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We give a quantum description of the ternary cold fission process within a stationary scattering formalism. The dynamics of the light particle and heavy fragments is described by a self-consistent system of equations for radial wavefunctions. We consider the spontaneous cold ternary fission of ²⁵²Cf accompanied by ⁴He and ¹⁰Be. The light cluster decays from some resonant eigenstate in the Coulomb plus nuclear potential. It turns out that for the angular momentum projection K &equal; 0 the light cluster emission is concentrated in the polar direction. By increasing K the maximum of the angular distribution moves towards the equator, as measured in the experiment. For ⁴He we predict short living decaying states. Due to a large repulsive core, proportional to K², such states are hindered in the case of ¹⁰Be. The motion of the two heavy fragments with −K compensates the rotation of the light fragment. We call this collective motion tri-rotor mode and it should be detected in the fragment yields by magnetic transitions.

We show that for osmium, platinum and mercury isotopes the α-particle preformation factors given by the standard shell model are not consistent with the barrier penetrabilities. The internal cluster formation amplitude and the outgoing Coulomb wavefunction should have the same logarithmic derivatives for the experimental Q-value. The usual shell model wavefunctions are not able to satisfy this condition along any isotopic chain. In order to correct this deficiency we use an effective procedure. We diagonalize the mean field using a single particle basis with two harmonic oscillator parameters, as proposed in a previous paper. In order to obtain correct tails of the wavefunctions, the second harmonic oscillator parameter should increase with the mass number. This is consistent with the suppression of α-clustering by increasing the proton–neutron asymmetry. A parabolic fit of this parameter versus the mass number enables us to ensure a consistency in experimental Q-values within a mean deviation of 300 keV.

We give a description of the binary cold fission process of ²⁵²Cf within the stationary scattering formalism. The decay of the dinuclear system (quasi-molecule) consists in the tunnelling of a metastable state from an internal region, where the nucleus–nucleus potential makes a quasi-molecular pocket due to the interplay of repulsive and attractive nuclear forces and the Coulomb force, to the asymptotic region which is governed solely by the Coulomb repulsion. As a transverse internal motion, we suppose angular oscillations of the fragments up to the scission point. In the external region these vibrations transform into rotations. The nuclear interaction is given by a double-folding procedure using M3Y forces plus a repulsive contact potential. For the experimental Q-value we find several resonant states of the binary system, depending on the repulsive strength. We predict a strong dependence of decay widths upon the internal structure of the considered resonant state. Therefore the measured yields of the two fragments with given angular momenta in coincidence are able to provide more insight into the internal molecular dynamics of the decaying dinuclear system.

The repulsion due to the nonlinearity of a Schrödinger equation for the elastic scattering of heavy ions is approximated by the compression energy stored in the region of contact of two colliding liquid drops with trapezoidal densities. Qualitative and quantitative estimates show the required repulsion to be in line with literature results. The absolute maximum for the projectile energy at which our model is still expected to be applicable is given byEp?6 MeV.