A new calculation formula of the nuclear cross-section of therapeutic protons

Waldemar Ulmer


Purpose: 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.

Method: 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. The mass number AN determines the strong interaction range, i.e. RStrong = 1.2·10-13·AN1/3cm. The threshold energy ETh of the energy barrier is determined by the condition Estrong = ECoulomb.

Results and Conclusion: 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 published papers.1-3


Cite this article as: Ulmer W. A new calculation formula of the nuclear cross-section of therapeutic protons. Int J Cancer Ther Oncol 2014; 2(2):020211. DOI: 10.14319/ijcto.0202.11


Nuclear interactions of protons; Threshold energy; Bethe-Wigner resonances; Gaussian representation of resonance interactions; Tunnel effect

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DOI: http://dx.doi.org/10.14319/ijcto.0202.11

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