Heavy-ion Reactions Research Articles

Systematic study of the fusion hindrance phenomenon using the proximity potential approach: signature of the energy-dependent effects of the surface energy coefficient

In the present study, we have systematically studied the role of surface energy coefficient as well as temperature dependence in the fusion hindrance phenomenon of the heavy-ion reactions using the proximity potential formalism. To this end, we have performed the calculations of the interaction potential using the original proximity potential 1977 (Prox. 77) and the fusion cross sections are calculated based on the coupled-channels (CC) approach. The considered fusion systems are including the heavy-ion reactions 11B+197Au, 12C+198Pt, 16O+208Pb, 28Si + 64Ni, 28Si + 94Mo, 58Ni+58Ni, 32S+89Y,34S+89Y, 12C+204Pb and 36S + 64Ni with conditions of Q <0 and charge product of the participant nuclei 392≤ Z1Z2 ≤784. Our preliminary calculations show the Prox. 77 model predicts the theoretical values ​​of the fusion cross-sections less than the corresponding experimental data especially in the energy regions below the fusion barrier. However, the imposing of the mentioned physical effects increases the calculated values of the fusion cross sections and thus improves their agreement with the experimental cross sections for the selected reactions. In addition, by considering the energy dependence on the surface energy constant γ0 of the proximity formalism at the low energy region we are able to reproduce well the fusion cross sections, the astrophysical factor S(E) as well as the logarithmic derivative L(E) in these regions.‎

Investigation of Fission Modes of $${}^{{248}}$$Cf and $${}^{{254,256}}$$Fm Nuclei Produced in Heavy-Ion Reactions

Investigation of Fission Modes of $${}^{{248}}$$Cf and $${}^{{254,256}}$$Fm Nuclei Produced in Heavy-Ion Reactions

An FPGA-based trigger system for CSHINE

A trigger system of the general function was designed using the commercial module of CAEN V2495 for heavy-ion nuclear reaction experiments at Fermi energies. The system was applied and verified on the compact spectrometer for heavy IoN experiment (CSHINE). Based on the field-programmable logic gate array technology of the command register access and remote computer control operation, trigger functions can be flexibly configured according to experimental physical goals. Using the trigger system on CSHINE, we conducted a beam experiment at 25 MeV/u $$^{86}\textrm{Kr}+ ^{124}\textrm{Sn}$$ on the Radioactive Ion Beam Line 1 in Lanzhou, China. The online results demonstrated that the trigger system worked normally and correctly. This system can be extended to other experiments as well.

Nuclear Structure and Decay Data for A=231 Isobars

The present evaluation of currently known nine nuclides of A=231: (231Rn, 233Fr, 231Ra, 231Ac, 231Th, 231Pa, 231U, 231Np and 231Pu) represents an update and revision of previous A=231 evaluation by 2013Br04. All the known decay and reaction data are evaluated, with recommended properties given in the Adopted Levels, Gammas datasets, for gamma-ray energies, photon branching ratios, level half-lives, spins, parities, transition probabilities, and configuration assignments. For 231Rn, only an identification of the nuclide has been made without an experimental determination of its half-life. For 231Fr, no excited states are known. About 30 levels in 231Ra up to 1774 keV excitation are known only from β− decay of 231Fr with level half-lives determined for five excited states. For 231Ac, excited states up to 3122 keV are known from β− decay, (t,α), and fragmentary information for high-spin levels from two heavy-ion reaction studies, with lifetimes of excited states measured for five levels. Extensive structure and rotational band information for 231Th is available for a large number of levels up to 1714 keV from β− and α decays, (n,γ) thermal and resonance, single-particle transfer reactions (d,p), (d,t) and (3He,α), with limited data for high-spin levels from one secondary reference, and half-lives available for five excited states. Very detailed structure data are available for 231Pa up to 2139 keV from β−, ε and α decays, (α,t), (d,d′) and high-spin data from heavy-ion Coulomb excitation and (p,2nγ) reaction, with level half-lives known for 34 excited states, mostly deduced by evaluators from transition probabilities determined in Coulomb excitation. Only eight excited states are known in 231U up to 1268 keV from ε and α decays, with no data for half-lives of excited states. For 231Np and 231Pu, only the ground-state is known from α decays, with a tentative level at 324 keV in 231Pu. Measurements of nuclear rms charge radius and isotope shifts for 231Ra have been made by 2018Ly01, and that for rms charge radius for 231Fr by 2014Bu06.235U is a well known nuclide for nuclear structure and reactor applications. There have been a large number of studies of its alpha decay to levels in 231Th, including some recent ones such as 2018Ma03 and 2017Le03, yet evaluators' analysis of the decay scheme suggests that, while α-particle transitions are well established, but several issues still remain about intricacies of gamma-ray and conversion electron spectroscopy which need to be resolved through dedicated experiments for a complete understanding of the decay scheme characteristics, although, this sort of research project would seem a challenging spectroscopic problem. As commented in individual datasets for other decays, important spectral information is lacking for most of the decay schemes, with almost no information available for some of these, resulting in many incomplete decay schemes in A=231 mass chain.

