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K - d 原子 の理論計算の現状と 今後の課題

K - d 原子 の理論計算の現状と 今後の課題. Shota Ohnishi (Tokyo Inst. Tech. / RIKEN). in collaboration with Yoichi Ikeda (RIKEN) Tetsuo Hyodo (YITP, Kyoto Univ. ) Emiko Hiyama (RIKEN) Wolfram Weise (ECT*). K bar N interaction. Experimental data used to determine model parameters.

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K - d 原子 の理論計算の現状と 今後の課題

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  1. K-d原子の理論計算の現状と今後の課題 Shota Ohnishi (Tokyo Inst. Tech. / RIKEN) • in collaboration with • Yoichi Ikeda (RIKEN) • Tetsuo Hyodo (YITP, Kyoto Univ.) • Emiko Hiyama (RIKEN) • Wolfram Weise (ECT*)

  2. KbarN interaction Experimental data used to determine model parameters K-pcross section: aboveKbarN threshold energy (w/ large error) Branching ratio kaonic atom L(1405) : below KbarN threshold energy (one pole or two pole <->L(1405) or L(1420)) : at/just below KbarN threshold energy

  3. Energy dependence of KbarN interaction Ikeda, Sato, PRC76, 035203(2007); Ikeda, Kamano, Sato, PTP124, 533(2010) WT Lagrangian E-independent Derivative coupling  E-dependent

  4. Signature of the KbarNN resonance Ohnishi, Ikeda, Kamano, Sato arXiv:1302.2301[nucl-th] to appear in PRC E-indep. E-dep. Significant difference on production spectra can be used to obtain KbarN interaction information

  5. Kaonic hydrogen Coulomb Only Coulomb Coulomb + strong int. 1s kaonic hydrogen 1s -8.6keV L(1405) Improved Deser formula Meissner, Raha, Rusetsky, Eur. Phys. J. C41 (2005) 213. Important constraint on K-p scattering length from the energy shift and width

  6. Kaonic hydrogen SIDDHARTA Collaboration Phys. Lett. B 704 (2011) 113. SIDDHARTA measurement of the energy shift and width of the 1s state : Improved Deser formula Ikeda, Hyodo, Weise Nucl. Phys. A 881 (2012) 98.

  7. Kaonic deuterium K-p andK-d scattering lengths  scattering lengths in I=0 and I=1 channels

  8. Deser formula K--nuclear optical potential of the tr form : neglect finite size effects

  9. Importance of multiple scattering • large cancelation of  impulse approx. does NOT work • strong charge exchange interaction between and  worse convergence of scattering series Impulse approx. Double scattering + … +

  10. Rusetsky formula impulse approximation double scattering Rusetsky formula (all orders of the multiple scattering) daK-d : three-body LECs neglect

  11. Improved Deser formula improved Deser formula Coulomb correction electronic vacuum polarization is amplified by powers of QED relativistic correction necessary

  12. full optical potential Here, multiple scattering, NN-pair correlations, finite nuclear size effect and so on are taken into account except for deuteron excitations.

  13. Uehling potential For kaonic atom, electron vacuum polarization effect is so large, that if we try to solve Schrödinger equation for K-pn three-body system to study deuteron excitations effect, we also need to consider about correction of Coulomb force. for non-relativistic limit

  14. modification of Coulomb potential • As a first step to study K-d atom, • K-p atom Deser formula imp. Deserformula

  15. K-p interaction • We employ the Gaussian local potential based on chiral effective field theory Parameters are fitted to reproduce the amplitude of Ikeda, Hyodo, Weise Nucl. Phys. A 881 (2012) 98.

  16. We study the 1s energy shift by solving the Schrodinger equation with only Coulomb potential and with Coulomb and strong interaction using the variational method. We obtain the value between Deser formula and improved Deser formula.

  17. electron vacuum polarization Coulomb vs Coulomb + strong -> Coulomb + Uehlingvs Coulomb + Uehling + strong

  18. Future work Summary • Deser formula and improved Deser formula • Effect of electron vacuum polarization • K-p • Uehling potential • How to handle the effect of electron vacuum polarization effect. • Lamb shift, K-d • Three-body caluculationof the K-pn • Faddeev calculation of AK-d

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