Measured Fusion Cross Sections Research Articles

Systematic study of fusion suppression and its dependency on projectile breakup threshold energy

Measurements of the excitation function (EF) of the observed evaporation residues (ERs) populated in the 20Ne + 93Nb reaction at E lab ≈ 91−145 MeV are carried out to explore the systematic of fusion suppression and its dependency on projectile breakup threshold energy, by employing the offline γ-ray detection method. The EF of the observed ERs populated through complete and/or incomplete fusion processes are analysed in the framework of statistical mode code PACE4. The fusion function, derived from the experimentally measured fusion cross section data, is compared with the universal fusion function (UFF) to estimate the degree of fusion incompleteness. Based on the observed results, an empirical formula is proposed to interrelate the degree of fusion suppression and breakup threshold energy of the incident projectile.

Influence of neutron transfer channels on fusion dynamics near the Coulomb barrier for 28Si + 116,120,124Sn systems

The phenomenon of enhanced fusion cross-section as compared to the theoretical predictions of 1-D BPM has been extensively studied over the past few decades. However, the unambiguous role of neutron transfer channels on the sub-barrier fusion enhancement is still elusive in most cases. Fusion cross-section measurements ≈ 15% below and above the Coulomb barrier were performed to elucidate the mechanisms responsible for the experimentally observed sub-barrier fusion enhancement. Coupled-channels calculations using CCFULL were used to decipher the reaction dynamics. CC calculations explained the fusion excitation function for 28Si + 116,120Sn systems after the inclusion of inelastic excitations along with a pair transfer. However, the observed behavior for the 28Si + 124Sn system could not be explained. The fusion barrier distribution has been extracted from the experimental data to unveil the various channels coupled in the concerned rection. A single uncoupled barrier was transformed into a distribution of barriers depicting the presence of different channels coupled in the reaction. The results indicate a significant effect from multi-neutron transfer channels on the fusion dynamics.

Sub-barrier fusion hindrance and absence of neutron transfer channels

The sub-barrier fusion hindrance has been observed in the domain of very low energies of astrophysical relevance. The measured fusion cross sections can be well estimated by using formula obtained by folding a Gaussian function for barrier height distribution with the expression for classical fusion cross section for fixed barrier. The parameters of the formula vary smoothly implying its usage in estimating the excitation function. In the present work, the effects of deformation and transfer on fusion reactions have been studied and the absence of neutron transfer channels has been correlated to the hindrance in heavy-ion fusion reactions.

Global approach for the reactions Be7+Si28 and Be7+Pb208 at near- and sub-barrier energies

Elastic scattering, total reaction, and fusion cross section measurements for the radioactive $^{7}\mathrm{Be}$ nucleus on a light and a heavy target, are treated in a global approach at near and sub-barrier energies for probing the optical potential and describing fusion at low energies. Elastic scattering data of $^{7}\mathrm{Li}$ on the same target were analyzed under the same context to support this analysis. It is found that for low mass targets, dispersion relations are not adequate for describing the potential or the fusion. On the contrary this is possible for heavy targets, where the standard potential threshold anomaly and fusion enhancement is observed. The consequences of the above on fusion hindrance at deep sub-barrier energies is discussed.

Fusion studies in C12+W182,184,186 reactions at energies below and near the Coulomb barrier

Background: The coupled-channels model has been highly successful in interpreting experimental subbarrier fusion. The statistical model framework has traditionally been used to explain the basic features of composite system de-excitation in the above Coulomb barrier region. However, in $^{12}\mathrm{C}$-induced reactions with $^{182,186}\mathrm{W}$, measured fusion cross sections are significantly lower than those predicted by various theoretical models and by fusion systematics.Purpose: To investigate the dynamics of heavy ion fusion at energies below and above the Coulomb barrier in the $^{12}\mathrm{C}$-induced reactions.Method: A mass spectrometer was used to study the evaporation residues for the $^{12}\mathrm{C}+^{182,184,186}\mathrm{W}$ reactions. The measurements ranged from $12%$ below to $45%$ above the Coulomb barrier energies. The measured fusion cross sections are compared with coupled channels and statistical model calculations.Results: The measured fusion cross sections for $^{12}\mathrm{C}+^{182,184,186}\mathrm{W}$ reactions show reasonably good agreement with coupled-channel calculations. Also, evaporation residue cross sections for $^{12}\mathrm{C}+^{182,184,186}\mathrm{W}$ reactions in the present experiment along with the fission cross sections from literature are described by statistical model calculations.Conclusions: We successfully explain the previously reported discrepancy between fusion measurements and calculations based on various theoretical models and by fusion systematics for $^{12}\mathrm{C}+^{182,186}\mathrm{W}$ reactions.

