  We discuss how to connect the energy levels of two-particle systems trapped
by a harmonic-oscillator force to scattering amplitudes, with nucleon-nucleon
scattering phase shifts in uncoupled channels as the application. At the center
of the proposed framework is the energy-dependent effective field theory that
aims to expand observables in a neighborhood around each reference energy,
often taken to be one of the energy levels. We also investigate how to
disentangle the trapping force at short distances and the intrinsic interaction
between the particles.
