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The crossover from thermal hopping to quantum tunneling is studied. We showthat the decay rate $\Gamma$ with dissipation can accurately be determined nearthe crossover temperature. Besides considering the Wentzel-Kramers-Brillouin(WKB) exponent, we also calculate contribution of the fluctuation modes aroundthe saddle point and give an extended account of a previous study of crossoverregion. We deal with two dangerous fluctuation modes whose contribution can'tbe calculated by the steepest descent method and show that higher ordercouplings between the two dangerous modes need to be taken into considerations.At last the crossover from thermal hopping to quantum tunneling in themolecular magnet Mn_{12}Ac is studied.Comment: 10 pages, 3 figure

physical review. b, condensed matter

Crossover from thermal hopping to quantum tunneling in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Mn</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">Ac</mml:mi></mml:math>

Crossover from thermal hopping to quantum tunneling inMn12Ac