  We give a sufficient condition for admissibility of generalized Bayes
estimators of the location vector of spherically symmetric distribution under
squared error loss. Compared to the known results for the multivariate normal
case, our sufficient condition is very tight and is close to being a necessary
condition. In particular we establish the admissibility of generalized Bayes
estimators with respect to the harmonic prior and priors with slightly heavier
tail than the harmonic prior. We use the theory of regularly varying functions
to construct a sequence of smooth proper priors approaching an improper prior
fast enough for establishing the admissibility. We also discuss conditions of
minimaxity of the generalized Bayes estimator with respect to the harmonic
prior.
