Cross Sections For Production Of Fragments Research Articles

Predicting 28Si projectile fragmentation cross sections with Bayesian neural network method* *Supported by the National Nature Science Foundation of China (11075100, 11347198, 11565001), the Natural Science Foundation of Shanxi Province, China (2011011001-2), the Shanxi Provincial Foundation for Returned Overseas Chinese Scholars (2011-058), and the Postgraduate Science and Technology Innovation Project of Shanxi Normal University (2023XBY004)

This study utilizes the Bayesian neural network (BNN) method in machine learning to learn and predict the cross-sectional data of 28Si projectile fragmentation for different targets at different energies and to quantify the uncertainty. The detailed modeling process of the BNN is presented, and its prediction results are compared with those of the Cummings, Nilsen, EPAX2, EPAX3, and FRACS models and experimental measurement values. The results reveal that, compared with other models, the BNN method achieves the smallest root-mean-square error (RMSE) and the highest agreement with the experimental values. Only the BNN method and FRACS model show a significant odd-even staggering effect; however, the results of the BNN method are closer to the experimental values. Furthermore, the BNN method is the only model capable of reproducing data features with low cross-section values at Z = 9, and the average ratio of the predicted to experimental values of the BNN is close to 1.0. These results indicate that the BNN method can accurately reproduce and predict the fragment production cross sections of 28Si projectile fragmentation and demonstrate its ability to capture key data characteristics.

Mean-field dependence of fragment-production cross sections in heavy-ion induced reactions calculated by antisymmetrized molecular dynamics

ABSTRACT Dependence of the fragment production cross-sections in heavy-ion induced reactions on employed mean-field models was investigated based on antisymmetrized molecular dynamics. For this purpose, five different sets of Skyrme mean-field potentials were employed. We found that there are differences of up to 20 times in production of fragments to forward angles in the systems of 12C + 16O at 6 and 100 MeV/u and 12C + 27Al at 6 MeV/u, where reactions with 12C projectile were selected due to its frequent use in cancer therapy. However, such a large difference tends to cease at backward angles. Therefore, a conclusion was drawn that the difference was due to the properties of the incident 12C nucleus. In order to verify this theoretical result, additional calculations were conducted for the 12C(p, n) and 27Al(p, n) reactions at 256 MeV, wherein a difference in the neutron yields was observed only in the former reaction.

Dynamical fluctuations in fragmentation reactions in a Boltzmann–Langevin approach

Based on the isospin-dependent Boltzmann–Langevin model, the dynamical fluctuations in the fragmentation reaction of 112Sn+112Sn are investigated. The quadrupole moment and octupole moment with zero magnetic quantum number have large fluctuations in the early time of the collisions. The dynamical fluctuations in momentum space show a strong dependence on the incident energy. The effects of using different fluctuations on the fragment cross sections are also studied in the fragmentation reactions. The results by using Q 20 + Q 30 fluctuation have a better agreement with the experimental data. Calculations using Q 20 + Q 30 fluctuation produce more proton-rich and neutron-rich nuclei than those using Q 20 fluctuation only. Besides, the difference between the production cross sections of fragments calculated by using Q 20 and Q 20 + Q 30 fluctuations is larger in the vicinity of the projectile. These results present that the dynamical fluctuations may affect the whole dynamical process of fragmentation reactions including the production of fragments, due to the nonlinear nature of the Boltzmann–Langevin equation.

The total and the partial charge-changing cross sections of 40Ar fragmentation on elemental targets at 500 A MeV

The total and the partial charge-changing cross sections of 40Ar fragmentation on CH2, C, Al, Cu and Pb targets at the highest energy of 495 A MeV were investigated using CR-39 plastic nuclear track detector. The total charge-changing cross-section for hydrogen target was calculated based on the results of polyethylene and carbon targets. It was found that the total charge-changing cross sections for fragmentation of 40Ar on H, C, Al, Cu and Pb targets were independent on the beam energy in our studied energies, and were consistent with the predictions of Bradt-Peters semi-empirical formula. Nilsen semi-empirical formula, NUCFRG2 and PHITS simulation codes given an underestimation of experimental data. The partial cross sections for projectile fragment production were independent on the beam energy in our studied energies for each target and do not show a significant odd-even effect. The partial cross sections for projectile fragment production were also compared with different empirical parametrization formulas, such as different version of Cummings, Nilsen, FRACS and EPAX3. Generally, EPAX3 and FRACS empirical parametrization can give a reasonable estimation of data within 25% relative errors.

