VOLUME 38, NUMBER 1 PHYSI t" AL REVIEW LETTERS 3 JxwvaRv 1977

Measurements of the Frequency Spectrum of Transition Radiation*

Michael L. Cherry and Dietrich Muller Enrico Ferjni Institute and DePartment of Physics, University of Chicago, Chicago, Ittinois 60637 (Received 28 June 1976) We report a measurement of the frequency spectrum of x-ray transition radiation. X rays were generated by electrons of 5 and 9 GeV in radiators of multiple polypropylene foils, and detected in the range 4 to 80 keV with a calibrated single-crystal Bragg spec- trometer. The experimental results closely reproduce the features of the theoretically predicted spectrum. In particular, the pronounced interference pattern of multifoil radia- tors and the expected hardening of the radiation with increasing foil thickness are clearly observed. The overall intensity of the radiation is somewhat lower than predicted by cal- culations.

The physical characteristics of x-ray transi- two media. " Using procedures that have been tion radiation have mainly been studied in mea- discussed earlier, 4' "we integrate Eq. (1) over surements of the total radiation yield. Various angles and take into account possible reabsorp- radiator-detector configurations' ' have led to tion of x rays inside the radiator. The resulting results which are in fair agreement with the the- frequency spectrum exhibits striking deviations oretical predictions' "(including the expected from that of a single interface: Pronounced max- saturation of the yield at high particle energies). ima and minima occur; and, for sufficiently high However, a precise measurement of the frequen- particle energy, the spectrum saturates, i.e., it cy sPectrum of this radiation is a much more sig- becomes independent of the particle energy. It nificant test of the theory, and, furthermore, should be pointed out that such oscillations do oc- leads to details crucial for the design of transi- cur even in the case of a single foil (N= 1). If tion-radiation detectors for relativistic particles. the ratio l,/l, is large (i.e. , l,/l, & 10), the shape The results of such a measurement are reported of the spectrum is largely determined by the sin- in this Letter. gle-foil interf erence, although the multiple-foil Let us denote the distribution of the transition- interference governs the saturation at high ener- radiation intensity with respect to the emission gies. '" The exact spectral shape and the posi- angle 8, and the frequency &o, as d'S/d8dcu. In tions of maximum intensity are determined by the idealized case of relativistic particles trav- the dimensions of the radiator. ~ Knowledge of ersing a single interface between two different these details is of prime importance for practi- media, this distribution yields, after integration cal applications. over angles, a frequency spectrum that is a mon- In the present experiment, performed at the otonic function of the x-ray energy "In p.ractice, Cornell University synchrotron, we have mea- intensity considerations require a radiator of sured the transition-radiation spectrum, gener- many interfaces. The radiator dimensions and ated by electrons of 5 and 9 GeV in radiators of the x-ray wavelengths may be comparable in the evenly spaced polypropylene foils (CH, ), with rest frame of a relativistic particle. Therefore, dimensions (200-1000 foils, thickness 16 to 82 the coherent addition of the radiation amplitudes ttm, spacing 1.4 mm) that are typical for practi- from the various interfaces leads to interference cal applications. A magnet was used to deflect phenomena which drastically modify the single- the electrons away from the x-ray detector. %e interface radiation pattern" d'S, /d8d~. For a have used a single-crystal Bragg spectrometer. transparent radiator of N foils of thickness ly Thus we avoided an intrinsic difficulty encount- equally spaced by distances l„one obtains ' "" ered in previous experiments"" "where a pro- portional or solid-state detector was used to measure the x-ray energy, such that single-pho- ton events became indistinguishable from events due to several simultaneous photons. One such sin'[N(l, + /Z, l,/Z, )] experiment has, however, been quite success- sin'(l, + /Z, I,/Z, ) ful" because only very short radiators were used. where Z, ,(8, cu) are the "formation zones" of the Both single- and multiple-foil interference phe- VOLUME 38, NUMBER I PHYSICAL REVIEW I.ETTKRS 5 JANUARY 1977

Scin t i I la tor 0 i f fraction ~ I I I I S4 crystal 9 GeV electrons Col lima tor Electron beam Helium Magnet 1000 Foils PXXi WX/8/XXXPXy CO 1. m C3 3 4 mm/16 p. SS CD

gl LLJ LIF, peak at 9. 1 keV I I I I I I I I I I I I I I I I I I I I I I I I I I II

