Total Reaction Cross Sections Research Articles

Measurement of He4 charge- and mass-changing cross sections on H, C, O, and Si targets in the energy range 70–220 MeV/u for radiation transport calculations in ion-beam therapy

Measured charge- and mass-changing cross sections for the systems $^{4}\mathrm{He}+^{12}C$, $^{4}\mathrm{He}+^{16}O$, $^{4}\mathrm{He}+^{28}\mathrm{Si}$, and $^{4}\mathrm{He}+^{1}\mathrm{H}$ in the energy range $70--220\phantom{\rule{4pt}{0ex}}\mathrm{MeV}/\mathrm{u}$ are presented. The cross sections were obtained via the attenuation method where a $\mathrm{\ensuremath{\Delta}}E\text{\ensuremath{-}}E$ scintillator telescope was used for particle identification. These new data have particular relevance for future applications of $^{4}\mathrm{He}$ ions in ion-beam radiotherapy because this technique relies on precise heavy ion transport models for an accurate dose calculation. The radiation transport codes applied for this purpose typically make use of parametrizations of the total reaction cross section ${\ensuremath{\sigma}}_{R}$. The widely used parametrization for nucleus-nucleus reaction cross sections by Tripathi et al. is shown to underpredict the new experimental cross sections for $^{4}\mathrm{He}$ ions in the therapeutic energy range by up to $30%$, which can lead to considerable dose calculation uncertainties. Therefore, modifications of the parameters in the Tripathi model are proposed to optimize it for applications related to $^{4}\mathrm{He}$ ion-beam therapy.

Reaction Cross Section of Heavy Projectiles Using Coulomb Modified Glauber Model

We investigated reaction cross section and inelastic collisions of the wide number of projectile and target nuclei using the Coulomb Modified Glauber Model (CMGM). The total reaction cross sections were calculated with and without accounting for in-medium effect for various heavy projectiles such as 56Fe26, 84Kr36, 132Xe54, 197Au79 and 238U92 that interact with Nuclear Emulsion Detector’s (NED) nuclei at incident energies at around 1 GeV/n. The calculated average values of reaction cross section are compared with the corresponding experimental data.

A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes

A dispersive optical model analysis of the proton scattering by titanium element nucleus and its natural isotopes is applied to the construction of the complex single-particle mean field starting from Fermi energy value to the energy value 100MeV and for constant input values of the parameters of this mean field. This mean field is called (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations were compared with these resulting from global parameterization of the optical model potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section, polarization for selected energy showed the excellent agreement with available experimental data and with these resulted from global parameterization of the optical model potential.

Study of The Breakup Channel Effect on The Semiclassical and Quantum Mechanical Calculations for The Light and Medium System

A semiclassical and full quantum mechanical approaches have been used to study the effect of channel coupling on the calculations of the total fusion reaction cross section , the fusion barrier distribution and the reaction probability for the systems 11B+237Np, 15N+54Fe and 58Ni +54Fe. The semiclassical approach used in the present work based on the method of the Alder and Winther for Coulomb excitation. The full quantum mechanical approach was based on solving the time dependent Schrödinger equationincluding the coupling effect. A comparison of our semiclassical calculations and full quantum mechanical calculations with the corresponding experimental data shows good agreement, above and below the Coulomb barrier.

Experimental Assessment of Lithium Hydride's Space Radiation Shielding Performance and Monte Carlo Benchmarking.

The harmful effects of space radiation pose a serious health risk to astronauts participating in future long-term missions. Such radiation effects must be considered in the design phase of space vessels as well as in mission planning. Crew radioprotection during long periods in deep space (e.g., transit to Mars) represents a major challenge, especially because of the strong restrictions on the passive shielding load allowed on-board the vessel. Novel materials with better shielding performance compared to the "gold standard" high-density polyethylene are therefore greatly needed. Because of the high hydrogen content of hydrides, lithium hydride has been selected as a starting point for further studies of promising candidates to be used as passive shielding materials. In the current experimental campaign, the shielding performance of lithium hydride was assessed by measuring normalized dose, primary beam attenuation and neutron ambient dose equivalent using 430 MeV/u 12C, 600 MeV/u 12C and 228 MeV proton beams. The experimental data were then compared to predictions from the Monte Carlo transport codes PHITS and GRAS. The experimental results show an increased shielding effectiveness of lithium hydride compared to reference materials like polyethylene. For instance, the attenuation length for 600 MeV/u 12C primary particles in lithium hydride is approximately 20% shorter compared to polyethylene. Furthermore, the comparison results between both transport codes indicates that the standard Tripathi-based total reaction cross-section model of PHITS cannot accurately reproduce the presented experimental data, whereas GRAS shows reasonable agreement.

