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Elizabeth Cunningham

Does the passage of low energy deuterons through a finite 12 C foil lead to small angle tensor polarisation?. Elizabeth Cunningham. Overview. Experimental motivation Brief description of tensor polarisation Nuclear scattering Atomic scattering Comparison with experiment Summary.

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Elizabeth Cunningham

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  1. Does the passage of low energy deuterons through a finite 12C foil lead to small angle tensor polarisation? Elizabeth Cunningham

  2. Overview Experimental motivation Brief description of tensor polarisation Nuclear scattering Atomic scattering Comparison with experiment Summary

  3. Deviation from randomness of approx. 10%. 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. [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. MI = ±1 b r MI = 0 b r 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:

  5. 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.

  6. T20= 0.18 ± 0.02 Experimental T20 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.

  7. V(r,I,) scattering centre  z r eikz incident plane wave f(,I) eikr scattered wave r Scattering Theory Asymptotic Wavefunction: Scattering amplitude connects wavefunction and observables: Used to calculate cross section and T20 polarization for deuterons elastically scattering from an individual 12C nucleus.

  8. Optical Potential Optical potential for d-12C 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: Vc = 119.0 MeV, Wc = 5.8 MeV, VLS = 6.2 MeV, VTR = 3.965 MeV

  9. T20 in forward direction is of order ~10-5 Results - Nuclear d-12C at 11.9 MeV

  10. Atomic Scattering e- 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: r ri R

  11. Atomic T20 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].

  12. Born approx. factor of 2 higher but both give T20 in forward direction of order ~10-5 Results - Atomic d-12C at 11.9 MeV

  13. Multiple scattering calculation givesT20 = 1.2x10-4 Multiple Scattering Estimate of the T20 from multiple atomic scattering events. Using qj2 = kj2 (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]

  14. 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.

  15. 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.

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