Shell Model Methods, Statistical Nuclear Reactions, and Beta-delayed Neutron Emission
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Physics - Nuclear physics and radiation physics↗
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Boundary-condition constraints for the shell model - a method for nuclear structure and nuclear reactions.
Asymptotic boundary conditions as constraints in shell model for scattering, reactions and nuclear structure calculations
NUCLEAR STRUCTURE↗
On modelling nuclear reactions in meteorites
An original method of experimental modeling depth distribution of radionuclides in sphere thick targets irradiated by protons in 4(pi)-geometry on JINR (Dubna) synchrocyclotron is described. Some results are presented.
Ustinova, G. K.↗
Investigating the time dependence of neutron-proton equilibration using molecular dynamics simulations
Neutron-proton equilibration has previously been studied experimentally in dynamically deformed nuclei in heavy ion collisions [Phys. Rev. Lett. 118, 062501 (2017); Phys. Rev. C 95, 044604 (2017)] using the NIMROD detector array at the Cyclotron Institute at Texas A&M University. Results indicated the composition of the two heaviest fragments originating from the excited projectile-like fragment evolved exponential with respect to their orientation angle to be more similar. Constrained Molecular Dynamics and Antisymmetrized Molecular Dynamics simulations were performed for different formulations of the density dependence of the asymmetry energy term of the nuclear equation of state. The simulations are compared to experimental results, which indicate a better agreement with a softer interaction in the nuclear equation of state.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Impact of composition and symmetry energy on the temperature of quasiprojectiles simulated with antisymmetrized molecular dynamics
The equation of state describes the emergent physical properties of matter. Experimental data is needed to help constrain the equation of state for nuclear matter. These constraints can help distinguish between an “asy-stiff” and an “asy-soft” equation of state, which has astrophysical implications. One path to help constrain the models is to analyze the nuclear caloric curve; some experiments have shown dependence on neutron excess, and may thus be sensitive to the asymmetry. A difference in the caloric curve based on the asymmetry of the reconstructed quasiprojectile (QP) had been observed using 70 Zn on 70 Zn at 35 MeV/nucleon taken with the NIMROD array. Antisymmetrized molecular dynamics calculations were performed for the same system and deexcited with gemini++. Both Gogny (asy-soft) and Gogny-as (asy-stiff) data sets were generated. The particles were then filtered based on detector geometric acceptance and thresholds. From the accepted particles, the excitation energy and temperature were calculated in the same way as for experimental data. Additionally, filter effects on the observed nuclear caloric curves were investigated. A tendency for the asy-stiff nuclear caloric curves to have higher temperatures than their asy-soft counterparts was observed for a number of probes. In addition, some probes may show sensitivity to the reconstructed composition of the QP, but this is inconclusive due to high statistical fluctuations and a large dependence on the exact method of event selection.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Systematic study of the validity of the eikonal model including uncertainties
Nuclear reactions at intermediate beam energies are often interpreted using the eikonal model. In the analysis of complex reaction probes, where few-body reaction methods are needed, the eikonal method may be used as an efficient way for describing the fragment-target reaction process. In this work, we perform a systematic study to test the validity of the eikonal approximation for nucleon-nucleus reactions. We also quantify uncertainties due to the nucleon optical potential on reaction observables. We inspect the validity of the eikonal model and its semiclassical correction by comparing it to exact solutions (obtained from solving the optical-model equation with a finite-differences method) for a wide range of reactions. We also study the effect of relativistic corrections, both kinematic and dynamic, by effectively incorporating the relativistic effects at intermediate energies. The uncertainties from a Bayesian global optical potential (KDUQ) are propagated to the observables of interest. Our study includes neutron and proton reactions on 27 Al , 40 Ca , 90 Zr , and 208 Pb , for a wide range of energies 𝐸 lab = 0–400 MeV. We calculate neutron-total cross sections (elastic and reactions) as well as proton-absorption cross sections as a function of beam energy, using the eikonal model, the eikonal model with a semiclassical correction, and the exact solution. Here, we also compute angular distributions for the methods above. Our results show that for the proton-absorption cross section, the eikonal model can be used down to around 60 MeV and the semiclassical correction extends its use to 30 MeV. However, the validity of the eikonal model for the neutron-total cross section only goes down to ≈120 MeV, a range extended to ≈ 50 MeV when using the semiclassical correction. We find the semiclassical correction to the eikonal model to be less effective in describing the angular distributions. The 1𝜎 uncertainty intervals on the observables we studied is less than 5% for most of the energies considered, but increases rapidly for higher energies, namely energies outside the range of KDUQ (𝐸 lab > 200MeV).
