Neutron inelastic scattering measurements on an undoped single crystal of C
uGeO3 and on a doped crystal CuGeo(0.997)Si(0.003)O(3) are performed in the
presence of a magnetic field H up to 12 T. In the present work, a particul
ar attention is given to the effect of H on the low-energy elementary excit
ations. This investigation is performed in the three different phases of th
e spin-Peierls system. In the dimerized D phase, the Zeeman splitting of th
e acoustic magnon branch is evaluated all along the dispersion branch (0<q<
less than or equal to>1/2). In the uniform U phase, it is established first
that, at finite temperature T not equal0, the low wave vector (q-->0) spin
on modes are little affected by the thermal fluctuations deltaE(T)similar o
r equal toT. Second, the effect of H on the same low-q mode results essenti
ally in a transfer of the fluctuations towards the Zeeman-shifted lower bou
ndary of the spinon continuum. Finally, our measurements an the doped compo
und establishes that an energy gap occurs in the elementary excitation spec
trum of the incommensurate I phase.