Precise machine learning models for fragment production in projectile fragmentation reactions using Bayesian neural networks * *Supported by the National Natural Science Foundation of China (11975091), the Program for Innovative Research Team (in Science and Technology) in University of Henan Province (21IRTSTHN011), China

Machine learning models are constructed to predict fragment production cross sections in projectile fragmentation (PF) reactions using Bayesian neural network (BNN) techniques. The massive learning for BNN models is based on 6393 fragments from 53 measured projectile fragmentation reactions. A direct BNN model and physical guiding BNN via FRACS parametrization (BNN + FRACS) model have been constructed to predict the fragment cross section in projectile fragmentation reactions. It is verified that the BNN and BNN + FRACS models can reproduce a wide range of fragment productions in PF reactions with incident energies from 40 MeV/u to 1 GeV/u, reaction systems with projectile nuclei from 40Ar to 208Pb, and various target nuclei. The high precision of the BNN and BNN + FRACS models makes them applicable for the low production rate of extremely rare isotopes in future PF reactions with large projectile nucleus asymmetry in the new generation of radioactive nuclear beam factories.

Production of neutron-rich N = 126 nuclei in multinucleon transfer reactions: Comparison between 136Xe + 198Pt and 238U + 198Pt reactions

The production cross sections for primary and residual fragments produced in two reaction systems 136Xe + 198Pt and 238U + 198Pt at incident energy 8 MeV/nucleon are calculated by improved quantum molecular dynamics (ImQMD) model incorporated with the statistical evaporation model (HIVAP code). It is found that the cross sections for n-rich N=126 residual fragments are several times larger in 238U+198Pt than in 136Xe+198Pt due to the larger cross sections and lower excitation energies of primary fragments in 238U induced reactions. In both systems, N=126 semi-magic residues are produced via neutron emission in the decay of primary fragments, which survive in the semi-central collisions and have lower excitation energies.

Strangeness and hypernuclear production in fragmentation reactions induced by antikaons

Formation mechanism of hyperfragments with strangeness s=-1 and s=-2 in collisions of antikaons on nuclei has been investigated within a microscopic transport model. Dynamics of pseudoscalar mesons and hyperons is modeled within the transport model, in which all possible reaction channels for creating hyperons such as the elastic scattering, resonance production and decay, strangeness exchange reaction and direct strangeness production in meson-baryon and baryon-baryon collisions have been included. A coalescence approach is developed for constructing hyperfragments in phase space and the decay process is described with a statistical approach. It is found that the $\Xi^{-}$ production is correlated to the K$^{+}$ formation and the hyperons $\Lambda$ and $\Sigma$ are created within a broad rapidity region. The production cross sections of nucleonic fragments and hyperfragments weakly depends on the incident momentum. The yields of $\Lambda-$ hyperfragments are the six order of magnitude of $\Xi^{-}-$ hyperfragments.

Approaching neutron-rich nuclei towards the r-process path in 86Kr-induced collisions at 15 MeV/nucleon

The production cross sections of projectile-like fragments from collisions of 15 MeV/nucleon 86Kr with 64,58Ni and 124,112Sn have been measured using a magnetic separator with emphasis on the neutron-rich isotopes. Neutron pick-up isotopes (with up to 6-8 neutrons picked-up from the target) were observed with large cross sections. The present results were also compared with our previous data of the same reactions at 25 MeV/nucleon. The data at 15 MeV/nucleon show enhanced production of neutron-rich isotopes very close to the projectile, relative to the corresponding data at 25 MeV/nucleon. The large cross sections of such reactions involving peripheral nucleon exchange, indicate that these reactions offer a novel route to access extremely neutron-rich rare isotopes towards the the astrophysical r-process path and the neutron-drip line.

