Sub-barrier Fusion Research Articles

α-nucleus potential for α-decay and sub-barrier fusion

The set of parameters for \ensuremath{\alpha}-nucleus potential is derived by using the data for both the \ensuremath{\alpha}-decay half-lives and the fusion cross sections around the barrier for reactions $\ensuremath{\alpha}+$$^{40}\mathrm{Ca}$, $\ensuremath{\alpha}+$$^{59}\mathrm{Co}$, and $\ensuremath{\alpha}+$$^{208}\mathrm{Pb}$. The \ensuremath{\alpha}-decay half-lives are obtained in the framework of a cluster model using the WKB approximation. The evaluated \ensuremath{\alpha}-decay half-lives and the fusion cross sections agreed well with the data. Fusion reactions between \ensuremath{\alpha} particles and heavy nuclei can be used for both the formation of very heavy nuclei and spectroscopic studies of the formed compound nuclei.

Transmission ion chamber: Design and application

A Transmission Ion Chamber (TIC) was constructed for use at the focal plane of the Fragment Mass Analyzer (FMA). The motivation for the construction of the TIC was to allow energy loss information to be added to the focal plane identification data. Three experiments immediately benefited form this information. First, an astrophysics experiment studying 69Br via the β decay of 69Kr would benefit greatly by adding a TIC to the existing implantation station. Second the study of extreme sub-barrier heavy-ion fusion evaporation reaction could be made more sensitive. Third, a study was performed using a PPAC–TIC–DSSD configuration to separate 101Sn from the other evaporation products of highly excited 108Te.

Low-energy nuclear reactions with weakly-bound systems

We discuss the problem of subbarrier fusion processes in reactions involving weakly-bound projectiles, in particular with respect to the effect of the strong coupling to break-up channels. Within a simple schematic coupled-channel model we show that the coupling to reaction channels (including continuum break-up channels) seems to predict enhancement of fusion below the barrier (for total fusion and, to a lesser degree, also for complete fusion), when the reaction process is treated within the conventional approach, with proper modifications due to weak-binding nature of halo systems (as for example the long range of formfactors and potentials)

Sub-barrier fusion induced by neutron-rich radioactive 132Sn

Evaporation residue cross-sections measured with short-lived 132Sn on 64Ni at energies near and below the Coulomb barrier were found to be enhanced as compared to those measured with stable Sn isotopes on 64Ni. Subsequent measurements of fission following fusion of 132Sn with 64Ni and extending the measurement of evaporation residues to higher energies were carried out.

Enhanced evaporation residue cross sections in neutron-rich radioactive 132Sn on 64Ni

Evaporation residue cross sections have been measured with neutron-rich radioactive $^{132}$Sn beams on $^{64}$Ni in the vicinity of the Coulomb barrier. The average beam intensity was $2\times 10^{4}$ particles per second and the smallest cross section measured was less than 5 mb. Large subbarrier fusion enhancement was observed. Coupled-channels calculations taking into account inelastic excitation and neutron transfer underpredict the measured cross sections below the barrier.

Quantum calculations of Coulomb reorientation for sub-barrier fusion.

Classical mechanics and time dependent Hartree-Fock (TDHF) calculations of heavy ions collisions are performed to study the rotation of a deformed nucleus in the Coulomb field of its partner. This reorientation is shown to be independent of the charges and relative energy of the partners. It only depends upon the deformations and inertias. TDHF calculations predict an increase by 30% of the induced rotation due to quantum effects while the nuclear contribution seems negligible. This reorientation modifies strongly the fusion cross section around the barrier for light deformed nuclei on heavy collision partners. For such nuclei a hindrance of the sub-barrier fusion is predicted.

