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

摘要

We have previously developed for nuclear cross-sections of therapeuticprotons a calculation model, which is founded on the collective model as wellas a quantum mechanical many particle problem to derive the S matrix andtransition probabilities. In this communication, we show that the resonancescan be derived by shifted Gaussian functions, whereas the unspecific nuclearinteraction compounds can be represented by an error function, which alsoprovides the asymptotic behavior. The energy shifts can be interpreted in termsof necessary domains of energy to excite typical nuclear processes. Thus thenecessary formulas referring to previous calculations of nuclear cross-sectionswill be represented in section 2. The mass number AN determines the stronginteraction range. The threshold energy ETh of the energy barrier is determinedby the condition Estrong = ECoulomb. A linear combination of Gaussians, whichcontain additional energy shifts, and an error function incorporate a possiblerepresentation of Fermi-Dirac statistics, which is applied here to nuclearexcitations and reaction with release of secondary particles. The newcalculation formula provides a better understanding of different types ofresonances occurring in nuclear interactions with protons. The present study ismainly a continuation of previous papers.