Fusion studies in O16+Nd142,150 reactions at energies near the Coulomb barrier

Background: Enhancement in fusion cross sections over one-dimensional barrier penetration model (1D-BPM) predictions has been observed at sub-barrier energies owing to the coupling of various internal degrees of freedom to the relative motion. On the other hand, hindrance in fusion is noticed at energies well above the barrier in a few cases.Purpose: The purpose is to probe the dynamics of heavy ion fusion at energies below and well above the Coulomb barrier.Methods: Fusion excitation functions for the $^{16}\mathrm{O}+^{142,150}\mathrm{Nd}$ reactions are measured using the Heavy Ion Reaction Analyzer (HIRA) at IUAC, New Delhi. Measurements have been performed in the range $12%$ below to $50%$ above the Coulomb barrier for both systems. The measured fusion cross sections are compared with coupled channels calculations using ccfull code. The cross sections are also compared with reactions using $^{16}\mathrm{O}$ beams with other isotopes of Nd to explore the systematic behavior of fusion.Results: Compared with 1D-BPM predictions, fusion enhancement is observed in both $^{16}\mathrm{O}+^{142}\mathrm{Nd}$ and $^{16}\mathrm{O}+^{150}\mathrm{Nd}$ reactions at below-barrier energies, with the latter reaction showing a higher enhancement. Coupled channels calculations incorporating the collective excitations of the target nuclei reproduce the fusion cross sections in both reactions. The collective excitations of the projectile nucleus do not seem to contribute to the observed fusion enhancement. Calculations using Aky\"uz-Winther potential parameters fail to reproduce the fusion cross sections at energies well above the barrier.Conclusions: Fusion enhancement is observed in both reactions studied. Degree of enhancement of sub-barrier fusion cross section is larger for the reaction using $^{150}\mathrm{Nd}$ target. Fusion hindrance is observed in both reactions at very high energies. The hindrance seems to increase with increasing beam energy. Larger value of diffuseness parameter compared with the value consistent with elastic-scattering measurements is required to reproduce the fusion excitation function at energies well above the barrier. This could be a strong indication of dynamical effects in fusion at very high energies.

Heavy-ion fusion cross sections in the barrier and high-energy regions: Signature of energy dependence in the repulsive core potential

The effect of incompressibility of cold nuclear matter (CNM) on the high-energy fusion data of the 26Mg+248Cm, 36S+238U, 48Ca+208Pb, 50Ti+209Bi and 40,48Ca+238U colliding systems with 1152≤Z1Z2≤1840 has been analyzed using coupled-channels (CC) calculations. To apply the effect of saturation property of nuclear matter, we use the M3Y double-folding model which is corrected with a repulsive term. The repulsive parameters are adjusted to provide an optimum fit to the available experimental fusion cross sections. For each of the 26Mg+248Cm, 36S+238U, 48Ca+208Pb colliding systems, the best fit to the measured fusion cross sections at high energies is achieved using the CC calculations based on the M3Y+Repulsion potential with a constant value for the strength of the repulsive contact term. While focusing on the heavy-ion fusion reactions existing in the mass range Z1Z2>1800 reveals that it is necessary to consider an energy-dependent behavior for the repulsive parameters. When these conditions are imposed on entrance channel potential, it is possible to obtain an excellent description of the fusion data for 50Ti+209Bi, 40Ca+238U, and 48Ca+238U reactions. Our findings indicate that the extracted values of the strength Vrep of the repulsive contact term increase with increasing incident energy Ec.m.. In addition, we conclude that the repulsive part of the density distribution becomes more diffused with an increase in bombarding energy.

