POLARIMETRY

1
Ed Stephenson Frascati (LNF-INFN) October 4, 2005
POLARIMETRY
For particles that decay (µ, ß-unstable nuclei)
the spin axis is also the preferred axis for the
emission of the (detected) product.
For stable particles (p, d, 3He) we must scatter
from a target. The dominant mechanism for
producing an effect is the action of the strong
spin-orbit force.
To see an effect (left/right rate difference)
requires
down
up
a cross section that varies (falls) with angle.
a scattering process that favors one side of the
nucleus over the other.
a strong spin-orbit force (attraction for
spin parallel to angular momentum).
angular momentum is up
so look for such effects
2
A typical experimental layout contains
y
left detector
(f0)
x
z
beam direction
?
polarization is up (along y)
target
right detector
scattering plane
A polarization of the beam (p) causes a
difference in the rates for scattering to the
left and right according to
analyzing power (determined by nuclear effects
in scattering) governs spin sensitivity
unpolarized cross section (determined by
nuclear effects in scattering) governs efficiency
3
Proton Scattering
Protons fall in between deuterons (rainbow
projectiles) and purely diffractive scattering
(where the near and far side amplitudes
are essentially equal).
The proton analyzing power is mostly positive.
Finding a suitable angle and energy range for
polarimetry depends on the details of the
diffraction pattern.
We want to operate at p 0.5-0.6 GeV/c.
The proton carbon maximum
The analyzing power goes through an A1 point at
189 MeV.
The proof requires
4
McNaughton analysis from LANL
rough efficiencies (defined as the number of
protons used for a polarization
measurement divided by the number of protons
hitting the target)
Polarimeter used thick carbon target and
recorded all forward angle protons, which are
mostly elastic.
The improvement is due mostly to the
increased target thickness.
1
4
5
The Indiana data between 100 and 200 MeV
This polarimeter selected for elastic scattering.
figure of merit is better with thinner target sA2
6
Important features of the IUCF polarimeter
thick scintillator gives energy to distinguish
elastic scattering
thin scintillator gives dE/dx to identify protons
wire chambers before and after carbon target give
scattering angle (? and f)
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Below 100 MeV, the forward peak in the analyzing
power fades. You then have to go to larger
angles.
factor between 4 and 5
multiply by 1/sin4(?/2) 9.3
You lose about a factor of 40 in cross section.
The solid angle can recovers about a factor of
two.
8
Osaka built a polarimeter for 65 MeV
(based on the Kato data)
Work here.
9
Deuteron polarization
m1 bigger than m-1
vector
m1 and m-1 the same but different from m0
tensor
10
Deuteron Scattering
Energies lt 70 MeV Coulomb rainbow scattering
estimated operating characteristics
Forward-angle trajectories curved in Coulomb field
efficiency ()


Spin-orbit force causes () to bend toward
smaller angles.
iT11
If the cross section is FALLING with angle, then
at any angle, spin () will dominate. This makes
iT11 lt 0.
momentum (GeV/c)
40 MeV design was here.
Work in this region.
11
Energy gt 40 MeV Nuclear rainbow scattering
efficiency ()