Cluster models↗
Kinetic approach of light-nuclei production in intermediate-energy heavy-ion collisions
We develop a kinetic approach to the production of light nuclei up to mass number A ≤ 4 in intermediate-energy heavy-ion collisions by including them as dynamic degrees of freedom. The conversions between nucleons and light nuclei during the collisions are incorporated dynamically via the breakup of light nuclei by a nucleon and their reverse reactions. We also include the Mott effect on light nuclei; i.e., a light nucleus will no longer be bound if the phase-space density of its surrounding nucleons is too large. With this kinetic approach, we obtain a reasonable description of the measured yields of light nuclei in central Au+Au collisions at energies of 0.25A GeV–1.0A GeV by the FOPI Collaboration. Our study also indicates that the observed enhancement of the α-particle yield at low incident energies can be attributed to a weaker Mott effect on the α particle, which makes it more difficult to dissolve in nuclear medium, as a result of its much larger binding energy.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Structures in the heavy-ion fusion excitation function at and above the Coulomb barrier
Contrary to descriptions from coupled-channels or other model calculations, heavy-ion fusion excitation functions are not smooth near and above the Coulomb barrier. There appear to be weak but noticeable oscillations or structures within the excitation functions that can be observed clearly in representation $d (σ E)/d E$ and in the comparison with theoretical calculations $σ (E) – σ_{th}(E)$. Importantly, a rather similar phenomenon has been studied before and can be explained in light symmetric systems as the influence of the centrifugal barrier penetration only on even angular momentum, but it cannot be extended to heavier, more asymmetric fusion systems. A more thorough investigation may be required to investigate this newly indicated behavior.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Search for beyond-mean-field signatures in heavy-ion fusion reactions
Examination of high-resolution, experimental fusion excitation functions for 16,17,18 O + 12 C reveals a remarkable irregular behavior that is rooted in the structure of both the colliding nuclei and the quasi-molecular composite system. The impact of the l-dependent fusion barriers is assessed using a time-dependent Hartree-Fock model, viewed as a mean-field reference. Barrier penetrabilities, taken directly from a density-constrained calculation, provide a significantly improved description of the experimental data as compared to the standard Hill-Wheeler approach. Furthermore, the remaining deviations between the parameter-free theoretical mean-field predictions and experimental fusion cross sections are exposed and discussed.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Role of isospin composition in low-energy nuclear fusion
We employ a microscopic approach that examines the impact of isospin dynamics on the process of low- energy nuclear fusion along an isotope chain and dependence on deformation. Our method utilizes the density constrained time-dependent Hartree-Fock theory (DC-TDHF), where isoscalar and isovector characteristics of the energy density functional (EDF) are examined in turn. This approach is applied to a series of fusion interactions of 176 Yb with increasingly neutron rich isotopes of calcium. By evaluating the contributions from the isoscalar and isovector components of the EDF, we look to quantify the influence of isospin composition on the conditions under which fusion is most likely to take place. Furthermore, our findings reveal that, in nonsymmetric systems, the isovector dynamics plays a significant role. Its typical effect is a reduction in the potential barrier, which turns into enhancement for neutron-rich systems.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
First simultaneous measurement of the γ-ray and neutron emission probabilities in inverse kinematics at a heavy-ion storage ring
The probabilities for γ-ray and particle emission as a function of the excitation energy of a decaying nucleus are valuable observables for constraining the ingredients of the models that describe the deexcitation of nuclei near the particle emission threshold. These models are essential in nuclear astrophysics and applications. In this paper, we have for the first time simultaneously measured the γ-ray and neutron emission probabilities of 208 Pb. The measurement was performed in inverse kinematics at the Experimental Storage Ring (ESR) of the GSI/FAIR facility, where a 208 Pb beam interacted through the 208 Pb (p,p') reaction with a hydrogen gas jet target. Instead of detecting the γ rays and neutrons emitted by 208 Pb, we detected the heavy beamlike residues produced after γ and neutron emission. These heavy residues were fully separated by a dipole magnet of the ESR and were detected with outstanding efficiencies. The comparison of the measured probabilities with model calculations has allowed us to test and select different descriptions of the γ-ray strength function and the nuclear level density available in the literature.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Comparing pion production in transport simulations of heavy-ion collisions at 270𝐴 MeV under controlled conditions
