| 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. |
