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Collisional Pumping of H$_2$O and CH$_3$OH Masers in C-Type Shock Waves

The collisional pumping of H$_2$O and CH$_3$OH masers in magnetohydrodynamic nondissociative C-type shocks is considered. A grid of C-type shock models with speeds in the range $5-70$ km s$^{-1}$ and preshock gas densities $n_{\rm H_2,0} = 10^4-10^7$ cm$^{-3}$ is constructed. The large velocity gradient approximation is used to solve the radiative transfer equation in molecular lines. The para-H$_2$O 183.3 GHz and ortho-H$_2$O 380.1 and 448.0 GHz transitions are shown to be inverted and to have an optical depth along the shock velocity $\vert τ\vert \sim 1$ at relatively low gas densities in the maser zone, $n_{\rm H_2} \gtrsim 10^5-10^6$ cm$^{-3}$. Higher gas densities, $n_{\rm H_2} \gtrsim 10^7$ cm$^{-3}$, are needed for efficient pumping of the remaining H$_2$O masers. Simultaneous generation of H$_2$O and class I CH$_3$OH maser emission in a shock is possible at preshock gas densities $n_{\rm H_2,0} \approx 10^5$ cm$^{-3}$ and shock speeds in the range $u_{\rm s} \approx 17.5-22.5$ km s$^{-1}$. The possibility of detecting class I CH$_3$OH and para-H$_2$O 183.3 GHz masers in star-forming regions and near supernova remnants is investigated.