Dependence of Chemical Abundance on the Cosmic Ray Ionization Rate in IC 348
Ions (e.g., H$_3^+$, H$_2$O$^+$) have been used extensively to quantify the cosmic-ray ionization rate (CRIR) in diffuse sightlines. However, measurements of CRIR in low-to-intermediate density gas environments are rare, especially when background stars are absent. In this work, we combine molecular line observations of CO, OH, CH, and HCO$^+$ in the star-forming cloud IC~348, and chemical models to constrain the value of CRIR and study the response of the chemical abundances distribution. The cloud boundary is found to have an $A_{\rm V}$ of approximately 4 mag. From the interior to the exterior of the cloud, the observed $^{13}$CO line intensities drop by an order of magnitude. The calculated average abundance of $^{12}$CO (assuming $^{12}$C/$^{13}$C = 65) is (1.2$\pm$0.9) $\times$10$^{-4}$, which increases by a factor of 6 from the interior to the outside regions. The average abundance of CH (3.3$\pm$0.7 $\times$ 10$^{-8}$) is in good agreement with previous findings in diffuse and translucent clouds ($A_{\rm V}$ $<$ 5 mag). However, we did not find a decline in CH abundance in regions of high extinction ($A_{\rm V}\simeq$8 mag) as previously reported in Taurus. By comparing the observed molecular abundances and chemical models, we find a decreasing trend of CRIR as $A_{\rm V}$ increases. The inferred CRIR of $ζ_{cr}$ = (4.7$\pm$1.5) $\times$ 10$^{-16}$ s$^{-1}$ at low $A_{\rm V}$ is consistent with H$^+_3$ measurements toward two nearby massive stars.