Role of microscopic temperature-dependent binding energies in the decay of Si*32 formed in the O20+C12 reaction

The investigation of fusion reactions involving light neutron-rich exotic nuclei is of paramount significance to understand nucleosynthesis in astrophysical scenarios. It is also estimated as a possible heat source to ignite $^{12}\mathrm{C}+^{12}\mathrm{C}$ reaction and production of x-ray superbursts from accreting neutron star. Recently, the fusion of neutron-rich $^{20}\mathrm{O}$ with $^{12}\mathrm{C}$ target has been studied with measurement of fusion cross-section $({\ensuremath{\sigma}}_{\text{fus}})$. Bass model under predicts the ${\ensuremath{\sigma}}_{\text{fus}}$ and time-dependent Hartree-Fock model also fails to explain the experimental data. To explicate the same, the investigation of $^{20}\mathrm{O}+^{12}\mathrm{C}$ reaction at near barrier energies has been made within quantum mechanical fragmentation-based dynamical cluster-decay model (DCM). Within DCM, the fragmentation potential comprises temperature-dependent Coulomb, nuclear and centrifugal potentials, along with temperature-dependent binding energies (T.B.E.) calculated within the macroscopic approach of Davidson mass formula. Recently, we have explored the temperature-dependence of different nuclear properties and nuclear symmetry energy within microscopic relativistic mean-field (RMF) theory [M. Kaur et al., Nucl. Phys. A 1000, 121871 (2020)]. In the present work, we inculcate the microscopic T.B.E. from RMF theory within DCM and investigate the structure of fragmentation potential for $^{32}\mathrm{Si}^{*}$ formed in $^{20}\mathrm{O}+^{12}\mathrm{C}$ reaction, comparatively for macroscopic (mac) and microscopic (mic) T.B.E. obtained from Davidson mass formula and RMF theory, respectively. The structure and magnitude of fragmentation potential are found to change drastically/notably along with a change in energetically favored/minimized fragments for both choices of T.B.E. The $\ensuremath{\alpha}$ particles $(^{4}\mathrm{He}$, $^{5}\mathrm{He})$ are favored at lower angular momenta in fragmentation profile for mic T.B.E. case only, which is in the agreement with predictions of statistical model results. This change in the nuclear structure embodied via fragmentation potential energy carries its imprints in the preformation probability ${P}_{0}$ of different fragments and affects the contribution of individual light-charged particle (LCP) channel in the ${\ensuremath{\sigma}}_{\text{fus}}$. A comparison of the relative cross-section of different LCP channels toward ${\ensuremath{\sigma}}_{\text{fus}}$ is quite different for both cases of T.B.E. The cross-section of $^{2}\mathrm{H}$ and $^{4}\mathrm{He}$ LCP channels is relatively enhanced for mic T.B.E. compared to mac T.B.E. Among different LCP channels, the $^{5}\mathrm{He}$ channel is the major contributor in ${\ensuremath{\sigma}}_{\text{fus}}$, which is in line with the results of the statistical EVAPOR model. The DCM-calculated ${\ensuremath{\sigma}}_{\text{fus}}$ is in agreement with the experimental data.

Exploring the fusion hindrance phenomenon: the case of 32,34S + 89Y

The sub-barrier fusion data of 32,34S + 89Y colliding systems are analyzed using the coupled-channels (CC) calculations, including couplings to the low-lying 2+ and 3− states in reacting nuclei as well as mutual and multi-phonon excitations of these states, based on the proximity potential model. In this scheme, we focus upon the the effect of surface energy coefficient γ and also thermal properties of liquids and hot nuclei on the inner part of the nuclear potential and thus on the fusion cross sections at bombarding energies far below the Coulomb barrier. As expected, our primary calculations using the original proximity potential 1977 show that this model underestimates the measured fusion cross sections at the whole energy region. It is shown that the mentioned physical effects bring significant cross sections enhancements for both reactions. The indications of the fusion hindrance phenomenon in the fusion cross sections at energies far below the Coulomb barrier show up. The observed S factors for the above-mentioned systems develop a maximum at low energies which can also be predicted by the phenomenological extrapolations. Our results within the framework of the modified form of the proximity potential reveal that the calculated fusion cross sections, S factors, and logarithmic slopes for the two systems are in good agreement with the corresponding experimental data even at the lowest energies.

