A Proposal to use Multiphoton Correlation Measurements to Solve the Phase Problem in X-Ray Crystallography
Kenneth Frankel
Lawrence Berkeley National Laboratory
We propose that by measuring the 2, 3 (and more) photon
correlation coefficients for an X-ray scattering experiment from a crystal
(or single molecule) one would be able to obtain initial phase information
that could be used to solve the molecular structure. We suggest a
preliminary design for the electron beam (for X-ray generation)
characteristics required to carry out the experiment. We will discuss the
initial design requirements (partially coherent illumination; intense,
nearly monochromatic, and femtosecond pulse beams). The requirements
suggest that the accelerator would be difficult to build but not impossible.
Previous experiments and theory support our proposal that multi-photon
correlation measurements could be applied to solving the phase problem in
X-ray crystallography. Two-particle boson correlation measurements have been
used over the past fifty years to measure the size of the boson emitting
source. The physics relies on the quantum mechanical phenomenon of bunching
(a consequence of Bose-Einstein statistics) and is equivalent to the
classical phenomenon of intensity interferometry (Hanbury-Brown Twiss (HBT)
effect). In HBT experiments, the results are a consequence of correlations
in the fluctuations of the electromagnetic field intensities. Two photon
correlation and intensity interferometry experiments have been conducted to
measure the angular size of stars, the source size in mercury lamps, and the
source size of synchrotron beams. Two and three-pion correlation experiments
have been used to study the source size in high energy and nuclear physics.
These experiments relied on a partially coherent, nearly thermal, and nearly
monochromatic radiation source. The radiation source itself was the object
under study. In a classic paper, Goldberger et al.1 showed that
the radiation source could be distinct from the object under study. They
showed that correlation measurements could be used to obtain the phase of
the scattering amplitude in two particle scattering experiments. While not
being crystallographers themselves, they did suggest applications for X-ray
crystallography in their paper.
For the general HBT experiment with two detectors, phase information is
lost, as the correlation measurement is proportional to the square of the
Fourier Transform of the source. While Goldberger et al. and others have
suggested that phase information can be obtained from a 2 particle
measurement from 2 independent sources, one needs to measure 3 or more
particles in coincidence to obtain phase information if there a single
radiation source. Some phase information has been extracted from three pion
correlations measured in relativistic heavy-ion collisions; however, the
results are difficult to interpret. Further studies will enable us to refine
the design requirements for our proposed experiment and to hopefully develop
a cost effective method of conducting the experiment in a timely manner.
References:
1. Goldberger, Lewis, and Watson, “Use of Intensity Correlations to Determine the Phase of a Scattering Amplitude”, Phys. Rev. (Dec 1963)
This work was supported by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
