Fusion Excitation Functions Research Articles

The extended optical model with dispersion relation for the fusion of light heavy-ion systems

Fusion excitation functions were calculated for light heavy-ion systems in the whole measured energy range. The calculations were performed by using the extended optical model for fusion which was applied with success for above-Coulomb-barrier energies. This model is based on the separate absorptive potential for fusion. The modification of the extended optical-model potential in the sub-barrier region occurs in its real and imaginary energy-dependent parts through the dispersion relation. The effect of the critical angular-momentum cut-off has been obtained by the decrease of W fus( E) at the high-energy region. A very good description of the experimental fusion cross sections were obtained for the following systems: 12C+ 12C, 12C+ 14N, 12C+ 16O, and 16O+ 16O. A detailed discussion of the parameters of the model is presented.

Interaction of aligned 23Na with 206Pb at the Coulomb barrier: Quasielastic scattering, fusion and fission

The interaction of 23Na with 206Pb at energies around the Coulomb barrier for quasielastic scattering and for fusion followed by fission has been investigated, partly with aligned projectiles. Quasielastic-scattering data are required to determine the energy dependence of the strength of the double-folding potential used in coupled-channel calculations. The real and imaginary part of the energy-dependent strength of the potential turn out to be correlated by a dispersion relation. The fusion excitation function and the associated second-rank-tensor analyzing powers can be described parameter-free using the real energy-dependent potential if channel coupling is considered as well. Finally, the transmission coefficients extracted from such calculations can be used as input for calculations of the fission angular distributions. Deviations are observed at the lowest bombarding energy.

Clear signatures of specific inelastic and transfer channels in the distribution of fusion barriers.

Fusion excitation functions for $^{144}\mathrm{Sm}$ + $^{16}\mathrm{O}$ and $^{17}\mathrm{O}$ have been measured to high precision. The extracted fusion barrier distributions show a double-peaked structure which is interpreted in terms of coupling to inelastic excitations of the target. The effect of the neutron stripping channel is evident in the reaction with $^{17}\mathrm{O}$. These barrier distributions show clearly the signatures of specific inelastic and transfer channels.

Fusion of 32S+154Sm at sub-barrier energies.

Fusion-evaporation cross sections for the $^{32}\mathrm{S}$${+}^{154}$Sm system at bombarding energies near the Coulomb barrier have been measured by off-line observation of the K x rays emitted in the radioactive decay of the residual nuclei. The total fusion cross sections were obtained by adding the contributions from evaporation and fission processes. The fusion excitation function for this system is compared with coupled-channel calculations that include the deformation of the target and vibrational states of both target and projectile.

Formation and decay of 164Yb* in near- and below-barrier fusion reactions.

A consistent description of the formation and decay of $^{164}\mathrm{Yb}^{\mathrm{*}}$ in the fusion of $^{16}\mathrm{O}$${+}^{148}$Sm and $^{64}\mathrm{Ni}$${+}^{100}$Mo is presented in a bombarding energy range from near to well below the entrance channel Coulomb barrier. Fusion excitation functions and angular momentum distributions are described well with a recently proposed one-dimensional barrier penetration model with energy-dependent fusion barriers. The main features of fusion and angular momentum distribution data in $^{64}\mathrm{Ni}$${+}^{100}$Mo are also reproduced with simplified coupled channel calculations. The statistical model accounts well for the decay of $^{164}\mathrm{Yb}^{\mathrm{*}}$ in the $^{16}\mathrm{induced}$ reaction and for most of the data in the $^{64}\mathrm{induced}$ reaction. The evaporation residue fractional cross sections as a function of the compound nucleus excitation energy show trends that correlate with the low- and high-spin regions of the compound nucleus angular momentum distributions populated in the two reactions.

Obtaining average angular momenta from fusion excitation functions near the Coulomb barrier

Strong coupling to direct reaction channels causes the fusion excitation function close to the Coulomb barrier to behave very differently from that due to a simple potential barrier. The average compound nucleus angular momentum 〈itl > 〉 is also strongly affected. It is shown how to obtain 〈 l〉 from a fusion excitation function using a model whose only parameter is the diffuseness of the nuclear potential.

Sub-barrier fusion of 16O+144Nd.

Fusion cross sections for $^{16}\mathrm{O}$${+}^{144}$Nd at bombarding energies ranging from ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=54.0 to 67.5 MeV were measured by observation of the delayed x rays emitted in the radioactive decay of the evaporation residues and their daughters. The experimental fusion excitation function was analyzed with a barrier penetration model which includes coupling to inelastic channels. The theoretical average angular momenta were calculated and compared with already existing data deduced from \ensuremath{\gamma}-multiplicity measurements.