I I I I I I I I I I I I I I I I I I I I I I I I I I It Sl s2 g :2- Scinti I lators Radiator Allfl COIOCldence scintillator A 0 p ply I I / ~ '% (Xe/CO~i Pb shielding FIG. 1. Diagram of the experimental setup. I l l I l 0 5 10 15 20 25 X-Ray Energy(keV) nomena were observed in this case. FIG. 2. Measured pulse-height distributions in the Figure 1 shows our experimental arrangement. proportional counter. The solid points show transition The x-rays reached the spectrometer through a radiation from 1000 CH& foils, while the open symbols obtained with background radiator. Note the good 0.5-cm wide collimator, 6 m from the radiator. are a agreement between the distributions outside the x-ray The spectrometer consisted of a LiF or an organ- peak. ic PET (polyethylene terephthalate) crystal, cov- ering the energy range 4 to 30 keV, and a xenon proportional counter, the signal of which was low differential yield, special efforts were re- pulse-height analyzed. The whole apparatus was quired to shield the apparatus from background. kept in a helium-filled enclosure to reduce x- The absolute ref lectivity of the crystals has ray absorption. Frequent tests were performed been calibrated with laboratory x-ray machines. throughout the runs to check the alignment be- The effective resolution varied between - 1 eV at tween spectrometer and beam. In order to nor- 4 keV and -40 eV at 29 keV. Details of these cal- malize the measured x-ray intensity to the elec- ibration measurements will be described in a tron flux, we assumed that transition-radiation separate publication. photons follow closely (i.e. , 8 =mc'/E) the tra- In Fig. 3 me show the results of our measure- jectory of their parent electrons in the absence ments for three radiators with different foil thick- of a magnetic field. This assumption was veri- nesses, normalized as photons per interface and fied by steering the beam across the spectrom- per electron. The number of foils in each radia- eter slit. With the magnet turned off, the flux tor is chosen such that the total mass (and hence of parent electrons was determined with scintil- the total photoelectric absorption) is approxi- lators by measuring the rate S1 S2 S3 2 (see Fig. mately the same in each case. Our data points 1), where A is a scintillator with an opening are corrected for the efficiency of the crystal through the center matching exactly the dimen- and the xenon counter, and for the transmission sions of the spectrometer slit. of the absorbing material (mainly helium) be- Figure 2 shows two superimposed pulse-height tween the radiator and the spectrometer. Typi- distributions, measured with the LiF crystal set cal errors are indicated. They are essentially for 9-keV x rays. One distribution mas generat- due to small changes in the electron beam and, ed with a radiator in place, while for the other mainly at low intensities, uncertainties in the the radiator was replaced by a solid block of background subtraction. For comparison with polyethylene of the same total mass. This back- the experimental results, the curves in Fig. 3 ground test has been performed for every run. show the shape of the expected distributions, cal- The distinct peak at 9 keV due to transition radi- culated as discussed above. Our data points re- ation is excellently resolved from background, produce the calculated spectral shapes excellent- and at 18 keV even a small second-order peak ly. The maxima and minima due to interference can be noticed. The width of the x-ray peaks is effects are mell resolved and appear exactly at determined by the resolution of the proportional the calculated frequencies. However, our over- counter. Because of the high resolution of the all intensity is somewhat lower than expected. crystal itself, more than 10' electrons are need- In order to fit the experimental data better, the ed for each 9-keV x-ray count. In view of this calculated spectra in Fig. 3 are scaled down by VQLUME 38, +UMBER 1 PHYSICAL REVIEW LETTERS $ JANUARY 1977

I I I I I I I I I I II IIlljllnllllli i plasmapressionn frequency of the foil material). This ex- Thickness= 4 82~m ~9 GeY 200 Foils assumes the radiator to be transparent at Io,„, and it also assumes that l,/l, » 1, i.e. , that the spectrum is determined primarily by sin- gle-foil interference. For the 82- and 50-pm ixIO— radiators, we measure the last maximum at 23 and 15 keg, respectively (see Fig. 3), while OId' =29 and 18 keV. This small but significant shift

