QUASI-MAGNETIC RESONANCE IN STORAGE RING ELECTRIC-DIPOLE-MOMENT EXPERIMENTS
Abstract
A general theoretical description of a magnetic resonance is presented. This description is necessary for a detailed analysis of spin dynamics in electric-dipole-moment experiments in storage rings. General formulas describing a behavior of all components of the polarization vector at magnetic resonance are obtained for arbitrary initial polarization. Quasimagnetic resonances for particles and nuclei moving in non-continuous perturbing fields of accelerators and storage rings are considered. Distinguishing features of quasi-magnetic resonances in storage ring electric-dipole-moment experiments are investigated. The formulas for the effect caused by the electric dipole moment are derived. Main systematical errors are discussed.
Supporting agencies: The author acknowledges the support by the Belarusian Republican Foundation for Fundamental Research (Grant No. Ф16D-004) and by the Heisenberg-Landau program of the German Ministry for Science and Technology (Bundesministerium für Bildung und Forschung).
About the Author
A. J. Silenko
Institute for Nuclear Problems of the Belarusian State University; Joint Institute for Nuclear Research
Belarus
Belarus
D. Sc. (Physics and Mathematics), Leading Researcher
11, Bobruiskaya Str., 220030, Minsk
Leading Researcher of the Bogoliubov Laboratory of Theoretical Physics
6, Joliot-Curie Str., 141980, Dubna, Moscow Region
References
1. Slichter C. P. Principles of Magnetic Resonance. 3rd ed. Berlin, Springer-Verlag, 1990. 640 p. Doi: 10.1007/978-3-662- 09441-9
2. Levitt M. H. Spin Dynamics: Basics of Nuclear Magnetic Resonance, 2nd ed. New York, Wiley, 2008. 714 p.
3. Thomas L. H. The Motion of the Spinning Electron. Nature (London), 1926, vol. 117, no. 2945, p. 514. Doi: 10.1038/117514a0; Thomas L. H. The Kinematics of an Electron with an Axis. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1927, vol. 3, no. 13, pp. 1–22. Doi: 10.1080/14786440108564170; Bargmann V., Michel L., Telegdi V. L. Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field. Physical Review Letters, 1959, vol. 2, no. 10, pp. 435–439. Doi: 10.1103/physrevlett.2.435; Frenkel J. Die Elektrodynamik des rotierenden Elektrons. Zeitschrift für Physik, 1926, vol. 37, no. 4-5, pр. 243–262. Doi: 10.1007/bf01397099.)
4. Nelson D. F., Schupp A. A., Pidd R. W., Crane H. R. Search for an Electric Dipole Moment of the Electron. Physical Review Letters, 1959, vol. 2, no. 2, pp. 492–495. Doi: 10.1103/physrevlett.2.492; Khriplovich I. B. Feasibility of search for nuclear electric dipole moments at ion storage rings. Physical Review Letters B, 1998, vol. 444, no. 1-2, pp. 98–102. Doi: 10.1016/ s0370-2693(98)01353-7
5. Fukuyama T., Silenko A. J. Derivation of Generalized Thomas-Bargmann-Michel-Telegdi Equation for a Particle with Electric Dipole Moment. International Journal of Modern Physics A, 2013, vol. 28, no. 29, p. 1350147. Doi: 10.1142/s0217751x 13501479
6. Silenko A. J. Spin precession of a particle with an electric dipole moment: contributions from classical electrodynamics and from the Thomas effect. Physica Scripta, 2015, vol. 90, no. 6, p. 065303. Doi: 10.1088/0031-8949/90/6/065303
7. Morse W. M., Orlov Y. F., Semertzidis Y. K. rf Wien filter in an electric dipole moment storage ring: The “partially frozen spin” effect. Physical Review Special Topics – Accelerators and Beams, 2013, vol. 16, no. 11, p. 114001. Doi: 10.1103/ physrevstab.16.114001
8. Mey S., Gebel R. A Novel RF E×B Spin Manipulator at COSY. International Journal of Modern Physics: Conference Series, 2016, vol. 40, p. 1660094. Doi: 10.1142/s2010194516600946
9. Slim J., Gebel R., Heberling D., Hinder F., Hölscher D., Lehrach A., Lorentz B., Mey S., Nass A., Rathmann F., Reifferscheidt L., Soltner H., Straatmann H., Trinkel F., Wolters J. Electromagnetic Simulation and Design of a Novel Waveguide RF Wien Filter for Electric Dipole Moment Measurements of Protons and Deuterons. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2016, vol. 828, pр. 116– 124. Doi: 10.1016/j.nima.2016.05.012
10. Silenko A. J. General classical and quantum-mechanical description of magnetic resonance: an application to electric-dipole-moment experiments. The European Physical Journal C, 2017, vol. 77, no. 5, p. 341. Doi: 10.1140/epjc/s10052-017-4845-2
