Proton-nucleus Total Reaction Cross Sections Research Articles

The effects of finite range of the NN force and in-medium NN cross-section on the proton–nucleus total reaction cross-section

The effects of the finite range of the NN force and medium modifications on the nucleon-nucleus total reaction cross sections are investigated in the framework of the Coulomb modified Glauber model (CMGM). Different models of the nuclear densities are used. Comparison with experiments is considered. It is found that the effects of finite range strongly increase the reaction cross section at low and intermediate energies. Medium modifications of the NN cross section reduced the reaction cross section at low and intermediate energies. Both effects are found to be important for a better description of the proton- and neutron-nucleus total reaction cross sections.

Neutron radii and neutron skin of neutron-rich nuclei deduced from proton-nucleus total reaction cross sections

A new method is proposed to deduce the neutron radii of neutron-rich nuclei. This method requires measuring the reaction cross sections of both the neutron-rich nucleus and its stable isotope at the same energy per nucleon on a proton target. Using this method and the available experimental data of 12,22C + p and 9,14Be + p at 40A MeV, the neutron radii of 22C and 14Be have been deduced.

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...

Effects of In-Medium Nucleon-Nucleon Cross Section and Nuclear Density Distribution on the Proton-Nucleus Total Reaction Cross Section

We present the proton-total reaction cross sections σR by comparing the experimental data with the Glauber model calculation using four sets of nucleon-nucleon cross sections used in literature (free nucleon-nucleon cross sections (NNCS), phenomenological NNCS, Bruckner-type NNCS and Pauli NNCS) and different nuclear densities for symmetric and asymmetric nuclei. For light symmetric target nuclei, the experimental σR data are well reproduced by the former three NNCS with the ground state density distributions of relativistic mean-field theory. On the other hand, for asymmetry heavier target nuclei, the calculations of the σR data depend significantly on the nuclear density distribution at large radius in the low energy region. The experimental σR of these nuclei are well reproduced by the empirical 3 pF density distribution and the in-medium NNCS. The neutron surface distributions are also discussed based on the 3 pF nuclear charge distributions.

Study of Different Forms of Density Distributions in Proton–Nucleus Total Reaction Cross Section and the Effect of Phase in NN Amplitude

Proton total-reaction cross-section (σR), measurements for about five nuclei in the range 12C to 208Pb at beam energies spanning 40–800 MeV have been analyzed in a systematic way by using the optical limit approximation of the Coulomb-modified Glauber multiple scattering theory. Two different phenomenological nuclear density distributions of the target nucleus in addition to the realistic one have been used in the present analysis. By applying the energy dependence in the slope parameter of nucleon–nucleon (NN) scattering amplitude, it is found that in general, the predictions of σ R with the phenomenological Gambhir and Patil density distribution agree fairly well with the experimental data. The inclusion of phase in the NN amplitude improves the theoretical results. Our analysis shows that the calculated total reaction cross sections closely reproduce the measured data over the whole range of energy considered in this work. To validate our analyses, we have also obtained a fairly good representation of elastic p-nucleus differential scattering cross section data. The effect of a Coulomb energy shift in the proton beam has also been studied.

30–300 MeV proton-nucleus total reaction cross sections

A functional form has been used to analyze proton total reaction cross sections on stable and unstable target nuclei. For proton or incident nuclei energy per nucleon in the range between 30 and 300 MeV, the parameter values in this functional are interpreted in terms of the nuclear-matter distribution by using reliable total reaction cross-sectional data.

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.

Scaling properties of proton-nucleus total reaction cross sections

We study the scaling properties of proton-nucleus total reaction cross sections for stable nuclei and propose an approximate expression in proportion to ${Z}^{2/3}{\ensuremath{\sigma}}_{\mathit{pp}}^{\mathrm{total}}+{N}^{2/3}{\ensuremath{\sigma}}_{\mathit{pn}}^{\mathrm{total}}$. Based on this expression, we can derive a relation that enables us to predict a total reaction cross section for any stable nucleus within $10%$ uncertainty at most, using the empirical value of the total reaction cross section of a given nucleus.

Study of proton total reaction cross section using a Helm model nuclear form factor

An analytic expression for proton–nucleus total reaction cross section has been developed within the framework of Coulomb modified Glauber multiple scattering theory using an approximate form of the Helm model form factor for the distributions of nucleons within nuclei. Without free parameters, the expression reproduces fairly well the proton total reaction cross section data at energies spanning 20–860 MeV. Excellent fits to the experimental data have been achieved using basically one free parameter, plus one other independent of beam energy.

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.

Predicting proton-nucleus total reaction cross sections up to 300 MeV using a simple functional form

Total reaction cross sections are predicted for proton scattering from various nuclei. A simple functional form has been used that reproduces the total reaction cross sections for the scattering of protons from (15) nuclei spanning the mass range from ${}^9$Be to ${}^{238}$U and for proton energies 10 to 300 MeV.

Simple functional form for proton-nucleus total reaction cross sections

A simple functional form has been found that gives a good representation of the total reaction cross sections for the scattering of protons from (15) nuclei spanning the mass range ${}^{9}$Be to ${}^{238}$U and for proton energies ranging from 20 to 300 MeV.

Nuclear absorption cross sections using medium modified nucleon–nucleon amplitudes

We extract the in-medium nucleon–nucleon amplitudes from the available proton-nucleus total reaction cross sections data. The retrieval of the information from the experiment makes these estimates very reliable. Simple expressions are then given for the in-medium nucleon–nucleon amplitudes for any system of colliding nuclei as a function of energy. Excellent agreement is demonstrated in ion-nucleus absorption cross sections.

Proton-Nucleus Total Reaction Cross Sections and Total Cross Sections Up to 1 GeV

In this paper are presented tables of all directly measured total reaction cross sections and total cross sections for protons interacting with all complex nuclei (2H and heavier) for proton energies up to 1 GeV. Some semiempirical fittings to the data are also included.

The proton-nucleus σ R in the microscopic relativistic and nonrelativistic model

The proton-nucleus total reaction cross section is evaluated in the energy range 100–1000 MeV using a microscopic optical model potential calculated both relativistically and nonrelativistically. The potentials are calculated in the impulse approximation and with medium effects taken into account. Both the relativistic and medium effects are found to be important at energies from 100–400 MeV.

Total reaction cross sections and the matter density of finite nuclei

A simple model for total reaction cross sections based on the impulse approximation and the use of an eikonal propagator is derived. Semiquantitative approximations are used to demonstrate that total reaction cross sections are determined by the radius at which the profile function is equal to one mean free path for the incident particle. A simple quantitative relation between the density and the profile function is also provided. The model is tested against existing data for proton-nucleus total reaction cross sections for $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{40,44,48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ targets at energies from 100 MeV to 1 GeV. The total reaction cross sections are generally found to be in agreement (with several exceptions) with neutron densities determined either theoretically or from other experiments.NUCLEAR REACTIONS Total reaction cross sections, matter densities and radii.