I I I I I I ( I I I I I I I I I t I I I I I I I I III II IIIIII' in frequency is caused by multifoil interference CD 4 —Thick effects. In the case of the 16-pm radiator, with 250 a measured maximum at 9 reabsorption CD keV, at C) low frequencies strongly influences the spectral CD shape, and leads to a suppression of the oscil-

CD latory structure at low frequencies. I x IO— Because of the interference phenomena, the C) transition-radiation yield saturates for high par- C) CL ticle energies. In the present experiment, this I I I I I I I I I I I I I I I I i I I IIIIIIIIIIIIIIIIII saturation is expected at electron energies be- tween 5 and 10 GeV. 4 Consequently very little energy dependence of our measured spectra is noticeable. The saturation energy should, how- I x IO— ever, increase slightly with increasing foil thick- ness, a tendency noticeable in our results around for the thicker radiators. Summarizing, the theoretical predictions of transition radiation, which are based on classi-

IO 20 50 40 cal electromagnetic theory, are confirmed by our X-Ray Energy(keV) results in great detail. The radiation appears exactly at the expected frequencies; the structure FIG. 8. Frequency spectra of transition radiation of the spectrum determined the dimensions emerging from three radiators with different foil thick- is by nesses. The points (solid points for 5-GeV and open of the radiator; and the expected saturation at symbols for 9-GeV electrons) are measured data; and high particle energies is observed. the curves (dashed lines for 5-GeV and solid line for We are greatly indebted to Dr. R. I.. Blake, 9-GeV electrons) are the results of calculations (see Los Alamos, for much advice, for loaning us es- text). sential parts of the spectrometer, and with Mr. D. Barrus, for help during the calibrations. We appreciate the help of S. Jordan, Dr. G. Hart- a constant factor of 0,64. We do not feel that this mann, Dr. G. Fulks, and R. Petre during the ex- overall normalization indicates a strong depar- periment. We acknowledge the services of the ture from the expected behavior of transition ra- staff of our laboratory, in particular Mr. W. John- diation, "but we note that in other experiments son and Mr. E. Drag. Finally, we are grateful the total yield of transition radiation has also to Dr. B. McDaniel, Dr. N. Mistry, Dr. G. Rouse, been found to be lower than calculated. 4' ' and the personnel of the Cornell University syn- From Fig. 3, we see that the radiation hardens chrotron for their generous help and support. with increasing thickness of the radiator foils. This feature (which is also apparent in the data of Ref. 17) is of prime importance for practical +Work supported in part by National Aeronautics and applications, since it makes possible "tuning" of Space Administration Grants No. NGL 14-001-005 and a transition-radiation system such that the radi- No. NGL 14-001-258. ation appears predominantly at frequencies where L. C. L. Yuan, C. L. Wang, H. Uto, and S. PrGnster, Phys. Lett. 81B, 608 (1970). the detector is most sensitive. For high particle H. Ellsworth, J. MacFall, G. Yodh, F. Harris, energies, one expects4 the bulk of the radiation T. Katsura, S. Parker, V. Peterson, L. Shiraishi, at frequencies close to the last maximum in the V. Stenger, J. Mulvey, B. Brooks, and J. Cobb, in spectrum, near &o,„=l,Io,'/27rc (where & ~, is the Proceedings of the Thirteenth international Confexenoe VOLUME )8, NUMBER 1 PHYSICAL REVIEW LETTERS 5 JANUARY 1977

—— — on Cosmic Bays, Denver, Colorado, l973 (Colorado =e /hc, and the dielectric constants are e& 2 1 &sf g /

Associated Univ. Press, Boulder, 1978), Vol. 4, with co~ 2 the plasma frequencies of the two media. p. 2819. (See G. M. Garibian, Zh. Eksn. Teor. Fiz. 99, 992 J. Fischer, S. Iwata, V. Radeka, C. L. Wang, and (1960) [Sov. Phys. JETP 12, 237 (1961)].) W. J. Willis, Phys. Lett. 49B, 398 (1974). X. Artru, G. Yodh, and G. Mennessier, Phys. Rev. 4 M. L. Cherry, G. Hartmann, D. MH11er, and T. A. D 12, 1289 (1975).

