Observational and theoretical evidence suggests that high-energy Galactic cosmic rays are primarily accelerated by supernova remnants . If also true for low-energy cosmic rays , the ionization rate near a supernova remnant should be higher than in the general Galactic interstellar medium ( ISM ) . We have searched for H _ { 3 } ^ { + } absorption features in 6 sight lines which pass through molecular material near IC 443—a well-studied case of a supernova remnant interacting with its surrounding molecular material—for the purpose of inferring the cosmic-ray ionization rate in the region . In 2 of the sight lines ( toward ALS 8828 and HD 254577 ) we find large H _ { 3 } ^ { + } column densities , N ( { H } _ { 3 } ^ { + } ) \approx 3 \times 10 ^ { 14 } cm ^ { -2 } , and deduce ionization rates of \zeta _ { 2 } \approx 2 \times 10 ^ { -15 } s ^ { -1 } , about 5 times larger than inferred toward average diffuse molecular cloud sight lines . However , the 3 \sigma upper limits found for the other 4 sight lines are consistent with typical Galactic values . This wide range of ionization rates is likely the result of particle acceleration and propagation effects , which predict that the cosmic-ray spectrum and thus ionization rate should vary in and around the remnant . While we can not determine if the H _ { 3 } ^ { + } absorption arises in post-shock ( interior ) or pre-shock ( exterior ) gas , the large inferred ionization rates suggest that IC 443 is in fact accelerating a large population of low-energy cosmic rays . Still , it is unclear whether this population can propagate far enough into the ISM to account for the ionization rate inferred in diffuse Galactic sight lines .