Hadronic cross section measurements with the DAMPE space mission using 20 GeV-10 TeV cosmic-ray protons and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>He</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math>

Precise direct cosmic-ray (CR) measurements provide an important probe to study the energetic particle sources in our Galaxy, and the interstellar environment through which these particles propagate. Uncertainties on hadronic models, ion-nucleon cross sections in particular, are currently the limiting factor toward obtaining more accurate CR ion flux measurements with calorimetric space-based experiments. We present an energy-dependent measurement of the inelastic cross section of protons and helium-4 nuclei (alpha particles) on a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>Bi</a:mi></a:mrow><a:mrow><a:mn>4</a:mn></a:mrow></a:msub></a:mrow></a:math><c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mtext>Ge</c:mtext><c:mn>3</c:mn></c:msub><c:msub><c:mi mathvariant="normal">O</c:mi><c:mn>12</c:mn></c:msub></c:math> target, using 88 months of data collected by the DAMPE space mission. The kinetic energy range per nucleon of the measurement points ranges from 18 GeV to 9 TeV for protons, and from <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mn>5</f:mn><f:mtext> </f:mtext><f:mi>GeV</f:mi><f:mo>/</f:mo><f:mi mathvariant="normal">n</f:mi></f:mrow></f:math> to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mn>3</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>TeV</i:mi><i:mo>/</i:mo><i:mi mathvariant="normal">n</i:mi></i:mrow></i:math> for helium-4 nuclei. Our results lead to a significant improvement of the CR flux normalization. In the case of helium-4, these results correspond to the first cross section measurements on a heavy target material at energies above <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:mn>10</l:mn><l:mtext> </l:mtext><l:mi>GeV</l:mi><l:mo>/</l:mo><l:mi mathvariant="normal">n</l:mi></l:mrow></l:math>. Published by the American Physical Society 2025