Model of the vibrationally excited H$_2$O maser at 658 GHz in
  circumstellar envelopes around asymptotic giant branch stars
  The model is presented of H$_2$O maser in the $1_{10}-1_{01}$ line within the
first excited vibrational state of the molecule around oxygen-rich asymptotic
giant branch stars. It is suggested that the maser cloud is located in the
inner layers of the circumstellar envelope where intense dust formation takes
place. The calculations took into account rotational levels belonging to the
five lowest vibrational states of the H$_2$O molecule. The model predicts the
gain values of the 658-GHz maser about $10^{-14} -10^{-13}$ cm$^{-1}$ at H$_2$
molecule concentrations $10^9 - 10^{11}$ cm$^{-3}$ and at high ortho-H$_2$O
concentrations $ \gtrsim 10^5$ cm$^{-3}$. The gas temperatures $1000 - 1500$ K
are considered to be a necessary condition for the effective maser operation.
Results are presented for other maser transitions of the excited vibrational
states of the molecule.
