by Glenn Roberts Jr.
The magic angle is all about mathematics, not hocus pocus, but it can work wonders in gathering useful data in scientific experiments and in medical imaging, too.
John Bozek, an instrument scientist at SLAC’s Linac Coherent Light Source, said the angle, which measures about 54.7 degrees, is important for a range of experiments with the X-ray laser, particularly those involving gases.
In photoelectron spectroscopy, a common research technique at LCLS, X-ray laser pulses strike a sample and eject electrons from it. Instruments called spectrometers measure the energy range, or spectrum, of the ejected electrons.
To get the most accurate measurements of the energy spectrum of those electrons, a detector can be placed at the magic angle relative to the path of the laser beam through the sample.
A detector placed at other angles can provide conflicting data, though it is possible to get an accurate measurement by comparing observations from multiple angles.
“If you measure the spectrum at 90 degrees, then measure it at zero degrees, some of the peaks in the spectra completely disappear; the intensity of the peaks will depend on the angle,” Bozek said. “So either you measure at a few angles, or you measure at the magic angle.”
One of the spectrometers at the LCLS’s Atomic, Molecular and Optical Science instrument is typically aligned at the magic angle, Bozek noted, to help cancel out such effects.
The magic angle is also useful in magnetic resonance imaging, among other applications.
The magic angle can be formed by drawing a line from a bottom corner in the inside of a cube diagonally to its opposite corner at the top of the cube, and measuring the angle between that diagonal line and the vertical line that rises from that bottom corner.