11. Silenko A. J. Equation of spin motion in storage rings in the cylindrical coordinate system. Physical Review Special Topics – Accelerators and Beams, 2006, vol. 9, no. 3, p. 034003. Doi: 10.1103/physrevstab.9.034003
12. Silenko A. J. Comparison of spin dynamics in the cylindrical and Frenet-Serret coordinate systems. Physics of Particles and Nuclei Letters, 2015, vol. 12, no. 1, pр. 8–10. Doi: 10.1134/s1547477115010197
13. Lehrach A., Lorentz B., Morse W., Nikolaev N., Rathmann F. Precursor Experiments to Search for Permanent Electric Dipole Moments (EDMs) of Protons and Deuterons at COSY. Available at: https://arxiv.org/pdf/1201.5773v1.pdf
14. Silenko A. J. Potential for measurement of the tensor polarizabilities of nuclei in storage rings by the frozen spin method. Physical Review C, 2009, vol. 80, no. 4, p. 044315. Doi: 10.1103/physrevc.80.044315
15. Silenko A. J. Connection between beam polarization and systematical errors in storage ring electric-dipole-moment experiments. JETP Letters, 2013, vol. 98, no. 4, pp. 191–194. Doi: 10.1134/s002136401317013x
16. Farley F. J. M., Jungmann K., Miller J. P., Morse W. M., Orlov Y. F., Roberts B. L., Semertzidis Y. K., Silenko A., Stephenson E. J. A new method of measuring electric dipole moments in storage rings. Physical Review Letters, 2004, vol. 93, no. 5, p. 052001. Doi: 10.1103/physrevlett.93.052001
17. Baryshevsky V. G. Birefringence effect in the nuclear pseudoelectric field of matter and an external electric field for a deuteron (nucleus) rotating in a storage ring. 2005. Available at: https://arxiv.org/pdf/hep-ph/0504064.pdf; Baryshevsky V. G. About influence of the deuteron electric and magnetic polarizabities on measurement of the deuteron EDM in a storage ring. 2005. Available at: https://arxiv.org/pdf/hep-ph/0510158.pdf; Baryshevsky V. G. Spin rotation of polarized beams in high energy storage ring. 2006. Available at: https://arxiv.org/pdf/hep-ph/0603191.pdf; Baryshevsky V. G., Gurinovich A. A. Spin rotation and birefringence effect for a particle in a high energy storage ring and measurement of the real part of the coherent elastic zero-angle scattering amplitude, electric and magnetic polarizabilities. 2005. Available at: https://arxiv.org/pdf/hep-ph/0506135.pdf
18. Baryshevsky V. G. Rotation of particle spin in a storage ring with a polarized beam and measurement of the particle EDM, tensor polarizability and elastic zero-angle scattering amplitude. Journal of Physics G: Nuclear and Particle Physics, 2008, vol. 35, no. 3, p. 035102. Doi: 10.1088/0954-3899/35/3/035102
19. Silenko A. J. Potential for measurement of the tensor magnetic polarizability of the deuteron in storage ring experiments. Physical Review C, 2008, vol. 77, no. 2, p. 021001(R). Doi: 0.1103/physrevc.77.021001
20. Silenko A. J. Tensor electric polarizability of the deuteron in storage-ring experiments. Physical Review C, 2007, vol. 75, no. 1, p. 014003. Doi: 0.1103/physrevc.75.014003
21. Baryshevsky V. G. and Silenko A. J. Potential for the measurement of the tensor electric and magnetic polarizabilities of the deuteron in storage-ring experiments with polarized beams. Journal of Physics: Conference Series, 2011, vol. 295, p. 012034. Doi: 10.1088/1742-6596/295/1/012034
22. Rathmann F., Saleev A., Nikolaev N. N. The search for electric dipole moments of light ions in storage rings. Journal of Physics: Conference Series, 2013, vol. 447, p. 012011. Doi: 10.1088/1742-6596/447/1/012011
23. Semertzidis Y. K. RFE and RFB effects. 2012. Available at: http://www.bnl.gov/edm/files/pdf/YkS_two_ RF_2012_0208.pdf
24. Nikolaev N. N. Duality of the MDM-transparent RF-E flipper to the transparent RF Wien-filter at all magnetic storage rings. 2012. Available at: http://www.bnl.gov/edm/files/pdf/NNikolaev_Wien_RFE.pdf (accessed 5 February 2016)
25. Lee S. Y. Spin resonance strength of a localized rf magnetic field. Physical Review Special Topics – Accelerators and Beams, 2006, vol. 9, p. 074001. Doi: 10.1103/physrevstab.9.074001
26. Orlov Y. F. On the partially-frozen-spin method. 2012. Available at: http://www.bnl.gov/edm/files/pdf/YOrlov_On_ partially-frozen-spin_3_21_12.pdf (accessed 5 February 2016).
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