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Muonic atom and anti-nucleonic atom

Muonic atom and anti-nucleonic atom. October 1, 2003 Akihiro Haga Workshop in RCNP. muon. ○Measured muonic transition in 208 Pb. Δ2p splitting 184.788(27) keV. Δ3p splitting 47.197(45) keV. At PSI. ○Experimental Allowable Regions of Nuclear Polarization.

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Muonic atom and anti-nucleonic atom

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  1. Muonic atom and anti-nucleonic atom October 1, 2003 Akihiro Haga Workshop in RCNP

  2. muon

  3. ○Measured muonic transition in 208Pb. Δ2p splitting 184.788(27) keV. Δ3p splitting 47.197(45) keV. At PSI.

  4. ○Experimental Allowable Regions of Nuclear Polarization Y. Yamazaki et al. Phys. Rev. Lett. 421470(1979) Values of the experimental NP correction Enp are determined by minimizing the χ2 function.

  5. ○Experimental Nuclear Polarization in muonic 208Pb Δ3p Δ2p P. Bergem et al. Phys. Rev. C, 37 2821(1988)

  6. ○Feynman diagrams for nuclear polarization in lowest order

  7. ○Nuclear Polarization Formula

  8. ○Relativistic correction

  9. ○Total nuclear polarization (eV) in muonic 208Pb States Feynman gauge Coulomb gauge Coulomb NP 1s1/2 -4470 -4466 -4231 2s1/2 -882 -878 -831 2p1/2 -1685 -1685 -1859 2p3/2 -1656 -1656 -1683 3p1/2 -501 -502 -564 3p3/2 -554 -555 -561 3d3/2 -230 -230 -255 3d5/2 -34 -33 -47 Haga et al., Phys. Rev. A, 65, 052509 (2002)

  10. ○Anomaly in Δp splitting energies of muonic 208Pb Δ3p Δ2p

  11. ○ QED corrections First order Second order

  12. ○ Relativistic treatment of nucleus 　　～ use of relativistic RPA ～ 250MeV with negative states 250MeV without negative states

  13. ○ Nuclear polarization in muonic 16O (eV)

  14. ○ Nuclear form factors for isoscalar 1- state -1-GeV state 8-MeV state

  15. ○ Energy-weighted sums of B(Eλ)(e２bλ・MeV) in 16O Classical sum rule

  16. まとめ ・208PbのΔ2p、 Δ3pの分裂エネルギー 　得られた結果からすると、Δ2pとΔ3pのAnomalyを同時に解決するのは困難ではないか？QEDの再計算を含め、何が問題なのかを確かめる必要があると思われる。Muonic atomの核分極補正は非常に大きく、この問題点を解決することにより核構造の情報を得るためのプローブとなりえるであろう。 ・Relativistic RPAを用いた核分極補正計算 Anti-nucleon state はゲージに依存しない結果を得るのに重要。この寄与はほとんど横波から生じ、Non-relativisticの場合のSeagull diagramに対応しているようである。またEffective mass のため、核分極補正の値はNon-relativistic より大きくなる。

  17. ○Relativistic picture of nucleus Proton single-particle states

  18. ○Proton single-particle energies MeV mN - mN Parameter set NLSH

  19. ○Transition probability Coulomb states

  20. G. Mao et al. nucl-th/112010

  21. まとめ • 原子核を相対論的に記述することにより、反陽子原子は原子核の特殊な励起状態として表すことができる。 • Relativistic Hartree Approach では負のエネルギー状態が非常に強く束縛される。この状態への遷移は小さい角運動量で大きくなる。 • 現在のRelativistic Hartree Approachは真空の補正が完全ではない。反陽子状態を記述する上でこの補正を正しく行うことが大切であると思われる。

  22. Particle-hole excitation – Vacuum correction Ordinary particle-hole excitation + Blocking effect

  23. Ordinary particle-hole excitation Blocking effect

  24. ○Nuclear polarization in hydrogenlike 208Pb Feynman Coulomb Haga et al., Phys. Rev. A, 65, 052509 (2002)

  25. ○Nuclear polarization in muonic 208Pb Feynman Coulomb Haga et al., Phys. Rev. A, 66, 034501 (2002)

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