Study of nucleus-nucleus potential by combined measurement of deep sub-barrier fusion and cluster decay

Study of nucleus-nucleus potential by combined measurement of deep sub-barrier fusion and cluster decay

Subbarrier fusion in the systems 11,10Be+ 209Bi

The subbarrier fusion cross sections with radioactive ion beams in the systems 10,11Be+ 209Bi have been measured and compared also with the stable system 9Be+ 209Bi. All three cross sections are similar within experimental accuracy; this is somehow unexpected since, in particular, the fusion process with 11Be should be influenced by its halo structure and small binding energy and could behave in a different way from the other two Be isotopes, in particular from 10Be, well bound. Extensive calculations were undertaken within the formalism of continuum discretized coupled channel ( CDCC) that considered only the coupling to two-body breakup, into n+core, of the projectile with excitation to continuum up to 10 MeV. The results are in agreement with the 11,10Be experimental data except at low energy where the cross sections could be influenced by target/projectile collective excitations. The CCFULL theoretical approach, compared to CDCC, seems to reproduce better the subbarrier region and worse the above barrier one. The 9Be cross sections are all underestimated by the CDCC approach while are well reproduced by CCFULL calculations. This suggests that, in this last case, the schematization of the breakup process into 2 only fragments maybe is not adequate and/or other excitations, properly handed by the CCFULL code, could be relevant.

Fusion and Heavy Ion Reactions

The purpose of this report is to review some simple aspects of heavy ion interactions which may be useful for understanding of sub-barrier fusion processes. The Christensen-Winther (CW) is a typical potential and is a useful starting point for a nucleus-nucleus interaction. It gives good values for the height and radius of the Coulomb barrier for many heavy ion pairs. With this and other similar interactions there is a rather large separation between the top of the Coulomb barrier and the point at which the densities come into contact. When used in conjunction with the coupled channels method potentials like the CW interaction give good fusion cross-sections near and for a few MeV below the top of the barrier. The coupled channels method fails in some cases when the energy is of the order of 5 Mev below the barrier. There is evidence that increasing the surface diffuseness of the ion-ion potential might help to resolve this problem. Cluster radioactivity is an inverse process to sub-barrier fusion, but the energies below the top of the Coulomb barrier are very different.

Sequential Fusion: Sub-Barrier Fusion Enhancement Due to Neutron Transfer

From the analysis of appropriate experimental data within a simple theoretical model it is shown that the intermediate neutron transfer channels with positive Q-values really enhance the fusion cross section at sub-barrier energies. The effect of sequential fusion was found to be very large especially for fusion of weakly bound nuclei. New experiments are proposed, which may shed additional light on the effect of neutron transfer in fusion processes.

FUSION03, Concluding Remarks

Fusion reactions below the Coulomb barrier provide new insights into multidimensional quantum tunneling, nuclear reaction dynamics and nuclear structure. These reactions are also of considerable interest to nuclear astrophysics. In this summary recent developments in the field are reviewed and open questions related to subbarrier fusion are presented.

Subbarrier Fusion and Barrier Distributions of48Ca+90,96Zr

We report on the measurement of subbarrier fusion cross sections for 4 8 Ca+ 9 0 , 9 6 Zr, with the aim to pin down the contribution of transfer and inelastic excitations in reactions involving 9 0 Zr and 9 6 Zr. We also present a re-evaluation of previously published data.

Sub-Barrier Fusion Enhancement in Neutron-Rich Radioactive132Sn on64Ni

Evaporation residue cross sections have been measured using neutron-rich radioactive 132Sn beams incident on a 64Ni target in the vicinity of the Coulomb barrier. This is the first experiment using accelerated 132Sn beams to study nuclear reaction mechanisms. The average beam intensity was 2x 104 particles per second and the smallest cross section measured was less than 5 mb. A large sub-barrier fusion enhancement was observed compared to evaporation residue cross sections for 64Ni on stable even Sn isotopes. The enhancement cannot be accounted for by a simple barrier shift due to the change in nuclear sizes. Coupled-channel calculations including inelastic excitation underpredict the measured cross sections below the barrier. The presence of several neutron transfer channels with large positive Q values suggests that multinucleon transfer may play an important role in enhancing the fusion of 132Sn and 64Ni.

Interplay of static and dynamic effects inHe6+U238fusion

We investigate the influence of the neutron halo and the breakup channel in 6He + 238U fusion at near-barrier energies. To include static effects of the 2n-halo in 6He nuclei, we use a single-folding potential obtained from an appropriate nucleon-238U interaction and a realistic 6He density. Dynamical effects arising from the breakup process are then included through coupled-channel calculations. These calculations suggest that static effects dominate the cross section at energies above the Coulomb barrier, while the sub-barrier fusion cross section appears to be determined by coupling to the breakup channel. This last conclusion is uncertain due to the procedure employed to measure the fusion cross-section.

