STABILITY OF LARGE BIPOLARONS IN THE PRESENCE OF A MAGNETIC-FIELD - ANALYTICAL ASYMPTOTIC LIMITS

The stability of large bipolarons in the presence of a static magnetic field was investigated in a previous paper on the basis of Feynman's path-integral approach. In general, the resulting analytical approxima tions E(estim) for the ground state energy had to be obtained by a num erical minimization procedure. In the present letter, analytical resul ts are derived for the first time for the (omega(c)-dependent) ground state energy of a bipolaron in a magnetic field in various limiting ca ses. In the limit of strong electron-phonon coupling (alpha much great er than 1) we obtain for omega(c) much less than 1 that E(estim) appro ximate to E(estim) (omega(c) = 0) + c (u)omega(c)/alpha(4) with c (u) an explicitly calculated constant, dependent on the ratio u = U/alpha where U is the strength of the Coulomb repulsion. For omega(c) much gr eater than alpha(2) much greater than 1 we find E(estim) approximate t o omega(c) - alpha(2)A(u) ln(2) omega(c)/alpha(2), also with an explic it analytical expression for A(u).