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Using a tadpole improved SU(2) gluodynamics action, the nonabelian potentialand the abelian potential after the abelian projection are computed. Rotationalinvariance is found restored at coarse lattices both in the nonabelian theoryand in the effective abelian theory resulting from maximal abelian projection.Asymptotic scaling is tested for the SU(2) string tension. Deviation of theorder of $6%$ is found, for lattice spacings between 0.27 and 0.06 fm. Evidencefor asymptotic scaling and scaling of the monopole density in maximal abelianprojection is also seen, but not at coarse lattices. The scaling behavior iscompared with analyses of Wilson action results, using bare and renormalizedcoupling schemes. Using extended monopoles, evidence is found that the gaugedependence of the abelian projection reflects short distance fluctuations, andmay thus disappear at large scales.Comment: 28 pages, RevTeX, 12 figures using epsfig (included); accepted for  publication in Physical Revie

Scaling and confinement aspects of tadpole-improved SU(2) lattice gauge theory and its Abelian projection