1. ”Optical” spin rotation phenomenon and spin-filtering of antiproton (proton, deuteron) beams in a nuclear pseudomagnetic field of a polarized nuclear target: the possibility of measuring the real and imaginary spin-depended part of the coherent zero-angle scattering amplitude
V. Baryshevsky, A. Rouba

2. Birefringence effect & Faradey effect
Could the “optical” effect exist for proton, neutron,
deuteron and other particles?

3. Refractive index If For particles with a spin
As a result of numerous studies (M.Lax, Rev.Mod.Phys. 23 (1951) 287…), a close relation between the amplitude f(0) of coherent elastic scattering at zero angle and the refraction index of a medium n can be established If
where k is the wave number of a particle, ρ is the number of particles per cm^3
For particles with a spin
For proton (antiproton) beam and target
is the target polarization

4. Pseudomagnetic field?
Suppose that particle absorption can be neglected, so
is the real vector
similar to Faraday effect
Experimentally observed for slow neutrons by A. Abragam (C.R. Acad. Sci. B274, ) and
M. Forte (Nuovo Cimento A18, )
If kRegz<<1 and kImgz<<1
- Is the particle
polarization
is the spin dichroism effect

5. Evolution of beam in a target
rotation
spin dichroism
V.Baryshevsky arXiv:

6. Evolution of beam in a target
Assume that target polarization is parallel or orthogonal to the
Transmission experiment with different absorption for
and without rotation of the
Case 1:
Direct measurement of imaginary part of spin dependent amplitude A1 and A2
Case 2:
Transmission experiment with rotation of the
Direct measurement of imaginary part of spin dependent amplitude A1 and A2

7. Evolution of beam in a target
Assume that target polarization is directed at some angle a to the beam momentum, and that the beam polarization is orthogonal to the plane
formed by vector of the target polarization and vector of momentum
Case 3:
Spin rotation above vector combined with spin dichroism
(absorption), determined by
In the transmission experiment it possible to measure ReA1 and ReA2, by measuring
beam lifetime for beam with the polarization and orthogonal to the orbit plane
of a storage ring
Inverse process:
Initially unpolarized proton (antiproton) beam becomes polarized
orthogonally to orbit plane of storage ring

8. Dichroism Transmission of unpolarized deuteron beam
through unpolarized (spinless) target
for Sz=±1
for Sz=0
from the optical
theorem
Dichroism
V. Baryshevsky and A. Rouba // Phys. Lett Vol. B P. 229

9. in front of target for unpolarized deuterons
Dichroism for deuterons
where Io and I±1 are the deuteron
occupation numbers with a spin
projection Sz=0 and Sz=±1, respectively
ρ is the number of scatterers per cm^-3,
z is the thickness in cm,
z’ is the thickness in g/cm^-2
in front of target for unpolarized deuterons
Pz=0, Pzz≠0
after target
Pz=0,
Pzz=0
Phys. Rev. Lett.,2010., 104.,
Phys. Part. and Nucl. Lett., 2010,7.,No 1, p. 27

10. Transmission (filtering) of unpolarized proton beam
through a polarized deuteron target in storage ring
Unpolarized proton beam
Unpolarized proton beam
Polarized deuteron target Pzz=-2, m=0
Polarized deuteron target Pzz=1, m=1

11. Transmission (filtering) of unpolarized proton beam
through a polarized deuteron target in storage ring ,
ρ is the target thickness in atoms/cm^2
ν is the revolution frequency
deuteron/cm^2 Hz mb mb
To obtain 10% difference in proton beam intensity due to spin dependent part
of total cross-section t should be about 4 hours.
Beam intensity drops in 4 times.

12. Summery
The real part of spindependent forward scattering amplitude for proton (antiproton)
can be directly determined by measuring of rotation of beam polarization relatively
polarization of an internal target at storage ring
The imaginari part of spindependent forward scattering amplitude for proton,
antiproton, deuteron can be directly determined by measuring of lifetime of beam,
passing through polarized (quadrupolarized) internal target at storage ring
The proton (antiproton) beam with polarization orthogonally to orbit plane
of storage ring can be obtained by transmission of unpolarized proton (antiproton)
beam through
internal target with vector polarization in orbit plane formed non right angle with beam
momentum