Heavy-ion fusion reactions of astrophysical interest

The hindrance in fusion of heavy-ion reactions crops up in the region of extreme sub-barrier energies. This phenomenon can be effectively analyzed using a simple diffused barrier formula derived assuming a Gaussian distribution of fusion barrier heights. Folding the Gaussian barrier distribution with the classical expression for the fusion cross section for a fixed barrier, the fusion cross section is obtained. The energy dependence of the fusion cross section provides good description to the existing data on sub-barrier heavy-ion fusion for lighter systems of astrophysical interest. Using this simple formula, an analysis has been presented from $^{16}$O + $^{18}$O to $^{12}$C + $^{198}$Pt, all of which were measured down to $<$ 10 $\mu$b. The agreement of the present analysis with the measured values is better than those calculated even from the sophisticated coupled channels calculations. The relatively smooth variation of the three parameters of this formula implies that it may be exploited to estimate the excitation function or to extrapolate cross sections for pairs of interacting nuclei which are yet to be measured. Possible extensions of the present methodology and its limitations have also been discussed.

Rules of thumb for synthesizing superheavy elements

Synthesizing any elements in the eighth period using either cold or hot fusion reactions remains a big challenge to date. The quasifission mechanism restricts complete fusion to an indeterminably low evaporation residue (ER) cross-section for superheavy nuclei. The entrance channel parameters of the heavy-ion reaction, the fission barrier of the compound nucleus, the deformation parameters of the projectile and target nuclei, and the kinetic energy of the projectile are mainly responsible for governing the scale of the quasifission. The role of these factors has been examined explicitly by the experimental ER cross-sections. Thorough comparisons lead us to infer that the entrance channel criteria contribute to a much lower extent than the deformation parameters do. The effect of deformation can be categorized into four rules as validated by all the reactions used except one Uue. The null result from this reaction is explained by the improper choice of the projectile energy, as shown theoretically by means of a statistical model approach, which is valid for a system having a large nucleon number so as to intrinsically have a high density of excited states. The optimal selection of the beam energy sets another rule. Therefore, these five rules can be treated as the rules of thumb for synthesizing the superheavy elements. Application of the first four rules can enable us primarily to spot a suitable reaction, and finally, exploitation of the fifth rule chooses the most appropriate reaction at a preferable excited energy to achieve the highest ER cross-section for a superheavy element.

Mean-field simulations of Es-254 + Ca-48 heavy-ion reactions

Einstenium-254 (Z = 99, N = 155), can be prepared as a target for research into nuclear reaction studies. This work presents structure and reaction calculations of Es-254 and Ca-48 (Z = 20, N = 28), using the Skyrme-(Time-Dependent)-Energy-Density-Functional formalism. The reaction calculations show the initial parts of the heavy-ion reaction between the nuclei which, depending on the interaction parameters, can lead to capture to a compound nucleus of element 119. For collisions with the spherical 48Ca impinging on the tip of the prolate 254Es no fusion events are found. For collisions where the calcium approaches the belly of the einsteinium, capture occurs with the compound nucleus outlasting the lifetime of the calculation, indicating a possible fusion candidate. For a sample center-of-mass collision energy of 220 MeV, slightly non-central collisions, up to an impact parameter of 1 fm, also form long-lived compound nuclei.

