Nucleon transfer in symmetric heavy-ion reactions at energies below the Coulomb barrier is investigated in the framework of a microscopic stochastic mean-field theory. Although mean field alone is known to significantly underpredict the dispersion of the fragment mass distribution, a considerable enhancement of the dispersion is obtained in the stochastic mean-field theory. The variance of the fragment mass distribution deduced from the stochastic theory scales with the number of exchanged nucleons. Therefore, the new approach provides the first fully microscopic theory consistent with the phenomenological analysis of the experimental data.
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