Sub-barrier Energies Research Articles

Effect of neutron rearrangement on subbarrier fusion reactions

Abstract The role of neutron transfer is investigated in the fusion process near and below the Coulomb barrier within the empirical channel coupling approach. The possibility of neutron transfer with positive Q-values considerably increases the barrier penetrability. The enhancement of fusion cross sections for 58Ni + 64Ni, 32S + 64Ni, 40Ca + 48Ca, and 40Ca + 124Sn is well reproduced at subbarrier energies by the empirical channel coupling approach including the coupling to the neutron-transfer channels. The predictions of the fusion cross sections for several combinations of colliding nuclei are also proposed which may shed additional light on the effect of neutron transfer in fusion processes. A huge enhancement of deep subbarrier fusion probability was found for light neutron-rich weakly bound nuclei. This may be quite important for astrophysical primordial and supernova nucleosynthesis.

Sub-barrier transfer in16O+208Pb and32S+208Pb and its role in understanding the suppression of fusion

A detailed analysis of the projectile-like fragments detected at backward angles in the reactions 16O, 32S+208Pb at energies below the fusion barrier is presented. Excitation functions corresponding to nucleon transfer with ΔZ = 1 and ΔZ = 2 were extracted, indicating surprisingly large absolute probabilities at sub-barrier energies. A comparison of 2p transfer probabilities with time-dependent Hartree-Fock calculations suggests strong pairing correlations between the two protons. Excitation energies in the projectile-like fragments up to ~ 15MeV for the 16O and ~ 25MeV for 32S-induced reactions demonstrate the population of highly excited states in the residual nuclei, indicating substantial dissipation of kinetic energy. These highly inelastic (large excitation energies) and complex (correlated few-nucleon transfer) processes may be closely related to the depletion of fusion through tunnelling at sub-barrier energies.

Reconstructing breakup at sub-barrier energies

Using a position sensitive detector array, back-angle coincidence measurements of breakup fragments at sub-barrier energies has enabled the complete characterisation of the breakup processes in the reactions of 6,7 Liw ith 208 PbB. reakup processes and their time-scales are identified through the reaction Q-values and the relative energy of the captured breakup fragments. The majority of breakup processes fast enough (~10-22 s) to affect fusion are triggered by transfer of a neutron from 6 Li, and of a proton to 7 Li. These breakup mechanisms should therefore have a major contribution to the ~30% suppression of complete fusion observed at above-barrier energies.

Role of neutron transfer and deformation effect in capture process at sub-barrier energies

The roles of nuclear deformation and neutron transfer in sub-barrier capture process are studied within the quantum diffusion approach. The change of the deformations of colliding nuclei with neutron exchange can crucially influence the sub-barrier fusion. The sub-barrier capture reactions following the neutron pair transfer are used for the indirect study of neutron-neutron correlation in the surface region of nucleus. The strong surface enhancement of the neutron pairing in nuclei 48 Ca, 64 Ni, and 116,124,132 Sn is demonstrated. Comparing the capture cross sections calculated without the breakup effect and experimental complete fusion cross sections, the breakup was analyzed in reactions with weakly bound projectiles 6,7,9 Li and 9 Be. A trend of a systematic behavior for the complete fusion suppression as a function of the target charge and bombarding energy is not achieved.

Effects of nuclear deformation and neutron transfer in capture processes, and fusion hindrance at deep sub-barrier energies

The roles of nuclear deformation and neutron transfer in sub-barrier capture process are studied within the quantum diffusion approach. The change of the deformations of colliding nuclei with neutron exchange can crucially influence the sub-barrier fusion. The comparison of the calculated capture cross section and the measured fusion cross section in various reactions at extreme sub- barrier energies gives us information about the fusion and quasifission.

