  The $\alpha$-decay rates for the nuclides $^{168,170,171,172,173,174,176}$Yb
and $^{148,150,152,154}$Gd have been estimated from transmission probabilities
in a systematic $\alpha$-nucleus potential and from an improved fit to
$\alpha$-decay rates in the rare-earth mass region. Whereas ${\alpha}$-decay of
$^{152}$Gd in natural gadolinium is a severe obstacle for the use of gadolinium
as a low-energy solar-neutrino detector, we show that
  ${\alpha}$-decay does not contribute significantly to the background in a
ytterbium detector. An extremely long ${\alpha}$-decay lifetime of $^{168}$Yb
is obtained from calculation, which may be close to the sensitivity limit in a
low-background solar neutrino detector.
