Heavy-ion Reaction Cross Sections Research Articles

Application of a universal reaction function to the description of heavy-ion reaction cross sections

Application of a universal reaction function to the description of heavy-ion reaction cross sections

Transfer reactions between odd-odd and even-even nuclei by using the interacting boson fermion fermion model and 0νββ decay in closure approximation

Spectroscopic amplitudes (SAs) in the interacting boson fermion fermion model (IBFFM) are necessary for the computation of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay but also for cross sections of heavy-ion reactions, in particular, double charge exchange reactions for the NUMEN Collaboration, if one does not want to use the closure limit. We present for the first time (i) the formalism and operators to compute in a general case the spectroscopic amplitudes in the IBFFM scheme from even-even to odd-odd nuclei, in a way suited to be used in reaction code, i.e., extracting the contribution of each orbital; (2) the odd-odd nuclei as described by the old IBFFM are obtained for the first time with the new implementation of machine learning (ML) techniques for fitting the parameters, getting a more realistic description. The one-body transition densities for $^{116}\mathrm{Cd}\ensuremath{\rightarrow}^{116}\mathrm{In}$ and $^{116}\mathrm{In}\ensuremath{\rightarrow}^{116}\mathrm{Sn}$ are part of the experimental program of the NUMEN experiment, which aims to find constraints on $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay matrix elements. As a first application of the spectroscopic amplitudes we present the calculation of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ nuclear matrix elements in the IBFFM formalism in closure approximation.

Evaporation residue cross section in the Cl37+Zn68 fusion reaction near the Coulomb barrier

Background: The measured subbarrier fusion cross sections in heavy-ion reactions are found to be significantly large as compared with those expected from the one-dimensional barrier penetration model (1d-BPM). Although attempts have been made to comprehend the enhancement in terms of different intrinsic degrees of freedom of the colliding nuclei, a clear understanding of the same is yet to come.Purpose: The objectives of this study is to understand the interplay of the channel coupling effect on fusion excitation function and explore the decay dynamics of the excited compound nucleus in the sub-and-near barrier region.Method: Fusion excitation function has been measured at energies from 7% below to 38% above the Bass barrier using a recoil mass spectrometer. Furthermore, cross sections of the different evaporation residues, such as 98, 99, 100, and 101 u, have been extracted.Results: The observed enhancement in the subbarrier fusion cross sections over the 1d-BPM predictions has been explained by considering the low-lying inelastic excitations among the interacting partners using ccfull code and by the barrier modification using the dynamical cluster-decay model (DCM). The cross sections of individual residual mass fractions (98, 99, 100, and 101 u) have been compared with the Hauser-Feshbach model.Conclusion: Coupled-channel calculations and DCM have successfully explained the total fusion cross sections data. The measured total fusion cross section ${\ensuremath{\sigma}}_{\mathrm{fus}}$ was found to be approximately equal to the sum of various residual mass fractions ($\mathrm{\ensuremath{\Sigma}}{\ensuremath{\sigma}}_{\mathrm{ER}}$) at energies above the Bass barrier. One-dimensional barrier height and radius parameters extracted from the measured data are in good agreement with the Bass model and DCM parameters.

The Glauber model and heavy ion reaction and elastic scattering cross sections

We revisit the Glauber model to study the heavy ion reaction cross sections and elastic scattering angular distributions at low and intermediate energies. The Glauber model takes nucleon–nucleon cross sections and nuclear densities as inputs and has no free parameter and thus can predict the cross sections for unknown systems. The Glauber model works at low energies down to Coulomb barrier with very simple modifications. We present new parametrization of measured total cross sections as well as ratio of real to imaginary parts of the scattering amplitudes for pp and np collisions as a function of nucleon kinetic energy. The nuclear (charge) densities obtained by electron scattering form factors measured in large momentum transfer range are used in the calculations. The heavy ion reaction cross sections are calculated for light and heavy systems and are compared with available data measured over large energy range. The model gives excellent description of the data. The elastic scattering angular distributions are calculated for various systems at different energies. The model gives good description of the data at small momentum transfer but the calculations deviate from the data at large momentum transfer.