Experimental determination of energy-dependent barriers for fusion

Experimental fusion excitation functions have been fitted for several systems using an energy-dependent barrier-penetration model as suggested in our earlier work where the barrier height is written as a function of the radial kinetic energy {var epsilon} at the interaction barrier. This form of the energy dependence of the fusion barrier leads also to an implied {ital l} dependence of the barrier. It is shown that the enhancement of {l angle}{ital l}{r angle} over {l angle}{ital l}{r angle}{sub {ital o}{ital d}} predicted by a simple energy-independent barrier-penetration model is maximum around the Coulomb barrier. A correlation has also been oberved between this maximum enhancement factor and the product of the charges of the colliding nuclei.

Dissipation-fluctuation dynamics for fusion, deep-inelastic collisions, and heavy-ion induced fission with particle evaporation

It is shown on selected examples how heavy-ion collisions (below 15 MeV/u) can be described by Langevin Monte Carlo dynamics. Fusion excitation functions, fusion spin distributions and Wilczynski diagrams of deep-inelastic collision (DIC) are calculated and compared with data. The bifurcation of fusion and DIC down to subbarrier energies is demonstrated. Time scales of DIC are obtained from calculating energy spectra of σ-electrons (atomic clock). By combining a (one-dimensional, overdamped) Langevin dynamics for the fission process with the statistical model (when the Kramers limit is reached after a transient time) we are not only able to calculate neutron multiplicities but also fission probabilities and (H.I.,xn) cross sections. Extending these investigations to a two-dimensional (elongation and neck) Langevin dynamics we obtain also kinetic energy distribution of fission fragments in coincidence with neutron multiplicities. By applying this model to a multi-dimensional decay rate for fission (derived with path integral methods) we calculate quantal corrections to the quasistationary Kramers result, which are not small even at temperatures reached in heavy-ion induced fission.

Nucleus-nucleus potential in the range -2<S<2.5 fm

The nucleus-nucleus potentials (${\mathit{V}}_{\mathit{N}}$) over a range of interaction distances (-2S2.5 fm) have been obtained from the analyses of the fusion excitation function data spanning a large range of energies. A three-parameter Fermi function adequately represents the observed variation of ${\mathit{V}}_{\mathit{N}}$/R\ifmmode\bar\else\textasciimacron\fi{}[R=${\mathit{R}}_{1}$${\mathit{R}}_{2}$/(${\mathit{R}}_{1}$+${\mathit{R}}_{2}$), with ${\mathit{R}}_{1}$ and ${\mathit{R}}_{2}$ the radii of the interacting nuclei] with S in the above-mentioned range.

Fusion limited by temperature

The effect of the temperature dependence of the free interaction energy on the fusion excitation function for the systems 40Ar + 27Al, 35Cl + 58Ni, 40Ca + 40Ca is investigated. The fusion cross section is found to vanish at energies around 25 MeV/u. Reduction of temperature due to dynamical preequilibrium particle emission may increase the limiting bombarding energy for disappearance of fusion considerably.

Fusion of 28Si + 68Zn, 32S + 64Ni, 37Cl + 59Co and 45Sc + 51V in the vicinity of the Coulomb barrier

Results of the measurements of fusion excitation functions and average angular momenta are presented for 37Cl + 59Co, 28Si + 68Zn, 32S + 64Ni and 45Sc + 51V, for centre-of-mass energies ranging from ∼5 MeV below to ∼10 MeV above the Coulomb barrier. These results are discussed in terms of the simplified coupled-channel model and the neutron-flow model due to Stelson. It is pointed out that simplified coupled-channel calculations including collective inelastic excitations alone do not reproduce the observed sub-barrier fusion cross section in most of the cases and that there is a need to include couplings to other channels, like transfer, in order to explain the observations. An analysis of 32S + 64Ni fusion excitation data has been performed to derive an empirical barrier distribution in order to investigate the relationship between the simplified coupled-channel model and the neutron-flow model. A simultaneous analysis of the fusion excitation function and average angular momentum seems to indicate that these two quantities are related to each other, as was pointed out by Balantekin and Reimer.

Experimental determination of the fusion-barrier distribution for the 154Sm+16O reaction.

The commonly held view that fusion excitation functions are featureless and do not provide a good test of models is challenged by high-precision measurements for the reaction $^{154}\mathrm{Sm}$${+}^{16}$O. The data yield a well-defined distribution of barrier heights using a recently proposed, novel analysis technique. The measured distribution is that expected from the quadrupole deformation of $^{154}\mathrm{Sm}$ and models using significantly different distributions cannot reproduce the measured excitation functions.

