Theoretical methods for the calculation of Bragg curves and 3D distributions of proton beams

The well-known Bragg-Kleeman rule RCSDA = A dot E0p has become a pioneer work in radiation physics of charged particles and is still a useful tool to estimate the range RCSDA of approximately monoenergetic protons with initial energy E0 in a homogeneous medium. The rule is based on the continuous-slowing-down-approximation (CSDA). It results from a generalized (nonrelativistic) Langevin equation and a modification of the phenomenological friction term. The complete integration of this equation provides information about the residual energy E(z) and dE(z)/dz at each position z (0 <= z <= RCSDA). A relativistic extension of the generalized Langevin equation yields the formula RCSDA = A dot (E0 +E02/2M dot c2)p. The initial energy of therapeutic protons satisfies E0 << 2M dot c2 (M dot c2 = 938.276 MeV), which enables us to consider the relativistic contributions as correction terms. Besides this phenomenological starting-point, a complete integration of the Bethe-Bloch equation (BBE) is developed, which also provides the determination of RCSDA, E(z) and dE(z)/dz and uses only those parameters given by the BBE itself (i.e., without further empirical parameters like modification of friction). The results obtained in the context of the aforementioned methods are compared with Monte-Carlo calculations (GEANT4); this Monte-Carlo code is also used with regard to further topics such as lateral scatter, nuclear interactions, and buildup effects. In the framework of the CSDA, the energy transfer from protons to environmental atomic electrons does not account for local fluctuations.Comment: 97 pages review pape

RECURSION RELATIONS AND SIMPLIFIED EXPRESSIONS FOR THE 6-j SYMBOLS

It is shown that the 144 symmetry properties of the 6-j symbols which were discovered by Regge can be displayed with a 4 x 4 array that is invariant to the ordering of three of the rows and all columns. The elements of the array are linear combinations of the quantum numbers. In addition, it is shown that a large set of three-term recursion relations exist. The recursion relations are used to deduce simplified expressions for the 6-j symbois in special cases. (auth

Office of Waste Isolation progress report, January 1978

This document, prepared to report progress on the National Waste Terminal Storage (NWTS) program, consists of project reports on work performed by organizations under subcontract to OWI, by DOE contractors, by OWI consultants, and by other federal agencies participating in the NWTS program. The project reports are made under the headings technical projects, facility projects, planning and analysis, and regulatory affairs. (DLC

Office of Waste Isolation progress report, December 1977

This document reports progress on the OWI's portion of the National Waste Terminal Storage (NWTS) program. It comprises project reports on work performed by organizations under subcontract to OWI, by DOE contractors, by OWI consultants, and by other federal agencies participating in the NWTS program. They are made under the headings technical projects, facility projects, planning and analysis, and regulatory affairs. (DLC

CALCULATION OF THE PULSE-HEIGHT RESPONSE OF NaI(Tl) SCINTILLATION COUNTERS

A Monte Carlo calculation to determine the pulse-height response of NaI(Tl) scintillation counters to gamma rays is described. Comparisons of several calculations with experiments using 3-in.-dia by 3-in.-high crystals for source energies from 0.32 to 7.48 Mev are presented and show good agreement at large pulse heights. At small pulse heights the calculations underestimated the experimental data and indicated that background radiation can contribute significantly to the experimental results. An extensive series of calculations are reported for a 3-in.-dia by 3-in.high crystal using monoenergetic, point isotropic sources placed on the crystal axis l0 cm from one end. The source energy ranged from 0.l to 6.0 Mev in this series of calculations. (auth

STUDIES OF THE LONGITUDINAL DEVELOPMENT OF HIGH-ENERGY ELECTRON-PHOTON CASCADE SHOWERS IN COPPER

Numerical results of the track lengths of photons and charged particles and the energy deposition as a function of depth out to 10 radiation lengths in Cu are presented for the case of electron-initiated electron-photon cascade showers. The incident energy varied from 50 to 45,000 Mev in these cases. Monte Carlo methods were used to calculate the longitudinal development of the showers in order to obtain the data that are presented. The Bethe-Heitler cross sections which include screening and the correct energy dependence were used for bremsstrahlung and pair production events. The Klein-Nishina formula was used for Compton scattering. Energy losses by ionization collisions were treated as a continuous energy degradation process. (auth

SOME SIMPLIFIED EXPRESSIONS FOR THE 3-j SYMBOLS

A general formalism is developed for obtaining simplified expressions for the 3-j symbol using the symmetry properties of the symbol discovered by Regge. Some new formulas are derived from the formalism for cases in which Racah's series for the symbol is summable. (auth

A COLLIMATOR STUDY FOR A 5-Gev ELECTRON BEAM

A calculation to determine the effectiveness of collimators in a high- energy electron beam is described. Numerical results for a 5-Bev electron beam incident on a 135.42-cm-thick aluminum collimator with an inside radius of 0.85 cm are reported. (auth