  A one-dimensional tight-binding Hamiltonian describes the evolution of a
single impurity interacting locally with $N$ electrons. The impurity spectral
function has a power-law singularity
$A(\omega)\propto\mid\omega-\omega_0\mid^{-1+\beta}$ with the same exponent
$\beta$ that characterizes the logarithmic decay of the quasiparticle weight
$Z$ with the number of electrons $N$, $Z\propto N^{-\beta}$. The exponent
$\beta$ is computed by (1) perturbation theory in the interaction strength and
(2) numerical evaluations with exact results for small systems and variational
results for larger systems. A nonanalytical behavior of $\beta$ is observed in
the limit of infinite impurity mass. For large interaction strength, the
exponent depends strongly on the mass of the impurity in contrast to the
perturbative result.
