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

2. 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

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

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

5. 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  G field in 1 meter

6. Small-angle scattering 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) Target positions Wave guides detector

7. Small-angle scattering 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 x10 -8 rad range Target positions Wave guides detector

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

9. 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

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

11. Scattering Cross section q<0.56 use Tsipenyuk and May results Tsipenyuk, May (arXiv:cond-mat/0207278 v1, 2002) -- unpublished data for S(0) q>0.56 use Sommers’ data Sommers, Dash and Goldstein (Phys Rev, 97)1954

12. Simulation energy at detector wavelength at detector

13. rotation angle for entire beam line – 477cm (no pi-coil) Rotation angle for B z =100  G  (all neutrons)  (scattered only)

14. rotation angle for entire beam line (pi-coil reverses rotation between targets) Rotation angle for B z =100  G Up Target  Down Target 

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

16. (U-D)/(U+D) Rotation angle for Bz=100  G  (mrad)

17. 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  G * initial angles chosen to be within critical angle of guide

18. 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

19. Neutron Transport 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] guideInput coiltargetsOutput coilASM 116cm89cm41.6cm 108cm28cm x z y Top View

20. Plots x-distribution entrancebefore target 1

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

22. Plots x-distribution Before ASMdetector