  We have previously developed for nuclear cross-sections of therapeutic
protons a calculation model, which is founded on the collective model as well
as a quantum mechanical many particle problem to derive the S matrix and
transition probabilities. In this communication, we show that the resonances
can be derived by shifted Gaussian functions, whereas the unspecific nuclear
interaction compounds can be represented by an error function, which also
provides the asymptotic behavior. The energy shifts can be interpreted in terms
of necessary domains of energy to excite typical nuclear processes. Thus the
necessary formulas referring to previous calculations of nuclear cross-sections
will be represented in section 2. The mass number AN determines the strong
interaction range. The threshold energy ETh of the energy barrier is determined
by the condition Estrong = ECoulomb. A linear combination of Gaussians, which
contain additional energy shifts, and an error function incorporate a possible
representation of Fermi-Dirac statistics, which is applied here to nuclear
excitations and reaction with release of secondary particles. The new
calculation formula provides a better understanding of different types of
resonances occurring in nuclear interactions with protons. The present study is
mainly a continuation of previous papers.
