Preliminary results in using Deep Learning to emulate BLOB, a nuclear interaction model

PURPOSE

A reliable model to simulate nuclear interactions is fundamental for Ion-therapy. We already showed how BLOB ("Boltzmann-Langevin One Body"), a model developed to simulate heavy ion interactions up to few hundreds of MeV/u, could simulate also ¹²C reactions in the same energy domain. However, its computation time is too long for any medical application. For this reason we present the possibility of emulating it with a Deep Learning algorithm.

METHODS

The BLOB final state is a Probability Density Function (PDF) of finding a nucleon in a position of the phase space. We discretised this PDF and trained a Variational Auto-Encoder (VAE) to reproduce such a discrete PDF. As a proof of concept, we developed and trained a VAE to emulate BLOB in simulating the interactions of ¹²C with ¹²C at 62 MeV/u. To have more control on the generation, we forced the VAE latent space to be organised with respect to the impact parameter (b) training a classifier of b jointly with the VAE.

RESULTS

The distributions obtained from the VAE are similar to the input ones and the computation time needed to use the VAE as a generator is negligible.

CONCLUSIONS

We show that it is possible to use a Deep Learning approach to emulate a model developed to simulate nuclear reactions in the energy range of interest for Ion-therapy. We foresee the implementation of the generation part in C++ and to interface it with the most used Monte Carlo toolkit: Geant4.

Preliminary results coupling "Stochastic Mean Field" and "Boltzmann-Langevin One Body" models with Geant4

PURPOSE

Monte Carlo (MC) simulations are widely used for medical applications and nuclear reaction models are fundamental for the simulation of the particle interactions with patients in ion therapy. Therefore, it is of utmost importance to have reliable models in MC simulations for such interactions. Geant4 is one of the most used toolkits for MC simulation. However, its models showed severe limitations in reproducing the yields measured in the interaction of ion beams below 100 MeV/u with thin targets. For this reason, we interfaced two models, SMF ("Stochastic Mean Field") and BLOB ("Boltzmann-Langevin One Body"), dedicated to simulate such reactions, with Geant4.

METHODS

Both SMF and BLOB are semi-classical, one-body approaches to solve the Boltzmann-Langevin equation. They include an identical treatment of the mean-field propagation, on the basis of the same effective interaction, but they differ in the way fluctuations are included. Furthermore, we tested a correction to the excitation energy calculated for the light fragments emerging from the simulations and a simple coalescence model.

RESULTS

While both SMF and BLOB have been developed to simulate heavy ion interactions, they show very good results in reproducing the experimental yields of light fragments, up to alpha particles, obtained in the interaction of ¹²C with a thin carbon target at 62 MeV/u.

CONCLUSIONS

BLOB in particular gives promising results and this stresses the importance of integrating it into the Geant4 toolkit.

Study of nuclear stopping in central collisions at intermediate energies

Nuclear stopping has been investigated in central nuclear collisions at intermediate energies by analyzing kinematically complete events recorded with the help of the 4π multidetector INDRA for a large variety of symmetric systems. It is found that the mean isotropy ratio defined as the ratio of transverse to parallel momenta (energies) reaches a minimum near the Fermi energy, saturates or slowly increases depending on the mass of the system as the beam energy increases, and then stays lower than unity, showing that significant stopping is not achieved even for the heavier systems. Close to and above the Fermi energy, experimental data show no effect of the isospin content of the interacting system. A comparison with transport model calculations reveals that the latter overestimates the stopping power at low energies.

Ising analogue to compact-star matter

By constructing an Ising analogue of compact-star matter at subsaturation density we explored the effect of Coulomb frustration on the nuclear liquid-gas phase transition. Our conclusion is twofold. First, the range of temperatures where inhomogeneous phases form expands with increasing Coulomb-field strength. Second, within the approximation of uniform electron distribution, the limiting point upon which the phase-coexistence region ends does not exhibit any critical behavior. Possible astrophysics consequences and thermodynamical connections are discussed.

Measurement of a complete set of nuclides, cross sections, and kinetic energies in spallation of 238U 1A GeV with protons

Spallation residues and fission fragments from 1A GeV 238U projectiles irradiating a liquid hydrogen target were investigated by using the fragment separator at GSI for magnetic selection of reaction products including ray-tracing, energy-loss and time-of-flight techniques. The longitudinal-momentum spectra of identified fragments were analyzed, and evaporation residues and fission fragments could be separated. For 1385 nuclides, production cross sections down to values of 10 microb with a mean accuracy of 15%, velocities in the uranium rest frame and kinetic energies were determined. In the reaction all elements from uranium to nitrogen were found, each with a large number of isotopes.