Fusion Reaction Cross Sections Research Articles

Experimental studies of fusion and fragmentation of fullerenes

Energy dependences of the fusion cross section for the collisions , and have been measured. Fusion occurs for energies above a sharp energetic barrier . The fusion barrier lies in the region between 60 and 80 eV and increases with increasing number of atoms participating in the collision. For energies beyond the barrier the fusion reaction cross section increases with collision energy to a maximum value and then decreases very rapidly. The highly excited fusion compound decays on the experimental timescale, and the resulting fragmentation pattern has been studied as a function of collision energy. For energies up to 200 eV the fragmentation behaviour can be modelled in terms of successive evaporation of units from the hot fusion product. At higher energies this model breaks down and another fragmentation mechanism has to be invoked. The overall results are in very good agreement with quantum molecular dynamics simulations and the predictions of simple phenomenological fusion models.

Generalized coulomb barrier transmission coefficient for solar neutrino and astrophysical problems

For astrophysical calculations, it is customary to extrapolate higher-energy (≳20keV) data using the Gamow transmission coefficient in estimating the nonresonance nuclear fusion reaction cross sections σ(E) for charged particles at low energies (<20 keV). We present a general extrapolation method based on a more realistic Coulomb barrier transmission coefficient, which can accommodate simultaneously both nonresonance and resonance contributions.

Improved Coulomb Barrier Transmission Coefficient for Nuclear Fusion Cross Sections

Higher energy (≳20 keV) data are customarily extrapolated by using the Gamow transmission coefficient to estimate the nonresonance nuclear fusion reaction cross sections σ(E) for charged particles at low energies (<20 keV), which are needed for fusion energy production and astrophysical calculations. A general extrapolation method is presented based on a more realistic Coulomb barrier transmission coefficient that can accommodate simultaneously both nonresonance and resonance contributions.

Elastic scattering and fusion calculations for 16O+63,65Cu.

Coupled channels calculations that simultaneously predict elastic scattering and fusion reaction cross sections are compared with the corresponding available measurements for $^{16}\mathrm{O}$${+}^{63,65}$Cu collisions. The calculations can reproduce the main features of the fusion and elastic scattering data sets but only separately by using significantly different ion-ion potentials.

Time independent description of thet(d, n)? fusion reaction in the presence of a muon

We describe the (α n μ)—(d t μ) continuum above and below thed+(t μ)1s threshold using theR-matrix formalism. The continuum is explicitly constructed in an adiabatic approximation, and the asymptotic phase shifts and amplitudes in all channels are obtained. The energy eigenstates are used to compute the fusion reaction cross section for in-flightd+(t μ) fusion, and fusion reaction rates involving transitions from thed+(t μ)1s continuum to be below threshold continuum states.

Calculations of complete fusion, incomplete fusion, and direct reaction cross sections for deuteron-induced reactions.

Two techniques that enable us to calculate cross sections of complete fusion and various incomplete fusion reactions within the framework of direct reaction theories are combined to calculate cross sections of various reactions initiated by d${+}^{93}$Nb with two incident energies of 15 and 25.5 MeV. It is shown that the predicted cross sections agree well with existing experimental data. This study provides a rather critical test of the two techniques used by examining the consistencies of the predictions of the total incomplete fusion plus direct reaction cross sections and also the regions where these reactions predominantly take place. One of these techniques can be easily used with any optical model code to obtain compound nucleus cross sections (excluding breakup and other direct reaction cross sections) for the Hauser-Feshbach calculations involving deuteron-induced reactions.

Cross Section for Cold Deuterium-Deuterium Fusion

Conventional estimates of cold deuterium-deuterium (D-D) fusion rate and branching ratio may not be reliable, since they are based on an extrapolation of the reaction cross sections at higher energies (≳ 4 keV) to lower energies where no direct measurements exist. Recent results of indirect measurements of the cross section indicate that the extrapolation method may not be valid at low energies. Direct measurements of the D-D fusion reaction cross section at low energies are suggested.

Effects of electron screening on low-energy fusion cross sections

The effects of electron screening on the low-energy cross sections of nuclear fusion reactions of astrophysical interest have been studied within the Born-Oppenheimer approximation using a simplified model. These studies indicate that a significant enhancement of the cross sections can occur already at beam energies, which are about a factor 100 higher than the electron binding energies. Cross sections near such energies can now be measured, in some cases, and several examples are discussed. For an understanding of the low-energy data as well as for a reliable extrapolation of the cross sections (for bare nuclei) to lower energies, the effects of electron screening must be well understood.