Nonequilibrium effects and transverse spherocity in ultrarelativistic proton-nucleus collisions

We investigate the effects of nonequilibrium dynamics in small colliding systems by comparing a nonequilibrium transport approach, Parton-Hadron-String Dynamics (PHSD), with a $(2+1)$-dimensional viscous hydrodynamic model, VISHNew. Focusing on $p+\mathrm{Pb}$ collisions at energies available at the Large Hadron Collider, we extract the initial conditions for the hydrodynamic model from PHSD, in order to reduce the impact of the early out-of-equilibrium dynamics and focus on the traces of nonequilibrium in the ensuing medium evolution. We find that in the transport approach quantities like energy density and bulk viscous pressure are highly inhomogeneous on the transverse plane during the whole evolution, whereas the hydrodynamic simulations dissolve more efficiently the initial spatial irregularities, still keeping a high degree of inhomogeneity due to the smaller size and lifetime of the medium produced in $p+\mathrm{Pb}$ collisions with respect to heavy-ion reactions. As a first step that will help to identify the impact of these nonequilibrium effects on final observables in proton-nucleus collisions, we perform an analysis of the transverse spherocity, an event-shape observable able to distinguish between jetty and isotropic configurations of transverse momenta. We found that the spherocity distribution in PHSD is slightly shifted towards the isotropic limit with respect to the hydrodynamic result. Even though this dissimilarity is partially due to the difference in the final charged particle production, it mainly comes from the different description within the two frameworks of the medium produced in small colliding systems. This finding supports the idea that multidifferential measurements, such as those based on event categorization according to multiplicity and spherocity, are useful to study final-state observables in ultrarelativistic proton-nucleus collisions.

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.

Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

The applicability of hydrodynamics in heavy ion collisions at sqrt{s_mathrm{NN}} = 2.4–7.7 GeV

To assess the degree of equilibration of the matter created in heavy-ion reactions at low to intermediate beam energies, a hadronic transport approach (SMASH) is employed. By using a coarse-graining method, we compute the energy momentum tensor of the system at fixed time steps and evaluate the degree of isotropy of the diagonal terms and the relative magnitude of the off-diagonal terms. This study focuses mostly on Au+Au collisions in the energy range {sqrt{s}_mathrm{NN}} = 2.4–7.7 GeV, but central collisions of lighter ions like C+C, Ar+KCl and Ag+Ag are considered as well. We find that the conditions concerning local equilibration for a hydrodynamic description are reasonably satisfied in a large portion of the system for a significant amount of time (several fm/c) when considering the average evolution of many events, yet they are rarely fulfilled on an event by event basis. This is relevant for the application of hybrid approaches at low beam energies as they are or will be reached by the HADES experiment at GSI, the future CBM experiment at FAIR as well as the beam energy scan program at RHIC.

Systematic study of two-proton radioactivity within various versions of proximity formalisms

In this work, we study the two-proton (2p) radioactivity half-lives for nuclei near or beyond the proton drip line within the Coulomb and proximity potential model (CPPM). We investigate the 28 versions of proximity potential formalisms, which were proposed for heavy-ion fusion reactions, heavy-ion elastic scattering, ternary fission and other applications. The results indicate that BW91 and Bass77 are inappropriate for handling 2p radioactivity since the classical turning point r in cannot be obtained for the depth of the total interaction potential between the released two protons and daughter nucleus being greater than the 2p radioactivity released energy. Among the other 26 proximity potential formalisms, the one proposed by Royer et al in 1984 denoted as Prox.77-8 is the best version with the lowest rms deviations between experimental data and relevant theoretical results. It is worth mentioning that the calculations of Coulomb and Proximity Potential Model for Deformed Nuclei (2021 PRC 104, 064 613) has least standard deviation (σ = 0.592) compared with present model and other models/formulae. Furthermore, we use CPPM with Prox.77-8 to predict the 2p radioactivity half-lives of 35 potential candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. The predicted results are consistent with previous theoretical models such as the unified fission model (UFM), generalized liquid drop model (GLDM) and effective liquid drop model (ELDM).

