  It has been recently proposed that helium white dwarfs may provide promising
conditions for the occurrence of the Bose-Einstein condensation. The argument
supporting this expectation is that in some conditions attained in the core of
these objects, the typical De Broglie wavelength associated with helium nuclei
is of the order of the mean distance between neighboring nuclei. In these
conditions the system should depart from classical behavior showing quantum
effects. As helium nuclei are bosons, they are expected to condense.
  In order to explore the possibility of detecting the Bose-Einstein
condensation in the evolution of helium white dwarfs we have computed a set of
models for a variety of stellar masses and values of the condensation
temperature. We do not perform a detailed treatment of the condensation process
but mimic it by suppressing the nuclei contribution to the equation of state by
applying an adequate function. As the cooling of white dwarfs depends on
average properties of the whole stellar interior, this procedure should be
suitable for exploring the departure of the cooling process from that predicted
by the standard treatment.
  We find that the Bose-Einstein condensation has noticeable, but not dramatic
effects on the cooling process only for the most massive white dwarfs
compatible with a helium dominated interior (\approx 0.50 M_\odot) and very low
luminosities (say, Log(L/L_\odot) < -4.0). These facts lead us to conclude that
it seems extremely difficult to find observable signals of the Bose-Einstein
condensation.
  Recently, it has been suggested that the population of helium white dwarfs
detected in the globular cluster NGC 6397 is a good candidate for detecting
signals of the Bose-Einstein condensation. We find that these stars have masses
too low and are too bright to have an already condensed interior.

Solar and Stellar Astrophysics;Quantum Gases