Channeling spin precession        updated October 25, 2007  D. Carrigan carrigan@fnal.gov (subject line must be sensible)

Channeling Formulary


Fermilab
Home
Pillars
Channel Home
Adv. Accel. Infrared/Dyson
SETI Biography Bibliography Nobel Prizes

Introduction

An interesting possible application of channeling in a bent crystal is the precession of the spin of a polarized particle. This may allow the measurements of magnetic moments in distances of only a few cm. The lifetimes of baryons containing charm quarks are so short that they travel only a few centimeters even at the highest available accelerator energies. Because of these short lifetimes, classical spin precession techniques using conventional magnets would produce negligibly small spin precession angles.

 

Baryshevskii and Pondrom independently pointed out that the magnetic moments of particles should precess if they were channeled in a bent crystal. The detailed precession theory has been developed by Lyuboshits and Kim. In a curved crystal the electrostatic field of the atomic planes deflecting the particle transforms into a magnetic field in the particle’s rest frame.

Channeling can be preserved for equivalent magnetic fields up to ~1000 T thus offering the potential of significant precession angles even when the length of the bent crystal is as small as 1
cm. More details on the process are given at Phys. Rev. Lett. 69, 3286 (1992).
spin precession

Spin precession

In this schenmatic a positive charged charm baryon is produced near or in a single crystal. The spin direction is perpendicular to the charm particle production plane which is parallel to a crystal plane. The crystal curvature produces an average centripetal electric field that causes the channeled particle to follow the crystal plane. That electric field transforms into the magnetic field B in the particle center of mass. The spin of the charm baryon precesses around this magnetic field. By observing the precession of the spin through the particle decay distribution it is possible to determine the magnetic moment of the baryon.
Spin precession apparatus

The apparatus

The Fermilab P-Center hyperon beam provided a tool for testing this concept. Using a beam of polarized Sigma+ hyperons we measured their spin precession in bent Si single crystals. With this result we determine the Sigma+ magnetic moment. The measurements were performed as part of Fermilab experiment E761. The apparatus consisted of a hyperon spectrometer (one dipole magnet and three clusters of silicon strip detectors) and a baryon spectrometer (two dipole magnets and four clusters of multiwire proportional chambers).

Two bent Si crystals were installed downstream of the hyperon spectrometer at the beginning of the decay region. The major faces of the crystals were cut along their (111) planes, which were oriented in the xz plane. Each crystal was 2.50 x 0.04 x 4.50 cm3. The beam was incident on the 2.50x0.04 cm* face. The upper crystal deflected the beam down and the lower crystal deflected the beam up. The deflections were approximately the same. The crystal curvature produced an equivalent magnetic field, Bx. which precessed the spins of the channeled particles in the yz plane. The bending of the two crystals was such that each crystal precessed the channeled particle’s spin in opposite directions. Energy loss detectors were implanted along the beam path in each of the crystals. These measured the energy loss of particles traversing the crystals and helped distinguish channeled particles, which have less energy loss, from non-channeled ones.

Results

The results


The measured polarizations are shown in the figure as solid arrows. The predicted precessions based on previous measurements are also shown as the dashed lines. The measured precessions agree with the predicted values within the measured errors As anticipated, the spins in the two crystals precess in opposite directions. Since the magnitude of the polarization after precession is consistent with the undeflected measurement, there is no evidence of depolarization during
channeling.

This experiment has confirmed spin precession for particles channeled in bent crystals. This phenomena could eventually open the way for magnetic moment measurements of short-lived particles such as charm baryons.