Total Kinetic Energy Loss Research Articles

Qualitative properties of the discrete random walk evolution of projectile-like ( N, Z) values on the dinuclear liquid-drop surface

A discrete random walk calculation of the evolution of the ( N, Z) distribution of projectile-like fragments from a nuclear heavy ion collision is presented. It incorporates energy conservation explicitly for each nucleon transfer, utilizing the liquid drop energies of osculating dinuclei to estimate the ( N, Z) dependence of the ground state energy of the system. The results show that energy conservation and the liquid-drop energy surface suffice to prescribe the characteristic shapes in ( N, Z) of the distributions when the transfer probabilities are defined by the total nuclear level densities; the rate at which the distribution spreads, on the other hand, is dominated by the fraction of the kinetic energy which is assumed to be dissipated by mechanisms other than nucleon transfer. Possible alternative prescriptions for the transfer probabilities are considered and shown to be qualitatively in disagreement with the observations at higher total kinetic energy loss (TKEL). Also it is shown that the overall width. σ 2 A , is less sensitive to such variations of the transfer probabilities than σ 2 Z , and how this feature is a natural consequence of the dinuclear energy surface. Finally, a residual discrepancy between calculation and observation at low TKEL values is identified as the most prominent remnant weakness of the description.

Proton transfer in quasi-elastic and deep-inelastic reactions in the systems86Kr on88Sr,90Zr and92Mo at energies close to the coulomb barrier

Reaction products corresponding to the transfer of one and several protons have been measured over a large angular range for incident energies of 380 MeV and 400 MeV in reactions of86Kr with88Sr,90Zr and92Mo. For transitions with smallQ-values (total kinetic energy loss TKEL≦10 MeV) the transfer probabilities are deduced. The magnitudes and slopes of these probabilities as function of the distance of closest approach between two nuclei are discussed. The results for single proton transfer are well described by tunneling, whereas the transfer of two and more nucleons into low lying states of the final nuclei seems to be influenced by intermediate transfer steps with larger TKEL. The data give the possibility to discuss the relation between deep-inelastic and quasi-elastic processes. The deep-inelastic data are analyzed successfully by including deformations, charge transfer and statistical fluctuations into the frictional model of Gross and Kalinowski.

Two-Dimensional Random Walk Process in Heavy Ion Collisions

Two-dimensional random walk model is applied to describe the interrelation between the energy loss and the mass transfer in heavy ion collisions. To take account of the energy loss associated with the mass transfer, we introduce the diagonal steps to the ordinary two-dimen­ sional random walk process. The average of the total kinetic energy loss Eo, as a function of the mass fragmentation, has a minimum at the initial mass fragmentation for the interaction time not very much exceeding the relaxation time. The results obtained from the present model are compared with some experimental data. They are in fairly good agreement with the experimental ones. The optimum values of the fractional energy or the distances of the neighboring sites LYE, are ~ 10 MeV for the 16 0(88 MeV) +27 Al reaction and ~ 24 Me V for the Ar(388 MeV)+' 32 Th reaction. These values of LYE are not contradictory to the assumptions inherent in the present model. We see that the smaller the magnitude of the step is, the less prominent the minima of the Eo as functions of the mass of the reaction products are. In the limit of the infinitesimal steps, i.e., the Fokker-Planck version, the minima disappear. So, in the context of the present model, the finite magnitude of the steps of the walker is suggested, together with the existence of diagonal steps.

Angular dependence of the products in the 86Kr + 166Er collision

The reaction 86Kr + 166Er is studied at a bombarding energy of 8.2 MeV/u. The results obtained in a one-particle inclusive measurement using a large-area position-sensitive ionisation chamber are studied in detail with respect to the experimental observables: nuclear charge Z, c.m. scattering angle θ and total kinetic energy loss TKEL. It is investigated which quantity is the most relevant in order to follow the evolution of dissipative phenomena. First and second moments of the angular distributions ( θ 0 and Γ θ ) are extracted as a function of energy loss using an unfolding procedure for the positive and negative scattering angles. A linear correlation between θ 0 and σ 2 z is evidenced. Using simplifying assumptions an upper limit of 310 mb is estimated for a long-living symmetric fragmentation component.