iT11
In attractive nuclear field, effect
reverses. These analyzing powers get very large
while the cross section falls exponentially.
momentum (GeV/c)
Data run out while spin sensitivity
improves. Higher energy data are needed.
12
More about nuclear rainbow scattering
NOTE Once analyzing power start to rise
for elastic scattering, it rises for ALL
inelastic and particle transfer channels. Thus
an inclusive polarimeter will gain efficiency.
(Estimates here consider only the elastic.)
Very large angle analyzing powers approach
their limit, could be used for in situ
calibration.
Most useful where analyzing power starts to rise
and cross section is still large. Sensitive to
inner angle cut.
Non-spin-orbit observables such as T21 or X2 are
small.
13
Oxygen target
rainbow at higher energy
Calcium target
T21
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Energy gt 200 MeV Absorptive spin-orbit
efficiency ()
Absorption eventually reduces nuclear rainbow.
But forward-angle spin-orbit effect grows in.
Efficiency rises while average iT11 falls.
average iT11
momentum (GeV/c)
AGS ring
At about 700 MeV, the use of an iron absorber to
separate the elastic scattering loses
its effectiveness. Then iT11 starts to decline.
Work here.
Forward-angle cross sections are large!
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Energy gt 700 MeV Absorptive spin-orbit no
particle identification
Higher efficiency but smaller analyzing power. Fo
r these cases the carbon target thickness was
held fixed at 30 cm.
efficiency ()
average iT11
momentum (GeV/c)
All angles past 1.5 are kept.
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Summary
Figure of merit effiency ? ? iT11 ?2
Absorptive spin-orbit inclusive
Absorptive spin-orbit
?
Coulomb rainbow
momentum (GeV/c)
Nuclear rainbow
Extrapolation of nuclear rainbow effect is not
known. This is the subject of studies at the KVI,
Groningen.
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KVI measurements of dC
Basic Plan
beam
126 MeV
55 MeV
lower limit without hitting negative
analyzing powers
Take data at two energies 80 and 110 MeV.
CH2 or C target
(typical it11 0.44)
points chosen as polarization reference
A y
KVI in-beam polarimeter with 8 detector arms
Hatanaka, NP A 426, 77 (84)
Sekiguchi, PR C 65, 034003 (02)
all other points AHEAD polarimeter, Witala FBS
15, 67 (93)
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beam
plastic ?E
NaI (stopping detector)
Temporary detector arrangement using the
horizontal arm position of the KVI in-beam
polarimeter
19
selected particle spectra
Sample spectra (110 MeV, 27)
particle identification
2 4.44
g.s.
triton
?E energy
deuteron
deuteron
proton
NaI energy
breakup
particle identification linearized
3.85 5/2
proton
deuteron
proton
triton
energy of particle emitted from target (MeV)
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Deuteron elastic scattering angular distributions
A y
80 MeV
70 MeV (data from Kato)
FOM s Ay2
cross section (mb/sr)
goes as 1/error2
figure of merit (mb/sr)
110 MeV
laboratory scattering angle (deg)
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Deuteron elastic scattering angular distributions
A y
80 MeV
Original concept based polarimeter on the use of
this peak in the figure of merit angular dist.
70 MeV (data from Kato)
cross section (mb/sr)
figure of merit (mb/sr)
110 MeV
laboratory scattering angle (deg)
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Deuteron elastic scattering angular distributions
A y
At the higher energy, another lobe in the
analyzing power is getting larger, making
possible greater efficiency at smaller angles.
This needs more investigation and data.
80 MeV
70 MeV (data from Kato)
cross section (mb/sr)
figure of merit (mb/sr)
110 MeV
laboratory scattering angle (deg)
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Deuterons and protons from the continuum
34.5
s (mb/sr/5 MeV)
s (mb/sr/4 MeV)
The positive analyzing powers from the
spin- orbit interaction extend into the continuum
for both deuterons and protons (neutron transfer
or breakup).
A y
A y
The design should include some of these regions.
FOM
FOM
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EDM polarimeter

• IDEA
• make thick target defining aperture
• scatter into it with thin target

lost to ring acceptance (2 kb)
40 MeV 10-5 1 GeV 6x10-4
cross section
(POMME efficiency several percent)
detector system
Coulomb
useful for spin (17 mb)
nuclear
U
defining aperture primary target
angle
L
extraction target - gas
R
D
R
?
D
Target could be Ar gas (higher Z).
Detector is far enough away that
doughnut illumination is not an acceptance
issue ? lt R.
Hole is large compared to beam. Every- thing
that goes through hole stays in the ring. (It
may take several orbits to stop scattered particle
.)
Events must imbed far enough from hole to not
multiple scatter out of primary target, thus ? ltlt
D. ?, which is a large fraction of the deuteron
range, sets scale for polarimeter.
Target extracts by Coulomb scattering
deuterons onto thick main target. Theres not
enough good events here to warrant detectors.
Primary target may need to be iris to allow
adjustment of position and inner radius. It may
also need to be removed during injection.
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What information is available from the
polarimeter?
To get pA
U
L
R
D
This asymmetry carries the EDM signal, which is a
rapid oscillation on top of a steady rise
with time.
This asymmetry carries the signal from
the precession of the spin in the plane of the
ring.
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What other sources arise for a left/right
asymmetry?
Polarimeter Systematic Errors
1
Displacement / angle errors
detectors
?
x
?
angle shift
position shift
Usual remedy measure on both sides (L/R)
flip initial spin use cross ratio formula
left/right efficiency differences cancel
spin
detector
/ luminosity differences cancel
27
Errors that are second-order in ? and upp
logarithmic derivatives of the analyzing power as
a function of scattering angle
We are helped by the small size of the asymmetry
and the expected time dependence.
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2
Polarimeter rotation
U
L
R
We are helped by the time dependence of eDU and
f-dependence in analysis of segmented detector.
target
D
f
3
Parity violation
Effects start to appear at e lt 10-6 associated
with px.
We are helped by time dependence.
29
Tensor polarization requires and equal population
of m1 and m-1 deuterons that is different from
m0.
4
For spin 1, tensor contributions (t21)
detectors
The left/right asymmetries oscillate as the spin
rotates in the ring plane. They do not grow with
time. The effect appears at 10-4 with 1 tensor
contamination of the polarized beam.
The left/right asymmetry is maximal along 45 but
reverses sign in the perpendicular direction.