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Observations by the Large Area Telescope (LAT) on the \textit{Fermi} missionof diffuse $\gamma$-rays in a mid-latitude region in the third quadrant(Galactic longitude $l$ from $200\arcdeg$ to $260\arcdeg$ and latitude $| b |$from $22\arcdeg$ to $60\arcdeg$) are reported. The region contains no knownlarge molecular cloud and most of the atomic hydrogen is within 1 kpc of thesolar system. The contributions of $\gamma$-ray point sources and inverseCompton scattering are estimated and subtracted. The residual $\gamma$-rayintensity exhibits a linear correlation with the atomic gas column density inenergy from 100 MeV to 10 GeV. The measured integrated $\gamma$-ray emissivityis $(1.63 \pm 0.05) \times 10^{-26} {\rm photons s^{-1} sr^{-1}H\mathchar`-atom^{-1}}$ and $(0.66 \pm 0.02) \times 10^{-26} {\rm photonss^{-1} sr^{-1} H\mathchar`-atom^{-1}}$ above 100 MeV and above 300 MeV,respectively, with additional systematic error of $\sim 10%$. The differentialemissivity in 100 MeV--10 GeV agrees with calculations based on cosmic rayspectra consistent with those directly measured, at the 10% level. The resultsobtained indicate that cosmic ray nuclei spectra within 1 kpc from the solarsystem in regions studied are close to the local interstellar spectra inferredfrom direct measurements at the Earth within $\sim 10%$.

Fermi LAT Observation of Diffuse Gamma-Rays Produced Through Interactions between Local Interstellar Matter and High Energy Cosmic Rays