Total Nuclear Reaction Cross Section Research Articles

Nuclear reaction cross sections for hadron therapy

Treatment planning in hadron therapy uses Monte Carlo techniques that require total nuclear reaction cross sections for a variety of interacting systems and over a wide range of energies. Current empirical models are tuned to reproduce cross sections for stable isotopes, but in some cases, overestimate measured cross sections by 20%. Here we discuss an alternative approach: the optical limit of Glauber theory, which describes existing measurements better and offers more reliable predictions for the many systems where there is no experimental information. We also suggest how existing implementations of empirical models within GEANT4 could be improved. Ultimately, these calculations should contribute to improvements in planning of hadron therapy treatments.

Effect of nuclear surface diffuseness on Coulomb excitation and total nuclear reaction cross sections

We investigate the effect of variation of nuclear surface diffuseness, through diffuseness parameter, on the evaluation of survival probability, absorption effects, Coulomb excitation cross section and total nuclear reaction cross section of Kr+80197Au system. The diffuseness parameter is found to be affecting all the above mentioned quantities appreciably. Specifically, the survival probability and Coulomb excitation cross section are found to be decreasing with increase in a while absorption effects and σR are found to be increasing.

Analysis of Various Projectile Interactions with Nuclear Emulsion Detector Nuclei at ~1 GeV per Nucleon Using Coulomb Modified Glauber Model

The total nuclear reaction cross section is calculated considering the cases with and without medium effect by employing Coulomb modified Glauber model (CMGM) for interactions of projectiles 56Fe26, 84Kr36, 132Xe54, 197Au79, and 238U92 with nuclear emulsion detector (NED) nuclei at around 1 GeV per nucleon incident kinetic energy. These calculated nuclear reaction cross sections are correlated with the different target groups of the NED nuclei. The average value of various parameters is also calculated and compared with the corresponding experimental results. The number of shower particles emitted in an interaction is also calculated and showed good agreement with the experimental result. We observed that the total nuclear reaction cross section increases with increasing the target mass number in case of all the considered projectiles. In addition, it is shown that the average value of reaction cross section with nuclear medium effect is in good agreement with the experimental results for projectiles 56Fe, 84Kr, and 132Xe, although results of projectiles 197Au and 238U are not in agreement with the experimental observations. This study sheds some light on the energy dependence of the nuclear reaction cross section.

Study of p-4Hetotal reaction cross-section using Glauber and Coulomb-modified Glauber models

The total nuclear reaction cross-section σRfor p-4He in the energy range from 25 MeV to 1000 MeV is calculated within Glauber and Coulomb-modified Glauber models. The Coulomb-modified Glauber model (CMGM) is introduced via modification of the Coulomb trajectory of the projectile from a straight line, and calculation of the effective radius of interaction. The effects of in-medium nucleon–nucleon (NN) total cross-section, phase variation, high order momentum transfer component of nucleon–nucleon elastic scattering amplitude and Pauli blocking are studied. It is pointed out that the phase variation of the nucleon–nucleon amplitude plays a significant role in describing σRwith γ = -1.6 fm2at in-medium nuclear density ϱ = 0 and γ = -2 fm2at ϱ = 0.17 fm-3in the whole energy range. A remarkable fit to the available experimental data is obtained by invoking Pauli blocking and high order momentum transfer of nucleon–nucleon (NN) elastic scattering amplitude for Ep< 100 MeV.

Nuclear reaction cross sections of exotic nuclei in the Glauber model for relativistic mean field densities

We have calculated the total nuclear reaction cross sections of exotic nuclei in the framework of the Glauber model, using as inputs the standard relativistic mean field (RMF) densities and the densities obtained from the more recently developed effective-field-theory-motivated RMF (the E-RMF). Both light and heavy nuclei are taken as the representative targets, and the light neutron-rich nuclei as projectiles. We found the total nuclear reaction cross section to increase as a function of the mass number, for both the target and projectile nuclei. The differential nuclear elastic scattering cross sections are evaluated for some selected systems at various incident energies. We found a large dependence of the differential elastic scattering cross section on incident energy. Finally, we have applied the same formalism to calculate both the total nuclear reaction cross section and the differential nuclear elastic scattering cross section for the recently discussed superheavy nucleus with atomic number Z = 122.