Fusion and direct reactions for the system6He+64Zn at and below the Coulomb barrier

Fusion and transfer $+$ breakup channels have been studied in the collision induced by the two-neutron-halo ${}^{6}$He on a ${}^{64}$Zn target at energies from below to above the Coulomb barrier. For comparison, the reaction induced by the stable isotope ${}^{4}$He on the same target has been studied. The fusion cross section has been measured by using an activation technique, detecting off-line the delayed x-ray activity following the electron capture decay of the evaporation residues. New measurements of the ${}^{4}$He $+$ ${}^{64}$Zn fusion cross section at sub-barrier energies have been performed in order to cover the same energy range of the ${}^{6}$He $+$ ${}^{64}$Zn fusion cross section and to compare the excitation functions for the two systems down to the lowest energy data point measured for ${}^{6}$He. From the new comparison a sub-barrier fusion enhancement has been observed in the ${}^{6}$He case with respect to the ${}^{4}$He one whereas no effect on the ${}^{6}$He fusion cross section has been seen at energies above the barrier. It has been concluded that such enhancement seems to be due to the diffuse halo structure properties of the ${}^{6}$He nucleus. Moreover, the reactions induced by ${}^{6}$He have shown a strong yield of $\ensuremath{\alpha}$ particles coming from direct processes.

Cluster transfer in the reaction16O+208Pb at energies well below the fusion barrier: A possible doorway to energy dissipation

The collision of the doubly-magic nuclei $^{16}$O+$^{208}$Pb is a benchmark in nuclear reaction studies. Our new measurements of back-scattered projectile-like fragments at sub-barrier energies show show that transfer of 2 protons ($2p$) is much more probable than $\alpha$-particle transfer. $2p$ transfer probabilities are strongly enhanced compared to expectations for the sequential transfer of two uncorrelated protons; at energies around the fusion barrier absolute probabilities for two proton transfer are similar to those for one proton transfer. This strong enhancement indicates strong $2p$ pairing correlations in $^{16}$O, and suggests evidence for the occurrence of a nuclear supercurrent of two-proton Cooper pairs in this reaction, already at energies well below the fusion barrier.

Effect of isospin on the fusion reaction cross section using various nuclear proximity potentials within the Wong model

Various versions of proximity potentials, with different isospin dependence, are used within the Wong model for fitting the fusion-evaporation cross sections from ${}^{58}$Ni + ${}^{58}$Ni, ${}^{64}$Ni + ${}^{64}$Ni, and ${}^{64}$Ni + ${}^{100}$Mo reactions in an intermediate mass region and capture cross sections from ${}^{48}$Ca + ${}^{238}$U, ${}^{244}$Pu, and ${}^{248}$Cm reactions in a superheavy mass region, known for fusion hindrance phenomena in coupled-channel calculations. It is found that proximity 1988 gives results close to experimental data in a comparison of proximity 1977 and proximity 2000 within the Wong formula, so this Proximity 1988 (Prox 1988) is then used within the extended Wong model. This combination can fit the cross sections for the ${}^{58}$Ni + ${}^{58}$Ni and ${}^{64}$Ni + ${}^{64}$Ni reactions but deviates a little from the experimental data for the ${}^{64}$Ni + ${}^{100}$Mo reaction at a center-of-mass energy below the Coulomb barrier. But the variation of ${\ensuremath{\ell}}_{\text{max}}$ with ${E}_{\text{c.m.}}$ at sub-barrier energies is absurd for these three reactions. So, a different type of strong nuclear interaction is required that accounts for isospin effect and asymmetry of the colliding nuclei, which is obtained here by a slight adjustment of the coefficient ${\ensuremath{\gamma}}_{0}$ of the nuclear surface energy constant of the Prox 1988 potential, in order to fit the experimental data for this reaction and named it mod-Prox 1988. The surface energy constant $\ensuremath{\gamma}$ depends on the neutron/proton excess, and change in one of its constants, ${\ensuremath{\gamma}}_{0}$, used in Prox 1988, introduces the required barrier modification for fitting the experimental data. Thus, change in $\ensuremath{\gamma}$ leads to change in barrier characteristics, i.e., barrier height (${V}_{B}^{\ensuremath{\ell}}$), position (${R}_{B}^{\ensuremath{\ell}}$), and oscillator frequency ($\ensuremath{\hbar}{\ensuremath{\omega}}_{\ensuremath{\ell}}$). Using this modified proximity potential within the extended Wong model, experimental data for all three Ni-induced reactions is fitted with a smooth variation of deduced ${\ensuremath{\ell}}_{\text{max}}({E}_{\text{c.m.}})$ at above- as well as below-barrier energies. The effect of isospin is more prominent at below-barrier energies. As an application, mod-Prox 1988 is then employed for the capture cross-section data from ${}^{48}$Ca + ${}^{238}$U, ${}^{244}$Pu, and ${}^{248}$Cm reactions in superheavy mass regions and it successfully fits the data point to point with a smooth variation of ${\ensuremath{\ell}}_{\text{max}}$ with ${E}_{\text{c.m.}}$. Thus, mod-Prox 1988 within the extended Wong model leads to a simultaneous explanation of several reactions displaying a hindrance to fusion. Thus, below the Coulomb barrier a stronger nuclear interaction is required as the $N/Z$ ratio increases and colliding nuclei become more and more asymmetric. The effects of multipole deformations are included here up to hexadecapole in the calculations, and orientation degrees of freedom are integrated for the coplanar configuration.

