50 th anniversary symposium on nuclear sizes and shapes 23/06/08 elizabeth cunningham does the...
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50th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08
Elizabeth Cunningham
Does the passage of low energy deuterons through a finite 12C foil lead to
small angle tensor polarisation?
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
Serious implications for designing polarimeters used in deuteron experiments.
Deviation from randomness of approx. 10%.
[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). IiiiiV. Baryshevsky and A. Rouba, arXiv:nucl-th/0706.3808, (2007).
50th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08
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.
Tensor Potential:
VTR(r,I)VTR(r)[(I ̂ r )2 2/3]
MI = ±1
MI = 0
b
br
r
50th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08
T20 Polarisation
T20 polarisation: measure of deviation from randomness.
The only type of tensor polarisation which does not tend to zero for scattering in the forward direction.
NMI = probability deuteron has Iz = MI in transmitted beam.
Unpolarised beam, N+1 = N-1 = N0 =1/3, gives: T20 = 0.
T203Iz
2 2
2
T203 N1N 1 2
2
1 3N0
2
50th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08
Experiment at Cologne University [1,2], measured tensor polarisation in the transmitted deuterons as large as
for small scattering angles and a carbon target thickness of 132 mg/cm2:
Transmitted deuterons are preferentially aligned with their long axis along incident beam direction.
Experimental T20
T20 = 0.18 ± 0.02
50th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08
Scattering Theory
z
eikz incident plane wave
f(,I) eikr scattered waver
r
V(r,I,) scattering centre Asymptotic Wavefunction:
Used to calculate cross section and T20 polarization for deuterons elastically scattering from an individual 12C nucleus.
Scattering amplitude connects wavefunction and observables:
(r) eikz f(,I)eikr
r
f(,I)
22 e ik.r V(r,I) (k,r) dr
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 ̂ r ]2 2 3 Coulomb[3] Central[3] Spin-Orbit[3] Tensor[4]
Extrapolation from polarisation data for angles greater than 1 deg. Potential depths:
Used to calculate scattering amplitude:
dd
13
Tr (ff)
T201
2
Tr(f [3Iz2 -2]f )
Tr(ff )
Vc = 119.0 MeV, Wc = 5.8 MeV, VLS = 6.2 MeV, VTR = 3.965 MeV
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
Coulomb interaction between deuteron and the atom:
Using Born approximation,
- first order approximation
- assumes effect of scattering potential is small
scattering amplitude for atom A A’ becomes:
Atomic Scattering
re-
riR
VdA Ze2
| R r/2|
e2
| R r/2 ri |i1
Z
fM I A M I 'A '
22 M I ' (r),A ' (ri),k' (R) VdA (R,r,ri) k(R),A (ri),M I(r)
50th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08
Using q = k - k’ and changing the variables so that R’=R+r/2,
gives a simplified expression for T20 polarisation for single atomic scattering of a deuteron from a carbon atom.
Qd = deuteron quadrupole moment = 0.2860 ± 0.0015 fm2 [5].
Atomic T20
T201
2
Tr([3Iz2 -2]MM)
Tr(M M)
23
Qdq2P2 cos(q)
fM IA M I 'A ' Tatom(q) MM I 'M I(q), MM I 'M I
dr e iqr/2M I '* (r)M I (r)
50th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08
Results - Atomic
Born approx. factor of 2 higher but both give T20 in forward direction of order ~10-5
d-12C at 11.9 MeV
50th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08
Estimate of the T20 from multiple atomic scattering events.
Using qj2 = kj
2 (scatt2)j and taking P2(cos(qj
)) = -0.5, most likely
value for small q:
To calculate specific case for comparison with experiment, use 2 [6]
Multiple Scattering
T2023
Qd qj2P2 cos(q j
) j=1
N
T2026
Qdk2 (scatt
2 ) jj=1
N
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
[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.
Thank you to my supervisors Ron Johnson and Jim Al-Khalili.
Thank you for listening…