Total Nuclear Reaction Cross Section Induced by Halo Nuclei and Stable Nuclei**The project supported by the State Key Basic Research Development Program of China under Contract No. G2000077400, the “100- Person Project” of the Chinese Academy of Sciences, National Natural Science Foundation of China under Grant Nos. 10175080, 10175082 10004012, and 19847002, and CAS Knowledge Innovation Project under Grant No.

We develop a method for calculation of the total reaction cross sections induced by the halo nuclei and stable nuclei. This approach is based on the Glauber theory, which is valid for nuclear reactions at high energies. It is extended for nuclear reactions at low energies and intermediate energies by including both the quantum correction and Coulomb correction under the assumption of the effective nuclear density distribution. The calculated results of the total reaction cross section induced by stable nuclei agree well with 30 experimental data within 10 percent accuracy.The comparison between the numerical results and 20 experimental data for the total nuclear reaction cross section induced by the neutron halo nuclei and the proton halo nuclei indicates a satisfactory agreement after considering the halo structure of these nuclei, which implies quite different mean fields for the nuclear reactions induced by halo nuclei and stable nuclei. The halo nucleon distributions and the root-mean-square radii of these nuclei can be extracted from the above comparison based on the improved Glauber model, which indicates clearly the halo structures of these nuclei. Especially, it is clear to see that the medium correction of the nucleon-nucleon collision has little effect on the total reaction cross sections induced by the halo nuclei due to the very weak binding and the very extended density distribution.

Energy dependence of the total reaction cross section of isomeric18Fmon silicon below 400 MeV

A 25 MeV/nucleon primary O-17 beam was used to produce an isomeric state F-18(m) beam via the single-nucleon transfer reaction O-17 (C-12, B-11)F-18(m). The total nuclear reaction cross section, sigma(R), of F-18(m) (metastable) on silicon was measured using a stack of silicon surface barrier detectors that included a position sensitive silicon detector (PSD). The total reaction cross sections were determined as a function of bombarding energy up to 400 MeV by measuring the energy loss in each detector. The reaction cross sections were measured both for a mixture of metastable- and ground-state ions and for a pure ground-state beam. The reaction cross sections for N-14 and O-16 beams were also measured simultaneously. The reaction cross sections for the metastable beam were deduced from the mixed- and the ground-state cross sections, corrected for the measured purity of the mixed-state beam. The observed reaction cross sections for F-18(m) are larger at low energies than the cross sections measured for the ground state. The isomeric cross sections can be reproduced by an optical model potential having a diffuseness of 0.8 fm, compared to a more conventional diffuseness parameter of 0.5 fm, which is adequate to reproduce the N-14, O-16, and F-18(g.s.) cross sections measured in this experiment.

In-medium nucleon-nucleon cross section and its effect on total nuclear reaction cross section

A phenomenological formula for in-medium nucleon-nucleon cross section is presented, in which nuclear matter density and incident energy dependencies are included. This formula is used to study total nuclear reaction cross section based on Coulomb-modified Glauber model. The calculated results can reproduce experimental total reaction cross section induced by the stable nuclei and the exotic nuclei over a wide energy range.

Isospin Physics in Heavy-Ion Collisions at Intermediate Energies

In nuclear collisions induced by stable or radioactive neutron-rich nuclei a transient state of nuclear matter with an appreciable isospin asymmetry as well as thermal and compressional excitation can be created. This offers the possibility to study the properties of nuclear matter in the region between symmetric nuclear matter and pure neutron matter. In this review, we discuss recent theoretical studies of the equation of state of isospin-asymmetric nuclear matter and its relations to the properties of neutron stars and radioactive nuclei. Chemical and mechanical instabilities as well as the liquid-gas phase transition in asymmetric nuclear matter are investigated. The in-medium nucleon-nucleon cross sections at different isospin states are reviewed as they affect significantly the dynamics of heavy ion collisions induced by radioactive beams. We then discuss an isospin-dependent transport model, which includes different mean-field potentials and cross sections for the proton and neutron, and its application to these reactions. Furthermore, we review the comparisons between theoretical predictions and available experimental data. In particular, we discuss the study of nuclear stopping in terms of isospin equilibration, the dependence of nuclear collective flow and balance energy on the isospin-dependent nuclear equation of state and cross sections, the isospin dependence of total nuclear reaction cross sections, and the role of isospin in preequilibrium nucleon emissions and subthreshold pion production.

