We show that, in a magnetic field parallel to the 2D electron layer, strong electron correlations change the rate of tunneling from the layer exponentially. It results in a specific density dependence of the escape rate. The mechanism is a dynamical Mossbauer-type recoil, in which the Hall momentum of the tunneling electron is partly transferred to the whole electron system, depending on the interrelation between the rate of interelectron momentum exchange and the tunneling duration. We also show that, in a certain temperature range, magnetic field can enhance rather than suppress the tunneling rate. The effect is due to the magnetic field induced energy exchange between the in-plane and out-of-plane motion. Magnetic field can also induce switching between intra-well states from which the system tunnels, and a transition from tunneling to thermal activation. Explicit results are obtained for a Wigner crystal. They are in qualitative and quantitative agreement with the relevant experimental data, with no adjustable parameters.
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