”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

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

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

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, 423-433) and M. Forte (Nuovo Cimento A18, 727-736) If kRegz<<1 and kImgz<<1 - Is the particle polarization is the spin dichroism effect

Evolution of beam in a target rotation spin dichroism V.Baryshevsky arXiv:1101.3146

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

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

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. 2010. Vol. B 683. P. 229

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., 222501 Phys. Part. and Nucl. Lett., 2010,7.,No 1, p. 27

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

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.

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