Deep Sub-barrier Energies Research Articles

Beyond the Coherent Coupled Channels Description of Nuclear Fusion

New measurements of fusion cross sections at deep sub-barrier energies for the reactions 16O+{204,208}Pb show a steep but almost saturated logarithmic slope, unlike 64Ni-induced reactions. Coupled channels calculations cannot simultaneously reproduce these new data and above-barrier cross-sections with the same Woods-Saxon nuclear potential. It is argued that this highlights an inadequacy of the coherent coupled channels approach. It is proposed that a new approach explicitly including gradual decoherence is needed to allow a consistent description of nuclear fusion.

Systematic study of the nuclear potential through high precision back-angle quasi-elastic scattering measurements

High precision quasi-elastic scattering excitation functions have been measured at energies well below the Coulomb barrier for the reactions of $^{32}\mathrm{S}$ with $^{208}\mathrm{Pb}$, $^{197}\mathrm{Au}$, $^{186}\mathrm{W}$, and $^{170}\mathrm{Er}$. Single-channel and coupled-channels calculations have been performed to extract the diffuseness parameter of the nuclear potential. For the reactions involving near-spherical targets, both theoretical analyses give the same diffuseness parameter. On the other hand, for deformed systems, couplings are important even at deep sub-barrier energies. In general, the effect of couplings is to reduce the diffuseness parameter value extracted from a single-channel potential. Single-channel fits to quasi-elastic scattering data result in $a=0.72\text{\ensuremath{-}}0.82$ fm, whereas coupled-channels calculations give diffuseness parameters in the range 0.58--0.75 fm.

Derivation of the surface diffuseness of the nucleus-nucleus interaction potential using large-angle quasielastic scattering at deep sub-barrier energies

We measured large-angle quasielastic scattering for the spherical 16,17,18 SO + 92 Mo systems at deep sub-barrier energies. This is a process sensitive to the surface region of the nuclear potential which can be used to probe surface diffuseness. The derived diffuseness values are of the order of 0.70 fm for the three systems, larger than predicted by previous works on similar systems.

Potential inversion with sub-barrier fusion data reexamined

We invert experimental data for heavy-ion fusion reactions at energies well below the Coulomb barrier in order to directly determine the internucleus potential between the colliding nuclei. In contrast to the previous applications of the inversion formula, we explicitly take into account the effect of channel couplings on fusion reactions, by assuming that fusion cross sections at deep sub-barrier energies are governed by the lowest barrier in the barrier distribution. We apply this procedure to the $^{16}\mathrm{O}+^{144}\mathrm{Sm}$ and $^{16}\mathrm{O}+^{208}\mathrm{Pb}$ reactions, and find that the inverted internucleus potential are much thicker than phenomenological potentials. A relation to the steep fall-off phenomenon of fusion cross sections recently found at deep sub-barrier energies is also discussed.

Role of neutrons in the fusion of nuclei

The problem of a quantum-mechanical description of a near-barrier fusion of heavy nuclei under conditions of a strong coupling of their relative motion to neutron degrees of freedom is studied. New mutually complementing efficient models employing the multidimensional time-dependent Schrodinger equation and methods for numerically solving the problems in question within these models are proposed. This makes it possible to study the evolution of wave functions for outer neutrons and to calculate nucleontransfer probabilities and occupation numbers for quasimolecular states over the entire energy range, including that of deep-subbarrier energies. It is shown that the valence-neutron wave functions extend over the volumes of both colliding nuclei before their surfaces come into contact and even before these nuclei overcome the Coulomb barrier (collectivization of outer nucleons). This gives rise to a substantial neutron-transfer effect on the fusion of nuclei and, in particular, to a sizable increase in the probability of subbarrier fusion for specific combinations of nuclei.

Existence of a one-body barrier revealed in deep subbarrier fusion

Based on the adiabatic picture for heavy-ion reactions, in which the neck formation in the one-body system is taken into account, we propose a two-step model for fusion cross sections at deep sub-barrier energies. This model consists of the capture process in the two-body potential pocket, which is followed by the penetration of the adiabatic one-body potential to reach a compound state after the touching configuration. We describe the former process with the coupled-channels framework, while the latter with the Wentzel-Kramers-Brillouin (WKB) approximation by taking into account the coordinate dependent inertia mass. The effect of the one-body barrier is important at incident energies below the potential energy at the touching configuration. We show that this model well accounts for the steep fall-off phenomenon of fusion cross sections at deep sub-barrier energies for the $^{64}\mathrm{Ni}$+$^{64}\mathrm{Ni}$ and $^{58}\mathrm{Ni}$+$^{58}\mathrm{Ni}$ reactions.

Surface diffuseness parameter for systems withZPZT≃780

We have investigated experimental quasielastic cross sections measured at backward angles and at deep sub-barrier energies for the {sup 35}Cl+{sup 105,106,110}Pd and {sup 32}S+{sup 110}Pd systems. Since coupling effects are almost negligible at very low bombarding energies, the quasielastic data allow one to determine the diffuseness parameter of the ion-ion potential. For the analyzed reactions we have obtained a surface diffuseness parameter value around 0.58{+-}0.04 fm.

