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Measurement of the nuclear polarization inoptically-pumped 37K:
Progress towards a measurement of theβ-asymmetry parameter
Benjamin Fenker
Texas A&M University Cyclotron InstituteTRIUMF Neutral Atom Trap
Symmetries in Subatomic PhysicsVictoria, BC
June 8 2015
1 / 28
Acknowledgments
The TRINAT Collaboration
TRIUMF - John Behr, Alexandre Gorelov, Konstantin Olchanski,Ioana Craiciu, Claire Warner, Claire Preston
Texas A & M - Spencer Behling, Michael Mehlman,Dan Melconian, Praveen Shidling, Eames Bennett
U of Manitoba - Melissa Anholm, Gerald Gwinner
Tel Aviv - Daniel Ashery, Iuliana Cohen
TRIUMF & ISAC Target & Beam Delivery GroupFunding Agencies
USA: DOE DE-FG02-93ER40773 & Early Career ER41747
Canada: NSERC, NRC through TRIUMF, WestGrid
Israel: Israel Science Foundation
2 / 28
Outline
Motivation - Testing the SM with nuclearphysics
TRINAT - TRIUMF’s Neutral Atom Trap
Polarization through optical pumping
Systematics in the polarizationmeasurement
Outlook and future plansshakeoff
Ion MCP
uniform E fieldB Coil Electrodes for
beta
electron MCP
3 / 28
Motivation: Fundamental Symmetries
Search for possible right-handed currents SU(2)L ⊗U(1)Y
?→ SU(2)R ⊗SU(2)L ⊗U(1)Y
Contribute to independent check on the value of Vud
Energy dependence tests recoil-order corrections, weakmagnetism, second-class currents
Angular correlations in β-decay are sensitive to new physics 10−3 precision constrains SM extensions, while 10−4 has
discovery potentiald5W
dEdΩedΩν∼ 1+aβν
pepν cos(θeν)
EeEν+b
me
Ee+
P
(
Aβpe
Eecos(θe)+Bν
pνEν
cos(θν)
)
+ . . .
θe
~pe ~pν
θνdud
duu
We
ν4 / 28
Overview
Magneto-Optical Trap (MOT) Provides a cold (∼ 1mK), localized (∼Ø1mm) source of atoms Shallow trap so products emerge unperturbed
Polarization Axis
Trap Light
OP Light
Nuclear DetectorsBC 408
Plastic Scintillator
Si−strip detector
Mirror
MCP
~E
5 / 28
Overview
Magneto-Optical Trap (MOT) Optical Pumping Polarizes the Atoms
σ± lasers drive biased random walk towards Pnucl =±1
Polarization Axis
Trap Light
OP Light
Nuclear DetectorsBC 408
Plastic Scintillator
Si−strip detector
Mirror
MCP
~E
5 / 28
Overview
Magneto-Optical Trap (MOT)
Optical Pumping Polarizes the Atoms Nuclear Detectors
β-telescopes measure position, energy along polarization axis
Polarization Axis
Trap Light
OP Light
Nuclear DetectorsBC 408
Plastic Scintillator
Si−strip detector
Mirror
MCP
~E
5 / 28
Overview
Magneto-Optical Trap (MOT)
Optical Pumping Polarizes the Atoms Nuclear Detectors
β-telescopes measure position, energy along polarization axis
BC 408Plastic Scintillator
Si−strip detector
Mirror
MCP
~E
5 / 28
β-detection
Scintillators record full energy; backgrounds from untrappedatoms, annihilation
Shake-off electron MCP tags events that decay from the trap Silicon ∆E detectors suppress background from γs Collected statistics for 0.2% measurement of Aobs
Energy [keV]0 1000 2000 3000 4000 5000 6000
Cou
nts
1
10
210
310
410
510 All Events-
Shakeoff eSi-strip detectorTriple coincidence
BC 408Plastic Scintillator
Si−strip detector
MCP
~E
6 / 28
Optical Pumping
Stretched state has F = 2, MF = 2 or equivalently Iz =32 , Jz =
12
Zeeman sublevels feel Bz = 2G along quantization axis Stretched state corresponds to atomic and nuclear polarization Photoionization is a monitor of excited state population Use this to monitor trap size, position, temperature, polarization
