Refractive-index measurement of Si at $\gamma$-ray energies up to 2 MeV

The refractive index of silicon at $\gamma$-ray energies from 181 to 1959 keV was investigated using the GAMS6 double crystal spectrometer and found to follow the predictions of the classical scattering model. This is in contrast to earlier measurements on the GAMS5 spectrometer, which suggested a sign change in the refractive index for photon energies above 500 keV. We present a reevaluation of the original data from 2011 as well as data from a 2013 campaign in which we show that systematic errors due to diffraction effects of the prism can explain the earlier data.

Figure 1

General layout and working principle of a double crystal spectrometer as used for the refractive-index measurement. The photon source is 15–20 m away from the first crystal inside the high flux reactor of the Institut Laue Langevin. Over this distance the beam is shaped by a system of fixed collimators. The spectrometer generates a low divergence monochromatic beam, which is separated from the primary beam by a system of movable collimators.

Figure 2

Experimental setup of the refractive-index experiment at GAMS5. The green cuboid indicates the collimated $\gamma$ beam. The red arrow demonstrates the direction of the shutter movement to alternate between refracted and reference beam.

Figure 3

Intensity of two selected $\gamma$ lines as a function of the rotation angle of the second spectrometer crystal. The blue (red) triangles (circles) are the experimental data and the black line shows a double Gaussian fit to the data. The fit is used to determine the position of the center of the rocking curve. The rocking curves at 181 keV (blue triangles) and 944 keV (red circles) are shown as examples. For high $\gamma$ energies the width of the rocking curve becomes smaller with the $\gamma$ energy as $E_{\gamma }^{-1}$ in accordance with dynamic diffraction theory [16].

Figure 4

Results of the real part $\delta$ of the complex index of refraction as a function of $\gamma$-ray energy. The experimental data is plotted after subtraction of the classical theoretical model (2). The GAMS6 measurement follows the classical model well with decreasing uncertainties to higher energies due to the narrower rocking curve. The GAMS5 measurements of 2011 and 2013 show significant deviations at 181 and >500 keV. These deviations are caused by different systematic effects: at 181 keV they originate due to beam passage through different parts of the GAMS5 crystal and for energies >500 keV they arise due to the onset of diffracting phenomena of the silicon prism (for details see text). The gray bar indicates the sensitivity limit of the GAMS6 measurement, as established via a run without refracting prisms.

Figure 5

Results of a radiography of the silicon prism as it was used for the GAMS5 experiments. The solid lines show the intensity profile, when the prism was not in diffraction orientation. The dashed lines show the same measurement, but with the prism in diffraction position. It can be seen that substantial amounts of intensity can be diffracted.

Figure 6

Data from the 2011 GAMS5 run compared to a model (4) describing the measured angular deviation in terms of superposition of a refraction and a diffraction component. The parameters of the model were fitted to the data showing an excellent agreement: $D=0.000040661148613035, E_c=978.78, \delta E=446.61$. The refraction part in (4) was not fitted, but calculated using the classical approximation model (2): $C=0.004146748006128347$. However, the data point at 181 keV is out of the combined model, as well as the refraction part, where the reason was explained in Sec. 3b. As shown in the inset, the primary beam is diffracted by the silicon lattice of the prism above a certain threshold energy. As illustrated, the incident, low-divergence beam enters the angular acceptance range for Bragg diffraction for higher energies. Note that the angles are exaggerated for clarity in the schematic and therefore the diffracted and refracted beam appear to separate spatially. However, for the small angles encountered at high photon energies, both possible paths through the prism overlap and can enter the detection system.

Figure 7

Schematic setup of the GAMS6 experiment, which illustrates the methodology of the experiment. Two prisms are shifted between the two crystals. This arrangement is less prone to systematic errors by ensuring that the same sections of the spectrometer crystals are used during the experiment and that refraction is measured in both positive and negative angles.

Figure 8

Red error bars: Time sequence of measured peak positions $c_{u,l,+,-}^{\left(i\right)}$ for the 517 keV measurement. The pattern of the 4-pack sequence can be clearly identified. From the data, the measured average Bragg angle (demeaned) and a slight linear drift of $-0.6$ nrad/h has been subtracted to visualize the corrective functioning of the 4-pack algorithm. Violet error bars: These are data from a measurement sequence without prisms. The data scatter randomly. The black lines indicate the sensitivity after 12 h measurement.