We present new measurements of the diffuse radio emission from the Coma cluster of galaxies at 1.4 GHz using the Effelsberg 100-m-telescope .
Even at that high frequency , the halo source Coma C has an extent down to noise of \sim 80 \arcmin corresponding to 3 Mpc ( { H _ { 0 } = 50 kms ^ { -1 } Mpc ^ { -1 } } ) in Coma .
The radio map reveals clear similarities with images of the extended X-ray halo of the Coma cluster .
However , the radio halo appears to be displaced from the X-ray halo by \sim 3 - 4 arcmin .
After subtracting the contributions from point sources we obtained an integrated diffuse flux density of { S _ { 1.4 GHz } } = 640 \pm 35 mJy from Coma C .

We derive relations between the various observationally determined spectral indices and the spectral index of the synchrotron emissivity , which allow one to achieve a rough estimate concerning the consistency of the presently available data at different frequencies and to place constraints on the emissivity index distribution .
In the halo ’ s core region , the inferred emissivity index between 0.3 GHz and 1.4 GHz appears to be in the range 0.4 - 0.75 implying that there must be some very effective mechanism for particle acceleration operating in the intracluster medium .
We discuss implications of our measurements and of the spectral index information on current theories for radio halo formation .
We stress the importance of having more measurements of Coma C at frequencies above 1.4 GHz , in order to be able to derive constraints on the physics of the formation process of the radio halo .