Akihisa Kohama

Nuclear transparency in the Glauber impulse approximation

Abstract We carefully construct a formalism, called the Glauber impulse approximation, for describing nuclear transparency for the semi-exclusive process of high-energy proton quasi-elastic scattering from nuclei. The formalism is based on the conventional multiple-scattering theory and uses the Glauber theory with impulse approximation. In the heavy nuclear limit, our formalism yields the familiar formula for the process based on the mean-free-path argument, except that the reaction cross section appears instead of the total cross section. Our nuclear transparency is thus larger than what could naively have been expected. The nuclear transparency calculated for various nuclei, agrees with the observation in overall magnitude, but fails to explain the energy variation.

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.

Elastic and total reaction cross sections of oxygen isotopes in Glauber theory

We systematically calculate the total reaction cross sections of oxygen isotopes, 15–24 O, on a 12 C target at high energies using the Glauber theory. The oxygen isotopes are described with Slater determinants generated from a phenomenological mean-field potential. The agreement between theoretical and experimental results is generally good, but a sharp increase of the reaction cross sections from 21 O to 23 O remains unresolved. To examine the sensitivity of the diffraction pattern of elastic scattering to the nuclear surface, we study the differential elastic-scattering cross sections of proton- 20,21,23 O at the incident energy of 300 MeV by calculating the full Glauber amplitude.

A model for nuclear transparency in high-energy quasi-elastic scatterings

Abstract The nuclear transparency is studied in a quantum-mechanical model for the internal structure of the proton. Only the breathing mode is considered for the internal motion and is described by the dynamical variation of the size parameter, b . The propagation of the dynamical proton in nuclear matter is calculated with its attenuation rate proportional to b 2 . The internal dynamics is found to enhance the transparency and gives rise to its monotonically increasing energy dependence.

Energy and mass-number dependence of hadron-nucleus total reaction cross sections

We thoroughly investigate how proton–nucleus total reaction cross sections depend on the target mass number A and the proton incident energy. In doing so, we systematically analyze nuclear reaction data that are sensitive to nuclear size, namely, proton–nucleus total reaction cross sections and differential elastic cross sections, using a phenomenological black-sphere approximation of nuclei that we are developing. In this framework, the radius of the black sphere is found to be a useful length scale that simultaneously accounts for the observed proton–nucleus total reaction cross section and first diffraction peak in the proton elastic differential cross section. This framework, which is shown here to be applicable to antiprotons, is expected to be applicable to any kind of projectile that is strongly attenuated in the nucleus. On the basis of a cross-section formula constructed within this framework, we find that a less familiar A1/6 dependence plays a crucial role in describing the energy dependence of...

Nuclear correlation and finite interaction-range effects in high-energy (e, e′p) nuclear transparency☆

Abstract Nuclear transparency is calculated for high-energy, semi-inclusive (e, e′p) reactions, by accounting for all orders of Glauber multiple-scattering and by using realistic finite-range pN interaction and (dynamically and statistically) correlated nuclear wave functions. The nuclear correlation effect is reduced due to the pN finite-range effect, and is only a few percent for a given one-body density, depending on details of the (presently poorly known) nuclear correlations in finite nuclei.

Anomalous mass number dependence of nuclear transparency

Abstract We examine the target mass number ( A ) dependence of the nuclear transparency calculated for ( e , e ′ p ) reactions. Generally, the transparency is proportional to A − 1 3 for large A s and has weaker A -dependence as A decreases. The conventional nuclear physics calculation yields a transparency whose A − 1 3 dependence is reached in rather light nuclei (around A = 20). If either the proton mean-free path in nuclei becomes substantially longer, or the internal structure of the proton is explicitly incorporated in the calculation, however, the A − 1 3 dependence is reached only in extremely heavy nuclei. The A -dependence should thus serve as a signature of the so-called color-transparency phenomenon.

Proton-Nucleus Total Reaction Cross Sections in the Optical Limit Glauber Theory Subtle Dependence on the Equation of State of Nuclear Matter

We calculate the proton-nucleus total reaction cross sections at different energies of incident protons within the optical limit approximation of the Glauber theory. The isospin effect has been taken into account. The nucleon distribution is obtained in the framework of macroscopic nuclear models in a way depending on the equation of state of uniform nuclear matter near the saturation density. We find that at an energy of order 40 MeV, the reaction cross section calculated for neutron- rich isotopes significantly increases as the parameter L characterizing the density dependence of the symmetry energy increases, while at energies of order 300 and 800 MeV, it is almost independent of L. This is a feature of the optical limit Glauber theory in which an exponential dependence of the reaction cross section on the neutron skin thickness remains when the total proton-neutron cross section is small enough.

Nuclear transparency in a relativistic quark model

Abstract We examine the nuclear transparency for the quasi-elastic (e,e′p) process at large momentum transfers in a relativistic quantum-mechanical model for the internal structure of the proton, using a relativistic harmonic oscillator model. A proton in a nuclear target is struck by the incident electron and then propagates through the residual nucleus suffering from soft interactions with other nucleons. We call the proton “dynamical” when we take into account of internal excitations, and “inert” when we freeze it to the ground state. When the dynamical proton is struck with a hard (large-momentum transfer) interaction, it shrinks, i.e. small-sized configuration dominates the process. It the travels through nuclear medium as a time-dependent mixture of nitrinsic excited states and thus changing its size. Its absorption due to the soft interactions with nuclear medium depends on its transverse-size. Since the nuclear transparency is a measure of the absorption strength, we calculate it in our model for the dynamical case, and compare the results with those for the inert case. The effect of the internal dynamics is observed, which is in accord with the idea of the “color transparency”. We also compare our results with the experimental data in regard of q2-dependence as well as A-dependence, and find that the A-dependence may reveal the color-transparency effect more clearly. Similar effects of the internal dynamics in the other semi-exclusive hard processes are briefly discussed.

Study of nuclear matter density distributions using hadronic probes

We briefly review our formula for a proton-nucleus total reaction cross section, σR, constructed in the black-sphere approximation of nuclei, in which a nucleus is viewed as a “black” sphere of radius “a”. Some years ago, using the Glauber model, one of the authors (A.K.) and his collaborators performed numerical simulations to examine the possibility to probe the nuclear matter density distributions of neutron-rich unstable nuclei from proton elastic scatterings “model-independently” [1]. The present study is another attempt to seek a “model-independent” framework for systematically analyzing scattering data for studying the matter density distributions of atomic nuclei.