A semiclassical formula for the reaction cross-section of heavy ions

We discuss an improvement to the expression for the heavy-ion reaction cross-section proposed long ago by Karol (P.J. Karol, Phys. Rev. C 11, 1203 (1975)) which describes the two-ion interaction through the nucleon-nucleon collisions in their overlap region when they come into contact. This improvement consists in considering the limitations due to the Pauli principle, which at low incident energies forbids many nucleon interactions, and in including a Coulomb factor. The final expression for which we also propose a new parametrization reproduces satisfactorily the known reaction cross-sections for many ion combinations using a global set of parameters. A decomposition of the reaction cross-section into the contributions of peripheral interactions, as a function of the impact parameter, is also discussed.

Effect of in-medium NN cross section and finite range force on the reaction cross section for a deformed target nucleus

A method is described to calculate the heavy ion reaction cross section ${\ensuremath{\sigma}}_{R}$ when one of the two nuclei is deformed. This method is based on both the double folding model and the optical limit approximation to Glauber theory. Both finite range of the nucleon-nucleon $(NN)$ interaction and in-medium effects of $NN$ cross section are included. The interacting pair $^{12}\mathrm{C}\text{\ensuremath{-}}^{238}\mathrm{U}$ is taken to study orientation, energy, and deformation dependence of ${\ensuremath{\sigma}}_{R}$. The finite range force increases the value of ${\ensuremath{\sigma}}_{R}$ by about $5%$. In-medium $NN$ cross section decreases ${\ensuremath{\sigma}}_{R}$ by about $1.9%$ compared to the free $NN$ cross section.

Glauber model and the heavy ion reaction cross section

We reexamine the Glauber model and calculate the total reaction cross section as a function of energy in the low and intermediate energy range, where many of the corrections in the model are effective. The most significant effect in this energy range is by the modification of the trajectory due to the Coulomb field. The modification in the trajectory due to nuclear field is also taken into account in a self-consistent way. The energy ranges in which particular corrections are effective are quantified, and it is found that when the center of mass energy of the system becomes 30 times the Coulomb barrier, none of the trajectory modification to the Glauber model is really required. The reaction cross sections for light and heavy systems, from the Coulomb barrier to intermediate energies, have been calculated. The exact nuclear densities and free nucleon-nucleon (NN) cross sections have been used in the calculations. The center of mass correction, which is important for light systems, has also been taken into account. There is an excellent agreement between the calculations with the modified Glauber model and the experimental data. This suggests that the heavy ion reactions in this energy range can be explained by the Glauber model in terms of free NN cross sections without incorporating any medium modification.

Description of Elastic and Reaction Cross-Sections of Heavy Ions Using Modified Glauber Model

The Glauber model for the description of the heavy ion reaction cross-sections and the elastic scattering differential cross-sections was extended to lower energies. This model was modified into modified Glauber model I to take into account the Coulomb distortion of the trajectory. The deflection effect of the trajectory due to the real nuclear potential in addition to the Coulomb effect in the modified Glauber model I were also taken into account in the Glauber model to get the modified Glauber model II. These models are satisfactorily applied for both elastic scattering differential cross-sections and reaction cross-sections for many collisions over a broad energy range. The obtained results reasonably well agree with the previous theoretical calculations and the experimental data. The corrected formula for the optical potential of A. Vitturi and F. Zardi is given. Results of this correction are discussed.

Modified Glauber model for the total reaction cross-section of 12C + 12C collisions

Glauber's theory has been adopted to calculate the total heavy-ion reaction cross-sections at high energies. At relatively low energies, Glauber's total reaction cross-section has been modified in order to take into account the Coulomb field effect and is called modified Glauber model I. In addition to the Coulomb field effect, the nuclear effect has also been taken into account in the Glauber model and is called modified Glauber model II. An analytical expression for the transparency function for heavy-ion reactions, involving the nuclear densities of the colliding ions and the nucleon-nucleon cross- section, has been obtained within the framework of the modified Glauber models I and II. The transparency and the total reaction cross-sections of the 12C + 12C collisions are calculated at different bombarding energies. The obtained results are in good agreement with the experimental data and with previous theoretical calculations.

Heavy-ion scattering at low energies: First-order correction to the eikonal phase shift

The first-order non-eikonal correction has been applied to calculate heavy-ion reaction cross sections at low energies. The numerical investigations show that, for many heavy-ion systems, reaction cross sections and elastic scattering angular distributions thus calculated, are in good agreement with the optical model calculations.