Prince, Phys. Rev. D 10, 8594 (1974). Explicitly, Z&,2=4c/(u(y + 6 +(ui, 2 /o) ) (see Ref T. A. Prince, D. MGller, G. Hartmann, and M. L. 4) Cherry, Nucl. Instrum. Methods 129, 291 (1975). K. Hoshino, Y. Ohashi, A. Okada, K. Taira, and 6L. C. L. Yuan, P. W. Alley, A. Bamberger, G. F. K. Yokoi, Acta. Phys. Acad. Sci. Hung. 29, Suppl. 4, Dell, H. Uto, Nucl. Instrum. Methods 127, 17 (1975). 448 (1970). C. Camps. V. Commichau, M. Deutschmann, H. Gbd- A. A. Frangian, F. B. Harutjunian, V. P. Kishinev- deke, K. Hangarter, W. Liesmann, U. PHtzhofen, and ski, A. A. Nazarian, and G. B. Torgomian, in Proceed- R. Schulte, Nucl. Instrum. Methods 181, 411 (1975). ings of the International Conference on Instrumentation A. I. Alikhanian, K. M. Avakina, G. M. Garibian, for High Energy Physics, Dubna, U. S. S. R., 8-12 Sep- M. P. Lorikian, and K. K. Shikhliarov, Phys. Bev. Lett. tember 1970 (unpublished); see also Bef. 11, Sect. 29f. 25, 625 (1970). C. W. Fabjan and W. Struczinski, Phys. Lett. 57B, M. L. Ter-Mikaelian, Nucl. Phys. 24, 48 (1961). 488 (1975). G. M. Garibian, Zh. Eksp. Teor. Fiz. 60, 89 (1971) 8The collimator (Fig. 1) absorbs x rays if emitted un- [Sov. Phys. JETP 88, 23 (1971)]. der angles much larger than the most probable angle M. L. Ter-Mikaelian, Irigh-Energy Electromagnetic (6 = 1/y). Although the radiation intensity drops very Processes in Condensed Medha (Wiley, New York, sharply with increasing 0, this effect accounts for part 1972). of the discrepancy between the measured and calculated For a single interface d $0/d0d&u = 2uAG /s[y ~+ g~ intensity. (We appreciate a comment on this point by +(ug /cu2) —(y +6 +(uq /(u ) j, where y=E/mc', u C. W. Fabjan and G. M. Garibian. )

Short-Range, High-Momentum Effects in the Reaction '50(y, po) for E7=100-300 MeV

J. L. Matthews, W. Bertozzi, M. J. Leitch, C. A. Peridier, B. L. Roberts, C. P. Sargent, and W. Turchinetz DePartment of Physics and Laboratory for ¹clearScience, Massachusetts institute of Technology, Cambridge, Massachusetts 02139"

and D. J. S. Findlay and R. O. Owens Department of Natural Philosophy, University of Glasgow, Glasgow, United Kingdomt (Received 8 November 1976)

The 60(p,po) cross section has been measured for a series of photon energies between 100 and 300 MeV at proton angles of 45', 90', and 135'. Above 250 MeV, the results ex- ceed simple shell-model predictions by several orders of magnitude. The data are com- pared with a calculation which involves & excitation in an intermediate state.

The (y,p) reaction at energies well above the are now available for photon energies up to 100 giant dipole resonance has long been recognized MeV. The comparison of recent theoretical cal- as a potential source of information about short- culations with these data does not in fact yield range effects in nuclei, on account of its sensi- any conclusive evidence that short-range effects tivity to high-momentum components in nucleon are important. A consistent explanation of a wide wave functions. If the experimental (y,p) cross range of data has been achieved' by a model section is found to exceed that predicted by a which introduces a residual interaction with the shell-model calculation assuming a single-step range of the one-pion exchange force, thus in- knock-out mechanism, this could be taken as evi- creasirig the cross section predicted by the sin- dence that short-range effects are operating to gle-step proton knock-out mechanism. However, increase the high-momentum amplitudes above the need for this medium-range residual interac- those of the simple shell-model wave functions. tion can be largely removed by an alternative and Precise (y,p) measurements"' on several nuclei perhaps more reasonable choice' of the potential-