1. 50 th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08 Elizabeth Cunningham Does the passage of low energy deuterons through a finite 12 C foil lead to small angle tensor polarisation?

2. 50 th 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

3. 50 th 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). Iiiii V. Baryshevsky and A. Rouba, arXiv:nucl-th/0706.3808, (2007).

4. 50 th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08 Tensor Interaction Deuteron has prolate quadrupole deformation along its spin axis. Different spin projection iiiiiiiiiiiM I = +1,0, -1 gives different apparent cross sectional area of deuteron ‘seen’ by target. Tensor Potential: M I = ±1 M I = 0 b b r r

5. 50 th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08 T 20 Polarisation T 20 polarisation: measure of deviation from randomness. The only type of tensor polarisation which does not tend to zero for scattering in the forward direction. N M I = probability deuteron has I z = M I in transmitted beam. Unpolarised beam, N +1 = N -1 = N 0 =1/3, gives: T 20 = 0.

6. 50 th 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/cm 2 : Transmitted deuterons are preferentially aligned with their long axis along incident beam direction. Experimental T 20 T 20 = 0.18 ± 0.02

7. 50 th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08 Scattering Theory  z e ikz incident plane wave f( ,I) e ikr scattered wave r r V(r,I,) scattering centre Asymptotic Wavefunction: Used to calculate cross section and T 20 polarization for deuterons elastically scattering from an individual 12 C nucleus. Scattering amplitude connects wavefunction and observables:

8. 50 th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08 Optical Potential Optical potential for d- 12 C nuclear scattering at 11.9 MeV: 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: V c = 119.0 MeV, W c = 5.8 MeV, V LS = 6.2 MeV, V TR = 3.965 MeV

9. 50 th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08 Results - Nuclear d- 12 C at 11.9 MeV T 20 in forward direction is of order ~10 -5

10. 50 th 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 r e-e- riri R

11. 50 th 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 T 20 polarisation for single atomic scattering of a deuteron from a carbon atom. Q d = deuteron quadrupole moment = 0.2860 ± 0.0015 fm 2 [5]. Atomic T 20

12. 50 th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08 Results - Atomic Born approx. factor of 2 higher but both give T 20 in forward direction of order ~10 -5 d- 12 C at 11.9 MeV

13. 50 th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08 Estimate of the T 20 from multiple atomic scattering events. Using q j 2 = k j 2 (  scatt 2 ) j and taking P 2 (cos(  q j )) = -0.5, most likely value for small q: To calculate specific case for comparison with experiment, use  2 [6] Multiple Scattering Multiple scattering calculation gives T 20 = 1.2x10 -4

14. 50 th Anniversary Symposium on Nuclear Sizes and Shapes 23/06/08 Summary - Measurement of T 20 = 0.18 ± 0.02 for 5-8 MeV deuterons passing through a 12 C target of thickness 132 mg/cm 2. - Calculation of T 20 ~ 10 -5 for 11.9 MeV deuterons scattering from a single 12 C nucleus. - Calculation of T 20 = 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.

15. 50 th 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…