  We formulate the quark sea contributions to the energy and various physical
observables in terms of Euclidean Green functions and their K-spin partial wave
reduction. In this framework it is not necessary to discretize the continuous
spectrum by introducing a finite boundary. Using this formulation we perform a
new self-consistent computation of the nucleon state in the Nambu-Jona-Lasinio
model. Besides this technical advantage such an alternative computation scheme
makes it possible to obtain the numerical predictions of the model in an
entirely independent way. We use the Pauli-Villars cutoff to define the model.
Our results for the nucleon energy, the mesonic profile, and various
observables essentially confirm results obtained by other groups using this
regularization. The results for $g\sub{A}$, obtained on the basis of quark
currents, are close to the experimental value.
