Inelastic scattering of20Ne and12C on58Ni and the three-body continuum

Using beams of²⁰Ne at 291 and 392 MeV and¹²C at 300 MeV the inelastic excitation of collective modes in⁵⁸Ni has been studied with a Q3D magnetic spectrometer. In the analysis different contributions are unfolded from the spectra:1. single lines,2. the inelastic continuum,3. the three-body continuum, which mainly originates from one-nucleon pick-up to unbound states followed by the nucleon emission. Special care was taken to calculate the spectral shape and strength of this process. The population of unbound²¹Ne-states is measured in a neutron-²⁰Ne coincidence experiment. Coupled channel calculations have been performed to extract the deformation parameters for the inelastic states, including mutual excitation. For the giant quadrupole resonance 70 % of the energy weighted sum rule is found. The excitation of higher multipoles is calculated and extrapolated to higher incident energies (50 MeV/u). The importance of the in-elastic excitation as a “doorway process” to more complex interactions is discussed. It is found that especially the excitation of the projectile (²⁰Ne) takes a large fraction (20–50 %) of the incoming flux in the first step.     

Influence of left-right asymmetry degrees of freedom in self-consistent calculations of 20Ne

Within a constrained Hartree-Fock calculation we investigate the effects of left-right asymmetric degrees of freedom associated with the channel ¹⁶O + ⁴He ? ²⁰Ne. We find a large softness of ²⁰Ne against octupole deformation. The optimal solution after restoration of the parity by means of a projection shows a pronounced ¹⁶O + ⁴He clustering. A generator coordinate calculation along the collective path confirms this conclusion. Once center-of-mass motion effects are taken into account a good agreement with experiment is found.     

The16O(α, γ)20Ne direct capture reaction at low energies

The¹⁶O(α, γ)²⁰Ne direct capture cross section has been calculated in a microscopically founded cluster model which reproduces simultaneously both the correct binding energies and the deformations of the²⁰Ne bound states. Theα+¹⁶O scattering states are derived from a microscopically derived local potential. The astrophysicalS-factor is found to increase linearly with energy in the energy rangeE _cm≈0.4–2 MeV and might therefore be determinable experimentally.     

Microscopic calculation of friction in heavy ion reaction using linear response theory

We present a realistic calculation of the frictional coefficients for²⁸Si+²⁰Ne system using the two-center shell model on the basis of the linear response theory. Adopting the center separationR and the deformationδ as collective variables we study the dependence of frictional coefficients γ _RR , γ _Rδ and γ_δδ on those variables, for various values of the neck parameter?, the temperatureT and the smearing widthΓ. The direct application of the linear response theory to the two-center potential gives non-vanishing friction for the simple translational motion of the two fragments even when they are far apart. A method to avoid this energy dissipation is proposed and is used in the calculation. Results show that the form factor of the frictional force is surface-peaked and the peak becomes lower as the prolate deformation or neck formation increases. Temperature dependence is mild, but is not negligible. We compare our γ _RR and γ_δδ with other models.     

Energy dissipation in light heavy ion reactions

Analysis of the energy dissipation for light heavy ions (¹²C,¹⁴N,¹⁶O,²²Ne) reactions has been attempted. Classical models with or without a friction term and the diffusion model have been compared to the data. Fragmentation and prompt collective excitation have been considered also.     

Dynamical effects on the way to fusion of very heavy nuclei

The central collision of ⁴⁰Ar and ²⁰⁸Pb is studied considering the ellipsoidal deformations and isovector dipole mode of motion in the approaching phase. The collective energy dissipation is suggested to originate from the Fermi surface deformation which is treated as a kinematically independent mode of motion within the canonical Lagrange-Rayleigh dynamics. The possible extensions of the approach are discussed. The potential energy surface, calculated using the generalized (folded) surface potential, is studied. The saddle point in the potential energy surface lying at the border of strongly deformed compact configurations is located. The potential energy at this point is about 10MeV smaller than that of the ions touching each other in the spherical shape. The examination of trajectories followed by the system in its evolution shows that the inertia forces strongly hinder the motion of ions along the potential energy valley. The collective energy dissipated during the approach is found to be smaller than the difference in the potential energies at saddle point and at the touching configuration of unpolarized ions.     

