  We discuss the origin of pathological behaviors that have been recently
identified in particle-number-restoration calculations performed within the
nuclear energy density functional framework. A regularization method that
removes the problematic terms from the multi-reference energy density
functional and which applies (i) to any symmetry restoration- and/or
generator-coordinate-method-based configuration mixing calculation and (ii) to
energy density functionals depending only on integer powers of the density
matrices, was proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041]
and implemented for particle-number restoration calculations in [M. Bender, T.
Duguet, D. Lacroix, arXiv:0809.2045]. In the present paper, we address the
viability of non-integer powers of the density matrices in the nuclear energy
density functional. Our discussion builds upon the analysis already carried out
in [J. Dobaczewski \emph{et al.}, Phys. Rev. C \textbf{76}, 054315 (2007)].
First, we propose to reduce the pathological nature of terms depending on a
non-integer power of the density matrices by regularizing the fraction that
relates to the integer part of the exponent using the method proposed in [D.
Lacroix, T. Duguet, M. Bender, arXiv:0809.2041]. Then, we discuss the spurious
features brought about by the remaining fractional power. Finally, we conclude
that non-integer powers of the density matrices are not viable and should be
avoided in the first place when constructing nuclear energy density functionals
that are eventually meant to be used in multi-reference calculations.