Enhancement of the subbarrier fusion reaction due to neck formation

Subbarrier fusion reaction cross sections have been calculated based on the idea of the neck formation. Barrier heights for the no neck configuration and for the neck formed one are calculated by the Krappe-Nix-Sierk model and the transition between them are calculated by the perturbation formula. The relative motion between two nuclei is treated by the semiclassical model introducing the imaginary time. The formulation was applied to the fusion of identical nuclei and for six systems we examined we got a good reproduction of the data. Our calculation shows that transfer of about one tenth of the incident flux to the neck formed configuration is necessary and enough to explain the experimental data.

Fusion reactions of polarized deuterons.

Polarized and unpolarized d+d..-->..n+ /sup 3/He fusion reaction cross sections in the center-of-mass energy region of 20-150 keV are calculated in a distorted-wave Born approximation. The calculated unpolarized cross sections and the anisotropy of the angular distributions are within 20% of the experimental data. The polarized cross sections are found to be --7.7% of the unpolarized ones despite the inclusion of the D-state component in /sup 3/He. This shows that the idea of a ''neutron-lean'' reactor may still be feasible. This result is consistent with the partial-wave analysis of the tensor analyzing power in the reaction d(d/sub pol/,p)t, but contrary to the findings of a recent resonating-group calculation.

Fusion and peripheral reactions in the systems 16O + 148,152Sm at sub-barrier energies

Cross sections for fusion and peripheral reactions in the sub-barrier region obtained with the coupled-channel and equivalent-spheres methods are compared for the systems 16O + 148,152 Sm. A barrier-like real potential plus a residual surface-imaginary potential is introduced as an alternative approach which allows the simultaneous fit of elastic, inelastic, fusion and peripheral reaction cross sections.

Influence of neck formation on heavy ion subbarrier fusion.

We calculate the effect of the neck degree of freedom on subbarrier fusion reaction cross sections. The potential energy and mass tensor are calculated on the basis of a two-dimensional representation of the liquid drop model. The WKB and Hill-Wheeler approximations are used to calculate the tunneling amplitudes for motion along the direction of the neck size degree of freedom. The resulting cross section for collisions between two identical Ni isotopes show a marked enhancement at low energies compared with the standard one-dimensional radial penetration calculations.

Nuclear structure effects in the fusion of calcium isotopes.

Fusion reaction cross sections are calculated for the /sup 40/Ca+ /sup 40,44,48/Ca systems taking into account their low lying collective excitations. The remaining differences with the low energy data are interpreted as being due to coupling effects of transfer reaction channels which increase strongly for the /sup 40/Ca+ /sup 44,48/Ca cases. Estimates for the observable transfer cross sections are given.

Energy dependence of fusion and reaction cross sections in the 9Be + 12C system

Angular distributions of protons, deuterons. tritons and α-particles were measured for the system 9Be + 12C at lab energies between 12 and 27 MeV. The compound nucleus model with level densities calculated according to the Gilbert-Cameron formula describes satisfactorily the measured proton, deuteron and triton data. In the α-particle spectra contributions from other processes seem to be present. In the analysis the fusion cut-off angular momentum was adjusted at each energy in order to reproduce correctly the proton, deuteron and triton channels. From this analysis the fusion cross section was determined as a function of the energy. The results were compared with fusion and total reaction cross section values calculated from a potential model with the real part of the interaction potential obtained from the double folding procedure of Satchler.

Reaction cross sections forC12+C12

The yields of the eleven most abundant nuclides produced in the $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$ reaction were determined in the energy range from 14-31 MeV (c.m.) via $\ensuremath{\gamma}$-ray techniques. Several reaction channels, including a few which involve only light-particle emission, show strong structure. Some of these anomalies are very narrow, having widths \ensuremath{\lesssim} 250 keV (c.m.). The $3\ensuremath{\alpha}$ evaporation cross section, as well as the yield of $^{12}\mathrm{C}$ via direct inelastic scattering, is determined. Further information is presented on the nature of a process leading to anomalously large $\ensuremath{\alpha}$-particle yields from the $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$ reaction at low energies. The strong gross-structure features of the fusion and total reaction cross sections are discussed in the context of the optical model, and also with reference to the limiting angular momentum for fusion. The latter analysis leads to some insight into the origin of the gross structure, but also suggests a striking correlation between the fusion cross section and the extended ground state band of $^{24}\mathrm{Mg}$ at high energies. This correlation, if it is not coincidental, has interesting consequences with regard to the behavior of $^{24}\mathrm{Mg}$ at high angular momentum and energy.NUCLEAR REACTIONS Complete fusion, $^{12}\mathrm{C}$+$^{12}\mathrm{C}$, ${E}_{\mathrm{c}.\mathrm{m}.}=14\ensuremath{-}31$ MeV, measured $\ensuremath{\sigma}(E)$ for production of 11 nuclides; $\ensuremath{\gamma}$ measurement, Ge(Li) detectors and natural target; deduced total fusion, $3\ensuremath{\alpha}$ evaporation, and direct inelastic scattering $\ensuremath{\sigma}$; deduced limiting angular momenta for fusion; discussed anomalous $\ensuremath{\alpha}$-particle yield from $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$ at low energies.

