Computer simulations of the n 4 He parityviolating

Computer simulations of the n 4 He parity-violating spin-rotation experiment at NIST Bret Crawford Gettysburg College DNP Oct. 28, 2006

Outline • Systematic Effects – Ambient magnetic field rotations – 4 He diamagnetism – Neutron slowing down in liquid He target – Small angle scattering • Simulation – Neutron transport – Modeling scattering cross section • Future Plans

Ambient Magnetic Field Rotations • Rotation angle • Magnetic field suppression, longitudinal B<100 m. G B=100 m. G, L=1 m, l=5 Ang Compare with experimental goal of • Subtracting Data from Upstream and Downstream targets cancels non-target related effects

4 He Diamagnetism • Reduces ambient external field B in target region • Neutrons in target cell precess slightly less than neutrons in empty cell

Neutron slowing down in target • Difference in indices of refraction between a full and empty target • Neutron slows in target causing larger rotation in ambient field • 100 m. G field in 1 meter

Small-angle scattering Target positions Wave guides detector • Upstream-downstream subtraction is incomplete – Lower energy for scattered neutrons (Up-target scatters travel farther at lower energy than down-target scatters) – path length of neutrons scattered in target is different for different target positions (down stream angle is larger)

Small-angle scattering Target positions Wave guides detector • different detector solid angles from target positions From simulation see ~3% more scattered neutrons in Detector from Down target than Up target • Amount of scattering into detector is small but not that small ~0. 2% of detected neutrons have a new angle and new energy from scattering (simulation) With Up-Down subtraction non-PV rotations are in the few x 10 -8 rad range

Neutron Transport Simulation* • • Random trajectories within critical angle of guide If wall angle < critical angle, bounce; otherwise absorbed. wave guide (qc=1 mrad/Ang) input coil (qc=1 mrad/Ang) target cell (empty LU, full RD)s pi-coil between target output coil ASM (apertures only; qc=3 mrad/Ang) *Murad Sarsour, Mike Snow, Bret Crawford

Modeling the Scattering Cross section : n-4 He • Absorption is negligible • Scattering is coherent • Detailed knowledge of scattering at low momentum transfer is a research question • Model for scattering in simulation code Choose q from S(q) Find energy from dispersion curve Calculate cross section from q and E Determine if scatters within target Follow new trajectory to target

arbitrary Modeling the Scattering Cross section : n-4 He Dispersion curve S(q) q(1/Ang)

Scattering Cross section • q<0. 56 use Tsipenyuk and May results Tsipenyuk, May (ar. Xiv: cond-mat/0207278 v 1, 2002) -unpublished data for S(0) • q>0. 56 use Sommers’ data Sommers, Dash and Goldstein (Phys Rev, 97)1954

Simulation energy at detector wavelength at detector

Rotation angle for Bz=100 m. G q (all neutrons) q (scattered only) rotation angle for entire beam line – 477 cm (no pi-coil)

Rotation angle for Bz=100 m. G Up Target q Down Target q rotation angle for entire beam line (pi-coil reverses rotation between targets)

Rotation angle for Bz=100 m. G Large rotation values Up Target q Down Target q rotation angle for entire beam line (pi-coil reverses rotation between targets)

Rotation angle for Bz=100 m. G (U-D)/(U+D) q (mrad)

Simulation: Preliminary Results • Neutron flux along beamline (z) * – Entering target 1 (UR): 23% – Entering target 2 (DL): 19% – Into detector: 11% • Scattering Info – 26% entering target scatter – 0. 2% entering detector have scattered, • Rotation after Up-Down Subtraction, averaged over all neutrons (angles, energies, positions) – 100 m. G *initial angles chosen to be within critical angle of guide

Future • Improve scattering model – Use x-ray data for low-q region of S(q) (R. Hallock, PRA 5, 1972) – Analytic calculation of double differential cross section • Include multiple scattering • Run for test targets

Neutron Transport Top View guide Input coil targets Output coil ASM x y 116 cm 89 cm 41. 6 cm • Guide and Input Coil x[-3. 05, -0. 35], [0. 35, 305] y[-2. 55, 2. 55] • Output Coil and targets x[-3. 0, -0. 35], [0. 35, 30] y[-2. 5, 2. 5] • Supermirror x[-2. 85, 2. 85] y[-2. 25, 2. 25] • Gaps [9. 0, 6. 8, 12. 0] 108 cm 28 cm z

Plots entrance x-distribution before target 1

Plots x-distribution after target 1 (UL) after target 2 (DR)

Plots x-distribution Before ASM detector