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We consider a small metallic grain coupled to a superconductor by a tunnelcontact. We study the interplay between proximity and charging effects in thepresence of the external magnetic field. Employing the adiabatic approximationwe develop a self-consistent theory valid for an arbitrary ratio of proximityand Coulomb strength. The magnetic field suppresses the proximity-inducedminigap in an unusual way. We find the phase diagram of the grain in thecharging energy - magnetic field plane. Two distinct states exist withdifferent values and magnetic field dependences of the minigap. The first-orderphase transition occurs between these two minigapped states. The transition tothe gapless state may occur by the first- or second-order mechanism dependingon the charging energy. We also calculate the tunneling density of states inthe grain. The energy dependence of this quantity demonstrates two differentgaps corresponding to the Coulomb and proximity effects. These gaps may beseparated in sufficiently high magnetic field.Comment: 11 pages (including 8 EPS figures). Version 3: extended. Final  version as published in PR

Proximity effect in the presence of Coulomb interaction and magnetic field