gms | German Medical Science

An analysis of total nuclear cross sections of various nuclei is presented, which provides detailed knowledge on the physical processes, e.g. potential/resonance scatter and nuclear reactions. The physical basis for potential/resonance scatter and the threshold energy E_Th resulting from Coulomb repulsion of nuclei are collective/oscillator models. These models only use as parameters the nuclear charge number Z and the number of all nucleons A_N. The outermost interaction distance R_strong of strong interactions amounts to R_strong = A_N ^1/3∙1.2∙10^-13 cm. For nuclei with Z ≤ 30 the threshold energy E_Th does not exceed 8.5 MeV; E_Th (oxygen): 6.9998 MeV.

The part pertaining to the nuclear reactions can only be determined by the microscopic theory. This theory is based on the nonlinear/nonlocal Schrödinger equation containing a combination of different types of Gaussian convolution kernels. They are used to describe strong interactions (π – and K – mesons), spin-orbit couplings between nucleons, and electrostatic repulsion of protons. The principle calculation procedure is the Hartree-Fock theory extended and generalized by configuration interactions (HF-CI). A low order approximation leads to the nuclear shell model based on the harmonic oscillator approach (models of Jensen/Mayer-Göppert and Elliot). Since harmonic oscillators are only reasonable for the ground state and lower excited states, we have also accounted for higher order solutions of excited/virtually excited states, which describe tensor forces and symmetry violations. Some essential calculation parameters of the collective model have been determined by that way. The determination of transition probabilities (contributions to the S matrix) yields possible reaction channels via excited and virtually excited states of all possible nuclear configurations represented by Slater determinants.

A physical impact is the fluence decrease of proton beams in different media, the contributions of secondary particles to Bragg curves, and their scatter behavior. A particular feature is that the resonance domain of the total nuclear cross section results from primary protons with energies E < 100 MeV inducing different kind of excitations, whereas for E > 100 resonance and potential scatter at the nucleus becomes a decreasing importance. With regard to secondary protons we have to differ between reaction protons resulting from a change of the isospin and non-reaction protons, which may either change the spin multiplicity or induce collective vibrations/rotations of the nucleus. The total cross sections Q^tot of nuclear interactions are characterized by following features: 1. Q^tot = 0 (if E < E_Th); 2. Gaussian behavior of Q^tot in the resonance domain; 3. Sequence of exponential functions up to the asymptotic behavior of Q^tot. The asymptotic behavior of Q^tot approximately obeys A_N ^2/3 (geometric cross-section).