Effects of nuclear orientation on fusion and fission process for reactions using 238U target nucleus

Fragment mass distributions for fission after full momentum transfer were measured in the reactions of 30Si,34,36S,31P,40Ar + 238U at bombarding energies around the Coulomb barrier. Mass distributions change significantly as a function of incident beam energy. The asymmetric fission probability increases at sub-barrier energy. The phenomenon is interpreted as an enhanced quasifission probability owing to orientation effects on fusion and/or quasifission. The evaporation residue (ER) cross sections were measured in the reactions of 30Si +238U and 34S+ 238U to obtain information on the fusion probability. In the latter reaction, significant suppression of fusion was implied. This suggests that quasifission has large fraction in the mass-symmetric fission events. The results are supported by a model calculation based on a dynamical calculation using Langevin equation, in which the mass distribution for fusion-fission and quasifission fragments are separately determined.

Probability of passing through a parabolic barrier and thermal decay rate: Case of linear coupling both in momentum and in coordinate

With the quantum diffusion approach, the probability of passing through the parabolic barrier and the quasistationary thermal decay rate from a metastable state are examined in the limit of linear coupling both in momentum and in coordinate between a collective subsystem and the environment. An increase of passing probability with friction coefficient is demonstrated to occur at subbarrier energies.

Fusion reaction cross-sections using the Wong model within Skyrme energy density based semiclassical extended Thomas Fermi approach

First, the nuclear proximity potential, obtained by using the semiclassical extended Thomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), is shown to give more realistic barriers in frozen density approximation, as compared to the sudden approximation. Then, taking advantage of the fact that, in ETF method, different Skyrme forces give different barriers (height, position and curvature), we use the l-summed extended-Wong model of Gupta and collaborators (2009) [1] under frozen densities approximation for calculating the cross-sections, where the Skyrme force is chosen with proper barrier characteristics, not-requiring additional “barrier modification” effects (lowering or narrowing, etc.), for a best fit to data at sub-barrier energies. The method is applied to capture cross-section data from 48Ca + 238U, 244Pu, and 248Cm reactions and to fusion–evaporation cross-sections from 58Ni + 58Ni, 64Ni + 64Ni, and 64Ni + 100Mo reactions, with effects of deformations and orientations of nuclei included, wherever required. Interestingly, whereas the capture cross-sections in Ca-induced reactions could be fitted to any force, such as SIII, SV and GSkI, by allowing a small change of couple of units in deduced lmax-values at below-barrier energies, the near-barrier data point of 48Ca + 248Cm reaction could not be fitted to lmax-values deduced for below-barrier energies, calling for a check of data. On the other hand, the fusion–evaporation cross-sections in Ni-induced reactions at sub-barrier energies required different Skyrme forces, representing “modifications of the barrier”, for the best fit to data at all incident center-of-mass energies Ec.m.ʼs, displaying a kind of fusion hindrance at sub-barrier energies. This barrier modification effect is taken into care here by using different Skyrme forces for reactions belonging to different regions of the periodic table. Note that more than one Skyrme force (with identical barrier characteristics) could equally well fit the same data.

