Direct Measurement of the Formation Length of Photons

We report the first observation of a shoulder in the radiation spectrum from GeV electrons in a structured target consisting of two thin and closely spaced foils. The position of the shoulder depends on the target spacing and is directly connected to the finite formation length of a low-energy photon emitted by an ultrarelativistic electron. With the present setup it is possible to control the separation of the foils on a $\mu \mathrm{m}$ scale and hence measure interference effects caused by the macroscopic dimensions of the formation length. Several theoretical groups have predicted this effect using different methods. Our observations have a preference for the modified theory by Blankenbecler but disagree with the results of Baier and Katkov.

Figure 1

Radiation intensity for a 197 GeV electron passing a gold target. The spectra have been normalized to the radiation length and the target thickness so that the Bethe-Heitler level is $4/3$. The Bethe-Heitler intensity is shown (black) together with the LPM effect (red), a simple model of the TSF effect (green) for a $26\mu \mathrm{m}$ Au target, a calculation using the formalism of Blankenbecler and Drell (BD) for a $26\mu \mathrm{m}$ Au target (green, dotted), a similar calculation using the theory of Baier and Katkov (BK) (blue, dotted) and for a sandwich target consisting of two $26\mu \mathrm{m}$ foils separated by $45\mu \mathrm{m}$ using BD (green, dashed) and BK (blue, dashed). The corrected BD theories (BD-$\delta$) are shown in black for the reference (dotted) and structured target (dashed). A BD-$\delta$ calculation for a target spacing of 1 mm is also shown (red, dashed) (see text for more details).

Figure 2

Experimental setup (not to scale). A 197 GeV electron beam passes the target assembly and is deflected by a magnet setup. Approximately 65 m downstream a BGO detector is placed in the photon beam and the deflected electron beam is measured by a lead glass calorimeter (LG).

Figure 3

BGO data and MC simulations. No target data are shown with red squares, reference data with green circles and $45\mu \mathrm{m}$ separation with black stars. MC is shown with lines. No target in red, reference in green, and $l_g=45\mu \mathrm{m}$ in black. The horizontal bar is the bin width.

Figure 4

The ratio between a measurement with $l_g=45\mu \mathrm{m}$ and the reference measurement. Both spectra have been background subtracted. The BGOA measurements are shown with black stars and BGO with red circles. Monte Carlo simulations using BD (green) and BD-$\delta$ (red) theories are also shown. Several theoretical curves based on BD and BK theory are shown for different gap sizes. The horizontal bar is the bin width and the vertical bar is the statistical errors.

Figure 5

The ratio between a measurement with $l_g=1\mathrm{mm}$ and a reference measurement. Both spectra have been background subtracted. The BGOA measurements are shown with black stars and BGO with red circles. Monte Carlo simulations using BD (green) and BD-$\delta$ (red) theories are also shown. The horizontal bar is the bin width and the vertical bar is the statistical errors.