Ene
rgy
355 nm light
F = 1
F = 2
F = 1
F = 2S1/2
P1/2
P3/2
Angular MomentumFz
Fz =−2 Fz =−1 Fz = 0 Fz = 1 Fz = 2
E−field
MC
P
K+
Note:~F =~I +~J
7 / 28
Optical Pumping
Stretched state has F = 2, MF = 2 or equivalently Iz =32 , Jz =
12
Zeeman sublevels feel Bz = 2G along quantization axis Stretched state corresponds to atomic and nuclear polarization Photoionization is a monitor of excited state population Use this to monitor trap size, position, temperature, polarization
Ene
rgy
Optical PumpingLight
Repump
F = 1
F = 2
F = 1
F = 2S1/2
P1/2
P3/2
Angular MomentumFz
Fz =−2 Fz =−1 Fz = 0 Fz = 1 Fz = 2
∆F z
=+
1
∆Fz =±1,0
E−field
MC
P
K+
Note:~F =~I +~J
7 / 28
Optical Pumping
Stretched state has F = 2, MF = 2 or equivalently Iz =32 , Jz =
12
Zeeman sublevels feel Bz = 2G along quantization axis Stretched state corresponds to atomic and nuclear polarization Photoionization is a monitor of excited state population Use this to monitor trap size, position, temperature, polarization
Ene
rgy
355 nm light
F = 1
F = 2
F = 1
F = 2S1/2
P1/2
P3/2
Angular MomentumFz
Fz =−2 Fz =−1 Fz = 0 Fz = 1 Fz = 2
E−field
MC
P
K+
Note:~F =~I +~J
7 / 28
Photoions monitor trap parameters
Polarized measurements must be done with MOT off
With MOT off, cloud expands; alternate counting/trappingP
hoto
ion
Eve
nts
1
10
210
310
410
BQuench MOT Collects, Cools
Optical Pumping
Time since MOT off / microseconds0 500 1000 1500 2000 2500 3000 3500 4000
z po
s / m
m∆
-10
-5
0
-5
8 / 28
Photoionization signal
With time-of-flight and position cuts, this signal is very clean
∆z position / mm
-20 -15 -10 -5 0 5 100
50
100
150
200
250
300
350
400
450
MOT / 1000.0FWHM = 3.2 mm
Optical PumpingFWHM = 2.3 mm
Photoion time-of-flight [ns]
1220 1260 1300 1340 1380 14200
50
100
150
200
250
300
MOT / 1000.0FWHM = 19 ns
Optical PumpingFWHM = 16 ns
9 / 28
Polarization Signal
This strong signal allows clean measurement of polarization
Initial peak proportional to number of atoms, laser power,provides normalization
Tail region provides information about the degree of polarization
Time [µs]-200 0 200 400 600 800 1000 1200 1400
Polarized
Pho
toio
nE
vent
s
0
10
20
30
40
50
60
70
Directly measurenon-stretchedpopulation, but
Polarization dependson how this smallpopulation isdistributed amongstsublevels
Small tail measuresdeviation from unity
10 / 28
Polarization Signal
This strong signal allows clean measurement of polarization
Initial peak proportional to number of atoms, laser power,provides normalization
Tail region provides information about the degree of polarization
Time [µs]-200 0 200 400 600 800 1000 1200 1400
Polarized
Pho
toio
nE
vent
s
0
10
20
30
40
50
60
70
Directly measurenon-stretchedpopulation, but
Polarization dependson how this smallpopulation isdistributed amongstsublevels
Small tail measuresdeviation from unity
10 / 28
Polarization Model
H = H0︸︷︷︸
Coulomb
+ Hso︸︷︷︸
Spin-Orbit
+ Hhf︸︷︷︸
Hyperfine
+ HB︸︷︷︸
Magnetic Field︸ ︷︷ ︸
Atomic Hamiltonian
−e~d ·~E(t)︸ ︷︷ ︸
Laser Term
HSO =~L ·~SHhf =~I · (~L+~S)~E(t) = E0 cos(kz −ωLt)εq
HB =−~µ·~B=−gF µB~B · (~I +~L+~S)
〈P〉= Tr(ρP) = Tr(ρIz) 〈T 〉 ∼ Tr(ρI2z )
Density Matrix:ρii - population of state iρij - correlation between i , j
Time evolution:d ρdt = 1
i~ [H (t), ρ]+R(t)
