  In perturbation theory, the wave function of domain-wall quarks decreases
exponentially with the fifth coordinate. We show that, regardless of the
quark's own momentum, the fall-off rate of the one-loop wave function is equal
to the slowest rate encountered at tree-level for any lattice four-momentum. We
propose new domain-wall actions involving beyond-nearest neighbor couplings in
the four physical dimensions, for which the perturbative wave function
decreases much faster. It is hoped that the new actions may preserve the good
chiral properties of domain-wall fermions up to larger values of the lattice
spacing.
