  Cross section data from the HARP experiment for pion production by protons
from a tantalum target have been convoluted with the acceptance of the
front-end channel for the proposed neutrino factory or muon collider and
integrated over the full phase space measured by HARP, to determine the
beam-energy dependence of the muon yield. This permits a determination of the
optimal beam energy for the proton driver for these projects. The cross section
data are corrected for the beam-energy dependent amplification due to the
development of hadronic showers in a thick target. The conclusion is that, for
constant beam power, the yield is maximum for a beam energy of about 7 GeV, but
it is within 10% of this maximum for 4<Tbeam < 11 GeV, and within 20% of the
maximum for Tbeam as low as 2 GeV. This result is insensitive to which of the
two HARP groups' results are used, and to which pion generator is used to
compute the thick target effects.