Theory of single-charge exchange heavy-ion reactions

The theory of heavy ion single charge exchange reactions is reformulated. In momentum space the reaction amplitude factorizes into a product of projectile and target transition form factors, folded with the nucleon-nucleon isovector interaction and a distortion coefficient which accounts for initial and final state ion-ion elastic interactions. The multipole structure of the transition form factors is studied in detail for Fermi-type non-spin flip and Gamow-Teller-type spin flip transitions, also serving to establish the connection to nuclear beta decay. The reaction kernel is evaluated for central and rank-2 tensor interactions. Initial and final state elastic ion-ion interaction are shown to be dominated by the imaginary part of the optical potential allowing to evaluate the reaction coefficients in the strong absorption limit, realized by the black disk approximation. In that limit the distortion coefficient is evaluated in closed form, revealing the relation to the total reaction cross section and the geometry of the transition form factors. It is shown that at small momentum transfer distortion effects reduce to a simple scaling factor, allowing to define reduced forward-angle cross section which is given by nuclear matrix elements of beta decay-type. The response function formalism is used to describe nuclear charge changing transitions. Spectral distributions obtained by a self-consistent HFB and QRPA approach are discussed for $\tau_\pm$ excitations of $^{18}O$ and $^{40}Ca$, respectively, and compared to spectroscopic data. The interplay of nuclear structure and reaction dynamics is illustrated for the single charge exchange reaction $^{18}O+^{40}Ca \to ^{18}F+^{40}K$ at $T_{lab}=270$ MeV.

Consistent account of deuteron-induced reactions on natCr up to 60 MeV

Purpose: Accurate new measurements of low-energy deuteron-induced reaction cross sections for natural Cr target can enhance the related database and the opportunity for an unitary and consistent account of the involved reaction mechanisms. Methods: The activation cross sections of $^{51,52,54}$Mn, $^{51}$Cr, and $^{48}$V nuclei for deuterons incident on natural Cr at energies up to 20 MeV, were measured by the stacked-foil technique and high resolution gamma spectrometry using U-120M cyclotron of the Center of Accelerators and Nuclear Analytical Methods (CANAM) of the Nuclear Physics Institute of the Czech Academy of Sciences (NPI CAS). They as well as formerly available data for deuteron interactions with Cr isotopes up to 60 MeV are the object of an extended analysis of all processes from elastic scattering until the evaporation from fully equilibrated compound system, but with a particular attention given to the BU and DR mechanisms. Results: The new measured activation excitation functions proved essential for the enrichment of the deuteron database, while the theoretical analysis of all available data strengthens for the first time their consistent account provided that (i) a suitable BU and DR assessment is completed by (ii) the assumption of PE and CN contributions corrected for decrease of the total-reaction cross section due to the leakage of the initial deuteron flux towards BU and DR processes. Conclusions: The suitable description of nuclear mechanisms involved within deuteron-induced reactions on chromium, taking into account especially the BU and DR direct processes, is validated by an overall agreement of the calculated and measured cross sections including particularly the new experimental data at low energies.

Simultaneous Optical Model Analysis of Elastic Scattering and Breakup Reaction Channels for 11Li + 208Pb System

Using the optical model (OM) potential, we perform simultaneous χ2 analysis of the elastic scattering and the breakup reaction data for 11Li + 208Pb system. We introduce Coulomb dipole excitation (CDE) and long-range nuclear (LRN) potentials to consider effects of long range interaction. By the simultaneous χ2 analysis, we obtain a variety of the parameter set with a large diffuseness parameter which is inferred by two valence neutrons of 11Li located in two different orbits moving into a wide region. From the extracted best parameter set, finally, we calculate the breakup, total fusion, and total reaction cross sections. The total reaction and the breakup reaction cross sections obtained from our present work well reproduced experimental data within 5% and 10%, respectively, whereas the total fusion cross sections overestimate experimental data. Detailed discussions regarding the disagreement with the fusion data are also addressed.

