Gamma Cherenkov-transition radiation of high energy electrons and methods for the measurement of the refractive index of MeV photons using total internal and external reflections (Invited talk)

It is given a review of the theoretical works showing that gamma ray Cherenkov-transition radiation (GCTR) is produced in some materials the refractive index of which in gamma region is greater than 1 according to the famous results of [1]. Since there are some published doubts [2] on the theoretical results of [1], and taking into account the difficulties of the experiment [1], in order to confirm or decline the results [1] it is proposed to study experimentally GCTR and an experimental method for the measurement of refractive index of MeV photons.


Introduction or formulation of the problem
In figure 1 it is shown qualitatively the behaviour of the dependence of the refractive index () n  of substances on photon energy   . As it is seen up to the X-ray region, excluding some narrow regions at anomaly dispersion frequencies, the refraction index is greater than 1, while when () n  >0.1 keV () n  <1.
where µ is the linear absorption coefficient. Now according to sensational experimental and theoretical results of [1] for silicon and gold ( ) 1, MeV. This has many important consequences and applications (see [3][4][5][6]) for nuclear physics, gamma optics, etc. Gold lenses, similar to Snigirev X-ray lenses, have been prepared in order to focus gamma ray beams. However, no new experimental results and answer to [2] has been published. The difficult experiment [1] has been carried out at Institut Laue-Langevin on the facility GAMS5 measuring the nanoradian relative diffraction angle for three lines of Cl 36 target bombarded by thermal neutrons when a Si wedge is inserted between the two crystals of a double Bragg diffraction spectrometer. The measured relative diffraction angles allowed to determine   (+1.83±1.57)x10 -10 , (+1.48±0.13)x10 -9 and (+1.11±0.30)x10 -9 , for 786, 1165 and 1951 keV photons, respectively, while the  measured for lower energies are negative according to the formula The authors of [1] using the cross section of various processes, mainly of the QED nonlinear process of Delbruck scattering calculated with the help of a complicated non-perturbative QED theory obtained good agreement between the experimental and theoretical results on  . However, A comment [2] on the work [1] has been published in which it has been shown that even using the Delbruck scattering cross sections given in [1] the contribution of Delbruck effect into δ is 10 -6 -10 -5 times less than it was estimated in [1]. Since there is no answer to [2] and no new experimental and theoretical results one can conclude that there is a problem in XXI century physics which it is better to solve experimentally.
On the other hand, it is well known that when a particle passes through a substance with 1 ) (   n it can produce Cherenkov radiation (CR) in radio-optical region (see [7,8]) and X-ray region (XCR) near K-, L-edges (see [9,10] it has been developed the theory of GCTR produced in a plate of material using the more confident experimental data of [1] in the region 786-2000 keV. In [11b] the theory of GCTR produced in a plate of material using the theoretical data of [1] in a wider region 786-10000 keV has been given, while the problems of the formation length and GCTR produced at a single interface and in stack of plate have been considered in [11c]. Looking for other methods of manifestation of the fact that in gamma ray region the refractive index can be greater than 1 in [11d] it is considered a simpler and direct method for the measurement of ) (   n using total internal (TIR) and external refection (TER) of MeV photons. In this work it is given a review of the works [11].

2.2a. GCTR produced at an interface between two media and its formation length
Let us first consider the formation length in medium of GCTR. According to [12,13] the formation length of XTR is a complex magnitude and is given by the expression From (1)  ( as for other types of radiation. As it follows from (8) when GCTR takes place and the condition The spectral-angular distribution of the number of photons of GCTR produced at an interface of two media (Si-vacuum) is derived substituting the values of χ' and χ'' into the formulae (1.59) [13] for XTR. In small angle and γ>>1 approximation one obtains (3)

2.2b. GCTR produced in a plate
Inserting the values of the complex  into the XTR spectral-angular distribution (formula (2.21) of [13] or formula (3.27) of [9] for a plate one derives the following formula for the spectral-angular distribution of GCTR where rad L is the thickness of the plate-radiator.