Probing the high-density nuclear symmetry energy with the Ξ−/Ξ0 ratio in heavy-ion collisions at sNN≈3 GeV

Recent beam energy scan experiments at the BNL Relativistic Heavy Ion Collider by the STAR Collaboration [Phys. Lett. B 827, 137003 (2022) and Phys. Rev. Lett. 128, 202303 (2022)] found that hadronic interactions dominate the collective flow and the proton cumulant ratios are driven by baryon number conservation in a region of high baryon density in $\sqrt{{s}_{NN}}=3$ GeV $\mathrm{Au}+\mathrm{Au}$ reactions, indicating that the dense medium formed in such collisions is likely hadronic matter. Within an updated a relativistic transport model with momentum dependent isoscalar and isovector single-nucleon mean-field potentials corresponding to different symmetry energies at suprasaturation densities, the $n/p, {\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}, {K}_{s}^{0}/{K}^{+}, {\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}/{\mathrm{\ensuremath{\Sigma}}}^{+}$, and ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}/{\mathrm{\ensuremath{\Xi}}}^{0}$ ratios are studied for central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=3$ GeV, where the maximum central density reaches about $(3.6--4.0){\ensuremath{\rho}}_{0}$. The doubly strange ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}/{\mathrm{\ensuremath{\Xi}}}^{0}$ ratio is found to have the strongest sensitivity to the variation of high-density nuclear symmetry energy. Thus, the ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}/{\mathrm{\ensuremath{\Xi}}}^{0}$ ratio in relativistic heavy-ion reactions at $\sqrt{{s}_{NN}}\ensuremath{\sim}3$ GeV may help probe sensitively the poorly known symmetry energy of dense neutron-rich matter critically important for understanding various properties of neutron stars.

Nucleon Density Distributions and Diabatic Potential in Heavy Ion Reactions

Nucleon Density Distributions and Diabatic Potential in Heavy Ion Reactions

Method for Approximately Taking into Account the Impact Parameter in Fusion–Fission Heavy-Ion Reactions within a Stochastic Model Featuring Three Dynamical Parameters

Method for Approximately Taking into Account the Impact Parameter in Fusion–Fission Heavy-Ion Reactions within a Stochastic Model Featuring Three Dynamical Parameters

Stochastic Variational Method for Viscous Hydrodynamics

In this short review, we focus on some of the subjects, related to J. Cleymans’ pioneering contribution of statistical approaches to the particle production process in heavy-ion collisions. We discuss these perspectives from the effects of stochastic processes in collective variables of hydrodynamic description, which is described by a stochastic variational method. In this connection, we stress also the necessity of the inclusion of surface and quantum effects in the study of relativistic heavy-ion reactions.

Evolution of the statistical disintegration of finite nuclei toward high energy

We develop a statistical approach for the description of complex nuclei formation from dynamically produced baryons in high energy heavy-ion reactions. We consider a finite highly-excited expanding nuclear system formed after central nucleus-nucleus collisions. This system is sub-divided into primary equilibrated nucleon clusters. The final nuclei are produced after the decay of these excited clusters. By the successful comparison with the FOPI experimental data we prove the possibility of such a local equilibrium in nuclear matter with the temperature corresponding to the phase coexistence region. The regularities obtained in this new nuclei production mechanism are shown.

Investigating effects of relativistic kinematics, dimensionality, interactions, and short-range correlations on the ratio of quartic over quadratic nuclear symmetry energies

