In a previous work 1 the authors have shown that thick single crystals can be used as polarizers and polarimeters for high-energy gamma rays. This possibility is due to the well known coherence effects in pair production, which cause a dependence of the absorption cross section on the linear polarization of the photons.In this paper we show that as a consequence of the effects discussed in A and B, single crystals are also birefringent. This opens interesting possibilities in the use of single crystals for the handling of circularly polarized gamma rays. In particular it is possible to use a crystal of appropriate thickness as the high-energy analog of a quarter-wavelength plate to convert linear into circular polarization, and vice versa. In this way it will be possible to produce and analyze circularly polarized gamma-ray beams of very high energy. As in the case of linear polarization 1 the efficiency is found to increase with the energy.As in A we consider a cubic crystal of thickness x and a photon whose momentum K is in the (001) plane of the crystal at an angle 6 from the (110) axis. The polarization vector e of the incoming photon will in general be a combination of two vectors t and y (see B), respectively, on the (001) plane and orthogonal to it: e = e 1 t + e 2 y. € can be considered as a two-component vector: € = ( € i> e 2)* Beyond the crystal the outgoing amplitude in the forward channel (photon of momentum K) will be connected to e by a 2x2 diagonal matrix of the form 2 (exp [in^((jo,x)where 3 co = IK I and the quantities n " and n L are the analogs of the refraction index in optics. The crystal acts as a \\ plate if the relative phase of the two components is changed by ^, i.e., if Re^-w ")wx = j>rr.The imaginary parts of these are connected with the absorption cross section, Imw(ou) = €(a>)/2a>, and were discussed and evaluated in A and B. The real parts can be derived from them by the use of dispersion relations. 4 We are interested in the difference of the real parts, which enters in the phase relations between the two components:CO' 2 -CO 2
In this note we propose a new method for the production and the analysis of a polarized beam of high-energy gamma rays. The method is based on the interference effects which are observable in high-energy electron pair production on crystals. As a consequence of these the absorption rate (inverse of the mean free path) of very highenergy photons in crystal matter depends on their linear polarization. This suggests the possibility of using a thick crystal for the polarization and analysis of high-energy gamma rays. The polarization is effected by preferential absorption of the unwanted polarization component, and the analysis by transmission measurements, as in the case of a polaroid filter for visible light. Extensive theoretical work on the interference effects of high-energy electrodynamic processes in crystals has been done by Uberall,^ and refined experiments have given results which are in excellent agreement with the theory.^ Another method for the production of linearly polarized gamma rays by means of interference effects in a crystal is based on bremsstrahlung.^ In this case the theory is also in excellent agreement with the experimental results obtained with electrons of --1 GeV.^ As a polarimeter the device we propose is perhaps unique in the high-energy region, where the application of other methods based on the angular distribution in pair production and elastic photoproduction of 7r° on nuclei of zero spin^ requires very difficult experiments. A unique characteristic of the device is that, since it is both a polarizer and an analyzer, one can build two or more of them and cross-calibrate them with each other. The polarizing power of the device can therefore be directly measured.The absorption of high-energy photons is mainly due to electron pair production, a process which is already known to give interference effects.^'^ Let us consider the case of a cubic crystal, where the momentum k of the incoming gamma rays is in the (001) plane and makes a small angle a with the (110) axis. The (001) plane is then a symmetry plane. We find that the total cross section for pair production depends in this situation on the linear polarization of the gamma rays.Let us denote by z" and T>^ the total cross sections per unit volume of the crystal for gamma rays which are linearly polarized in the (001) plane and orthogonal to it. The two polarization components will be absorbed with different mean free paths; i.e., after having penetrated a thickness X of the crystal the intensities of the two components will be reduced according to® /V)=/"(0)exp[-T:V],If the beam was originally unpolarized [/" (0) = / (0)], we now have a polarization: P{x)-[l\x) -l''{x)]/[l\x)^I^{x)]^tanh[iAr(S -S )].(2) From Eq.(2) one can see that this method could, in principle, produce any degree of polarization, with an appropriate choice of the thickness x. This is achieved with a loss of the original intensity which can be expressed in terms of the polarization P{x) and of a param-270
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