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. P n is the neutron beam polarization, ε rf 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 A ϒ.

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

RF Spin Flipper In the RFSF there is a static field B 0 =9.7G from the guide field and a RF field B rf 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 B 0. If the RF field oscillates at the Larmor frequency of the neutron magnetic moment in the guide field ω L =ϒB 0 =29kHz then the frequency of B rf is on resonance and one rotating component of B rf 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 B rot. 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 3 He spin filter SNS 60Hz 10cm × 12cm Supermirror polarizer

Field Uniformity S. Balascuta The rf field B rf in the RFSF is not uniform because B rf 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. The efficiency of the RFSF off axis is determined by the integral of the amplitude of B rf experienced by the neutron over the length of the RFSF.

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

3 He is polarized through spin exchange with optically pumped alkali metal such as Rb or K. How do we polarize 3 He? Only electrons in the S 1/2 state with m s =-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 P 1/2 m s =+1/2 state. The excited electron will decay back to the S 1/2 ground state with either value for the spin state. Since only the ground state electron in the m s =-1/2 spin state can absorb a photon but the excited electron can decay to either spin state, the m s =+1/2 spin state will eventually become populated. The 3 He 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 3 He cell is polarized in a static magnetic field of 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 3 He polarization takes several hours to saturate and is usually pumped over night. The spin-lattice relaxation time of a 3 He cell will often be over 100 hours, which will provide a stable 3 He polarization for polarimetry measurements.

3 He Analyzer Cells Five 3 He analyzer cells have been produced for the polarimetry measurement and named Maxwell, Nambu, Oppenheimer, Ramsey, and Szilard. The 3 He cells are 1in diameter cylindrical cells made of GE180 glass. They are filled with 3 He, N 2, and trace amounts of Rb for polarization of the 3 He. So far three of the 3 He cells have been characterized. Length 3 He Thickness 3 He Pressure T1 Lifetime Max. Polarization Maxwell 2.5” 0.97 Å bar 18.1hr 19% Nambu 4” 1.24 Å bar 10.8hr 32% Oppenheimer 3” 1.14 Å bar 11.6hr 37%

3He Analyzer in the Beamline

Neutron Transmission through a 3 He Cell Neglecting normalization, the measured neutron flux of an unpolarized neutron beam through an unpolarized and polarized 3 He cell are given by: Where κ is the 3 He cell thickness, which is a function of the 3 He density n, the length of the cell l, and a normalizing reference cross-section σ 0 and neutron wavelength λ 0. 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 3 He cell.

Transmission of a Polarized Neutron Beam through a 3 He 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 3 He cell can then be determined from a polarized neutron beam. Where R ↑ =N ↑ /N 0 and R ↓ =N ↓ /N 0 are ratios of the flux measurements.

Polarization of the Neutron Beam The effective efficiency of the supermirror polarizer and the polarized 3 He cell is the product of their polarization efficiencies, P n P n He. The detected neutron flux through the supermirror and the 3 He 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 3 He cell will be measured corresponding to the RFSF on and off and the two 3 He spin states tuned by AFP. Where N 0 (λ)=e -κλ is the neutron flux through an unpolarized 3 He cell. These measurements will also be done at several 3 He polarizations. Since the polarization of the neutron beam is independent of the polarization of the 3 He, 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 10 8 n/cm 2 s, an aperture of 1 cm 2, 20 time bins, 5×10 2 n/time bin, a relative neutron transmission of 0.01 through a thick 3 He 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.