Tremblay, P. and Jacques C. PRA 41(9), 4989 (1990)Renzoni, F. et al. PRA 63(6), 065401 (2001)
Systematics in the polarization measurement
Photoionization signal is an indirect measure of the polarization
Light ellipticity and a transverse magnetic field affect thephotoionization curve similarly but result in different polarization
-Steady state P1/2 population
0 0.02 0.04 0.06 0.08 0.1 0.12×10−3
Nuc
lear
Pol
ariz
atio
n
0.994
0.995
0.996
0.997
0.998
0.999
1 Bx = 0.0, Vary s3
s3 = 1.0, Vary Bx
s3 = 1.0
s3 = 0.993Bx = 0.0G
Bx = 0.15 G
Off-line studies:Bx ≤ 66mG
Stokesparameter:
〈s3〉=I+− I−I++ I−
≥+0.9893
≤−0.9983
CPT “dark” statesare minimized
11 / 28
Depolarizing mechanisms - Stokes Parameter s3
s3 characterizes the degree of circular polarization
s0 is equivalent to the total power contained in the beams3
s0=
I+− I−I++ I−
If |s3|/s0 < 1.0, atoms can be pumped out of the stretched state
Ene
rgy
F = 1
F = 2
F = 1
F = 2S1/2
P1/2
P3/2
Angular MomentumFz
Fz =−2 Fz =−1 Fz = 0 Fz = 1 Fz = 2
Equilibrium is reached withnot all atoms in the fullystretched state
12 / 28
Depolarizing mechanisms - Stokes Parameter s3
s3 characterizes the degree of circular polarization
s0 is equivalent to the total power contained in the beams3
s0=
I+− I−I++ I−
If |s3|/s0 < 1.0, atoms can be pumped out of the stretched state
Ene
rgy
F = 1
F = 2
F = 1
F = 2S1/2
P1/2
P3/2
Angular MomentumFz
Fz =−2 Fz =−1 Fz = 0 Fz = 1 Fz = 2
Equilibrium is reached withnot all atoms in the fullystretched state
12 / 28
UHV Viewport
SiC Mirror
s3 =−0.9950
s3 =−0.9980
s′3 =−0.9959 s′3 =−0.9938
Warneret al. RSI 85, 113106 (2014).
Depolarizing mechanisms - Transverse magnetic field
Magnetic field perpendicular to polarization axis causesprecession
Atoms in the stretched state precess toother ground states
~B = Bx x +Bz zH~B =−~µ·~BHBx = gF µBBxFx = gF µBBx
F++F−2
13 / 28
Depolarizing mechanisms - Transverse magnetic field
Magnetic field perpendicular to polarization axis causesprecession
Atoms in the stretched state precess toother ground states
~B = Bx x +Bz zH~B =−~µ·~BHBx = gF µBBxFx = gF µBBx
F++F−2
13 / 28
Trim coils minimize transverse magnetic fieldScan current and minimize optical pumping tail to find Iideal
Compare Iideal and Iactual , find Bx = 33mG.
Conservatively assign 100% uncertainty → Bx ≤ 66 mG
Preliminary Results
Depolarizing mechanisms are almost 100% correlated
Perform separate fits with either s3 or B⊥ fixed
Cou
nts
/mic
rose
cond
0
1
2
3
4
5
6
7
8
σ− −2log(L)comb/ν = 757/1168
Time / microsecond200 400 600 800 1000 1200 1400 1600 1800
Polarized
Polarized
Cou
nts
/mic
rose
cond
0
2
4
6
8
10
12 σ+
Cou
nts
/mic
rose
cond
0
1
2
3
4
5
6
7
8
σ− −2log(L)comb/ν = 771/1169
Time / microsecond200 400 600 800 1000 1200 1400 1600 1800
Polarized
Polarized
Cou
nts
/mic
rose
cond
0
2
4
6
8
10
12 σ+
Bx = 66mG
I(σ−) = 2.2(3)Wm−2
s3(σ−) =−0.9967(9)
P =−0.994(1)stat
I(σ+) = 2.1(2)Wm−2
s3(σ+) = +0.9915(16)
P =+0.990(2)stat
Bx = 4(36)mG
I(σ−) = 2.0(2)Wm−2
s3(σ−) =−0.9938
P =−0.9916(4)stat
I(σ+) = 2.0(2)Wm−2
s3(σ+) = +0.9893
P =+0.9890(3)stat
14 / 28
Preliminary Results - Global Fit
Vary delay-time after AC-MOTFit with common s3 and Bx
σ− σ+
Cou
nts
/ 2.0
mic
rose
cond
s
0
0.51
1.52
2.5
3
3.54
E = 395 V/cm8.4 hours−2logL/d.o.f.=5617/8028
Cou
nts
/ 1.0
mic
rose
cond
s
0
1
2
3
4
5
6
E = 535 V/cm15.2 hours
Cou
nts
/ 10.
