Determination of pion intranuclear rescattering rates in ${\nu }_{\mu }-\mathrm{N}\mathrm{e}$ versus ${\nu }_{\mu }-\mathrm{D}$ interactions for the atmospheric $\nu$ flux

Intranuclear rescattering rates are determined for low energy pions created within neon nuclei by muon neutrinos with energies between 0.4 and 6.0 GeV. Specifically, charged current ${\nu }_{\mu }$-neon and ${\nu }_{\mu }$-deuteron interactions from two accelerator bubble chamber experiments are $E_{\nu }$ weighted to match the shape of the atmospheric neutrino spectrum. The relative populations of final states within the weighted event samples imply rates for pion absorption and pion charge exchange, which expressed as probabilities per final state pion, are 0.22±0.05 and 0.10±0.08, respectively. Inclusive ${\pi }^{\pm }$ momenta and production angle distributions from neon are found to be similar to those from deuteron targets; sizable kinematic distortions attributable to inelastic rescattering are absent. However, the fraction of ${\pi }^{+} \left({\pi }^{-}\right)$ momenta in neon which are less than 300 MeV/c and backward in the laboratory system slightly exceeds the deuteron fraction, by 0.03±0.04 (0.11±0.10). Our measurements indicate the extent to which pion intranuclear rescattering may distort final states resulting from atmospheric neutrino reactions or from nucleon decays in nuclei having mass number near $A=20\mathrm{}$.