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Approximate formulas are derived for the critical density and pressure at which the atoms of hydrogen-like plasmas become ionized due to overlapping of the wave functions. By this mechanism, not only the thermally excited but also the ground state atoms of alkali plasmas become ionized already at moderate pressures. Numerical examples are given for H, Li, Na, K, Rb, and Cs plasmas. It is shown that the (negative) electron-ion interaction energy balances the (positive) thermal energy for sufficiently high electron densities (e.g., n ~ 1020 cm-3 for T ~ 104 K) so that the plasma assumes a cohesive state similar to that of a (liquid) metal. From the quantum effects, the electron exchange energy contributes significantly to this "self-containment" of dense plasmas.