0 m
icro
seco
nds
0
1
2
3
4
5
6
7
E = 395 V/cm2.8 hours
Cou
nts
/ 1.0
mic
rose
cond
s
0
1
2
3
4
5
67
8
E = 415 V/cm7.6 hours
Time [microseconds]200 400 600 800 1000 1200 1400 1600 1800
Cou
nts
/ 4.0
mic
rose
cond
s
0
1
2
3
4
5E = 415 V/cm
1.6 hours
0
0.51
1.52
2.5
3
3.54
0
1
2
3
4
5
6
0
1
2
3
4
5
6
7
0
1
2
3
4
5
67
8
Time [microseconds]200 400 600 800 1000 1200 1400 1600 1800
0
1
2
3
4
5
15 / 28
Preliminary Results
Uncertainties / 10−4
σ+ σ−
Polarization Alignment Polarization AlignmentDepolarizing Mechanism 8 15 4 5
Global Fit vs. Average 1 3 1 2Fit ∆ vs. Fit I 3 6 3 6
Uncertainty in Bz 1 3 1 1Binning 2 3 2 5
Initial Alignment (T0 =−1) 18 42 15 36Hyperfine Pumping 1 2 1 3Sum Systematics 20 45 16 37
Statistics 6 16 8 19Uncertainty 22 48 18 42
Central Value 0.9898 -0.9761 -0.9920 -0.9808
P = 〈MI〉I = 0.991(2) T =
I(I+1)−3〈M2I 〉
I(2I−1) =−0.978(5)
16 / 28
Conclusions
Nuclear polarization gives access to more β-decay observables Optical pumping achieves high polarization in an open geometry
→ P = 0.991±0.002 Will not dominate the uncertainty for present data set We expect
dAβAβ
≤ 0.5% (ASMβ =−0.5706(7))
Future plans include modeling our MOT to reduce uncertaintyfrom initial sublevel distribution
Polarization measurement at 10−4 precision requires moresystematic studies
Uncertainty / 10−4
2012 2014
Asymmetry (Stat.) 62 20Polarization (Stat.) 60 7Polarization (Systematics) 56 18Detector Response 64Asymmetric Number of Trapped Atoms 25Trap Movement 18Timing Errors 9Mirror Thickness 2
S. Behling “Measurement Of The Standard Model Beta Asymmetry Parameter, Aβ, in 37K” Ph. D Thesis. Texas A & M University, 2015. 17 / 28
THANK YOU
Backup slides . . .18 / 28
Acknowledgments
The TRINAT Collaboration
TRIUMF - John Behr, Alexandre Gorelov, Konstantin Olchanski,Ioana Craiciu, Claire Warner, Claire Preston
Texas A & M - Spencer Behling, Michael Mehlman,Dan Melconian, Praveen Shidling, Eames Bennett
U of Manitoba - Melissa Anholm, Gerald Gwinner
Tel Aviv - Daniel Ashery, Iuliana Cohen
TRIUMF & ISAC Target & Beam Delivery GroupFunding Agencies
USA: DOE DE-FG02-93ER40773 & Early Career ER41747
Canada: NSERC, NRC through TRIUMF, WestGrid
Israel: Israel Science Foundation
19 / 28
Comparison with Geant4
Cou
nts
0
200
400
600
800
1000Data
Geant4 SimulationPRELIMINARY
χ2/ν = 1.6
Energy [keV]1000 2000 3000 4000 5000
y dat
a−
y mc
√y m
c
-4
-2
0
2
4
20 / 28
Preliminary Results
Uncertainties / 10−4
σ+ σ−
Polarization Alignment Polarization AlignmentDepolarizing Mechanism 8 15 4 5
Global Fit vs. Average 1 3 1 2Fit ∆ vs. Fit I 3 6 3 6
