Polarized Neutrons in RHIC Page: 2 of 7
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RIKEN-BNL Workshop on RHIC Spin Physics, April 27-29, 1998
Polarized Neutrons in RHIC*
Ernest D. Courant
RHIC Project
April 20, 1998
There does not appear to be any obvious way to accelerate neutrons, polarized or otherwise, to
high energies by themselves. To investigate the behavior of polarized neutrons we therefore have to obtain
them by accelerating them as components of heavier nuclei, and then sorting out the contribution of the
neutrons in the analysis of the reactions produced by the heavy ion beams.
The best "neutron carriers" for this purpose are probably 3He nuclei and deuterons. A polarized
deuteron is primarily a combination of a proton and a neutron with their spins pointing in the same
direction; in the 3He nucleus the spins of the two protons are opposite and the net spin (and magnetic
moment) is almost the same as that of a free neutron.
Polarized ions other than protons may be accelerated, stored and collided in a ring such as RHIC
provided the techniques proposed for polarized proton operation can be adapted (or replaced by other
strategies) for these ions.
To accelerate polarized particles in a ring, one must make provisions for overcoming the
depolarizing resonances that occur at certain energies. These resonances arise when the spin tune (ratio of
spin precession frequency to orbit frequency) resonates with a component present in the horizontal field.
The horizontal field oscillates with the vertical motion of the particles (due to vertical focusing); its
frequency spectrum is dominated by the vertical oscillation frequency and its modulation by the periodic
structure of the accelerator ring. In addition, the magnet imperfections that distort the closed orbit vertically
contain all integral Fourier harmonics of the orbit frequency.
The spin precession frequency in a plane machine is
Vp = Gy(1)
in the frame of reference turning with the particle, where G = (g-2)/2 is the magnetic moment anomaly of
the particle. Resonances due to betatron oscillations ("intrinsic resonances") occur at those energies where
ry = v,+ kP (2)
where v,, is the vertical betatron oscillation tune, P is the periodicity of the lattice, and k is any integer. In
addition "imperfection" resonances, associated with orbit distortion, occur at all integer values of G y. Each
resonance is characterized by a strength >, which depends on the amplitude of oscillations and/or orbit
distortion as well as on the details of the lattice and, of course, on G. The resonance strengths can be
calculated by the program DEPOL.
For protons G = 1.793, and therefore the imperfection (integer) resonances are spaced by Mc2/G =
523 MeV. In the RHIC lattice (6 insertions, the equivalent of about 81 FODO cells, P=3) intrinsic
resonances for each sign in (2) are 3x523 MeV apart, but the strong ones only occur with spacing of about
81 units of Gy The strongest imperfection resonances tend to occur at those integer values of G y which
are near the ones for strong intrinsic resonances.
* Work performed under the auspices of the U.S. Department of Energy.1
BNL-65606
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Courant, E. D. Polarized Neutrons in RHIC, report, May 1, 1998; United States. (https://digital.library.unt.edu/ark:/67531/metadc863956/m1/2/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.