  Time-of-flight neutron spectroscopy has been used to determine the
crystalline electric field (CEF) Hamiltonian, eigenvalues and eigenvectors
appropriate to the $J$ = 7/2 Yb$^{3+}$ ion in the candidate quantum spin ice
pyrochlore magnet $\rm Yb_2Ti_2O_7$. The precise ground state (GS) of this
exotic, geometrically-frustrated magnet is known to be sensitive to weak
disorder associated with the growth of single crystals from the melt. Such
materials display weak "stuffing" wherein a small proportion, $\approx$ 2\%, of
the non-magnetic Ti$^{4+}$ sites are occupied by excess Yb$^{3+}$. We have
carried out neutron spectroscopic measurements on a stoichiometric powder
sample of Yb$_2$Ti$_2$O$_7$, as well as a crushed single crystal with weak
stuffing and an approximate composition of Yb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ with
$x$ = 0.046. All samples display three CEF transitions out of the GS, and the
GS doublet itself is identified as primarily composed of m$_J$ = $\pm$1/2, as
expected. However,"stuffing" at low temperatures in
Yb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ induces a similar finite CEF lifetime as is
induced in stoichiometric Yb$_2$Ti$_2$O$_7$ by elevated temperature. We
conclude that an extended strain field exists about each local "stuffed" site,
which produces a distribution of random CEF environments in the lightly stuffed
Yb$_{2+x}$Ti$_{2-x}$O$_{7+y}$, in addition to producing a small fraction of
Yb-ions in defective environments with grossly different CEF eigenvalues and
eigenvectors.
