Rashba precession of spins moving along a one-dimensional quantum channel i
s calculated, accounting for Coulomb interactions. The Tomonaga-Luttinger m
odel is formulated in the presence of spin-orbit scattering and solved by B
osonization. Increasing interaction strength at decreasing carrier density
is found to enhance spin precession and the nominal Rashba parameter due to
the decreasing spin velocity compared with the Fermi velocity. This result
can elucidate the observed pronounced changes of the spin splitting on app
lied gate voltages that are estimated to influence the interface electric f
ield in heterostructures only a little.