A. Winther

Channel-coupling effects in heavy-ion fusion reactions

Abstract A coupled-channel framework for fusion reactions is considered where an ingoing-wave boundary condition allows the effect of strong coupling in the barrier region to be studied. It is shown analytically within the sudden limit and, more generally, with model calculations that the couplings to reaction channels act to enhance the transmission through the barrier at low energies. This appears to be a natural mechanism for explaining the relatively large sub-barrier heavy-ion fusion cross sections which have recently been observed.

Relativistic coulomb excitation

Abstract Coulomb excitation of both target and projectile in relativistic heavy ion collisions is evaluated including the lowest order correction for the deviation from a straight line trajectory. Explicit results for differential and total cross sections are given in the form of tables and figures.

The evidence of the ion-ion potentials from heavy ion elastic scattering

Abstract From classical perturbation theory it is concluded that elastic scattering mainly determines the real part of the optical potential in a point slightly inside the distance of closest approach for a trajectory leading to the rainbow angle. With this rule the emperical evidence is compared to some ion-ion potentials given in the litterature. An empirical expression is given for the potential as well as for the radius of the Coulomb barrier.

A study of Q-value effects on barrier penetration

Abstract Coupled-channel equations for barrier penetration problems are solved analytically to show the effects which finite Q-values have on the total transmission function.

On the absorptive potential in heavy ion scattering

Abstract A preliminary investigation of the nuclear imaginary potential to be used for the analysis of elastic scattering data of heavy ions is presented. The derivation is carried out in the framework of the semiclassical description. The resulting potential is angular momentum independent and shows two components. A long range part due to transfer reactions and a short range part due to nuclear inelastic scattering. Coulomb excitation has not been taken into account. Simple closed expressions are derived for the transition amplitudes associated with the transfer and inelastic processes, including the Q -value dependence which can be used for the analysis of reaction data.

Transient fields acting on heavy ions during slowing-down in magnetized materials

Abstract This paper treats the theory of transient fields acting on the nucleus of an energetic ion during slowing-down in magnetized materials. The enhancement of density, at the ion nucleus, of atomic electrons scattered by the ion is χ ≈ 10 2 −10 3 . This implies a strong magnetic field from polarized electrons in a ferromagnetic material. Estimates of the enhancement and knowledge of energy loss permit a calculation of the total magnetic precession of a nucleus during slowing-down. Effects of screening are discussed and the sizable relativistic correction is computed. Fluctuation phenomena are also treated, as well as transient electric field gradients due to electron scattering. There is good agreement with the trend of experimental results, and relative values in different ferromagnetics agree within experimental error. But the measurements remain ∼ 50 % above the formulae. The discrepancy may be due to some of the more complicated corrections, which have not yet been estimated.

Calculation of the imaginary part of the heavy ion potential

Abstract The paper contains a numerical evaluation of the expressions for the absorptive potential in heavy ion reactions given earlier. With a standard folding expression for the real part of the ion-ion potential general good agreement is found with experimental data for the angular distributions of elastic and inelastic scattering. Special interest is attached to the case of 16 O + 28 Si where the calculated imaginary potential is very small at low bombarding energies.

Transfer reactions between heavy ions

Abstract The theory of transfer reactions between heavy ions is formulated in a semi-classical approximation in terms of coupled differential equations in time which include the effects of excitation in entrance and exit channel and the non-orthogonality of the wave functions. The main effects of the exchange of energy, mass and charge are taken into account.

Reaction mechanism of two-nucleon transfer between heavy ions

Abstract A quantal formulation of the two-nucleon transfer process is given, and the basic coupled-channel equations are solved by iteration up to second order. The first order corresponds to simultaneous transfer, the second order to successive (sequential) transfer of two nucleons. Different representations of the T -matrix are derived. For the first order a post form and a prior form, which correspond to the representations of the DWBA, are obtained. For the second order we derive several representations which give different decompositions into a pure successive and a non-orthogonality term. A semiquantal approximation is introduced which leads to a simplification of description and computation. The transfer amplitude for each partial wave is calculated in the semiclassical way and then a partial wave summation using the JWKB elastic phase shifts is performed. Numerical results obtained by this approximation show good agreement with quantal calculations for simultaneous transfer even above the Coulomb barrier, provided the attractive part of the potential is not too strong. The method is used for an investigation of the relative importance of the successive process in the reactions 94 Mo( 18 O, 16 O) 96 Mo and 208 Pb( 16 O, 14 C) 210 Po. It is found that the contributions from successive and simultaneous transfer have the same order of magnitude.

On the reaction mechanism of two-nucleon transfer between heavy ions

Abstract The competition between simultaneous and successive transfer of two nucleons between heavy ions is studied in the semiclassical approximation. It is shown that second order effects often dominate the reaction.