the energy dependence of the cross section measured for stable nuclei without introducing any adjustable energy dependent parameter. We finally discuss whether or not the reaction cross section is affected by an extremely low density tail of the neutron distribution for halo nuclei.

Energy dependence of proton-nucleus reaction cross sections

Reaction-cross-section data for proton-nucleus scattering up to 1 GeV have been analyzed in a black-disk model. Simple phenomenological relations are derived, which make it possible to predict the energy dependence of proton-nucleus reaction cross sections. The relations require only the total cross sections in nucleon-nucleon scattering and the matter densities of the proton and the target nucleus.

Reaction cross section described by a black sphere approximation of nuclei

We identify a length scale that simultaneously accounts for the observed proton-nucleus reaction cross section and diffraction peak in the proton elastic differential cross section. This scale is the nuclear radius, $a$, deduced from proton elastic scattering data of incident energies higher than $\sim800$ MeV, by assuming that the target nucleus is a ``black'' sphere. The values of $a$ are determined so as to reproduce the angle of the first diffraction maximum in the scattering data for stable nuclei. We find that the absorption cross section, $\pi a^2$, agrees with the empirical total reaction cross section for C, Sn, and Pb to within error bars. This agreement persists in the case of the interaction cross section measured for a carbon target. We also find that $\sqrt{3/5}a$ systematically deviates from the empirically deduced values of the root-mean-square matter radius for nuclei having mass less than about 50, while it almost completely agrees with the deduced values for $A\gtrsim50$. This tendency suggests a significant change of the nuclear matter distribution from a rectangular one for $A\lesssim50$, which is consistent with the behavior of the empirical charge distribution.

Global analysis of proton nucleus reaction cross sections

Glauber theory in the optical limit is used in a global analysis of proton-nucleus reaction cross sections. A large body of data with target mass $9l~Al~238$ and energies $6l~El~800$ MeV has been analyzed. A good description is obtained in the entire range of mass and energy. The extracted rms radii are consistent with the corresponding values from high energy electron scattering and muonic atom x-ray measurements, as well as with relativistic mean field calculations.

Empirical determination of the mean free path of a nucleon in the nuclear medium

The mean free path of a nucleon in the nuclear medium extracted from measured neutron-nucleus total cross sections is compared with the values determined from the energy-momentum dispersion relation. The optical potentials used in the dispersion relation are the relativistic global energy-dependent Lorentz scalar and vector potentials of Dirac phenomenology. Excellent agreement between the values extracted from either total neutron-nucleus cross sections or proton-nucleus reaction cross sections and the calculated values is achieved when the optical potentials are evaluated using radial values corresponding to approximately 80% of nuclear matter density.

PROTON-NUCLEUS REACTION CROSS SECTIONS COMPUTED FROM ELASTIC-SCATTERING DATA

Proton-nucleus reaction cross sections in the energy region from 90 to 300 MeV are computed from elastic-scattering data. The interference of the nuclear scattering amplitude with the calculable Coulomb scattering amplitude determines the magnitude and phase of the nuclear amplitude when the differential elastic-scattering cross section is known. The reaction cross section is then obtained by an application of the optical theorem.