Fragment charge identification technique with a plastic scintillator detector using clinical carbon beams

Nuclear physics processes are an important source of uncertainty in dose calculations in particle therapy and radioprotection in space. Accurate cross section measurements are a crucial ingredient in improving the understanding of these processes. The FOOT (FragmentatiOn Of Target) experiment aims at measuring the production cross sections of fragments for energies, beams and targets that are relevant in particle therapy and radioprotection in space. An experimental apparatus composed of several sub-detectors will provide the mass, charge, velocity and energy of fragments produced in nuclear interactions in a thin target. A crucial component of the FOOT apparatus will be the ΔE-TOF detector, designed to identify the charge of the fragments using plastic scintillators to measure the energy deposited and the time of flight with respect to a start counter. In this work, we present a charge reconstruction procedure of produced fragments at particle therapy energies. We validate it by measuring the charges of various fragments at an angle of 3.2°and 8.3°with respect the beam-axis, using a small-scale detector and clinical beams of carbon ions at the CNAO oncology center. Experimental results agree well with FLUKA Monte Carlo simulations.

Charge identification performance of a [formula omitted]E-TOF detector prototype for the FOOT experiment

FOOT (FragmentatiOn On Target) is an applied nuclear physics experiment aimed at measuring the production cross sections of fragments for energies, beams and targets relevant in particle therapy and radioprotection in space. The ΔE-TOF detector will measure the energy deposited by the fragments in a wall of plastic scintillators and the time of flight with respect to a start detector. These two quantities allow to determine the charge Z of the fragment. In this work, we summarize the charge identification procedure of a detector prototype with two scintillator modules.

Spallation reactions induced by 4.4 GeV deuterons on lead isotopes

Independent and cumulative production cross sections for radioactive nuclear fragments from the deuteron-irradiation of isotopically enriched lead (204Pb, 206Pb, 207Pb, and 208Pb) targets were obtained for the first time. The experiment has been performed with a 4.4 GeV deuteron beam from the Nuclotron of the Laboratory of High Energy Physics (LHE), Joint Institute for Nuclear Research (JINR) at Dubna. The production cross sections of target fragments were determined by off-line γ-ray spectroscopy. Charge dispersion and mass-yield distributions were deduced from these data. The results are discussed in terms of the relative importance of different reaction mechanisms (evaporation–spallation, fission and multifragmentation). Comparison of our results with the data from the reaction induced by protons of about the same kinetic energy per nucleon, has been performed. The coexistence of the different decay modes in the formation of the reaction residues, such as spallation, fission and multifragmentation is suggested.

Microscopic studies of production cross sections in multinucleon transfer reaction Ni58+Sn124

Background: Multinucleon transfer reactions at low-energy collisions are considered to be promising for the production of new exotic nuclei, which are difficult to produce by other methods. Theoretical studies are required to provide reliable predictions for the experiments and to help understand the microscopic mechanism in multinucleon transfer reactions.Purpose: We provide a predictive approach for production cross sections and show how and to what extent the microscopic approach works well in multinucleon transfer reactions.Methods: We employ the $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ approach, which combines the microscopic time-dependent Hartree-Fock (TDHF) model with the state-of-art statistical model $\text{GEMINI}\phantom{\rule{0.16em}{0ex}}++$, to take into account both the multinucleon transfer dynamics and the secondary de-excitation process. The properties of primary products in multinucleon transfer process, such as transfer probabilities and primary cross sections, are extracted from TDHF dynamics using the particle-number projection method. Production cross sections for secondary products are evaluated using the statistical model $\text{GEMINI}\phantom{\rule{0.16em}{0ex}}++$.Results: We investigate the influence of colliding energies and deformation orientations of target and projectile nuclei on multinucleon transfer dynamics in the reaction $^{58}\mathrm{Ni}+^{124}\mathrm{Sn}$. More nucleons are observed to transfer in the tip collision than in the side collision. The production cross sections for secondary fragments with $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ calculations well reproduce the experimental measurements at energies close to the Coulomb barrier. At sub-barrier energy, the theoretical results gradually deviate from the experimental data with the increase of the number of transferred neutrons, showing the limitations of a single mean-field approximation in the TDHF approach. Possible origins for this discrepancy are discussed. The total cross sections integrated over all the neutron transfer channels are in good agreement with the experimental data for all the energies. We compare the production cross sections of $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ calculations with those from GRAZING model and find that our approach gives a description as quantitatively good as the semiclassical model, although there is no adjustable parameters for the reaction dynamics in the microscopic TDHF method.Conclusions: The microscopic $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ approach reasonably reproduces the experimental data at energies close to the Coulomb barrier and well accounts for the multinucleon transfer mechanism. The present studies clearly reveal the applicability of $\text{TDHF}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\text{GEMINI}$ method in multinucleon transfer reactions, which thus is a promising tool for predicting the properties of new reactions.

