An easy tool for the Monte Carlo simulation of the passage of photons and electrons through matter

A simple Monte Carlo (MC) algorithm for the simulation of the passage of low-energy gamma rays and electrons through any material medium is presented. The algorithm includes several approximations that accelerate the simulation while maintaining reasonably accurate results. Systematic comparisons for both photons and electrons have been made against the MC code PENELOPE and experimental data to validate the algorithm, showing deviations in the deposited energy smaller than or around 10% in the energy interval of 0.1 - 5 MeV in light media. The simulation is also valid for heavy media, but with less accuracy at high energy. The algorithm has been implemented in an open-source Python package called LegPy, which provides an easy-to-use framework for rapid MC simulations aiming to be useful for applications that do not require the level of detail of available well-established MC programs.Comment: 14 Figures, 9 pages. Submitted to Radiation Measurement

Diffeomorphism-invariant covariant Hamiltonians of a Pseudo-Riemannian metric and a linear connection

\noindent Let $M\to N$ (resp.\ $C\to N$) be the fibre bundle of pseudo-Riemannian metrics of a given signature (resp.\ the bundle of linear connections) on an orientable connected manifold $N$. A geometrically defined class of first-order Ehresmann connections on the product fibre bundle $M\times_NC$ is determined such that, for every connection $\gamma$ belonging to this class and every $\mathrm{Diff}N$-invariant Lagrangian density $\Lambda$ on $J^1(M\times_NC)$, the corresponding covariant Hamiltonian $\Lambda ^\gamma$ is also $\mathrm{Diff}N$-invariant. The case of $\mathrm{Diff}N$-invariant second-order Lagrangian densities on $J^2M$ is also studied and the results obtained are then applied to Palatini and Einstein-Hilbert Lagrangians