Context : The radio spectra of many shell-type supernova remnants show deviations from those expected on theoretical grounds .

Aims : In this paper we determine the effect of stochastic reacceleration on the spectra of electrons in the GeV band and at lower energies , and we investigate whether or not reacceleration can explain the observed variation of radio spectral indices .

Methods : We explicitely calculate the momentum diffusion coefficient for 3 types of turbulence expected downstream of the forward shock : fast-mode waves , small-scale non-resonant modes , and large-scale modes arising from turbulent dynamo activity .
Noting that low-energy particles are efficiently coupled to the quasi-thermal plasma , a simplified cosmic-ray transport equation can be formulated and is numerically solved .

Results : Only fast-mode waves can provide momentum diffusion fast enough to significantly modify the spectra of particles .
Using a synchrotron emissivity that accurately reflects a highly turbulent magnetic field , we calculate the radio spectral index and find that soft spectra with index \alpha \lesssim - 0.6 can be maintained over more than 2 decades in radio frequency , even if the electrons experience reacceleration for only one acceleration time .
A spectral hardening is possible but considerably more frequency-dependent .
The spectral modification imposed by stochastic reacceleration downstream of the forward shock depends only weakly on the initial spectrum provided by , e.g. , diffusive shock acceleration at the shock itself .

Conclusions :