The total charge-changing cross sections and the partial cross sections of 56Fe fragmentation on Al, C and CH2 targets

The total charge-changing cross sections and the partial cross sections of 56Fe fragmentation on polyethylene, carbon and aluminum targets at the highest energy of 496 A MeV are investigated using CR-39 plastic nuclear track detector. The total charge-changing cross-section for hydrogen target is calculated based on the results of polyethylene and carbon targets. It is found that the total charge-changing cross sections for fragmentation of 56Fe on hydrogen, carbon and aluminum targets are independent on the beam energy in our studied energies, and are consistent with the predictions of Bradt–Peter semi-empirical formula, Nilsen parameterized formula, NUCFRG2 and QMSFRG theoretical simulation codes. The partial cross sections for projectile fragment production are independent on beam energy in our studied energies for each targets and do not show a significant even-odd effect.

Systematic Study of Neutron-Rich Rare Isotope Production in Peripheral Heavy-Ion Collisions at Beam Energies 15–25 MeV/nucleon

The production cross sections of projectile-like fragments from collisions of 86Kr projectiles with 64,58Ni and 124,112Sn targets at 15 and 25 MeV/nucleon are studied systematically with emphasis on the neutron-rich isotopes. Our recent experimental data are compared with calculations for the above collisions employing a hybrid approach. The dynamical stage of the projectile-target interaction was described with either the phenomenological deep-inelastic transfer (DIT) model or with the the microscopic constrained molecular dynamics model (CoMD). Subsequently, for the de-excitation of the projectile-like fragments, the statistical multifragmentation model (SMM) or the binary-decay code GEMINI were employed. An overall good agreement with the experimental results was obtained. We point out that our current understanding of the reaction mechanism at beam energies below the Fermi energy suggests that such nuclear reactions, involving peripheral nucleon exchange, can be exploited as a novel route to access extremely neutron-rich rare isotopes toward the r-process path and the hard-to-reach neutron drip-line. For this purpose, we believe that the use of re-accelerated neutron-rich radioactive beams may offer unique and exciting opportunities toward unexplored regions of the nuclear landscape.

Isospin influence on fragments production in 78Kr + 40Ca and 86Kr + 48Ca collisions at 10 MeV/nucleon

In heavy ion collisions at low energy (E/A < 10–15 MeV/nucleon) the N/Z ratio in the entrance channel is closely related to the isospin degree of freedom and can influence the reaction mechanisms and consequently the production of the fragments in the exit channel. We analyse the fragment production cross sections in the reactions 86Kr + 48Ca and 78Kr + 40Ca , at the laboratory energy of 10 MeV/nucleon. The experiment was conducted at the INFN Laboratori Nazionali del Sud in Catania, by using the \( 4\pi\) detector CHIMERA. For the two reactions, elastic scattering measurements are performed to extract the normalization factor used to evaluate the absolute cross sections. Velocity and energy spectra, mass and charge distributions, as well as dynamic features of reaction products, are studied. The study of the characteristics of mass and charge distributions, energy and velocity spectra of the reaction products shows mainly a relaxed component, related to fusion reaction followed by evaporation or binary decay. Nevertheless signals ascribable to a non equilibrated component are present. Structure effects are evident in the staggered shape of emitted fragments cross sections and are more pronounced in the neutron poor system. The analysis highlights clear differences for the two systems in the contributions arising from different reaction mechanisms. Besides, a study of the overall influence from the entrance channel energy is performed. Comparisons to DNS (DiNuclear System) and GEMINI++ models are reported. The data analysis indicates a slightly higher fusion-evaporation cross section and a strongly pronounced probability of fission-like processes for the neutron poor system with respect to the neutron rich one. The neutron enrichment seems thus to limit the formation of the composite system and to inhibit the fission decay channel.

Isotopic Dependence of Fragment Production Cross Sections in the Reactions of Deuterons on Enriched Lead and Tin Isotopes

The isoscaling behavior of the fragment production cross section was studied for reactions with deuterons on enriched lead targets (204Pb, 206Pb, 207Pb, 208Pb). The information about the reaction mechanism as well as the origin of the residues in the mass range 20 ≤ A ≤ 100 were obtained. During the analysis it was found the same behavior of the reactionmechanism as in the reactions with deuteron on enriched tin isotopes (112Sn, 118Sn, 120Sn, 124Sn). In the present article the estimation of the temperature and the symmetry energy coefficient of composite systems was done.

