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

Exigências de triptofano e padrão de recuperação do desempenho de poedeiras comerciais após alimentação com rações deficientes em triptofano Tryptophan requirements and recovery performance pattern of commercial laying hens after feeding tryptophan-deficient diets

Este experimento foi conduzido para avaliar as exigências de triptofano e o padrão de recuperação do desempenho de poedeiras alimentadas com rações deficientes em triptofano. Foram utilizadas 160 poedeiras comerciais da linhagem Hisex White distribuídas em um delineamento inteiramente casualizado com cinco níveis de triptofano nas dietas (0,13; 0,15; 0,17; 0,19 e 0,21%), com oito repetições de quatro aves. As poedeiras permaneceram por duas semanas em adaptação (51 a 52 semanas), por seis semanas para avaliação da exigência de triptofano (53 a 58 semanas) e por quatro semanas para determinação do padrão de recuperação do desempenho (59 a 62 semanas). A produção e a massa de ovos foram prejudicadas quando as poedeiras foram alimentadas com rações contendo 0,13% de triptofano, no entanto, o desempenho foi recuperado após uma semana de alimentação com ração contendo 0,21% desse aminoácido. A qualidade interna dos ovos não foi influenciada pelos níveis de triptofano estudados (ingestão de 137,1 a 228,0 mg triptofano/dia). As exigências de triptofano foram estabelecidas entre 161 e 188 mg/dia, dependendo da característica avaliada (produção ou massa de ovos) e do modelo de regressão aplicado (polinomial, exponencial ou segmentado).<br>This experiment was carried out to evaluate the tryptophan (Trp) requirements and the recovery performance pattern of laying hens fed Trp-deficient diets. One hundred sixty Hisex White commercial laying hens were randomly distributed in five Trp levels in the diets (0.13, 0.15, 0.17, 0.19 and 0.21% ) with eight replicates of four birds. The laying hens remained for two weeks in adaptation (51 to 52 weeks), for six weeks for evaluation of Trp requirements (53 to 58 weeks) and for four weeks for the determination of the recovery performance pattern (59 to 62 weeks). Egg production and egg mass were impaired when laying hens were fed diets containing 0.13% of Trp, however, the performance was recovered after one week of feeding under a diet containing 0.21% of this amino acid. Internal egg quality was not influenced by the Trp levels studied (intake among 137.1 to 228.0 of Trp mg/day). Tryptophan requirements ranged from 161 to 188 mg/ay, depending on the characteristics evaluated (egg production or egg mass) and the regression model applied (polynomial, exponential or broken line)