Within the TMEP, we present a detailed study of the performance of different transport models in Sn+Sn collisions at 270A MeV, and put particular emphasis on the production of pions and Delta resonances, which have been used as probes of the nuclear symmetry energy. We prescribe a common and rather simple physics model, and follow in detail the results of 4 BUU models and 6 QMD models. The nucleonic evolution of the collision and the nucleonic observables in these codes do not completely converge, but the differences among the codes can be understood as being due to several reasons: the basic differences between BUU and QMD models in the representation of the phase-space distributions, computational differences in the mean-field evaluation, and differences in the adopted strategies for the Pauli blocking in the collision integrals. For pionic observables, we find that a higher maximum density leads to an enhanced pion yield and a reduced pi- pi+ yield ratio, while a more effective Pauli blocking generally leads to a slightly suppressed pion yield and an enhanced pi- pi+ yield ratio. We specifically investigate the effect of the Coulomb force, and find that it increases the total pi- pi+ yield ratio but reduces the ratio at high pion energies, although differences in its implementations do not have a dominating role in the differences among the codes. Taking into account only the results of codes that strictly follow the homework specifications, we find a convergence of the codes in the final charged pion yield ratio to a 1 sigma deviation of about 5%. Furthermore, the uncertainty is expected to be reduced to about 1.6% if the same or similar strategies and ingredients, i.e., an improved Pauli blocking and calculation of the non-linear term in the mean-field potential, are similarly used in all codes.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Proton and neutron density distributions at supranormal density in low- and medium-energy heavy-ion collisions. II. Central Pb + Pb collisions
This paper represents a continuation of our investigation into the limitations on total, proton, and neutron particle number densities, as well as the asymmetry of proton and neutron density distributions achievable in central heavy-ion collisions. We explore these aspects at low and medium energies within the framework of the Boltzmann-Uhlenbeck-Uehling (pBUU) transport and time-dependent Hartree-Fock (TDHF) models. Previous studies, focusing on symmetric and asymmetric collisions of Ca and Sn nuclei [1], and initial results on Pb-nuclei collisions [2], emphasized the role of the Coulomb interaction in these events. Our findings indicated that: (i) the highest total densities predicted at 𝐸 beam = 800 MeV/nucleon were on the order of ≈ 2.5𝜌 0 (𝜌 0 = 0.16 fm −3 ), (ii) the proton-neutron asymmetry for maximal densities, 𝛿=(𝜌$^{max}_{n}$− 𝜌$^{max}_{p}$)/(𝜌$^{max}_{n}$+𝜌$^{max}_{p}$), did not generally exceed the asymmetry in the initial state of the collision at all beam energies and tended to decrease during the reaction, and (iii) a significant portion of this asymmetry had its microscopic origin in Coulomb forces, masking the pure nuclear contribution. These new findings, particularly relevant in the astrophysical context, are further examined in this work, focusing on the heaviest target-projectile combination 212,208 Pb accessible in an experiment. We introduce the SkT3 Skyrme force model, not previously used for the Pb system, and compare it to the SV-bas and SV-sym34 models to explore the symmetry-energy dependence of the results. Contour plots of nucleonic densities are presented, contrasting the time evolution of the density distributions in low (TDHF) and high (pBUU) models. We also present the evolution of normalized maximal proton, neutron, and total nucleon number density with increasing beam energy in the full pBUU model and the Vlasov approximation, aiming to explore the impact of correlations in the reaction. The time evolution of the proton and neutron density distributions in the plane transverse to the beam direction is illustrated at both low and high beam energy. In conclusion, our detailed examination of the Pb system in this work provides further essential evidence that the aforementioned findings (i)–(iii) are only weakly dependent on system size and a symmetry-energy model, and thus, they are of more general importance.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Low-energy 17 O(𝑛,𝛾) 18 O reaction within the microscopic potential model and its role for the weak 𝑟 process
The neutron radiative capture reaction 17 O (𝑛,𝛾) 18 O plays a pivotal role in both nuclear structure studies and astrophysical nucleosynthesis, particularly in the formation of elements during hydrostatic and explosive stellar environments. We calculated the 17 O (𝑛,𝛾) 18 O cross section within the Skyrme Hartree-Fock potential model and analyzed electric dipole 𝐸1 transitions to both positive- and negative-parity states below the α-decay threshold in 18 O. Our cross sections are significantly different from the data available in commonly used libraries. We further investigate the impact of the new calculated cross section on weak 𝑟-process nucleosynthesis using large-scale reaction network calculations across a wide range of electron fractions and entropies. Our results show that the 17 O (𝑛,𝛾) 18 O reaction rate significantly influences the production of first 𝑟-process peak elements, such as strontium, under specific astrophysical conditions. This study highlights the importance of accurate nuclear data for light isotopes in modeling heavy-element synthesis and provides updated reaction rates for future nucleosynthesis simulations.