Langevin description of the charge distribution of fragments originating from the fission of excited nuclei

The charge distribution of fragments originatingfrom the fission of the ²³⁶U compound nucleus is calculated within a stochastic approach based on Langevin equations. The elongation coordinate, the neck-thickness coordinate, and the charge-asymmetry coordinate are chosen as collective variables. The friction parameter of the charge mode is calculated on the basis of two nuclear-viscosity mechanisms, that of one-body and that of two-body dissipation. It is shown that the Langevin approach is applicable to studying isobaric distributions. In addition, the charge distribution in question is studied as a function of the excitation energy of the compound nucleus and as a function of the coefficient of two-body viscosity.     

Two particle — two hole mixing in Hartree-Fock calculations

The constrained Hartree-Fock theory is used for studying the stability of the solutions against two particle — two hole excitations. Quadropole and hexadecapole deformation are imposed on the Hartree-Fock equations to get the true energy minimum and the equilibrium shape. Energy corrections are calculated using second-order perturbations and complete diagonalization. Applications are made to the ²⁰Ne and ²⁸Si nuclei.     

Nuclear dissipation with residual interactions studied by means of the Mori formalism

We apply correlation function techniques to the calculation of nuclear friction within the framework of a linear response theory. We make use of the fluctuation dissipation theorem to relate the response function to the correlation function which is evaluated by exploiting projection operator techniques. We go beyond the one-body dissipation approximation in the sense that we have taken into account the decay of particle-hole excitations into more complicated configurations. A rather simple formula for the frequency and temperature dependence of the friction coefficient is derived which we have applied to the high energy fission of²³⁸U. The friction coefficients for deformations around the first and second minima of the fission barrier have been calculated using this approach.     

Coupling of one and two quasiparticles to a Bohr-Mottelson core in195,196,197,198Hg

A new model for coupling the motion of particles to that of a quadrupole collective core with rotations andβ andγ vibrations is proposed. The Hamiltonian describing the core is obtained by quantising the classical Hamiltonian associated with the quadrupole degrees of freedom. The inertial parameters and the deformation energy surface are determined microscopically. The spherical shell model particles interacting among themselves by pairing are coupled to the core by aλ ²-pole (λ=0, 2, 4) potential. The theory is applied to^195–198Hg. The predicted results agree very well the experimental data. A comparison of the present model to the other formalism is also given.     

Comparison of the fusion reactions12C+20Ne and16O+16O near the Coulomb barrier

The partial cross sections of heavy residual nuclei produced in the heavy ion fusion of¹²C+²⁰Ne have been measured atE _c.m.=6–15 MeV viaγ-ray spectroscopy with a Ge(Li) detector. Windowless and recirculating gas target systems have been used. The dominant residual nuclei are²⁴Mg,²⁷Al,²⁸Si,³⁰Si,³⁰P and³¹P, which arise from two- and three-body breakups in the exit channels. The observed excitation functions are smooth in their energy dependence and give no indications for the existence of pronounced resonance structures, in contrast to theoretical predictions. The Coulomb excitation of²⁰Ne served as an intrinsic calibration standard in the determination of absolute partial and total fusion cross sections. The same experimental set-up was also used in the reaction studies of¹⁶O+¹⁶O atE _c.m.=7–14 MeV, going through the same compound nucleus³²S at similar excitation energies. The observed energy dependence in the excitation functions is in good agreement with previous work. The total fusion cross section agrees fairly well with two sets of values reported previously, but deviates significantly from other reported absolute cross section values. The relative evaporation distributions of the residual nuclei are similar for both heavy ion reactions. However, the ratio of their total fusion cross sections deviates from model predictions and suggests that compound nucleus formation does depend on the microscopic structure of the colliding nuclei in the entrance channel. From the observed energy dependence of the above ratio, particularly at subcoulomb energies, geometrical effects in the entrance channel (due to deformed and spherical nuclei) appear to be weak. The astrophysical aspects of the data in the context of late stellar nucleosynthesis are discussed.     

The angular momentum dependence of correlations in the ground state rotational spectra of20Ne and22Ne

Multi-Configuration-Hartree-Fock (MCHF) calculations with angular momentum projection before the variation of the internal degrees of freedom have been performed for the nuclei²⁰Ne and²²Ne. This procedure yields different correlated intrinsic states for the different members of a rotational band. Thus the angular momentum dependence of correlations has been studied. Experimentally, the ground state spectra of²⁰Ne and²²Ne show properties similar to the phase transitions observed in some rare earth nuclei which have been well reproduced through the present calculations. The calculated spectra andBE2-values show a significant improvement compared to the ones obtained by variation before the angular momentum projection is effected.     