Analysis of total reaction cross sections for deuterons on 1p-shell-nuclei

This study aims to analyze the differential cross sections (DCSs) of elastic scattering and total reaction cross sections (TRCSs) of the loosely-bound deuteron projectile impinging on 1 p -shell nuclei, such as $^{9}$Be, $^{12}$C, and $^{16}$O, at incident energies ranging between 10.6 and 171 MeV using the continuum discretized coupled channel (CDCC) method. By fitting the experimental data for the DCSs and TRCSs, energy-dependent renormalization factors for the real and imaginary parts of the nucleon-nucleus optical-model potentials deduced from the studies proposed by Koning and Delaroche (KD02) and by Watson, Singh, and Segel (WSS), are obtained.It is found that with the WSS potential, which was obtained specifically for $1p$-shell nuclei, the CDCC calculations can simultaneously reproduce both the DCSs and the TRCSs. The results show that it is important to choose appropriate optical potentials to describe deuteron-induced reactions.

Effect of resonance states of the weakly bound 6Li on total fusion in reactions with targets 28Si, 96Zr and 209Bi

Continuum Discretized Coupled-Channel calculations of total fusion cross sections for reactions induced by the weakly bound nucleus 6Li with targets 28Si, 96Zr and 209Bi at energies around the Coulomb barrier are presented. In the cluster structure frame of 6Li → α+d, short-range absorption potentials are considered for the interactions between the α- and d-fragments with the targets. In the model, the effect of resonance (l = 2, Jπ = 3+, 2+, 1+) and non-resonance breakup states of 6Li on fusion is studied by using two approaches: (1) by omitting the resonance states from the full discretized CDCC breakup space and 2) by considering only the resonance discretized sub-space. Among other things, it is found that resonance breakup states produce strong repulsive polarization potentials that lead to fusion suppression. The particular effect on fusion of a single resonance is calculated. It is found that resonances 2+ and 1+ have a more significant role on incomplete fusion, while the 3+ on complete fusion.

Strong absorption model with antisymmetric S-matrix

We present a strong absorption model with an [Formula: see text]-matrix in a new form of an antisymmetrized Fermi distribution for describing diffraction patterns of neutron–nucleus scattering at intermediate energies. The proposed antisymmetric [Formula: see text]-matrix has a form close to the conventional one and allows to obtain exact analytical expressions for the damping factor that determines the elastic scattering amplitude and the total cross-sections for interaction, reactions and elastic scattering. The use of an antisymmetrized Fermi function instead of the usual Fermi function in successful strong absorption models basically does not notably affect the calculated nucleon–nucleus elastic scattering differential cross-sections in the intermediate energy region.

Reaction Dynamics for the Systems 7Be, 8B + 208Pb at Coulomb Barrier Energies

In this contribution we describe the first results obtained for the investigation of the elastic scattering process in the reactions induced by the Radioactive Ion Beams 7Be and 8B on a 208Pb target at Coulomb barrier energies. The experimental data were analyzed within the framework of the optical model in order to extract the total reaction cross section. The comparison with data available in literature for reactions induced on 208Pb by light ions in the mass range A = 6-8 shows that the loosely-bound 8B has the largest reactivity.

New method to calculate the nuclear radius from low energy fusion and total reaction cross sections

New method to calculate the nuclear radius from low energy fusion and total reaction cross sections

Evidence of a Proton Halo in 23Al: A Mean Field Analysis

We have studied the nuclear structure properties like binding energy, charge radius, quadrupole deformation parameter for various isotopes of Al from the valley of stability to drip line region using the well known relativistic mean field formalism (RMF) with NL3 parameter set. We have compared our results with experimental data and found reasonable agreement. Further, we have taken spherical and deformed RMF densities to estimate the reaction dynamics of $^{23-28}$Al isotopes as projectiles and $^{12}$C as target by conjunction in Glauber model. The estimated results are also compared with the experimental data. The analysis of angular elastic differential and one proton removal cross sections are also studied with Glauber model many body system to investigate the structural feature of $^{23}$Al. The evidence of enhanced total reaction cross section, higher value of rms radius, narrow longitudinal momentum distribution and small proton separation energy of $^{23}$Al support its proton halo structure.

Elastic scattering of 17F nuclei from 58Ni target: Comparison with three different models

In this study, elastic scattering for the system 17F + 58Ni at the energies 58.5 MeV and 170 MeV were examined theoretically by using optical model, cluster model, double folding model and optical model. The results were compared with data in the literature and experimentally data. Total reaction cross sections were determined. The results obtained have been successful in explaining experimental data.