Dynamical properties of heavy-ion reactions deduced from coupled-channels calculations

The distribution of the total reaction, fusion, and direct reaction cross section in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{l}}$ space are studied using coupled-channels calculations. These calculations also provide information about such quantities as the polarization of highly excited states, the energy dependence of the fusion cross section, and the dependence of the total kinetic energy loss on the spins of the excited states.NUCLEAR REACTIONS Model coupled-channels calculations; deduced ${\ensuremath{\sigma}}_{R}$, ${\ensuremath{\sigma}}_{F}$, ${\ensuremath{\sigma}}_{D}$, polarization; dependence on angular momentum transfer and interactions.

Reaction cross sections forO16+C12

The yields of the eleven most abundant nuclides produced in the $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$ reaction were determined in the energy range from 14-31 MeV (c.m.) via $\ensuremath{\gamma}$-ray techniques. Several reaction channels, including a few which involve only light-particle emission, show strong structure. Some of these anomalies are very narrow, having widths \ensuremath{\lesssim} 250 keV (c.m.). The $3\ensuremath{\alpha}$ evaporation cross section, as well as the yield of $^{12}\mathrm{C}$ via direct inelastic scattering, is determined. Further information is presented on the nature of a process leading to anomalously large $\ensuremath{\alpha}$-particle yields from the $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$ reaction at low energies. The strong gross-structure features of the fusion and total reaction cross sections are discussed in the context of the optical model, and also with reference to the limiting angular momentum for fusion. The latter analysis leads to some insight into the origin of the gross structure, but also suggests a striking correlation between the fusion cross section and the extended ground state band of $^{24}\mathrm{Mg}$ at high energies. This correlation, if it is not coincidental, has interesting consequences with regard to the behavior of $^{24}\mathrm{Mg}$ at high angular momentum and energy.NUCLEAR REACTIONS Complete fusion, $^{12}\mathrm{C}$+$^{12}\mathrm{C}$, ${E}_{\mathrm{c}.\mathrm{m}.}=14\ensuremath{-}31$ MeV, measured $\ensuremath{\sigma}(E)$ for production of 11 nuclides; $\ensuremath{\gamma}$ measurement, Ge(Li) detectors and natural target; deduced total fusion, $3\ensuremath{\alpha}$ evaporation, and direct inelastic scattering $\ensuremath{\sigma}$; deduced limiting angular momenta for fusion; discussed anomalous $\ensuremath{\alpha}$-particle yield from $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$ at low energies.

Complete Fusion Nuclear Reactions Induced by Krypton Ions. Effective Threshold and Minimum Distance of Approach for the ReactionsCd116+Kr84andGe72+Kr84

Effective energy thresholds have been measured for the cross sections of complete fusion reactions induced by krypton ions on ${\mathrm{Cd}}^{116}$ and ${\mathrm{Ge}}^{72}$. They show that the minimum distance of approach for the reaction is shorter than with lighter projectiles and corresponds to a Coulomb repulsion at a distance of ${r}_{0}({{A}_{1}}^{\frac{1}{3}}+{{A}_{2}}^{\frac{1}{3}})$ fm with ${r}_{0}=1.32$ fm instead of 1.45 fm.

Thermonuclear Reaction Waves at High Densities

The initiation, development, and propagation of thermonuclear reaction waves in a solid density deuterium-tritium plasma are presented. Physical effects due to thermonuclear reactions, heat conduction, electron-ion equilibration, bremsstrahlung, and fluid dynamics are contained in the analysis. The qualitative behavior of the physical variables is discussed and solutions of the equations are obtained by employing finite difference numerical techniques. Due to plasma properties and the form of the fusion reaction cross section, important differences exist between fusion and chemical detonation waves. Threshold ignition energy is found for simple geometries and the complete history of the development of the wave is studied. The structure of a fully developed fusion reaction wave is presented. Finally, the thermonuclear energy yield from small D-T pellets is presented.