2.2c. GCTR produced in a stack of plates
The necessary expressions obtained with the help of corresponding formulae (3.15) of [13] as well as numerical results are given in [11c] and will not be discussed here. Before proceeding it is important to note the following: In contrast to XTR, due to the facts that for GCTR   abs rad L L a few cm, and the requirement that the particle velocity must be changed insignificantly, therefore, it is necessary to have is the radiation length of the radiator material), GCTR produced in a stack of plates as well as at one interface have no practical values since the GCTR yield from a stack of plates can not exceed the GCTR yield from a plate and it is not reasonable to consider GCTR production at one interface because one can not replace the infinite medium of a single interface with a plate thinner than abs L . Therefore, further it will be considered only GCTR produced in a plate with  rad L 1 cm given by (4)

Numerical results on GCTR produced in a plate
The below given numerical results described in details in

The angular distribution of GCTR
obtained integrating (4) over   in the interval 800-10000 keV is shown in figure 3. From figure 3 it follows that GCTR is emitted mainly in the angular interval from 30  rad up to 50  rad.

The dependence of GCTR on the electron energy
The energy dependence of the total number of GCTR (solid curve) and bremsstrahlung (dashed curve) photons is shown in figure 4. As it seen in figure 4 the number of the GCTR photons as in case of XTR exceed the background and begins to increase sharply beginning from a "threshold" energy about 12 GeV. Then with the increase of E a "saturation" achieves with  GCTR N 3.4. As it is has been shown still in [12,14] the number of the XTR photons in transition radiation detectors (TRD) from a stack of plates without and with taking into account the absorption is equal to XTR N ~11 and ~2 and exceeds the background bremsstrahlung only in a relatively narrow region    ) ( (2-30) keV, and this allows to construct TRD detectors, which found wide application for particle identification. Therefore one can use GCTR also for the same purpose.  Figure 5 shows how GCTR N depends on rad L . Around L rad = 1 cm GCTR N is proportional to rad L , and the electron energy losses are still small. Therefore, it is reasonable to take rad L~(2-10) % X 0 , and as the calculations (see [11]) show the use of a stack of plates instead of a plate has no advantage.

Experimental possibilities
One can use an experimental arrangement similar to those used at SLAC [15] and CERN SPS [16] and [17] for the study of various types of radiation of 1-200 GeV electrons. Without discussing the proposed arrangement let us note that the SLAC beam has the difficulty that it must contain 1 electron per pulse, while the SPS beam being much longer, allows to detect a few GCTR photons per pulse.
The analysis of the spectra measured by 25 GeV electrons in   = (1-10) MeV region did not reveal any exceeding over the calculated spectra of bremsstrahlung of various theories [15]. Probably, one cannot use this fact to decline the results of [1] may be because no measurements on Si have been performed.

Measurement of the reflection index of MeV photons using total internal and external reflection
It is well known that if ) ( n >1 (optical) it can take place TIR at the boundary medium-vacuum with TIR cr  = arcsin(1/n). Similarly, if ) ( n <1 (X-rays) it can take place TER at the boundary vacuummedium with TER cr  = (2δ) 1/2 . If δ~ 10 -9 , TER cr  = 45 μrad, which is not very small, rad  , as the angles in [1]. In many works of the past (see, [18]) it has been proposed, but not realized, to use TER for various purposes, in particular, for the "monochromatization" of MeV photon beams. However, such MeV experiments become realistic only recently connected with the advance of the method of inverse Compton scattering intense photon sources [19]. Suitable parameters are available at present at the facility HiGS of Duke university, which provides 10 8 -10 11 ph/s in a ~10 % BW, and soon at the ELI facility in Romania, which will provide ~10 13 ph/s in a ~1 % BW.   Therefore, for HiGS one expects to detect ~1-10 3 TER ph/s, and the experiment is feasible. However, in reality one must take into account that the HiGS beam is available after 2 collimators at a distance of  liquid xenon time projection chamber (LXeTPC) [20] or proposed LXeTPC on the basis of graphene [21].

Conclusion
At present it is possible to study the predicted GCTR using  E 20 GeV electrons at SLAC or of CERN and to measure directly ) ( n of various materials in MeV region using TER or TIR. These experiments can confirm or decline the discovery of [1].