Single and pair neutron transfers at sub-barrier energies

Multinucleon transfer cross sections in the ${}^{96}$Zr+${}^{40}$Ca system have been measured, in inverse kinematics, at bombarding energies ranging from the Coulomb barrier to $\ensuremath{\sim}$25$%$ below. Targetlike recoils have been identified in A, Z and velocity with the large solid angle magnetic spectrometer PRISMA. The experimental data for one- and two-neutron transfer channels have been compared with semiclassical microscopic calculations. For the two-neutron transfer channels the relevance of the transitions to the ground state and to the 0${}^{+}$ excited states of ${}^{42}$Ca are discussed by employing, for the reaction mechanism, the successive approximation. It is found that the transition to the 0${}^{+}$ state at $\ensuremath{\sim}$6 MeV, whose wave function is dominated by the two neutrons in the $2{p}_{3/2}$ shell, is much larger than the ground state one. The comparison with the inclusive data reveals that transitions to states with high multipolarity and non-natural parity are important. This suggests that more complex two-particle correlations have to be incorporated in the treatment of the transfer process.

The decay of the compound nucleus 215Fr* formed in the 11B+204Pb and 18O+197Au reaction channels using the dynamical cluster-decay model

The decay of 215Fr* nucleus, formed in 11B+204Pb and 18O+197Au reactions, is studied by using the dynamical cluster-decay model (DCM) with effects of deformations and orientations of nuclei included in it. The observed decay is mainly via fusion–fission, with data collected for both the fission excitation functions and fission fragment anisotropies. The chosen reaction channels have entrance channel mass asymmetries lying on either side of the Bussinaro–Gallone critical asymmetry parameter. In agreement with experimental data and conclusions based on the statistical code PACE2, for fission excitation functions, our DCM calculations with ℓmax value used in accordance with the sticking moment of inertia also show no contribution of the quasi-fission component in fission cross-sections for both the reaction channels, measured at incident center-of-mass energy spread on either side of the Coulomb barrier. Due to deformation and orientation of nuclei, the fission mass distribution is asymmetric, and nearly independent of the entrance channel. Interestingly, for a best fit to data on fission cross-sections, an in-built ‘barrier lowering’ seems operative at sub-barrier energies for both the reactions under study. Also, the fission fragment anisotropies, calculated on DCM for the first time, using non-sticking moment of inertia are found consistent with experimental data for both the reaction channels, confirming beyond doubt the entrance channel's independence of the decay of 215Fr*.

Fusion Reactions with the One-Neutron Halo NucleusC15

The structure of (15)C, with an s(1/2) neutron weakly bound to a closed-neutron shell nucleus (14)C, makes it a prime candidate for a one-neutron halo nucleus. We have for the first time studied the cross section for the fusion-fission reaction (15)C+(232)Th at energies in the vicinity of the Coulomb barrier and compared it to the yield of the neighboring (14)C+(232)Th system measured in the same experiment. At sub-barrier energies, an enhancement of the fusion yield by factors of 2-5 was observed for (15)C, while the cross sections for (14)C match the trends measured for (12,13)C.

Fusion excitation functions of 64Ni+112–132Sn reactions studied on the dynamical cluster-decay model

The dynamical cluster-decay model (DCM) of Gupta and Collaborators has been used to study the decay of various Pt-isotopes 176, 182, 188, 196Pt* formed in 64Ni+112, 118, 124Sn and 132Sn+64Ni reactions. The evaporation residue (ER) and fission cross-sections (σER and σfiss) are calculated in reference to available experimental data at near- and sub-barrier energies. The calculated σER show excellent agreement with experimental data at all incident center-of-mass (c.m.) energies, with the characteristics of emitted light particles (LPs) showing a change with the increase of the iso-spin N/Z ratio of compound nucleus (CN). The only parameter of DCM, the neck-length parameter, for 196Pt* becomes much smaller, compared to other 176, 182, 188Pt*isotopes, and more so at higher c.m. energies, possibly due to additional eight neutrons of the radioactive 132Sn nucleus. Another interesting result of the DCM calculation is that, similar to other well-known Ni-induced (58, 64Ni+58, 64Ni and 64Ni+100Mo) reactions, an inbuilt ‘barrier lowering’ effect is also shown operating for σER as well as σfiss at sub-barrier energies in these reactions. Furthermore, the calculated σfiss shows a significant contribution of quasi-fission (σqf) at the highest one or two energies, and, due to the deformation and orientation effects of fission fragments, shows a change of the mass distributions from a predominantly symmetric to a predominantly asymmetric one with the increase in the N/Z ratio of CN. This change in fission mass distributions provides the possibility of fine-/sub-structure in fission products of Pt* isotopes.Communicated by Professor S Bass.