Enhanced fusion-evaporation cross sections in neutron-rich 132Sn on 64Ni.

Evaporation residue cross sections have been measured with neutron-rich radioactive 132Sn beams on 64Ni in the vicinity of the Coulomb barrier. The average beam intensity was 2 x 10(4) particles per second and the smallest cross section measured was less than 5 mb. Large sub-barrier fusion enhancement was observed. Coupled-channel calculations taking into account inelastic excitation significantly underpredict the measured cross sections below the barrier. The presence of several neutron transfer channels with large positive Q values suggests that multinucleon transfer may play an important role in enhancing the fusion of 132Sn and 64Ni.

Sub-barrier fusion enhancement due to neutron transfer

From the analysis of appropriate experimental data within a simple theoretical model, it is shown that the intermediate neutron transfer channels with positive Q values really enhance the fusion cross section at sub-barrier energies. The effect is found to be very large, especially for fusion of weakly bound nuclei. New experiments are proposed, which may shed additional light on the effect of neutron transfer in fusion processes.

Fusion rate enhancement due to energy spread of colliding nuclei

Experimental results for sub-barrier nuclear fusion reactions show cross section enhancements with respect to bare nuclei which are generally larger than those expected according to electron screening calculations. We point out that energy spread of target or projectile nuclei is a mechanism that generally provides fusion enhancement. We present a general formula for calculating the enhancement factor and provide quantitative estimate for effects due to thermal motion, vibrations inside atomic, molecular, or crystal system, and due to finite beam energy width. All these effects are marginal at the energies that are presently measurable; however, they have to be considered in future experiments at still lower energies. This study allows us to exclude several effects as a possible explanation of the observed anomalous fusion enhancements, which remain a mystery.

Transfer reactions and sub-barrier fusion in 40Ca + 90, 96Zr

The two systems 40Ca + 90,96Zr have been studied by measuring nucleon transfer reactions at two energies near the Coulomb barrier, thus complementing the available sub-barrier fusion cross-sections. Angular distributions for various transfer channels have been determined. Significantly larger neutron transfer cross-sections are found for the target 96Zr that exhibits the larger enhancement in the sub-barrier fusion cross-sections. All data have been analyzed with a new model for heavy-ion collisions that calculates simultaneously transfer cross-sections, fusion excitation functions and barrier distributions. The model gives a good account of both transfer and fusion data.

Collective and Transfer Modes in the Sub-Barrier Fusion of Several A ~ 100 Systems CN _"

By using some simple model assumptions, the relative contribution of collective and transfer degrees of freedom to the sub-barrier fusion of several systems is investigated. Previously measured data for 32S + 58,64Ni, 37Cl + 58,60,62,64Ni, 37Cl + 70,72,73,74,76Ge, and 27Al + 70,72,73,74,76Ge are analyzed. Even though the effects of collective degrees of freedom are dominant, transfer effects are shown to be important for many systems in order to account for the trend of the lower energy points. Under simplified assumptions for the transfer strength, a distance for transfer is estimated for some systems. An apparent inconsistency found in previous analysis of the Cl + Ge data is solved.

Dominance of collective over proton transfer couplings in the fusion of32Sand34Swith89Y

Fusion excitation functions have been measured to high precision for the reactions ${}^{32}\mathrm{S}{+}^{89}\mathrm{Y}$ and ${}^{34}\mathrm{S}{+}^{89}\mathrm{Y}.$ The sub-barrier fusion cross sections for ${}^{32}\mathrm{S}{+}^{89}\mathrm{Y}$ are found to be more enhanced over single-barrier penetration calculations than those for ${}^{34}\mathrm{S}{+}^{89}\mathrm{Y},$ and the shapes of the two experimental barrier distributions are significantly different. The effects of proton transfer and double phonon excitations have been examined using exact coupled channels calculations. These suggest that the difference between the two systems lies mainly in the collectivity of the projectiles, whilst proton transfer has only a minor effect.