Probing surface diffuseness of nucleus-nucleus potential with quasielastic scattering at deep sub-barrier energies

We perform a systematic study on the surface property of nucleus-nucleus potential in heavy-ion reactions using large-angle quasielastic scattering at energies well below the Coulomb barrier. At these energies, the quasielastic scattering can be well described by a single-channel potential model. Exploiting this fact, we point out that systems which involve spherical nuclei require the diffuseness parameter of around 0.60 fm in order to fit the experimental data, while systems with a deformed target between 0.8 fm and 1.1 fm.

Surface diffuseness anomaly in heavy-ion potentials for large-angle quasielastic scattering

Recent high precision experimental data for heavy-ion fusion reactions at sub-barrier energies systematically show that a surprisingly large surface diffuseness parameter for a Woods-Saxon potential is required in order to fit the data. We point out that experimental data for quasielastic scattering at backward angles also favor a similar large value of the surface diffuseness parameter. Consequently, a double folding approach with a short-range imaginary potential for the compound nucleus formation fails to reproduce the experimental excitation function of quasielastic scattering for the $^{16}\mathrm{O}+^{154}\mathrm{Sm}$ system at energies around the Coulomb barrier. We also show that the deviation of the ratio of the quasielastic to the Rutherford cross sections from unity at deep sub-barrier energies offers an unambiguous way to determine the value of the surface diffuseness parameter in the nucleus-nucleus potential.

Effect of nonlocality on sub-barrier fusion enhancement

The effect of nonlocality on heavy ion fusion is discussed at sub-barrier energies. It is shown that a simple barrier penetration model with a nonlocal ion-ion potential cannot reproduce the coupled channel results, though it gives rise to fusion enhancement at low energies. It is further shown that the coupled channel effects are important for fusion around the Coulomb barrier energies whereas the nonlocal effects give a large cross section enhancement at deep sub-barrier energies.

Optical model approach for heavy ion fusion.

The differences between optical model (OM) and the barrier transmission approaches for fusion are studied in detail at low energy. In the heavy ion case at deep subbarrier energies, the absorption mean square spin of an optical model calculation using a short ranged imaginary potential differs significantly from the results of the WKB transmission method. This discrepancy of OM results is shown to be due to absorption occurring beyond the barrier position. The coupled reaction channel calculations for fusion based on OM approach are shown to be sensitive to the choice of imaginary fusion potentials, whereas the coupling effects on fusion are dominant for energies only around the barrier. \textcopyright{} 1996 The American Physical Society.

Nuclear clusters in dissipative medium

An exact solution of channel coupling equations describing the relative motion of two heavy clusters was analyzed without additional (commonly used) simplifications concerning a restricted number of the channels and low excitation energy in comparison with the total energy. It was found that excitation of even very simple quantum system with only one degree of freedom may reveal the dissipative features at slow collisions if the spectra of this system is sufficiently random. An excitation of such a system at sub-barrier tunnelling increases significantly (by several orders) the transmission probability, in spite of the large dissipation of relative motion kinetic energy occurs. At deep sub-barrier energies the soft degrees of freedom are excited with the most probability. Dynamics of wave packet in dissipative environment was also analyzed and a new effect of wave packet sticking to a potential wall due to its tangling and time delay inside the inelastic channels was found.

Subbarrier photofission ofU238

Subbarrier photofission cross sections and the fission half-lives have been calculated for $^{238}\mathrm{U}$ in terms of a suitable double-hump fission barrier model. The competition due to the gamma deexcitation to the shape isomeric state in the second well (and its consequent fission) has been included by introducing an absorptive part in the potential in the second well region. The calculated cross sections reproduce satisfactorily the recently observed "shelf" in the deep-subbarrier energy region and result in a resonance structure in the threshold region consistent with that observed. The calculation also predicts several low energy resonances in the cross sections and a detailed competition of the prompt and the delayed fission contributions suggests that an angular anisotropy measurement might be more sensitive in detecting the relatively small contribution of delayed fission in the energy region 4.5-5.5 MeV.NUCLEAR REACTIONS Fission calculated subbarrier photofission cross sections and fission half lives using a suitable two-hump fission barrier in $^{238}\mathrm{U}$. The results reproduce the observed "shelf" in the cross sections in the deep-subbarrier energy region and the observed resonance structure in threshold region.

Three-hump fission barrier inTh232

Subbarrier photofission cross-sections and the fission half-lives have been calculated for $^{232}\mathrm{Th}$ in terms of a suitable three-hump fission barrier model consistent with the suggestion of M\"oller and Nix. The competition due to the gamma deexcitation to the shape-isomeric state in the second well (and its consequent fission) has been included by introducing an absorptive part in the potential in the second well region. The calculated cross sections reproduce satisfactorily the recently observed "shelf" in the deep-subbarrier energy region and provide a further quantitative evidence in favor of resolving the "thorium anomaly" along the lines suggested by M\"oller and Nix.NUCLEAR REACTIONS Fission, calculated subbarrier photofission cross-sections and fission half-lives using a three-hump fission barrier in $^{232}\mathrm{Th}$. Results reproduce the observed "shelf" in the cross-sections in deep-subbarrier energy region.