  We extend a recent chiral approach to nuclear matter of Lutz et al. [Phys.
Lett. B474 (2000) 7] by calculating the underlying (complex-valued)
single-particle potential U(p,k_f) + i W(p,k_f). The potential for a nucleon at
the bottom of the Fermi-sea, U(0,k_{f0})= - 20.0 MeV, comes out as much too
weakly attractive in this approach. Even more seriously, the total
single-particle energy does not rise monotonically with the nucleon momentum p,
implying a negative effective nucleon mass at the Fermi-surface. Also, the
imaginary single-particle potential, W(0,k_{f0}) = 51.1 MeV, is too large. More
realistic single-particle properties together with a good nuclear matter
equation of state can be obtained if the short range contributions of
non-pionic origin are treated in mean-field approximation (i.e. if they are not
further iterated with 1pi-exchange). We also consider the equation of state of
pure neutron matter $bar E_n(k_n)$ and the asymmetry energy A(k_f) in that
approach. The downward bending of these quantities above nuclear matter
saturation density seems to be a generic feature of perturbative chiral
pion-nucleon dynamics.