While ample evidence for the so-called empirical parabolic law of the equation of state (EOS) of isospin asymmetric nuclear matter (ANM) has been obtained in many studies within both nonrelativistic and relativistic nuclear many-body theories using various interactions, it has been unclear if there is any fundamental physics reason for the small quartic symmetry energy compared to the quadratic one even as the ANM approaches pure neutron matter. Within both relativistic and nonrelativistic free Fermi gas (FFG) models in coordinate spaces of arbitrary dimension $d$ with and without considering short-range correlations (SRCs) as well as nonlinear relativistic mean field models, we study effects of relativistic kinematics, dimensionality, interactions, and SRC on the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ of quartic over quadratic symmetry energies in ANM EOSs. We found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ in the FFG model depends strongly on the dimension $d$. While it is very small already in the normal three-dimensional space, it could be even smaller in spaces with reduced dimensions for subsystems of particles in heavy-ion reactions and/or whole neutron stars due to constraints, collectivities, and/or symmetries. We also found that the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ could theoretically become very large only at the ultrarelativistic limit far above the density reachable in neutron stars. However, nuclear interaction directly and/or indirectly through SRC-induced high-momentum nucleons affects significantly the density dependence of $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ compared to the relativistic FFG model prediction. The SRCs affect significantly not only the kinetic energy of symmetric nuclear matter but also the ratio $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ while the relativistic corrections are found negligible. Although we found no fundamental physics reason for the $\mathrm{\ensuremath{\Psi}}(\ensuremath{\rho})$ to be very small especially at high densities, the results may help better understand the EOS of dense neutron-rich matter.

Systematic study of fusion barrier characteristics within the relativistic mean-field formalism

Background: The nuclear interaction potential and hence the fusion barrier formed between the interacting nuclei are the keys to understanding the complex fusion process dynamics. Purpose: This work intends to explore the fusion barrier characteristics of different target-projectile combinations within the relativistic mean-field (RMF) formalism. Methods: The density distributions of interacting nuclei and the microscopic R3Y NN interaction are obtained from relativistic mean-field (RMF) formalism for non-linear NL1, NL3, TM1, and relativistic-Hartree-Bogoliubov (RHB) approach for DDME2 parameter sets. The fusion and/or capture cross-section for the different reaction systems is calculated using the well-known $\ell$-summed Wong model. Results: The barrier height and position of 24 heavy-ion reaction systems are obtained for different nuclear density distributions and effective NN interaction potentials. The comparison of fusion and/or capture cross-section obtained from the $\ell$-summed Wong model is made with the available experimental data. Conclusions: The phenomenological M3Y NN potential is observed to give higher barrier heights than the relativistic R3Y NN potential for all the reaction systems. The comparison of results obtained from different relativistic parameter sets shows that the densities from NL1 and TM1 parameter sets give the lowest and highest barrier heights for all the systems under study. We observed higher barrier heights and lower cross-sections for DDR3Y NN potential as compared to density-independent R3Y NN potentials obtained for considered non-linear NL1, NL3 and TM1 parameter sets. According to the present analysis, it is concluded that the NL1 and NL3 parameter sets provide comparatively better overlap with the experimental fusion and/or capture cross-section than the TM1 and DDME2 parameter sets.

Investigation of isotopic dependence on the O + Ni fusion cross section near barrier energies

Fusion excitation functions have been measured for $^{16}\mathrm{O}+^{61}\mathrm{Ni}$ and $^{18}\mathrm{O}+^{61,62}\mathrm{Ni}$ systems around the Coulomb barrier ($\ensuremath{\approx}0.7{V}_{B}$--$1.3{V}_{B}$) using the recoil mass spectrometer, heavy ion reaction analyzer. The ground state $Q$ value for two neutron stripping is positive for both systems with $^{18}\mathrm{O}$ as the projectile. Strong enhancement of the experimental fusion cross sections were observed below the barrier for all the systems compared to that of the predictions of the one-dimensional barrier penetration model. To understand such enhancement, a coupled-channels formalism has been used. A comparative study of these systems indicated that the coupling of two neutron transfer channels with the collective excitations could play the role behind the sub-barrier fusion enhancement for $^{18}\mathrm{O}$ induced reactions. However, the sub-barrier enhancement for $^{16}\mathrm{O} + ^{61}\mathrm{Ni}$ is found to be due to the coupling of quadrupole vibrations of both the interacting nuclei. Also after comparing these systems with other systems of different Ni isotopes, we have found that the signature of the role of coupling to neutron transfer channels due to ground state positive $Q$ value for neutron transfer is ambiguous.