Power counting is applied to relativistic mean-field energy functionals to
estimate contributions to the energy from individual terms. New estimates f
or isovector, tensor, and gradient terms in finite nuclei are shown to be c
onsistent with direct, high-quality fits. The estimates establish a hierarc
hy of model parameters and identify how many parameters are well constraine
d by bulk nuclear observables. We conclude that four (possibly five) isosca
lar, non-gradient parameters, one gradient parameter, and one isovector par
ameter are well determined by the usual bulk nuclear observables. (C) 2000
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