Waves in central fields. Scattering of alpha particles from nuclei

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2020, Tutor: Francesc Salvat PujolThe quantum problem of a particle in a central field of force has been studied. A robust numerical algorithm has been utilized for solving the radial wave equation for both bound and free states. The general expression of distorted waves has been employed in calculations of elastic scattering of alpha particles from nuclei. The absorptive effect of the imaginary component of the optical-model potential has been analyze

Optimal navigability of weighted human brain connectomes in physical space

The architecture of the human connectome supports efficient communication protocols relying either on distances between brain regions or on the intensities of connections. However, none of these protocols combines information about the two or reaches full efficiency. Here, we introduce a continuous spectrum of decentralized routing strategies that combine link weights and the spatial embedding of connectomes to transmit signals. We applied the protocols to individual connectomes in two cohorts, and to cohort archetypes designed to capture weighted connectivity properties. We found that there is an intermediate region, a sweet spot, in which navigation achieves maximum communication efficiency at low transmission cost. Interestingly, this phenomenon is robust and independent of the particular configuration of weights.Our results indicate that the intensity and topology of neural connections and brain geometry interplay to boost communicability, fundamental to support effective responses to external and internal stimuli and the diversity of brain functions.Comment: 49 pages (10 main text, 39 Supplementary Material

Inelastic collisions of fast charged particles with atoms: Bethe asymptotic formulas and shell corrections

The relativistic plane-wave Born approximation is applied to the study of inelastic collisions of charged particles with atoms, by considering atomic wave functions calculated from the independent-electron approximation with the self-consistent Dirac-Hartree-Fock-Slater potential. A database of longitudinal and transverse generalized oscillator strengths (GOSs) has been computed by using accurate numerical methods for all the subshells of the ground-state configurations of the elements with atomic numbers from 1 (hydrogen) to 99 (einsteinium). The calculated GOS do not satisfy the Bethe sum rule; departures from the sum rule are in accordance with previous theoretical estimates. Asymptotic high-energy formulas for the total cross section, the stopping cross section, and the energy-straggling cross section are derived with proper account of the relativistic departure from the Bethe sum rule. The shell correction is calculated as the energy-dependent term that, when added to the asymptotic formula, reproduces the value of the atomic cross section calculated by integrating the energy-loss differential cross section. Shell corrections to the stopping cross section obtained from the present approach are presented and compared with previous estimates

Generation of a database of differential cross sections for nuclear elastic scattering of α\alpha particles on nuclei

The general-purpose code for the simulation of radiation transport FLUKA accounts for the elastic scattering of charged projectiles on the screened electrostatic potential of target atoms. However, no dedicated model for the nuclear elastic scattering of ions heavier than the proton is implemented. A prospective study has been carried out to examine the extent to which nuclear elastic scattering of alpha particles can be systematically modelled. In this work we have examined an effective optical potential model for the alpha-nucleus interaction, we have numerically solved the radial Schrodinger equation and we have evaluated the differential cross section for elastic scattering (DCES) using the partial-wave method. A preliminary database of DCES has been generated for alpha particles of up to 400 MeV on targets ranging from 12C to 209Bi for the sampling of nuclear elastic scattering events