Uncertainty in Bz 1 3 1 1Binning 2 3 2 5
Initial Alignment (T0 =−1) 18 42 15 36Hyperfine Pumping 1 2 1 3Sum Systematics 20 45 16 37
Statistics 6 16 8 19Uncertainty 22 48 18 42
Central Value 0.9898 -0.9761 -0.9920 -0.9808
P = 〈MI〉I = 0.991(2) T =
I(I+1)−3〈M2I 〉
I(2I−1) =−0.978(5)
21 / 28
Preliminary Results
Uncertainties / 10−4
σ+ σ−
Polarization Alignment Polarization AlignmentDepolarizing Mechanism 8 15 4 5
Global Fit vs. Average 1 3 1 2Fit ∆ vs. Fit I 3 6 3 6
Uncertainty in Bz 1 3 1 1Binning 2 3 2 5
Initial Alignment (T0 =−1) 18 42 15 36Hyperfine Pumping 1 2 1 3Sum Systematics 20 45 16 37
Statistics 6 16 8 19Uncertainty 22 48 18 42
Central Value 0.9898 -0.9761 -0.9920 -0.9808
P = 〈MI〉I = 0.991(2) T =
I(I+1)−3〈M2I 〉
I(2I−1) =−0.978(5)
21 / 28
Future work: Initial sublevel distribution?
Has little effect on equilibrium state but can affect theshape of the initial peak
Polarization is limited by “unpolarized” β-asymmetry
Alignment (T ) unconstrained (for now)
Initi
al P
opul
atio
n F
ract
ion
0
0.1
0.2
0.3
0.4
0.5
T = 0.0
Initi
al P
opul
atio
n F
ract
ion
0
0.1
0.2
0.3
0.4
0.5
T = -0.34
|1, -1> |1, 0> |1, 1> |2, -2> |2, -1> |2, 0> |2, 1> |2, 2>
Initi
al P
opul
atio
n F
ract
ion
0
0.1
0.2
0.3
0.4
0.5
T = -1.0
Preliminary Results
Uncertainties / 10−4
σ+ σ−
Polarization Alignment Polarization AlignmentDepolarizing Mechanism 8 15 4 5
Global Fit vs. Average 1 3 1 2Fit ∆ vs. Fit I 3 6 3 6
Uncertainty in Bz 1 3 1 1Binning 2 3 2 5
Initial Alignment (T0 =−1) 18 42 15 36Hyperfine Pumping 1 2 1 3Sum Systematics 20 45 16 37
Statistics 6 16 8 19Uncertainty 22 48 18 42
Central Value 0.9898 -0.9761 -0.9920 -0.9808
P = 〈MI〉I = 0.991(2) T =
I(I+1)−3〈M2I 〉
I(2I−1) =−0.978(5)
21 / 28
Future work: Initial sublevel distribution?
Has little effect on equilibrium state but can affect theshape of the initial peak
Polarization is limited by “unpolarized” β-asymmetry
Alignment (T ) unconstrained (for now)
0 20 40 60 80 100 120 140 160 180 2000
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
0.0045 =00T=-0.340T=-10T
ES Population
Preliminary Results
Uncertainties / 10−4
σ+ σ−
Polarization Alignment Polarization AlignmentDepolarizing Mechanism 8 15 4 5
Global Fit vs. Average 1 3 1 2Fit ∆ vs. Fit I 3 6 3 6
Uncertainty in Bz 1 3 1 1Binning 2 3 2 5
Initial Alignment (T0 =−1) 18 42 15 36Hyperfine Pumping 1 2 1 3Sum Systematics 20 45 16 37
Statistics 6 16 8 19Uncertainty 22 48 18 42
Central Value 0.9898 -0.9761 -0.9920 -0.9808
P = 〈MI〉I = 0.991(2) T =
I(I+1)−3〈M2I 〉
I(2I−1) =−0.978(5)
21 / 28
Future work: Initial sublevel distribution?
