**Beam Polarimetry** Matthew Musgrave NPDGamma Collaboration Meeting Oak Ridge National Laboratory Oct. 15, 2010

**Introduction** The neutron beam polarization and the spin flip efficiency of the RFSF need to be determined to obtain the parity violating physics ϒ-ray asymmetry from the measured ϒ-ray asymmetry. Pn is the neutron beam polarization, εrf is the efficiency of the RFSF, and C is a constant representing the rest of the corrections to the measured asymmetry. The goal of the polarimetry measurement is to obtain the polarization of the neutron beam to within 5% to help achieve a statistical precision of ~10-8 for Aϒ.

**Polarimetry** The neutron beam polarization will be determined from relative neutron flux measurements through a polarized 3He analyzer cell. The neutron spin will be flipped by a RFSF and the 3He spin will be flipped by adiabatic fast passage to provide redundant methods of measuring the signal of opposing spin states of the neutrons. RFSF 3He analyzer cells

**RF Spin Flipper** In the RFSF there is a static field B0=9.7G from the guide field and a RF field Brf produced by the RFSF oscillating in the direction of the neutron beam. The RF field can be approximated as two counter rotating fields, rotating normal to the guide field B0. If the RF field oscillates at the Larmor frequency of the neutron magnetic moment in the guide field ωL=ϒB0=29kHz then the frequency of Brf is on resonance and one rotating component of Brf follows the precession of the neutron magnetic moment. The other component is off resonance by twice the Larmor frequency and has a negligible effect on the precession of the neutron magnetic moment. In the rotating frame of reference of the neutron magnetic moment there is only a field in the ẑ direction.

**RF Spin Flipper** In the rotating reference frame on resonance, the neutron magnetic moment precesses about the effective magnetic field at the Larmor frequency for Brot. To achieve a spin flip of the neutron beam, the neutrons need to remain in the RFSF for the time required to rotate the neutron spins by π radians. Where n=1, 3, 5… The time spent in the RFSF is dependent on the neutron’s velocity, which for the NPDGamma experiment is characterized by the neutron’s time of flight. Where L is the length of the RFSF and l is the distance to the neutron moderator. To rotate the neutron spins by π radians, the rf field of the RFSF must be varied with the time of flight.

**Efficiency of RFSF at LANL** The efficiency of the RFSF at LANL was measured to be 98.8±0.5%. Differences in the design of the beam line and the method of polarizing the neutrons will affect the efficiency of the RFSF and how it is calculated. LANSCE 20Hz 9.5cm × 9.5cm 3He spin filter SNS 60Hz 10cm × 12cm Supermirror polarizer

**Field Uniformity** The rf field Brf in the RFSF is not uniform because Brf is produced by a finite solenoid. If the RFSF is tuned to maximize efficiency in the center of the beam, the RFSF efficiency will be less than unity off axis. S. Balascuta The efficiency of the RFSF off axis is determined by the integral of the amplitude of Brf experienced by the neutron over the length of the RFSF.

**Neutron Polarization by Capture on Polarized 3He** The cross-section for neutrons with spin anti-parallel to the 3He nuclear spin is very large. Twice the cross-section for unpolarized neutrons. p n n n p p n p The cross-section for neutron capture on 3He with nuclear spin parallel to the neutron spin is nearly zero. p n n n p p n p The strong spin dependence of the neutron capture cross-section of polarized 3He makes it an effective neutron polarizer and analyzer.

**How do we polarize 3He?** 3He is polarized through spin exchange with optically pumped alkali metal such as Rb or K. • Only electrons in the S1/2 state with ms=-1/2 can absorb the laser light because the light is circularly polarized with magnetic projection of +1. • The valence electron in the alkali metal absorbs a photon with angular momentum of +1 and magnetic projection of +1 and is excited to the P1/2 ms=+1/2 state . • The excited electron will decay back to the S1/2 ground state with either value for the spin state. • Since only the ground state electron in the ms=-1/2 spin state can absorb a photon but the excited electron can decay to either spin state, the ms=+1/2 spin state will eventually become populated. • The 3He is then polarized through spin exchange hyperfine interactions with the electrons of the alkali atoms.

