Computer simulations of the n-4He parity-violating spin-rotation

experiment at NIST

Bret CrawfordGettysburg College

DNPOct. 28, 2006

Outline

• Systematic Effects – Ambient magnetic field rotations– 4He 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<100G

B=100G, L=1m, =5Ang

Compare with experimental goal of

• Subtracting Data from Upstream and Downstream targets cancels non-target related effects

v

BLt NL

8.3

radA

35

104.2

radPV7103

4He Diamagnetism

• Reduces ambient external field B in target region

• Neutrons in target cell precess slightly less than neutrons in empty cell

6101 B

B

radA

95

102

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

• 100G field in 1 meter

oute

foutin n

n

1

6105.2 fe nn

radA

95

106

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)

cmLL 003.0~10~ 5

Target positions Wave guides detector

radA

65

107

E

Eo 2

rad

A45

51010

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 With Up-Down subtraction non-PV rotations are in the few xthe few x1010-8-8radrad range range

Target positions Wave guides detector

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

Modeling the Scattering Cross section : n-4He

• 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 curveCalculate cross section from q and EDetermine if scatters within targetFollow new trajectory to target

,

0

22

qSk

kb

dEd

d

Modeling the Scattering Cross section : n-4He

S(q)

S(q) Dispersion curve

arbi

trar

y

q(1/Ang)

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

221

0

44 qr

SqS

d

d

c

bb

Simulation

energy at detector wavelength at detector

rotation angle for entire beam line – 477cm (no pi-coil)

Rotation angle for Bz=100G

(all neutrons) (scattered only)

rotation angle for entire beam line (pi-coil reverses rotation between targets)

Rotation angle for Bz=100G

Up Target Down Target

Large rotation values

Up Target Down Target

rotation angle for entire beam line (pi-coil reverses rotation between targets)

Rotation angle for Bz=100G

(U-D)/(U+D)

Rotation angle for Bz=100G

(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) – 100G

*initial angles chosen to be within critical angle of guide

initialfinal EE

radsim8108

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

• 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]

• Supermirrorx[-2.85,2.85] y[-2.25,2.25]

• Gaps [9.0, 6.8, 12.0]

guide Input coil targets Output coil ASM

116cm 89cm 41.6cm 41.6cm 108cm 28cm

x

zy

Top View

Plots x-distribution

entrance before target 1

Plots x-distribution

after target 1 (UL) after target 2 (DR)

Plotsx-distribution

Before ASM detector