Nucleus-nucleus reaction cross section at low energies: Modified Glauber model.

The Glauber model approach for the description of the heavy-ion reaction cross section is extended to lower energies. A simple analytic expression for the transparency function is obtained by evaluating the overlap integral of the nuclear densities over the hyperbolic trajectory. Using this transparency function the reaction cross section of a large number of heavy-ion systems is predicted reasonably well at low energies.

Coulomb-modified Glauber model description of heavy-ion reaction cross sections.

A simple closed-form analytic expression for the heavy-ion reaction cross section, involving nuclear densities of colliding ions and the nucleon-nucleon cross section, has been obtained within the framework of the Glauber model modified for the Coulomb field effect. Reaction cross sections for a large number of heavy-ion systems have been predicted reasonably well over an energy range beginning with the Coulomb barrier to a few GeV/nucleon.

Microscopic inelastic form factors for heavy-ion reactions

Inelastic form factors for one-step reactions are computed with a microscopic force comprising both central and tensor forces for calculating cross sections of heavy-ion reactions. A second quantization formalism is applied and one-body transition densities between initial and final wave functions are exposed.

Inclusive γ and π0cross sections in heavy-ion reactions

Perturbation theory in a time-dependent basis is used to derive formal expressions for pion and gamma emission in heavy-ion reactions. The structure of the theory motivates an external mean-field phenomenology as a representation of the actual mean field plus lowest-order collision dynamics. The source function for the emission process is identified as a Wigner function constructed from the time Fourier transform of the nuclear wavefunctions. A simple model of the Wigner function is constructed and used to relate the production cross section for pi 0 and gamma in the reaction 14N+Ni at a laboratory bombarding energy per nucleon of 35 MeV. A direct relation between pi 0 and gamma cross sections is predicted to hold in the region of high gamma ray energy where the gamma emission is dominated by spin currents.

CCFUS — A simplified coupled-channel code for calculation of fusion cross sections in heavy-ion reactions

CCFUS — A simplified coupled-channel code for calculation of fusion cross sections in heavy-ion reactions

Heavy-ion reaction cross sections from elastic scattering data

The generalized optical theorem for charged particles is rederived. Its use for the determination of the reaction cross section and forward nuclear elastic scattering amplitude is discussed. Nonforward angles are considered. An error analysis is applied to theoretical as well as experimental data.

Resonant fluctuations in heavy-ion reaction cross sections: 16O(16O, alpha )28Si.

Synthetic small-angle excitation functions and angular distributions are calculated for the reaction $^{16}\mathrm{O}$,${\ensuremath{\alpha}}_{0}$)${}^{28}$Si by use of a compound-nucleus decay model which includes angular momentum conservation. Fluctuations in the synthesized cross sections are shown to exhibit all the general characteristics of measured ${\ensuremath{\alpha}}_{0}$ cross sections, including features usually attributed to resonances.

Excitations in grazing heavy-ion reactions

We show that a model of independent particle-hole excitations in a two-center basis is able to produce resonance-like structures in the cross sections of heavy-ion reactions. A fit to the experimental data on the system 40Ca on 40Ca at 400 MeV beam energy yields a relative transfer probability close to one. The resonance-like structures are quite well reproduced.

Direct Measurement of theC12+C12Reaction Cross Section between 10 and 83 MeV/Nucleon

The first results of direct measurements of heavy-ion reaction cross sections, sigma/sub R/, with use of the beam attenuation method are reported. For the /sup 12/C+ /sup 12/C system sigma/sub R/ was measured at three incident energies, 112, 360, and 996 MeV. The data show deviations from the geometrical reaction cross section and agree with recent theoretical predictions based on Glauber theory.

Cross sections for production of transfermium elements

Complete fusion cross sections in heavy-ion reactions are studied for various systems in the entrance channel. It is shown that the maximum of the complete fusion cross sections for obtaining low excited transfermium elements corresponds to the same target-projectile combination as suggested by the fragmentation theory. Calculations based on the computer code OVERLAID ALICE show also that the cross sections for light-particle evaporation are maximum for the same target-projectile combination. The calculations are illustrated for the compound nucleus 252102.