Has little effect on equilibrium state but can affect theshape of the initial peak
Polarization is limited by “unpolarized” β-asymmetry
Alignment (T ) unconstrained (for now)
Model MOT dynamics to limit initial alignment
Work in progress
Optics Layout
30 mW, 770 nm Laser
AOM for ON/OFF
1/2-wave plate
Polarizing beam-splitter
Polarizing beam-splitter
Polarizing beam-splitter
Polarization Maintaining Fiber
Deflects poorly polarized light
ON OFF
High quality polarizer
High quality polarizer LCVR - 1/2-wave plate or zero
High quality1/4-wave plate
High quality1/4-wave plate
UHV Viewport w/PCTFE Gasket
UHV Viewport w/PCTFE Gasket
SiC Mirror
SiC Mirror
TRAP
Control Computer
Controls Optical Pumping ON/OFF
LCVR - 1/2-wave plate or zero
Controls Polarization State
22 / 28
Why 37K?
Atomic structure allows for laser-trapping AND optical pumping
Isobaric analogue decay simplifies nuclear structure corrections
Strong branch to ground state is a very clean decay
Iπ = 32+ → 3
2+
is a mixed Fermi-Gamow Teller decay
∆t1/2 = 0.08%(Shidling et al. 2014)∆BR = 0.14%∆QEC = 0.003%
3/2+
3/2+
5/2+
MIRROR
MIRROR
β+
3718Ar19
3719K18
2.07% QEC = 3.4 MeV
97.89% QEC = 6.1 MeV
23 / 28
Why 37K?
Atomic structure allows for laser-trapping AND optical pumping
Isobaric analogue decay simplifies nuclear structure corrections
Strong branch to ground state is a very clean decay
Iπ = 32+ → 3
2+
is a mixed Fermi-Gamow Teller decay
∆t1/2 = 0.08%(Shidling et al. 2014)∆BR = 0.14%∆QEC = 0.003%
∆F t = 0.18%∆ρ = 0.4%
3/2+
3/2+
5/2+
MIRROR
MIRROR
β+
3718Ar19
3719K18
2.07% QEC = 3.4 MeV
97.89% QEC = 6.1 MeV
23 / 28
Why 37K?
Atomic structure allows for laser-trapping AND optical pumping
Isobaric analogue decay simplifies nuclear structure corrections
Strong branch to ground state is a very clean decay
Iπ = 32+ → 3
2+
is a mixed Fermi-Gamow Teller decay
∆t1/2 = 0.08%(Shidling et al. 2014)∆BR = 0.14%∆QEC = 0.003%
∆F t = 0.18%∆ρ = 0.4%
Aβ(0) =−0.5706(7)→∆Aβ = 0.12%
3/2+
3/2+
5/2+
MIRROR
MIRROR
β+
3718Ar19
3719K18
2.07% QEC = 3.4 MeV
97.89% QEC = 6.1 MeV
23 / 28
Photoionization Events
BC408 Plastic Scintillator
Silicon Strip Detector
rMCPeMCP
Nuclear polarization
355 nm light ~E
~B
Photoelectrone−
K+ Monitor of trapposition, size,temperature
Ultra-clean measure ofnuclear polarization P
24 / 28
Measure Vud with mirror nuclei
Nuclearcorrection
RadiativecorrectionExperimental
unce
rtain
ty
0+−→ 0+ neutron
mirrorpionnuclei
Vud
25 / 28
TRINAT’s x2-MOT System
Collection trap is coupled to TRIUMF-ISAC beam line
Transfer atoms to second trap for precision measurement
MCP
MCP
Push
beam 14"
Collection chamber Detection chamber
Ion
Neutralizer
beam
Electrostatichoops
26 / 28
Initial Polarization
Atoms can be polarized in a MOT if beams are unbalanced. Weavoid this
Use β-asymmetry of trapped (unpolarized) atoms to constraininitial polarization
S. Behling “Measurement Of The Standard Model Beta Asymmetry Parameter, Aβ, in 37K” Ph. D Thesis. Texas A & M University, 2015.
27 / 28
Correlation measurements with polarized nuclei
LTNO
Brute-forcealignment ofnuclear spin
P calculatedknowing thetemperature
Backscatteringfrom sourceholder
Stern-Gerlach
Physicallyseparatepolarized atoms
Very highpolarization, butinefficient
Optical Pumping
MI
γ
State selection;very high P
Open geometryminimizesbackscattering
Must measurepolarization
28 / 28