Fusion reactions around the barrier for Be+238U * *Supported by the National Natural Science Foundation of China (12005314, 11805289, 11875328, 11775316), and the ELI-NP Phase II, a project co-financed by the Romanian Government and the European Union through the European Regional Development Fund - the Competitiveness Operational Programme (1/07.07.2016, COP, ID 1334)

Fusion-evaporation cross sections of U( Be, 5n) Cm are measured over a wide energy range around the Coulomb barrier. These measured cross sections are compared with model calculations using two codes, namely HIVAP2 and KEWPIE2. HIVAP2 calculations overestimate the measured fusion-evaporation cross sections by a factor of approximately 3. In KEWPIE2 calculations, two approaches, namely the Wentzel-Kramers-Brillouin (WKB) approximation and the empirical barrier-distribution (EBD) method, are used for the capture probability; both of them properly describe the measured cross sections. Additionally, fusion cross sections of Be+ U measured in two experiments are applied to constrain model calculations further through three codes, i.e., HIVAP2, KEWPIE2, and CCFULL. Parameters in these codes are also examined by comparison with measured fusion cross sections. All the comparisons indicate that the KEWPIE2 calculations using the WKB approximation agree well with the measured cross sections of both fusion reactions Be+ U and the fusion-evaporation reaction U( Be, 5n) Cm. Calculations using the fusion code CCFULL are also in good agreement with the measured fusion cross sections of Be+ U.

Fusion of the Borromean nucleus Be9 with a Au197 target at near-barrier energies

To probe the role of the intrinsic structure of the projectile on sub-barrier fusion, measurement of fusion cross sections has been carried out in $^{9}$Be + $^{197}$Au system in the energy range E$_{c.m.}$/V$_B$ $\approx$ 0.82 to 1.16 using off-beam gamma counting method. Measured fusion excitation function has been analyzed in the framework of the coupled-channel approach using CCFULL code. It is observed that the coupled-channel calculations, including couplings to the inelastic state of the target and the first two states of the rotational band built on the ground state of the projectile, provide a very good description of the sub-barrier fusion data. At above barrier energies, the fusion cross section is found to be suppressed by $\approx$ 39(2)\% as compared to the coupled-channel prediction. A comparison of reduced excitation function of $^{9}$Be + $^{197}$Au with other $x$ + $^{197}$Au shows a larger enhancement for $^9$Be in the sub-barrier region amongst Z=2-5 weakly and tightly bound projectiles, which indicates the prominent role of the projectile deformation in addition to the weak binding.

Interpretation of the anomaly in the diffuseness parameter of the Woods–Saxon potential for light fusion reactions using the effects of nuclear matter equation of state

The present study has been aimed at understanding the role of nuclear matter (NM) incompressibility effects on the description of the problem of the abnormally large diffuseness parameter of the Woods–Saxon (WS) potential for the fusion reactions induced by the light-mass nuclei. In order to assess this aim, we simulate theoretically the saturation properties of NM within the framework of the double-folding (DF) model for a total of 26 colliding systems with condition 64 ≤ Z1Z2≤ 204 for charge product of their participant nuclei. It is shown that the DF model supplemented with the effects of nuclear matter equation of state (EOS) provides an appropriate description for measured fusion cross sections of our selected systems at around and above barrier energies. We find that the diffuseness parameters of the equivalent WS potential fitted to the DF model in the fusion barrier region are ranging from 0.62 to 0.71 fm, whereas this range is increased to aWS=0.66−0.81 fm after modeling the incompressibility effects. Our results show that the extracted values of the diffuseness parameter based on the modified form of the DF model follow an increasing trend with the charge product Z1Z2. We also present for the first time a discussion on a decreasing linear dependence of the diffuseness parameter of the nucleus–nucleus potential on the nuclear incompressibility constant K.

