  In light and medium-mass nuclei, two-body weak currents from chiral effective
field theory account for a significant portion of the phenomenological
quenching of Gamow-Teller transition matrix elements. Here we examine the
systematic effects of two-body axial currents on Gamow-Teller strength and
$\beta$-decay rates in heavy nuclei within energy-density functional theory.
Using a Skyrme functional and the charge-changing finite amplitude method, we
add the contributions of two-body currents to the usual one-body linear
response in the Gamow-Teller channel, both exactly and though a density-matrix
expansion. The two-body currents, as expected, usually quench both summed
Gamow-Teller strength and decay rates, but by an amount that decreases as the
neutron excess grows. In addition, they can enhance individual low-lying
transitions, leading to decay rates that are quite different from those that an
energy-independent quenching would produce, particularly in neutron-rich
nuclei. We show that both these unexpected effects are related to changes in
the total nucleon density as the number of neutrons increases.
