  Transverse-momentum ($p_{\rm T}$) differential yields of electrons from
semileptonic heavy-flavour hadron decays have been measured in the most central
(0-10%) and in semi-central (20-40%) Pb-Pb collisions at $\sqrt{s_{\rm NN}} =
2.76$ TeV. The corresponding production cross section in pp collisions has been
measured at the same energy with substantially reduced systematic uncertainties
with respect to previously published results. The modification of the yield in
Pb-Pb collisions with respect to the expectation from an incoherent
superposition of nucleon-nucleon collisions is quantified at mid-rapidity
($|y|$ $<$ 0.8) in the $p_{\rm T}$ interval 0.5-3 GeV/$c$ via the nuclear
modification factor, $R_{\rm AA}$. This paper extends the $p_{\rm T}$ reach of
the $R_{\rm AA}$ measurement towards significantly lower values with respect to
a previous publication. In Pb-Pb collisions the $p_{\rm T}$-differential
measurements of yields at low $p_{\rm T}$ are essential to investigate the
scaling of heavy-flavour production with the number of binary nucleon-nucleon
collisions. Heavy-quark hadronization, a collective expansion and even
initial-state effects, such as the nuclear modification of the Parton
Distribution Functions, are also expected to have a significant effect on the
measured distribution.