**Spin Exchange Optical Pumping** Collision Mixing

**Optical Pumping Station** The 3He cell is polarized in a static magnetic field of 12-14 Gauss, and its polarization and spin-lattice relaxation time are determined in the lab by NMR. During optical pumping the Rb’s polarization becomes saturated in under a second, but the 3He polarization takes several hours to saturate and is usually pumped over night. The spin-lattice relaxation time of a 3He cell will often be over 100 hours, which will provide a stable 3He polarization for polarimetry measurements.

**3He Analyzer Cells** Five 3He analyzer cells have been produced for the polarimetry measurement and named Maxwell, Nambu, Oppenheimer, Ramsey, and Szilard. The 3He cells are 1in diameter cylindrical cells made of GE180 glass. They are filled with 3He, N2, and trace amounts of Rb for polarization of the 3He. So far three of the 3He cells have been characterized. Length 3He Thickness 3He Pressure T1 Lifetime Max. Polarization Maxwell 2.5” 0.97 Å-1 2.1 bar 18.1hr 19% Nambu 4” 1.24 Å-1 1.7 bar 10.8hr 32% Oppenheimer 3” 1.14 Å-1 2.0 bar 11.6hr 37%

**3He Analyzer in the Beamline**

**Neutron Transmission through a 3He Cell** Neglecting normalization, the measured neutron flux of an unpolarized neutron beam through an unpolarized and polarized 3He cell are given by: Where κ is the 3He cell thickness, which is a function of the 3He density n, the length of the cell l, and a normalizing reference cross-section σ0 and neutron wavelength λ0. The polarization of the neutron beam is given by: If the wavelength of the neutrons is known, the polarization can be rewritten as a function of neutron flux measurements through the cell. This is the analyzing power of the 3He cell.

**Transmission of a Polarized Neutron Beam through a 3He Cell** Assuming the neutron spin can be flipped with unit efficiency, the transmission of an unpolarized neutron beam can be approximated from a polarized neutron beam by flipping the neutron spins and averaging the flux measurements of the two neutron spin states. The analyzing power of the 3He cell can then be determined from a polarized neutron beam. Where R↑=N↑/N0 and R↓=N↓/N0 are ratios of the flux measurements.

**Polarization of the Neutron Beam** The effective efficiency of the supermirror polarizer and the polarized 3He cell is the product of their polarization efficiencies, PnPnHe. The detected neutron flux through the supermirror and the 3He cell can be determined from the effective efficiency. The polarization of the neutron beam as a function of neutron wavelength can then be calculated from relative neutron flux measurements.

**Neutron Flux Measurements** Four neutron flux measurements through a polarized 3He cell will be measured corresponding to the RFSF on and off and the two 3He spin states tuned by AFP. Where N0(λ)=e-κλis the neutron flux through an unpolarized 3He cell. These measurements will also be done at several 3He polarizations. Since the polarization of the neutron beam is independent of the polarization of the 3He, these additional measurements will provide a redundant check on the beam polarization. The efficiencies of the RFSF and the AFP coils can also be determined from the neutron flux measurements.

**RFSF Efficiency** The 3He polarization can be flipped with nearly 100% efficiency by adiabatic fast passage. By assuming no loss in polarization of the 3He, the efficiency of the RFSF can be determined by ratios of sums and differences of neutron flux measurements.

**Statistical Precision** To determine the polarization of the neutron beam to within 5%, the statistical precision of each neutron flux measurement will be measured to better than 1.5%. This equates to about 5000 neutrons detected by the neutron detector. Neutron flux measurements will be taken for about 20 time bins to determine the polarization at different neutron wavelengths . Assuming a neutron flux of 108 n/cm2s, an aperture of 1 cm2, 20 time bins, 5×102 n/time bin, a relative neutron transmission of 0.01 through a thick 3He cell, and a 10% capture efficiency in the neutron detector. A conservative estimate for the time of a statistically significant neutron flux measurement can be calculated. The time required to make a neutron flux measurement is small enough that the polarimetry measurement will not be statically limited.