  Metastable He$_{2}^{*}$ excimer molecules have been utilized as tracer
particles of the normal component in superfluid $^4$He (He II) which can be
imaged via laser-induced fluorescence. These excimer molecules form tiny
bubbles in He II and can bind to quantized vortices at sufficiently low
temperatures, thereby allowing for direct visualization of vortex dynamics in
an inviscid superfluid. However, the
$a^{3}\Sigma^+_{u}$${\rightarrow}$$c^{3}\Sigma^+_{g}$ optical absorption line,
which is responsible for the fluorescence imaging of the He$_{2}^{*}$
molecules, is controlled by fluctuations on the bubble shape, and its exact
line profile is not known at low temperatures. In this paper, we present a
bubble model for evaluating the surface fluctuation eigenmodes of the excimers
in He II. The line profile of the
$a^{3}\Sigma^+_{u}{\rightarrow}c^{3}\Sigma^+_{g}$ transition is calculated at
different temperatures by considering both the zero-point and thermal
fluctuations on the bubble shape. We show that, as the temperature drops from
2~K to 20 mK, the peak absorption strength is enhanced by a factor of about
five, accompanying a blueshift of the peak location by about 2 nm. A
double-peak line profile due to the rotational levels of the molecular core can
be resolved. This bubble model also allows us to evaluate the stiffness of the
He$_{2}^{*}$ bubbles and hence their diffusion constant in He II due to
scattering off thermal phonons. Our results will aid the design of future
experiments on imaging quantized vortices in He II using He$_{2}^{*}$ tracers.
