  The solution of the scattering problem based on the Lippmann-Schwinger
equation requires in many cases a discretization of the spectrum in the
continuum which does not respect the unitary equivalence of the S-matrix on the
finite grid. We present a new prescription for the calculation of phase shifts
based on the shift that is produced in the spectrum of a Chebyshev-angle
variable. This is analogous to the energy shift that is produced in the energy
levels of a scattering process in a box, when an interaction is introduced. Our
formulation holds for any momentum grid and preserves the unitary equivalence
of the scattering problem on the finite momentum grid. We illustrate this
procedure numerically considering the non-relativistic NN case for $^1S_0$ and
$^3S_1$ channels. Our spectral shift formula provides much more accurate
results than the previous ones and turns out to be at least as competitive as
the standard procedures for calculating phase shifts.