6 ≤ A ≤ 19↗
Negative components in the representation $\frac{𝑑^{2}(𝜎𝐸)}{𝑑𝐸^2}$ of heavy-ion fusion cross sections
Negative components are observed in the representation $\frac{𝑑^{2}(𝜎𝐸)}{𝑑𝐸^2}$ in heavy-ion fusions related to recent studies of noticeable oscillations in the high-energy region of the fusion excitation functions. A modified multiGaussian model has been developed, which includes contributions for both positive and negative components in the $\frac{𝑑^{2}(𝜎𝐸)}{𝑑𝐸^2}$ representation. The model reproduces the heavy-ion fusion excitation functions very well, including oscillations. The property of these negative components in the $\frac{𝑑^{2}(𝜎𝐸)}{𝑑𝐸^2}$ spectrum and the reaction mechanism of fusion at energies above the Coulomb barrier are investigated. Finally, the model also reproduces well light heavy-ion fusion reactions between 12 C and 16 O at high energy; results imply that the compound nucleus channel effect may have an important contribution at the high energy region for all fusion systems.
low & intermediate energy heavy-ion reactions↗
Universal function for heavy-ion fusion cross sections
A universal function for heavy-ion fusion cross sections, Y = $\sqrt{π}$ Xerfc (- X ) + exp(- X 2 ) is proposed. By scaling both the cross section σ(E) and the energy E, heavy-ion fusion cross section data are found to follow closely a universal function over the whole energy range. The scaling is developed from either a simple, empirical single-Gaussian barrier distribution model for the representation d 2 (σE)/dE 2 , or the modified Siwek-Wilczynski model. The cross section expressions of these models are analytical, and can be easily used for all heavy-ion fusion excitation functions. Thus a bench marking of heavy-ion fusion excitation functions has been achieved. Finally, a general discussion regarding the universal function is given.
low & intermediate energy heavy-ion reactions↗
Cross sections for the formation of Rb84m,g, Rb83, and Rb82m in Sr86(d,x) reactions up to deuteron energies of 49 MeV: Competition between α-particle and multinucleon emission processes
Cross sections of Sr86(d,x) reactions leading to the products Rb84m,g, Rb83, and Rb82m were measured by the stacked-sample activation technique up to deuteron energies of 49 MeV. Nuclear model calculations were performed using the codes talys and empire, which combine the statistical, precompound, and direct interaction components. In all cases, the empire results were much higher than the talys calculation. Fairly good agreement was obtained between measured data and the talys calculation after some optimization of the input model parameters. Insight into competition between α-particle and multinucleon emission in the Y88 compound-nucleus system was also gained.
59 ≤ A ≤ 89↗
Quantifying uncertainties due to optical potentials in one-neutron knockout reactions
One-neutron knockout reactions have been widely used to extract information about the single-particle structure of nuclei from the valley of stability to the drip lines. The interpretation of knockout data relies on reaction models, where the uncertainties are typically not accounted for. In this work, we quantify uncertainties of optical potentials used in these reaction models and propagate them, for the first time, to knockout observables using a Bayesian analysis. We study two reactions in the present paper, the first of which involves a loosely bound halo projectile, 11 Be, and the second a tightly bound projectile, 12 C. We first quantify the parametric uncertainties associated with phenomenological optical potentials. Complementing this approach, we also quantify the model uncertainties associated with the chiral forces that can be used to construct microscopic optical potentials. For the phenomenological study, we investigate the impact of the imaginary terms of the optical potential on the breakup and stripping components of the knockout cross sections as well as the impact of the angular range. For the 11 Be case, the theoretical uncertainty from the phenomenological method is on the order of the experimental uncertainty of the knockout observables; however, for the 12 C case, the theoretical uncertainty is significantly larger. Additionally, the widths of the uncertainty bands for the knockout observables obtained for the microscopic study and the phenomenological approach are of similar orders of magnitude. Based on this work we conclude that structure information inferred from the ratio of the knockout cross sections will carry a theoretical uncertainty of at least 20% for halo nuclei and at least 40% for tightly bound nuclei.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