  Recent experiments have shown that fullerene and fluorofullerene molecules
can produce interference patterns. These molecules have both rotational and
vibrational degrees of freedom. This leads one to ask whether these internal
motions can play a role in degrading the interference pattern. We study this by
means of a simple model. Our molecule consists of two masses a fixed distance
apart. It scatters from a potential with two or several peaks, thereby
mimicking two or several slit interference. We find that in some parameter
regimes the entanglement between the internal states and the translational
degrees of freedom produced by the potential can decrease the visibility of the
interference pattern. In particular, different internal states correspond to
different outgoing wave vectors, so that if several internal states are
excited, the total interference pattern will be the sum of a number of
patterns, each with a different periodicity. The overall pattern is
consequently smeared out. In the case of two different peaks, the scattering
from the different peaks will excite different internal states so that the path
the molecule takes become entangled with its internal state. This will also
lead to degradation of the interference pattern. How these mechanisms might
lead to the emergence of classical behavior is discussed.
