A simple determination of the halo size \(L\) from \(^{10}\)Be/\(^9\)Be data

The AMS-02 and HELIX experiments should soon provide \(\mathrm{^{10}Be/^9Be}\) cosmic-ray data of unprecedented precision. We propose an analytical formula to quickly and accurately determine \(L\) from these data. Our formula is validated against the full calculation performed with the propagation code \usine{}. We compare the constraints on \(L\) set by Be/B and \(\mathrm{^{10}Be/^9Be}\), relying on updated sets of production cross-sections. The best-fit \(L\) from AMS-02 Be/B data is shifted from 5 kpc to 3.8 kpc when using the updated cross-sections. We obtained consistent results from the Be/B analysis with USINE, \(L=3.8^{+2.8}_{-1.6}\) kpc (data and cross-section uncertainties), and from the analysis of \(\mathrm{^{10}Be/^9Be}\) data with the simplified formula, \(L=4.7\pm0.6\) (data uncertainties) \(\pm2\) (cross-section uncertainties) kpc. The analytical formula indicates that improvements on \(L\) thanks to future data will be limited by production cross-section uncertainties, unless either \(\mathrm{^{10}Be/^9Be}\) measurements are extended up to several tens of GeV/n, or nuclear data for the production of \(\mathrm{^{10}Be}\) and \(\mathrm{^9Be}\) are improved; new data for the production cross-section of \(\mathrm{^{16}O}\) into Be isotopes above a few GeV/n are especially desired.