Mass and charge flow in the reaction 7.1 MeV/u197Au+63Cu

Mass-yield and angular-distribution data are presented for products from the reaction of 7.1 MeV/μ 197Au with63Cu. With help from information derived from the latter, the former are classified into components corresponding to quasielastic transfer (580±80 mb), deep-inelastic transfer plus quasifission (1300±130 mb), fusionfission (≦195 mb), and sequential fission (195±45 mb). The fusion excitation function calculated with the Dynamic Capture model standard parameter set reproduces our deduced fusion-fission cross section well. Moreover, using this cross section as well as additional published data for the same reaction system, we extract ans-wave fusion-barrier shift (“extra push”) for this system of 35±7 MeV, which is in good agreement with the systematics derived from other fusion-barrier shifts which have been reported in the literature. Lastly, support is found for the Dissipative Diabatic Dynamics model prediction that dynamically-hindered fusion trajectories are reflected into quasielastic channels.

Velocity spectra and angular distributions of evaporation residues from 32S +12C at 145 MeV.

Velocity spectra and angular and mass distributions for the evaporation residues of the $^{32}\mathrm{S}$${+}^{12}$C system at ${\mathit{E}}^{32}$S=145 MeV in the angular range 3\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}${\mathrm{\ensuremath{\vartheta}}}_{\mathit{L}}$\ensuremath{\le}12\ifmmode^\circ\else\textdegree\fi{} have been measured. In order to separate compound nucleus evaporation residues from other heavy reaction products, a kinematic analysis based on simple statistical assumptions relative to the velocity spectra was performed. The structures in the mass distribution are compared with the lilita code predictions. The fusion excitation function of the existing results is compared with theoretical models. The total reaction cross section has been extracted by means of the modified sum of differences method.

A Langevin description of the competition between fusion and deep-inelastic collisions close to the barrier

A Langevin Monte Carlo method based on the surface friction model is used to investigate the competition between fusion and deep-inelastic collisions close to the barrier. Data for the58Ni+112,124Sn systems are analyzed. The measured excitation functions for fusion are well reproduced, whereas the calculated deep-inelastic cross sections deviate somewhat from experiment. Predictions for the corresponding spin distributions are made. Contrary to what is usually assumed they are not well separated in 1-space.

Observation of mean-spin barrier bump in sub-barrier fusion of 28Si with 154Sm.

We have measured the fusion excitation function and gamma-ray multiplicities, M{sub gamma}, for the {sup 28}Si + {sup 154}Sm system. We have also measured M{sub {gamma}} for the {sup 16}O + {sup 166} Er system that leads to the same compound nucleus, {sup 182}Os. This is used to calibrate the connection between M{sub {gamma}} and the first moment of the spin distribution of the compound nucleus, {l angle}{ell}{r angle}. We find that the deduced {l angle}{ell}{r angle} in {sup 28}Si + {sup 154}Sm agrees reasonably well with theoretical expectations, and in particular exhibits the barrier bump expected when another degree of freedom is strongly coupled to the relative motion. 17 refs., 2 figs.

Sub-barrier fusion and elastic scattering in S+Ni systems.

The elastic scattering of $^{32}\mathrm{S}$ on $^{58,64}\mathrm{Ni}$ and fusion excitation functions for $^{32}\mathrm{S}$${+}^{58,64}$Ni and $^{34}\mathrm{S}$${+}^{64}$Ni have been measured at energies near the Coulomb barrier. Our results differ in several important respects from previous measurements on these systems. Coupled-channels calculations which explicitly allow for collective inelastic excitations and single-nucleon transfer reactions simultaneously reproduce the main features of the new elastic-scattering and fusion data.

A new optical model approach for heavy ion fusion

Fusion excitation functions and compound nucleus spin distributions have been investigated within the framework of the optical model using an energy dependent imaginary potential. The decrease in the strength of the imaginary potential for fusion with decreasing bombarding energy near the Coulomb barrier has been parametrised in terms of the relative kinetic energy at the interaction barrier rather than the center of mass bombarding energy, as is usually done. This results in an l-dependent imaginary potential in the optical model. With this new parametrisation, it has been possible to reproduce the measured fusion cross sections and mean square spin values of the compound nucleus in the reaction of the 16O+ 208Pb system.

Anomalous anisotropies of fission fragments for the 16O+232Th sub-barrier fusion-fission reaction.

Fission cross sections and angular distributions have been measured for the $^{16}\mathrm{O}$${+}^{232}$Th reaction at the bombarding energies from 76 to 86 MeV. The fission excitation function is rather well reproduced on the basis of the Wong model. However, the model that reproduces the enhancement observed in the sub-barrier fusion excitation function fails to account for the experimental anisotropies. It is found that the observed anisotropy is much larger than expected, and as a function of center-of-mass energy it exhibits a peak around 76 MeV with a width (FWHM) of 3.7\ifmmode\pm\else\textpm\fi{}0.5 MeV. A comparison with our previous data of $^{19}\mathrm{F}$${+}^{232}$Th reaction reveals that the anomaly is strongly related to the nuclear structure property of the projectile nucleus.