COMPLETE CHARACTERIZATION OF BREAKUP OF 9Be BY α-α COINCIDENCE MEASUREMENTS

The breakup mechanisms for 9 Be have been studied through coincident detection of the breakup α particles at sub-barrier energies, where the probability of capture of a charged breakup fragment by the target nucleus is negligible. Combining the reconstructed reaction Q-value and the relative energy of the two coincident breakup α particles a complete picture of breakup dynamics has been obtained. The measurements reveal breakup processes which are fast enough (~ 10-22 s) to affect fusion, called prompt breakup. It is shown that prompt breakup is triggered predominantly by the transfer of a neutron -a two-step process. The prompt breakup probabilities are shown to have an exponential dependence on the surface-to-surface separation of the interacting nuclei, but are independent of the target nuclei, ranging from 144 Sm to 209 Bi . These results provide significant input towards a complete quantal model aiming to describe the breakup of weakly bound stable and halo nuclei.

NEAR BARRIER REACTIONS INDUCED BY WEAKLY BOUND CLUSTER NUCLEI

Experimental excitation functions are presented for complete fusion and transfer reactions in the interaction of 6 He and 6,8,9 Li with 206 Pb , 209 Bi , and nat Pt targets. The data on fusion in the 6 He -induced reactions at energies close to the Coulomb barrier differ from predictions within the framework of the statistical model for compound nucleus decay. For these exit channels a strong enhancement has been observed. Enhancement of the cross section for neutron transfer (with the 6 He and 8,9 Li beams) and deuteron transfer (with the 6 Li beam) reactions is observed at deep sub-barrier energies. The results are discussed from the viewpoint of how the nuclear cluster structure influences the probability of interaction at near-barrier energies.

Sub-barrier capture with quantum diffusion approach: Actinide-based reactions

With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed nuclei at subbarrier energies. The calculated results are in a good agreement with existing experimental data. With decreasing bombarding energy under the barrier the external turning point of the nucleusnucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is expected at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum of captured system on the bombarding energy. From the comparison of calculated and experimental capture cross sections, the importance of quasifission near the entrance channel is shown for the actinide-based reactions leading to superheavy nuclei.

Peculiarities of sub-barrier reactions with heavy ions

With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed and spherical nuclei at sub-barrier energies. The calculated results are in a good agreement with existing experimental data. With decreasing bombarding energy under the barrier the external turning point of the nucleus-nucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is expected at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum of captured system on the bombarding energy. From the comparison of calculated capture cross sections and experimental capture (fusion) cross sections, the importance of quasifission near the entrance channel is shown for the actinide-based reactions and reactions with medium-heavy nuclei at sub-barrier energies.

Halo effects on fusion cross section in 4,6He+64Zn collision around and below the coulomb barrier

The structure of the halo nuclei is expected to influence the fusion mechanism at energies around and below the Coulomb barrier. Here new data of 4He+64Zn at sub-barrier energies are presented which cover the same energy region of previous measurements of 6He+64Zn. The fusion cross section was measured by using an activation technique where the radioactive evaporation residues produced in the reaction were identified by the X-ray emission which follows their electron capture decay. By comparing the two system, we observe an enhancement on the fusion cross section in the reaction induced by 6He, at energy below the Coulomb barrier. It is shown that this enhancement seems to be due to static properties of halo 2n 6He nucleus.