Maximizing specific energy by breeding deuterium

Specific energy (i.e. energy per unit mass) is one of the most fundamental and consequential properties of a fuel source. In this work, a systematic study of measured fusion cross-sections is performed to determine which reactions are potentially feasible and identify the fuel cycle that maximizes specific energy. This reveals that, by using normal hydrogen to breed deuterium via neutron capture, the conventional catalyzed D–D fusion fuel cycle can attain a specific energy greater than anything else. Simply surrounding a catalyzed D–D reactor with water enables deuterium fuel, the dominant stockpile of energy on Earth, to produce as much as 65% more energy. Lastly, the impact on space propulsion is considered, revealing that an effective exhaust velocity exceeding that of deuterium-helium-3 is theoretically possible.

Isotopic effects in sub-barrier fusion of Si + Si systems

Background: Recent measurements of fusion cross sections for the 28Si+28Si system revealed a rather unsystematic behavior ; i.e., they drop faster near the barrier than at lower energies. This was tentatively attributed to the large oblate deformation of 28Si because coupled-channels (CC) calculations largely underestimate the 28Si+28Si cross sections at low energies, unless a weak imaginary potential is applied, probably simulating the deformation. 30Si has no permanent deformation and its low-energy excitations are of a vibrational nature. Previous measurements of this system reached only 4 mb, which is not sufficient to obtain information on effects that should show up at lower energies. Purpose: The aim of the present experiment was twofold: (i) to clarify the underlying fusion dynamics by measuring the symmetric case 30Si+30Si in an energy range from around the Coulomb barrier to deep sub-barrier energies, and (ii) to compare the results with the behavior of 28Si+28Si involving two deformed nuclei. Methods: 30Si beams from the XTU tandem accelerator of the Laboratori Nazionali di Legnaro of the Istituto Nazionale di Fisica Nucleare were used, bombarding thin metallic 30Si targets (50 μg/cm2) enriched to 99.64% in mass 30. An electrostatic beam deflector allowed the detection of fusion evaporation residues (ERs) at very forward angles, and angular distributions of ERs were measured. Results: The excitation function of 30Si+30Si was measured down to the level of a few microbarns. It has a regular shape, at variance with the unusual trend of 28Si+28Si. The extracted logarithmic derivative does not reach the LCS limit at low energies, so that no maximum of the S factor shows up. CC calculations were performed including the low-lying 2+ and 3− excitations. Conclusions: Using a Woods-Saxon potential the experimental cross sections at low energies are overpredicted, and this is a clear sign of hindrance, while the calculations performed with a M3Y + repulsion potential nicely fit the data at low energies, without the need of an imaginary potential. The comparison with the results for 28Si+28Si strengthens the explanation of the oblate shape of 28Si being the reason for the irregular behavior of that system.

Dynamical explanation for the anomaly in the diffuseness parameter of the nucleus-nucleus potential in heavy-ion fusion reactions

The abnormally large diffuseness parameter of the Woods-Saxon (WS) potential in heavy-ion fusion reactions is explained for the first time based on the microscopic dynamics simulations. With the improved quantum molecular dynamic (ImQMD) model, we systematically explore the dynamical processes in the fusion reactions $^{12}\mathrm{C}+^{92}\mathrm{Zr}$, $^{16}\mathrm{O}+^{92}\mathrm{Zr}$, $^{28}\mathrm{Si}+^{92}\mathrm{Zr}$, $^{35}\mathrm{Cl}+^{92}\mathrm{Zr}$, $^{40}\mathrm{Ca}+^{46}\mathrm{Ti}$, and $^{16}\mathrm{O}+^{154}\mathrm{Sm}$. Without introducing any free model parameters or additional assumptions, the microscopic ImQMD model can reproduce the measured fusion cross sections of all selected colliding systems with good accuracy. Due to the dynamical evolutions of the density distributions in the fusion processes, the energy dependence of nucleus-nucleus potential can be clearly observed. Based on the dynamical nucleus-nucleus potential of the ImQMD simulations, we extract the corresponding diffuseness parameters of the WS potential. The obtained values locate in a range between $\mathit{a}=0.83$ and $1.17\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$ at different incident energies. In addition, the regular decreasing trend for the diffuseness parameter with the increase of the incident energies is also observed.

