Average polarization in deep inelastic collisions of heavy ions

The polarization averaged over many quantal channels is analyzed. The analytical expressions for probability distribution function and average polarization are derived in cases of pure statistical reactions as well as the planar ones.     

A one-dimensional statistical model of friction in deeply inelastic heavy ion collisions

We use the semiclassical approximation for the relative motion (which is simplified and taken to be one-dimensional), neglect other collective degrees of freedom, and describe the coupling between relative motion and intrinsic degrees of freedom by a random-matrix model. This leads to an explicit expression for the friction coefficient. Numerical calculations show qualitative agreement with the data.     

Cross sections of inelastic processes in collisions between relativistic structured heavy ions and atoms

A nonperturbative method is developed for the calculation of cross sections of inelastic processes in collisions between structured high-charge heavy ions moving at relativistic velocities and atoms. By structure ions are meant partly stripped ions consisting of an ion nucleus and a number of bound electrons which partly compensate the core charge and form the electron “coat” of the ion. The single ionization cross section of hydrogen atom and single and double ionization cross sections of helium atom are calculated. It is demonstrated that the inclusion of the extent of ion charge may bring about a marked variation of the respective cross sections compared to ionization by point ions of the same charge and energy.     

Polarization effects in nucleus-nucleus collisions: (II). Elastic and inelastic cross sections

We solve the coupled-channel equations based on the perturbed stationary-state approach in the rotating coordinate frame for heavy-ion collisions. We propose a method for treating a large number of coupled equations by a truncation in the space spanned by perturbed states. Polarization effects due to the coupling to high-lying collective states are discussed for ¹²C + ¹²C scattering.     

Large-angle scattering of heavy ions: (II). General structure of inelastic cross section

Closed-form expressions are derived for the differential cross section of inelastic heavy-ion scattering at large angles. The inelastic transition amplitude given by the distorted-waves theory for excitation of low-lying collective states is evaluated by an extension of analytic methods developed in the preceding paper for elastic large-angle scattering. The very close relation between the inelastic and elastic cross sections is displayed. In particular it is shown that the angular distributions have a universal form, and that the backward-angle inelastic excitation function has, aside from a slowly varying overall energy dependence, an oscillatory gross structure of diffractive origin which is nearly identical to that of the elastic excitation function, irrespective of the physical mechanism involved.     

The critical distance in collisions of heavy ions

There is a large discrepancy in published values of the critical distance in heavy-ion collisions. We have recalculated the critical distance by a more accurate method for symmetric collisions of point nuclei as a function of Z. The reasons for the discrepancy are discussed.     

Excitation energy partition in deeply inelastic collisions between40Ar and Ag at 27 MeV per nucleon

The dynamics of the two partners produced in dissipative collisions has been experimentally studied for the system⁴⁰Ar + Ag at 27 MeV per nucleon. Primary masses of the fragments can then be calculated; the excitation energy partition between the two fragments is derived from the number of particles evaporated by each fragment. We found that this division evolves from equipartition to a repartition close to thermal equilibrium in the excitation energy range 300–350 MeV or interaction times 5-10×l0^?22 s.     

Polarization effects in nucleus-nucleus collisions: (I). Distortion of nuclear intrinsic states

Polarization effects due to the interaction between two complex nuclei are investigated in the rotating frame whose z-axis lies in the direction connecting the two nuclei. This allows one to define intrinsic states of the dinuclear system including these polarization effects. We present here a modified coupled-channel formalism whose basis states are these intrinsic states. Results on energy shifts and particle density and B(E2) value modifications in a schematic microscopic model are presented and compared with those of the phenomenological surface-vibrational model. In the case of the rotational model the influence of the nucleus-nucleus interaction on the directivity of nuclear symmetry axes is also analyzed.     

Large-angle scattering of heavy ions: (I). General structure of elastic cross section

Closed-form expressions are derived for the differential cross section of elastic heavy-ion scattering at large angles. The derivation is based on the general form of the elastic partial-wave S-matrix in real l-space. By a generalization of analytic techniques developed in earlier work, it is shown that the large-angle scattering cross section has a universal structure involving combinations of Bessel functions and the Fourier transforms of the rapidly varying parts of the S-matrix, irrespective of their dynamical origin. Anomalous large-angle scattering is attributed to deviations of the S-matrix from its “normal strong-absorption profile”, and general conditions for backward-angle enhancement are given. Our model-independent formulation provides the framework for an “inductive” method of analyzing experimental angular distributions and excitation functions aimed at identifying, as uniquely as possible, the dynamical mechanisms that operate in large-angle heavy-ion scattering. Extensions of the formalism to inelastic scattering and transfer reactions, and applications of the analytic method, will be described in subsequent papers.     

Unified model of deep inelastic heavy ion collisions: Collectivity and statistics

Deep inelastic heavy ion collisions are viewed as multi-step processes described in terms of coupled-channel equations. Including both statistical and collective excitations, it is shown that in the semi-classical limit the coupled-channel equations reduce to a classical equation of motion for the relative coordinate with frictional force, master equation for the intrinsic occupation probabilities, and a damped forced harmonic oscillation for the mean deformation of the ions. We therefore succeed in unifying the approaches of Agassi et al. and Broglia et al., and in justifying the phenomenological models of Deubler et al. and Abul-Magd et al.     

Can perturbation theory of nuclear friction explain the rapid and strong energy damping,found in deeply inelastic heavy ion collisions?

It is shown that the lowest order perturbation theory for the excitation of each single particle state due to the time dependent variation of the combined two centers s.p. potential is a promising candidate to account for most of the energy loss occuring in the deeply inelastic collisions of heavy ions. The linear response theory of nuclear friction is at T=0 a special case of the simpler perturbation theory. Important improvements are presented.     