Unusual energy dependence of the total nuclear reaction cross section for a secondary isomeric nuclear beam (18Fm, Jπ = 5+, Ex = 1.1 MeV)

A primary 17 O beam has been used to produce a 22.3 MeV/nucleon 18 F m isomeric secondary beam via a single nucleon transfer reaction on a carbon target. The total nuclear reaction cross sections for 18 F m and 18 F g . s . in silicon were measured in a stack of seven silicon solid-state detectors. The cross section for 18 F m exhibits some unusual features at low energy not seen for 18 F g . s . or other ions.

Closed-form expressions for cross sections of exotic nuclei

We study p+11Li cross sections, in the intermediate-energy region, with the nucleus characterized by a halo structure. The eikonal approximation and “tϱ” optical potential are used to get an intuitive picture of the reaction mechanism. By using gaussian nucleon densities for 11Li, 9Li and the halo, we obtain similar expressions for the total nuclear reaction and two-neutron removal cross section in the Glauber approximation. Closed-form analytical expressions for those cross sections are derived. By comparing the results with the exact ones, we can conclude that we have derived a fair approximation to them. We also estimate the “in-medium” Pauli-blocking effect on the cross sections.

Total cross sections of reactions induced by neutron-rich light nuclei

Total nuclear reaction cross-sections are determined by means of a 4π-γ method. The results cover a wide span of targets for various stable beams. The validity of the method is shown in a combined systematics including also the results of transmission-type experiments. The data are very well described by the formula developed by Kox et al. The same method is applied to secondary fragment beams produced from a 44 MeV/u22Ne beam on a 332mg/cm2 181Ta target. Using the LISE spectrometer the fragments4, 6He,6–9, 11Li,7, 9–12, 14Be,10–15, 17B11–19C,13–19N,15–21O,18– 21F and20,21 Ne are analyzed and transported to interact with a 199.4 mg/cm2 Cu target surrounded by a 4π-γ counter. The measured total reaction cross-sectionsσ R are discussed in terms of the reduced strong absorption radiusr 0 and compared with other experimental results.

Deep inelastic reactions of32S on27Al

A time-dependent Hartree-Fock analysis of the collision of 32S with 27Al is carried out for a laboratory energy of 175 MeV. Using the sharp cut-off approximation a total nuclear reaction cross section of 2.27 b is obtained, corresponding to a grazing angular momentum of approximately 64h(cross). A complete fusion cross section of 1.06 b arises from an angular momentum fusion window 17h(cross)<or approximately=lin<or approximately=47h(cross). The deep inelastic reactions on either side of the fusion window lead to two separate components in the energy spectrum of the products of strongly damped collisions with distinct Q values.

Nucleus-nucleus reaction cross sections at high energies: Soft-spheres model

A simple analytical expression is derived for the total nuclear reaction cross section in heavy-ion heavy-ion collisions at high energies based on the semiclassical optical model. Tapered nuclear density distributions are used in conjunction with nucleon-nucleon collision cross sections. NUCLEAR REACTIONS Nucleus-nucleus, high-energy; semiclassical calculation of total reaction cross sections, tapered density distributions.

Interactions of Negative Pions in Carbon and Lead

A cloud chamber investigation of the nuclear interactions of 125-Mev negative pi mesons has been carried out. Carbon and lead were employed as the scattering material. The experimental arrangement was designed to observe the charge-exchange process: ${\ensuremath{\pi}}^{\ensuremath{-}}+\mathrm{C}\ensuremath{\rightarrow}{\mathrm{B}}^{(\mathrm{exc})}+[{\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}].$ High-energy photons, probably attributable to charge exchange, are found to arise from nuclear interaction, with a small but finite cross section. Total and differential cross section for elastic and inelastic scattering, as well as total nuclear reaction cross sections, are presented. A square well (optical model) analysis fits the data with a potential whose real part is attractive and 30 Mev deep, and whose imaginary part corresponds to a mean free path in nuclear matter of 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm. The optical model parameters are found to be energy dependent, the well depth increasing and the mean free path decreasing as the energy is raised.