Statistics of the energy dissipation rate and local enstrophy in turbulent channel flow

Using high-resolution direct numerical simulations, the height and Reynolds number dependence of high-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully developed turbulent channel flow. The statistics are studied over a range of wall distances, spanning the viscous sublayer to the channel flow centerline, for friction Reynolds numbers Re_τ=180 and Re_τ=381. The high resolution of the simulations allows dissipation and enstrophy moments up to fourth order to be calculated. These moments show a dependence on wall distance, and Reynolds number effects are observed at the edge of the logarithmic layer. Conditional analyses based on locations of intense rotation are also carried out in order to determine the contribution of vortical structures to the dissipation and enstrophy moments. Our analysis shows that, for the simulation at the larger Reynolds number, small-scale fluctuations of both dissipation and enstrophy show relatively small variations for z⁺?100.     

Pion and photon bremsstrahlung in a heavy ion reaction model with friction

Based on a classical dynamical model of nuclear motion with a velocity dependent friction force we calculate pionic and electromagnetic bremsstrahlung emitted in heavy ion collisions with bombarding energies between 20 and 84 MeV/n. For arbitrary projectile-target combinations and with a fixed value of the only parameter of the model, the friction coefficientκ, our calculations reproduce the observed beam energy and target mass dependence for pions. The gamma yields, calculated with the same value ofκ, reproduce the measured dependence of the cross-section on energy and target mass, but underestimate the published data by a factor two. This is a good agreement in view of the discrepancies between different experimental groups.     

Studies on strongly damped components in relatively light heavy ion reaction systems

Strongly damped components have been studied in relatively light heavy ion reaction systems;²⁰Ne(E _lab=93, 120 and 146MeV)+⁵⁰Cr,²⁰Ne(E _lab=146MeV)+⁵⁴Cr and²⁰Ne(E _lab=146MeV)+⁹²Mo,¹⁰⁰Mo. The kinetic energy, angular and charge distributions have been observed for those products. The yields of symmetric-mass-splitting products for²⁰Ne+⁵⁰Cr were found about three times larger than those for²⁰Ne+⁵⁴Cr. There was also observed a similar difference in the cross sections of the symmetric-mass-splitting products between²⁰Ne+⁹²Mo and²⁰Ne+¹⁰⁰Mo reactions. In order to explain the bombarding energy dependence of the cross sections of symmetric-mass-splitting products by the transport theory, it was found necessary to assume that the mean life of the composite nucleus was dependent on the bombarding energy. However, the target isotope dependence of the cross sections could not be explained by such an assumption. They could be partly explained by fission calculations.     

DSA lifetime measurements in21Ne at high recoil velocity

States in²¹Ne up to 5 MeV excitation energy have been populated using the inverted reaction²H(²⁰Ne,pγ). The Doppler shift attenuation (DSA) analysis of thepγ coincidence spectra taken in a Ge(Li) detector at 45° and 135° and an annular silicon surface barrier detector near 0° yielded the lifetimes of 8 states in²¹Ne. Due to the large recoil ofπ _i/c～ 4% three new lifetimes were determined for the short lived levels at 2.80, 4.68 and 4.73 MeV, namely 10±4 fs, 16±4 fs and 10±4 fs, respectively. The results are compared with rotational and shell model calculations.     

The influence of correlations on the odd-mass Nuclei21Ne and25Mg

Excitation energies and electromagnetic properties of the low energy spectra of²¹Ne and²⁵Mg have been calculated using the Multi-Configuration-Hartree-Fock (MCHF) model. BothT=0 andT=1 pairing correlations are found to be simultaneously important in those odd mass nuclei. Furthermore, though axial symmetry was requested, quite good agreement with the experimental data is reached.     

Reaction cross sections and radii of A=17 and A=20 isobars

Reaction cross sections and root-mean-square (rms) radii of A=17 and A=20 isobars are calculated by using a simplified Glauber model and spherical and deformed Hartree-Fock (HF) wave functions. The small separation energy effect is discussed on the reaction cross sections of A=17 isobars and possible proton halo in ¹⁷Ne by using modified spherical HF wave functions. The calculated rms mass radii of A=20 isobars are increased appreciably by the deformation effect and show a similar irregular pattern as a function of the isospin to that of the observed radii.