Total reaction cross section for the 11B + 58Ni system and application of a recent new reduction methodology

The investigation is made to extract the total reaction cross section from a previous work where the elastic scattering of the tightly bound 11B on the 58Ni target was measured, at energies close to the Coulomb barrier. Total reaction cross sections were extracted from the elastic scattering analysis using the Optical Model with double-folding type potentials. We have also taken the total reaction cross section of the systems with almost the same mass range targets and different projectiles from the literature and tried to compare with our system by reducing the cross sections, for the elimination of trivial effects due to different sizes and different Coulomb barriers. In addition to that, for all the systems considered, one-channel calculations that account only for fusion have been performed to study the quantitative effect of the direct reaction channels on the total reaction cross section.

Examination of the C22 radius determination with interaction cross sections

A nuclear radius of $^{22}$C is investigated with the total reaction cross sections at medium- to high-incident energies in order to resolve the radius puzzle in which two recent interaction cross section measurements using $^1$H and $^{12}$C targets show the quite different radii. The cross sections of $^{22}$C are calculated consistently for these target nuclei within a reliable microscopic framework, the Glauber theory. To describe appropriately such a reaction involving a spatially extended nucleus, the multiple scattering processes within the Glauber theory are fully taken into account, that is, the multi-dimensional integration in the Glauber amplitude is evaluated using a Monte Carlo technique without recourse to the optical-limit approximation. We discuss the sensitivity of the spatially extended halo tail to the total reaction cross sections. The root-mean-square matter radius obtained in this study is consistent with that extracted from the recent cross section measurement on $^{12}$C target. We show that the simultaneous reproduction of the two recent measured cross sections is not feasible within this framework.

Systematic continuum-discretized coupled-channels calculations of total fusion for Li6 with targets Si28, Co59, Zr96, Pt198 , and Bi209 : Effect of resonance states

Continuum discretized coupled-channel (CDCC) calculations of total fusion cross sections for reactions induced by the weakly bound nucleus $^{6}\mathrm{Li}$ with targets $^{28}\mathrm{Si}, ^{59}\mathrm{Co}, ^{96}\mathrm{Zr}, ^{198}\mathrm{Pt}$, and $^{209}\mathrm{Bi}$ at energies around the Coulomb barrier are presented. In the cluster structure frame of $^{6}\mathrm{Li}\ensuremath{\rightarrow}\ensuremath{\alpha}+d$, short-range absorption potentials are considered for the interactions between the $\ensuremath{\alpha}$ and $d$ fragments with the targets. The effect of resonance ($l=2, {J}^{\ensuremath{\pi}}={3}^{+},{2}^{+},{1}^{+}$) and nonresonance states of $^{6}\mathrm{Li}$ on fusion is studied by using two approaches: (1) by omitting the resonance states from the full discretized CDCC breakup space and (2) by considering only the resonance subspace. A systematic analysis of the effect on fusion from resonance breakup couplings is carried out from light to heavy mass targets. Among other things, it is found that resonance breakup states produce strong repulsive polarization potentials that lead to fusion suppression. Couplings from nonresonance states give place to weak repulsive potentials at high energies; however, these become attractive for the heavier targets at low energies.

Role of external neutrons of weakly bound nuclei in reactions with their participation

The paper presents the results of measurement of the total cross sections for reactions 4,6He+Si and 6,7,9Li+Si in the beam energy range 5–50 A MeV. The enhancements of the total cross sections for reaction 6He+Si compared with reaction 4He+Si and 9Li+Si compared with reactions 6,7Li+Si have been observed. The performed microscopic analysis of total cross sections for reactions 6He+Si and 9Li+Si based on numerical solution of the time-dependent Schrödinger equation for external neutrons of projectile nuclei 6He and 9Li yielded good agreement with experimental data.

Calculation of total reaction cross sections of 6He, 8,9Li on nuclei within the microscopic optical potential model

Experimental data on total reaction cross sections of exotic nuclei 6He, 8,9Li interaction with the 181Ta, 59Co, 28Si and 9Be targets in a wide energy range are analyzed in the framework of a hybrid model of microscopic optical potential (OP). The real part of OP is obtained on the basis of the double folding model, while the imaginary part of OP is calculated within the high energy approximation. This theoretical approach demonstrates the fairly well agreement with experimental data at the wide energy regions.