Transcript Document

Does the passage of low energy deuterons through a
finite 12C foil lead to small angle tensor polarisation?
Elizabeth Cunningham
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Overview
Experimental motivation
Brief description of tensor polarisation
Nuclear scattering
Atomic scattering
Comparison with experiment
Summary
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Experimental Result
At University of Cologne using deuterons up to 16 MeV [1] :
‘First attempt to measure spin dichroism, i.e. creation of
tensor polarisation in an unpolarised deuteron beam by
unpolarised carbon targets.’ [2]
Observed tensor polarization for small scattering angles
Deviation from randomness of approx. 10%.
Serious implications for designing polarimeters used in
deuteron experiments.
[1] A. Rouba et al., Proc. 17th Int. Spin Physics Symp.; SPIN06, 2-7 Oct.,
Kyoto, Japan, AIP Conf. Proc. 915 (2007).
50th
[2] V. Baryshevsky et al., arXiv:hep-ex/0501045, (2005).
Anniversary
Symposiumand
on A.
Nuclear
Sizes
and Shapes
23/06/08
V. Baryshevsky
Rouba,
arXiv:nucl-th/0706.3808,
(2007).
Iiiii
Tensor Interaction
Deuteron has prolate
quadrupole deformation
along its spin axis.
Different spin projection
iiiiiiiiiiiMI = +1,0, -1
gives different apparent
cross sectional area of
deuteron ‘seen’ by target.
MI = ±1
r
MI = 0
r
2
ˆ
V
(r,I)

V
(r)[(I
r
)
 2/3]
Tensor Potential:
TR
TR
50th Anniversary Symposium on Nuclear Sizes and Shapes
b
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b
T20 Polarisation
T20 polarisation: measure of deviation from randomness.
T20 
3I2z  2
2
The only type of tensor polarisation which does not tend to zero
for scattering in the forward direction.
3N1  N1   2 1 3N0
T20 

2
2

NMI = probability deuteron has Iz = MI in transmitted beam.
Unpolarised beam, N+1 = N-1 = N0 =1/3, gives: T20 = 0.

50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Experimental T20
Experiment at Cologne University [1,2], measured tensor
polarisation in the transmitted deuterons as large as
T20 = 0.18 ± 0.02
for small scattering angles and a carbon target thickness of
132 mg/cm2:
Transmitted deuterons are preferentially
with their long axis along incident
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
aligned
beam direction.
Scattering Theory
V(r,I,) scattering centre
Asymptotic Wavefunction:
e
 (r)  e  f (,I)
ikz

ikr
z
r
Scattering amplitude connects
wavefunction and observables:

f(,I)  
2
2
e
ik.r
r
eikz
incident
plane wave ikr
f(,I) e scattered
r
wave
V(r,I)  (k, r) dr

Used to calculate cross section and T20 polarization for deuterons
elastically scattering from an individual 12C nucleus.
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Optical Potential
Optical potential for d-12C nuclear scattering at 11.9 MeV:
V(r,s)  VC (r) Vc (r) iWc (r) VLS(r)L  I  VTR (r)[I ˆr ]2  2 3
Coulomb[3]
Central[3]
Spin-Orbit[3]
Tensor[4]
Extrapolation from polarisation data for angles greater than 1 deg.
Potential depths:
Vc = 119.0 MeV, Wc = 5.8 MeV, VLS = 6.2 MeV, VTR = 3.965 MeV
Used to calculate scattering amplitude:
d 1

 Tr(ff )
d 3
1 Tr(f [3I2z - 2] f  )
T20 
Tr(ff  )
2
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Results - Nuclear
d-12C at 11.9 MeV
T20 in forward direction is of order ~10-5
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Atomic Scattering
Coulomb interaction between
deuteron and the atom:
VdA
er
R
Z
Ze 2
e2


|R  r/2| i1 |R  r/2  r i |
ri
Using Born approximation,
- first order approximation
- assumes effect of scattering potential is small
scattering amplitude for atom A  A’ becomes:

f MI A MI 'A ' 
MI ' (r),A' (r i ),k' (R) VdA (R,r,r i ) k (R),A (r i ),MI (r)
2
2
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Atomic T20
Using q = k - k’ and changing the variables so that R’=R+r/2,
fMI A MI 'A'  Tatom(q) MMI 'MI (q),
MMI 'MI 
 dr e
iqr/2
*M ' (r)M (r)
I
gives a simplified expression for T20 polarisation for single
atomic scattering of a deuteron from a carbon atom.
1 Tr([3I2z - 2]M M)
T20 
Tr(M M)
2
2
  Qd q 2 P2 cos( q )
3
Qd = deuteron quadrupole moment = 0.2860 ± 0.0015 fm2 [5].
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
I
Results - Atomic
d-12C at 11.9 MeV
Born approx. factor of 2 higher but both give T20 in
forward direction of order ~10-5
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Multiple Scattering
Estimate of the T20 from multiple atomic scattering events.


N
2
T20   Qd q 2j P2 cos(q j )
3
j=1
Using qj2 = kj2 (scatt2)j and taking P2(cos(qj)) = -0.5, most likely
value for small q:
N

2
2
T20  Qd k2 (scatt
)j
6
j=1
To calculate specific case for comparison with experiment, use
2 [6]
Multiple scattering calculation gives
T20 = 1.2x10-4

50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Summary
- Measurement of T20 = 0.18 ± 0.02 for 5-8 MeV deuterons
passing through a 12C target of thickness 132 mg/cm2.
- Calculation of T20 ~ 10-5 for 11.9 MeV deuterons scattering
from a single 12C nucleus.
- Calculation of T20 = 1.2x10-4 for 11.9 MeV deuterons
scattering from atomic electrons.
- Theoretical calculation about 3 orders of magnitude smaller
than experimental measurement.
- Major discrepacy which could have serious implications for
designing polarimeters used in deuteron experiments.
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08
Acknowledgements
Thank you to my supervisors Ron Johnson and Jim Al-Khalili.
Thank you for listening…
[1] A. Rouba et al., Proc. 17th Int. Spin Physics Symp.; SPIN06, 2-7 Oct., Kyoto, Japan, AIP
Conf. Proc. 915 (2007).
[2] V. Baryshevsky et al., arXiv:hep-ex/0501045, (2005).
iiiiiiV. Baryshevsky and A. Rouba, arXiv:nucl-th/0706.3808, (2007).
[3] H. Wilsch and G. Clausnitzer, Nucl. Phys. A160, 609 (1971).
[4] G. Perrin et al., Nucl. Phys. A282, 221 (1977).
[5] D. M. Bishop and L. M. Cheung, Phys. Rev. A20, 381 (1979).
[6] R. C. Johnson and E. J. Stephenson, in preparation.
50th Anniversary Symposium on Nuclear Sizes and Shapes
23/06/08