  Coherent control of nuclear pumping in a three level system driven by x-ray
light is investigated. In single nuclei, the pumping performance is determined
by the branching ratio of the excited state populated by the x-ray pulse. Our
results are based on the observation that in ensembles of nuclei, cooperative
excitation and decay leads to a greatly modified nuclear dynamics, which we
characterize by a time-dependent cooperative branching ratio. We discuss
prospects of steering the x-ray pumping by coherently controlling the
cooperative decay. First, we study an ideal case with purely superradiant decay
and perfect control of the cooperative emission. A numerical analysis of x-ray
pumping in nuclear forward scattering with coherent control of the cooperative
decay via externally applied magnetic fields is presented. Next, we provide an
extended survey of nuclei suitable for our scheme, and propose
proof-of-principle implementations already possible with typical M\"ossbauer
nuclear systems such as $^{57}\mathrm{Fe}$. Finally, we discuss the application
of such control techniques to the population or depletion of long-lived nuclear
states.