Analysis of the low- and high-energy fusion cross sections: the case of 58Ni+54Fe

The importance of the saturation effect of cold nuclear matter (NM) on describing the fusion hindrance phenomenon at extremely low incident energies is investigated for the medium-heavy mass system of 58Ni+54Fe. From the theoretical viewpoint, for considering the mentioned property during the fusion process one can use the double-folding (DF) model which is modified through the repulsive core effects as a basic heavy ion–ion potential. The theoretical calculations of the fusion cross sections are performed using the coupled-channel technique, including couplings to the low-lying and states in target and projectile. It is shown that the corrective effects of the cold NM provide an appropriate description for the energy-dependent behavior of the measured fusion cross sections at extremely low incident energies. Moreover, we find that the calculated results of the astrophysical S factor and the logarithmic derivative based on the modified form of the DF model are in good agreement with the corresponding experimental data at these energies. A discussion is also presented about the predictions of the present sudden approach for the behavior of the fusion cross sections at high incident energies. The obtained results reveal that this behavior depends on the nuclear structure of the reacting nuclei.

Dependence of fusion on isospin dynamics

We introduce a new microscopic approach to calculate the dependence of fusion barriers and cross-sections on isospin dynamics. The method is based on the time-dependent Hartree-Fock theory and the isoscalar and isovector properties of the energy density functional (EDF). The contribution to the fusion barriers originating from the isoscalar and isovector parts of the EDF is calculated. It is shown that for non-symmetric systems the isovector dynamics influence the sub-barrier fusion cross-sections. For most systems this results in an enhancement of the sub-barrier cross-sections, while for others we observe differing degrees of hindrance. We use this approach to provide an explanation of recently measured fusion cross sections which show a surprising enhancement at low $E_\mathrm{c.m.}$ energies for the system $^{40}$Ca+$^{132}$Sn as compared to the more neutron-rich system $^{48}$Ca+$^{132}$Sn, and discuss the dependence of sub-barrier fusion cross-sections on transfer.

Fusion cross section measurements of astrophysical interest for light heavy ions systems within the STELLA project

This contribution is focused on the STELLA project (STELlar LAboratory), which aims at the measurement of fusion cross sections between light heavy ions like 12 C+12 C, 12 C+16 O or 16 O+16 O at deep subbarrier energies. The gamma-particle coincidence technique is used in order to reduce background contributions that become dominant for measurements in the nanobarn regime.The experimental setup composed of an ultra high vacuum reaction chamber, a set of 3 silicon strip detectors, up to 36 LaBr3 (Ce) scintillators from the UK FATIMA collaboration, and a fast rotating target system will be described. The 12 C+12 C fusion reaction has been studied from Elab = 11 to 5.6 MeV using STELLA at the Andromede facility in Orsay, France. Preliminary commissioning results are presented in this article.

Influence of neutron transfer channels on fusion enhancement in sub-barrier region

Fusion cross-section measurements were performed for system 40 Ca + 70 Zn around the Coulomb barrier energies using Heavy Ion Reaction Analyzer (HIRA). The observed enhancement in experimental fusion cross-sections was investigated via coupled-channels formalism. The coupling of inelastic excitations alone could not reproduce the experimental data, however, the effect of octupole state of the projectile was observed to be significant. The multi-neutron positive Q-value transfer channels were also included in the calculations using semi-classical model. It was observed that two neutrons pick-up channel gave a major contribution to the fusion enhancement and successfully reproduce the experimental data at above as well as below barrier energies. The coupling of more than two neutrons transfer could not give any significant enhancement to subbarrier fusion.

Sub-barrier fusion cross section measurements with STELLA

The experimental setup STELLA (STELlar LAboratory) is designed for the measurement of deep sub-barrier light heavy ion fusion cross sections. For background suppression the γ-particle coincidence technique is used. In this project, LaBr3 detectors from the UK FATIMA (FAst TIMing Array) collaboration are combined with annular silicon strip detectors customized at IPHC-CNRS, Strasbourg, and the setup is located at Andromede, IPN, Orsay. The commissioning of the experimental approach as well as a sub-barrier 12C +12C → 24Mg∗ cross section measurement campaign are carried out.