Local equilibration and diffusive phenomena in40Ar+27Al and14N+27Al heavy ion reactions

Extensive analysis of the energy dissipation and nucleon exchange has been done with heavier systems. Here we choose the two light systems40Ar+27Al (Elab=340 MeV) and14N+27Al (Elab=100 MeV) in order to study the correlation of the energy dissipation with the variance of the charge distributions as a function of total kinetic energy loss bins. Considerable energy damping is found to occur in the approach phase which cannot be explained by a simple Fokker-Planck diffusion model. Indeed a model which interprets the collision as a local equilibration followed by diffusive phenomena is more appropriate to fit the data.

The PbPb collision

The reaction 208Pb on 208Pb was studied at bombarding energies of 7.0 and 7.57 MeV/u. One-particle inclusive measurements using a large-area position-sensitive ionisation chamber delivered the kinetic energy, charge and scattering angle of the reaction products. A precise calibration of the stopping power for very heavy ions in the detector gas was performed. The measured Wilczynski diagrams show, for increasing loss of kinetic energy, an increase of the mean scattering angle. It is attributed to the dominance of the repulsive Coulomb forces with respect to the attractive nuclear forces. The element distribution for the 208Pb on 238U reaction at 7.5 MeV/u was also measured and compared to the PbPb and UU reactions. Fission probabilities are derived as a function of charge and total kinetic energy loss. The most striking result is seen in the σ z 2 versus TKEL correlation: the average rate of energy loss per nucleon exchange is abnormally large. It is shown that this behaviour is associated with the double magic closed shell character of the colliding nuclei. Nuclear structure information is extracted through a simple parametrisation.

Structure effects in dissipative collisions

An ansatz representing a generalisation of the one-body recoil formula is proposed on the basis of the total kinetic energy loss versus σ Z 2 correlation systematics observed in collisions between very heavy nuclei. It is shown that such correlations are surprisingly sensitive to the shell structure of the colliding nuclei. The mechanism of energy dissipation appears also to be strongly influenced by the structure effects.

Shape relaxation in heavy-ion collisions

It is proposed to treat the slow evolution of fragment deformations in deeply inelastic heavy-ion collisions as a dissipative process. For spheroidal fragment shapes and the corresponding driving potential we obtain expressions for mean value and variance of the deformation and for the associated scission-configuration energy fluctuations. Results for the correlation between dissipated angular momentum and total kinetic energy loss as well as for the energy spectra are in good agreement with recent data.

Charge and mass transfer in the reaction136Xe+208Pb at energies close to the coulomb barrier

Mass and charge transfer was investigated for the system136Xe+208Pb at 5.9 MeV/nucleon incident energy with aΔE —E-time of flight telescope. The angle and energy integrated cross section for the strongly damped events was found to be 510 mb, very close to the total reaction cross section. The width of the mass distribution as function of the total kinetic energy loss was measured and is compared to the width of the corresponding charge distribution. An upper limit of 1 μb has been found for processes with very large mass transfer.

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.

Evidence for a short lifetime and a long lifetime regime in the deep inelastic collisions between 40Ca and 64Ni at 182 MeV

Deep inelastic collisions have been studied in the reaction 40Ca + 64Ni at 182 MeV bombarding energy. It is clearly shown that provided the energies over the interaction barrier are similar, heavy and light systems show the same trends. The charge distributions and the total kinetic energy loss are shown to be related to the interaction time and are discussed in the framework of a diffusion model. The total cross section of the DIC process is compared with other exit channel cross sections.

Dissipation, mass exchange and the microscopic time scale of heavy-ion collisions

The time scale provided by the nucleon exchange mechanism in heavy-ion reactions is employed to study kinetic energy damping. The experimental kinetic energy lost per nucleon exchanged in Kr- and Xe-induced reactions is observed to decrease linearly with the total kinetic energy loss. These results, which are consistent with energy dissipation and nucleon exchange occuring on a similar time scale, are compared with the predictions of a one-body dissipation mechanism and a diffusion model.