By Coblentz W.W., Lampland C.O.
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Belarusian Acad. Sci. 18, 499 (1974) 22 12. G. D. Feranchuk: J. Phys. (Paris) 44, 913 (1983) 38 13. G. D. O. V. Ivashin: Nucl. Instrum. Methods A 249, 306 (1986) 22 14. B. Batterman, H. Cole: Rev. Mod. Phys. 36, 681 (1964) 38 15. A. K. Zhevago: Radiation from High Energy Particles in Media and External Fields (Nauka, Moscow 1988) 20, 21 16. M. Born, E. Wolf: Principles of Optics (Pergamon Elmsford, New York 1975) p 328 23 17. D. Feranchuk: Coherent phenomena in the processes of X-ray and gammaradiation from relativistic charged particles in crystals.
For the plane sets with reciprocal vectors 28 2 Classical Theory of Radiation gm = 2π d{hkl} mZ {hkl} , m = 1, 2, . . , d{hkl} = √ h2 a , + k 2 + l2 where a is a lattice constant and Z {hkl} is a normal to the planes. The angle (m) θB does not depend on m because sin θB = (Z {hkl} v)/v, and frequencies ωB (m) and vectors kB follow from (m) ωB (m) kB πc , d{hkl} sin θB ω{hkl} v 2π = + Z {hkl} . 35) which leads to sin2 νL ≈ πLδ(ν) = 2πLvδ[ω + v(gz − kz )] . 36) The most specific feature of PXR is that peak distribution is independent of the energy of a particle.
32) for PGR in a thin crystal is modified to [17] Wg(s) = (j k es )([pg v][pg j kg ]) 2K + 1 q2 ngr Q(k, kg ) 2 4π ωr2 c3 2K0 + 1 2(ω − ωr + iΓ/2) × 1 [(k − g)2⊥ + ω2 v2 γ 2 4 sin2 (ω/v − kz + gz )L/2 . 56) Here ngr is a Fourier component of the density distribution of resonant nuclei; kg = k+g; K and K0 are the moments of principal and excited nucleus states, respectively, and j k is a matrix element of the electromagnetic current, which defines the resonant transition between principal |0 and excited |1 nucleus states: ˆ n e−ikrn |0 , j k = 1|e(v) where |j 0 |2 = cΓ1 /2 and Γ1 is an elastic width of transition.
New Measurements of Planetary Radiation and Planetary Temperatures by Coblentz W.W., Lampland C.O.
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