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##

Fitting Strategy and Error Analysis

One of the still-unsolved questions is an appropriate selection of
experimental data that would allow for a
more-or-less unique determination
of the coupling constants defining the energy functional. To this end,
one usually uses certain constraints obtained by extrapolating nuclear
data to an infinite system and selected data for finite nuclei. The
sensitivity of the final fit to the choice of this data set leads to a
plethora of parameterizations currently available in the literature.

Most of the currently used density functionals correctly reproduce
generic trends in nuclear masses - as selected masses are usually
considered in the data set - but their descriptions of other
quantities vary. Moreover, they often significantly differ in parameters
or coupling constants [8]. This suggests that yet-unresolved
correlations may exist between these parameters, and only certain
combinations thereof are important [76,51]. Such
correlations would explain the fact that widely different
parameterizations lead to fairly similar results.

The present stage of theory requires constructing new energy density
functionals supplemented by a complete error and covariance
analysis. It is not sufficient to ``predict'' properties of exotic
nuclei by extrapolating properties of those measured in experiment.
One must also quantitatively determine errors related to such an
extrapolation. Moreover, for experimental work it is essential
that an improvement gained by measuring one or two more isotopes be
quantitatively known. From a theoretical perspective, one must also
know the confidence level with which the parameters of the
functional are determined. An analysis of this type constitutes a
standard approach in other domains of physics, but they are seldom
performed in theoretical nuclear structure research.

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Jacek Dobaczewski
2006-01-17