Nuclear fission with mean-field instantons

We present a description of nuclear spontaneous fission, and generally of quantum tunneling, in terms of instantons, that is, periodic imaginary-time solutions to time-dependent mean-field equations. This description allows comparisons to be made with the more familiar generator coordinate (GCM) and adiabatic time-dependent Hartree-Fock (ATDHF) methods. It is shown that the action functional whose value for the instanton is the quasiclassical estimate of the decay exponent fulfills the minimum principle when additional constraints are imposed on trial fission paths. In analogy with mechanics, these are conditions of energy conservation and the velocity-momentum relations. In the adiabatic limit, the instanton method reduces to the time-odd ATDHF equation, with collective mass including the time-odd Thouless-Valatin term, while the GCM mass completely ignores velocity-momentum relations. This implies that GCM inertia generally overestimates the instanton-related decay rate. The very existence of the minimum principle offers hope for a variational search for instantons. After the inclusion of pairing, the instanton equations and the variational principle can be expressed in terms of the imaginary-time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The adiabatic limit of this theory reproduces ATDHFB inertia.