Production mechanism of neutron-rich nuclei around N = 126 in the multi-nucleon transfer reaction 132Sn + 208Pb**Supported by National Natural Science Foundation of China (11705118, 11475115, 11647026) and Natural Science Foundation of SZU (2016017)

The time-dependent Hartree-Fock approach in three dimensions is employed to study the multi-nucleon transfer reaction 132Sn + 208Pb at various incident energies above the Coulomb barrier. Probabilities for different transfer channels are calculated by using the particle-number projection method. The results indicate that neutron stripping (transfer from the projectile to the target) and proton pick-up (transfer from the target to the projectile) are favored. De-excitation of the primary fragments is treated by using the state-of-art statistical code GEMINI++. Primary and final production cross sections of the target-like fragments (with Z=77 to Z=87) are investigated. The results reveal that fission decay of heavy nuclei plays an important role in the de-excitation process of nuclei with Z > 82. It is also found that the final production cross sections of neutron-rich nuclei depend only slightly on the incident energy, while those of neutron-deficient nuclei depend strongly on the incident energy.

Inverse Quasifission in 156,160Gd + 186W Reactions

To investigate the impact shell effects have in the formation of neutron-rich fragments in multinucleon transfer reactions, a series of experiments to explore the binary channel in 156,160Gd + 186W reactions at energies near and above the Coulomb barrier is performed at the Flerov Laboratory’s U-400 accelerator using the CORSET setup. These experiments are aimed mainly at obtaining the production cross sections of leadlike fragments in the process of inverse quasifission. The mass, energy, and angular distributions of the binary reaction products are measured at energies of 860 and 935 MeV of 160Gd ions and 878MeV in the case of 156Gd ions. The excitation energies of primary fragments are estimated using their measured mass–energy distributions. Enhanced yields of products with masses of 200–215 amu are observed for both reactions. At energies above the barrier for side-to-side collisions (935 MeV), the yield of lead-like fragments is an order of magnitude larger than at energies near the Coulomb barrier, due possibly to the influence of orientation effects. The enhancement observed in the yield of reaction products with masses heavier than the target mass confirms that multinucleon transfer reactions can be used to obtain new neutron-rich isotopes, and to synthesize new superheavy elements.

Empirical parametrization for production cross sections of neutron-rich nuclei by photofission of U238 at low energies

An empirical parametrization for the production cross sections of $^{238}\mathrm{U}$ photofission fragments at low energies (${E}_{\ensuremath{\gamma}}l30$ MeV) is developed. This parametrization, $\mathrm{GIF}^{238}\mathrm{U}$, consists of three parts, namely, the photofission cross section, the mass yield, and the isobaric charge distribution. The photofission cross section is parametrized to reproduce measured data over a wide energy range. The mass yield distribution is described by the energy-dependent multimodal fission model. The isobaric charge distribution is improved, relative to other parametrizations, to describe many experimental data sets over a broad mass range. Comparisons with different measured $^{238}\mathrm{U}$ photofission data sets at various energies reveal that $\mathrm{GIF}^{238}\mathrm{U}$ is in very good agreement with measured elemental and mass yields and can accurately reproduce experimental isotopic yields. Production cross sections (yields) of photofission fragments calculated by this parametrization indicate that many neutron-rich nuclei approaching the $r$-process path can be accessed via photofission of $^{238}\mathrm{U}$ at radioactive-beam facilities.

Theoretical study on production cross sections of exotic actinide nuclei in multinucleon transfer reactions**Supported by National Natural Science Foundation of China (11605296) and Natural Science Foundation of Guangdong Province, China (2016A030310208)

Within the dinuclear system (DNS) model, the multinucleon transfer reactions 129,136Xe + 248Cm, 112Sn + 238U, and 144Xe + 248Cm are investigated. The production cross sections of primary fragments are calculated with the DNS model. By using a statistical model, we investigate the influence of charged particle evaporation channels on production cross sections of exotic nuclei. It is found that for excited neutron-deficient nuclei the charged particle evaporation competes with neutron emission and plays an important role in the cooling process. The production cross sections of several exotic actinide nuclei are predicted in the reactions 112Sn + 238U and 136,144Xe + 248Cm. Considering the beam intensities, the collisions of 136,144Xe projectiles with a 248Cm target for producing neutron-rich nuclei with Z=92−96 are investigated.