The motion behaviours of the channelling particles have been controlled by an interaction potential of a particle with a crystal.Assuming to the interaction potential is the sine-squared potential

then the channelling effects and the channeling radiation are described analytically.In a harmoric approximation only one line is discovered in the channelling radiation spectra.The width of spectrum line is effected by Doppler effect

thermal vibration of lattice

electron multi-scattering and double-pole effect

besides the non-linearity of the system.Thus width of the spectra line has expanded almost.However

these factors may be decreased to minimum by effort

but the intrinsical extended width of the spectrum line by the radiation is not overcomed.Va-(rious) interaction potentials were compared

sine-squared potential is introduced to describte the interaction of the particle with the crystal.In a harmoric approximation of the sine-squared potential one disscused the intrinsical width and the frequency shift of the spectrum line for channelling radiations. Of course

the intrinsical width and the frequency shift of the spectrum line are very small in a classical approximation

However

this effect is obvious in a quantum mechanic frame

the shift magnitude is almost the same to the line width

this is so-called Lamb shift discovered by Soviet Physicist Lamb.In addition

in this paper the motion equation is derived in a classical mechanic frame

the solution of the equation is found by using pertubation method.The channelling radiation energy is calculated by a classical electro-dynamics.As example

the radiation energy for 1st order harmonic is for a positron with energy 56.0 MeV.It shows that the intrinsical width and the (frequency) shift of the spectra line are very small in all truth.