The competition between fusion-fission and deeply inelastic reactions in the medium mass systems

The competition between fusion-fission and deeply inelastic reactions in the Cl + Ni system has been studied by investigating the exit channelQ-value dependence of theZ-distributions of fission-like fragments. TheZ-, kinetic energy- and angular distributions of the fission-like fragments produced in the³⁷Cl +⁶⁴Ni system atE _lab=170, 186 MeV and in the²⁸Si +⁷⁴Ge system atE _lab=176 MeV have been measured by counter telescopes. TheZ-distribution of the³⁷Cl +⁶⁴Ni system was found to be essentially the same as that of the³⁵Cl +⁶²Ni system at the same bombarding energy. It is shown that this result can not be explained by the statistical fusion fission model but is consistent with a deeply inelastic model. A systematic study of the fission-like phenomenon in this mass region indicates that the maximum angular momenta for fusion reactions as well as the minimum angular momenta for DIC can be reproduced by the Bass model in the sliding limit (f=1.0) while the maximum angular momenta for fully energy-damped deeply inelastic reactions are governed by the strong interaction radius as predicted by the successive critical distance fusion model. The significance of these results are discussed.Communicated by V. Metag     

The coulomb glory effect in collisions of antiprotons with heavy ions

The Coulomb glory effect in the back scattering of antiprotons with energies of from 100 eV to 3 keV from a bare nucleus of uranium and from uranium ions with closed shells is considered in terms of nonrelativistic and relativistic quantum theory. The appearance of Coulomb glory in collisions with multiply charged ions is caused by nucleus charge screening by filled electron shells. In scattering from a bare nucleus, the effect appears because of the screening properties of the vacuum polarization potential.     

Elaborate treatment of the inelastic collisions of positrons with alkali atoms and alkaline-earth positive ions using a restricted coupled-static approximation

Summary We present the results of a very elaborate investigation of the inelastic collisions of positrons with the ground states of the first four alkali atoms (³Li,¹¹Na,¹⁹K and³⁸Rb) and their electronically resemblant alkaline-earth positive ions,i.e. ⁴Be⁺,¹²Mg⁺,²⁰Ca⁺ and³⁹Sr⁺, respectively, using a restricted coupled-static approximation in which the reactance matrices are adjusted to be symmetrical. Our interest is concentrated on the calculation of the total elastic and positronium formation cross-sections and their behaviour in the low-energy region (below 10 eV for the atoms) or the regions above the positronium formation thresholds (when the ions are considered). Our results are the most accurate cross-sections expected from the approximation employed. They reveal, within their limits, the most important characteristics of these cross-sections and provide us with a satisfactory comparison between the main features of positron-atom and positron-ion collisions. Present address.     

Velocity effects in atomic and molecular collisions: Study by coherent transients

The effect of translational velocity of active atoms and molecules on the properties of photon echo is investigated using the technique of coherent transient processes. A variation in the photon-echo decay with a frequency detuning of the excitation radiation relative to the center of the vibrational-rotational transition 0 ? 1 ν₃ R(4, 3) is observed in a mixture of ¹³CH₃F with atomic buffers. The results are interpreted using the dependence of the echo decay rate on the magnitude of the translational velocity of active particles. The dependence of the relaxation matrix on the direction of the velocity of active atoms results in a new phenomenon of the collision-induced echo, which is investigated at the transition 0 ? 1 ¹⁷⁴Yb in mixtures with atomic buffers.     

Boson expansions and quantization of time-dependent self-consistent fields (I). Particle-hole excitations

Two concrete methods are presented for quantizing the time-dependent Hartree equations in terms of boson operators. The first is the well-known infinite boson expansion analogous to the Holstein-Primakoff representation of angular momentum operators. The second, a new development, consists of finite boson quadratic forms, and is analogous to the Schwinger representation of angular momenta. In each case, a physical boson subspace can easily be constructed within which the full fermion dynamics is exactly duplicated. It therefore follows that quantization of the time-dependent Hartree equations, including all degrees of freedom, retrieves the exact many-body problem. The discussion in this paper is limited to particle-hole excitations of an N-particle system. A generalization to one-nucleon transfer processes on the N-particle system is also given in terms of ideal odd nucleons, but this brings in infinite expansions.     

Proton reactions with 17O: (I). Elastic and inelastic scattering reactions

Differential cross sections for the elastic and inelastic scattering of protons by ¹⁷O have been measured at 8.62, 9.45 and 10.5 MeV. Excitation functions at 110° and 140° were measured from 8.5 to 10.5 MeV. The elastic scattering angular distributions were used to find optical model parameters for the scattering. The angular distributions of inelastically scattered protons were analysed using the effective interaction method of Satchler, and also with the microscopic theory of Geramb and Amos.     

Dynamics of ionization mechanisms in relativistic collisions involving heavy and highly-charged ions

The dynamics of mechanisms associated with the ionization of inner-shell electrons in relativistic collisions involving heavy and highly-charged ions is investigated within a nonperturbative approach formulated explicitly in the time domain. The theoretical treatment is based on the exact numerical solution of the time dependent Dirac equation for two Coulomb centers on a lattice in momentum space. We present results for ionization in encounters between 100 MeV/u Au⁷⁹⁺ projectile ions impinging on a hydrogen-like uranium target. By directly visualizing the collision dynamics we identify a new ionization mechanism in which electrons are emitted from the internuclear region preferentially in the transverse direction with respect to the projectile trajectory. A striking characteristic of this ionization mechanism is that the velocity of the electron is higher than the projectile velocity. Received 26 June 2001 and Received in final form 27 November 2001