# Nuclear fission with mean-field instantons - Nuclear Theory

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Abstract: We present a description of nuclear spontaneous fission, and generally ofquantum tunneling, in terms of instantons - periodic imaginary-time solutionsto time-dependent mean-field equations - that allows for a comparison with morefamiliar and used generator coordinate GCM and adiabatic time-dependentHartree-Fock ATDHF methods. It is shown that the action functional whosevalue for the instanton is the quasiclassical estimate of the decay exponentfulfils the minimum principle when additional constraints are imposed on trialfission paths. In analogy with mechanics, these are conditions of energyconservation and the velocity-momentum relations. In the adiabatic limit theinstanton method reduces to the time-odd ATDHF equation, with collective massincluding the time-odd Thouless-Valatin term, while the GCM mass completelyignores velocity-momentum relations. This implies that GCM inertia generallyoverestimates instanton-related decay rate.The very existence of the minimum principle offers a hope for a variationalsearch for instantons. After the inclusion of pairing, the instanton equationsand the variational principle can be expressed in terms of theimaginary-time-dependent Hartree-Fock- Bogolyubov TDHFB theory. The adiabaticlimit of this theory reproduces ATDHFB inertia.

Author: ** J. Skalski**

Source: https://arxiv.org/