1. DIRAC status π + K ‒ - and π ‒ K + -atoms π + π ‒ -atoms (   ) Run 2011 Future magnet   level scheme, Stark effect and energy splitting measurement 1 Leonid Nemenov 21. October 2011

2. I Status of π + K ‒ -atoms 2 Run 2008-2010, statistics with low and medium background (⅔ of all statistics). Point-like production of all particles. The e + e ‒ background was not subtracted. Q Q – relative momentum in the πK c.m.s. A. Benelli, V. Yazkov Coulomb pairs Atomic pairs non-Coulomb pairs

3. II Status of π - K + -atoms 3 Run 2008-2010, statistics with low and medium background (⅔ of all statistics). Point-like production of all particles. The e + e ‒ background was not subtracted. A. Benelli, V. Yazkov Q – relative momentum in the πK c.m.s. Coulomb pairs Atomic pairs non-Coulomb pairs

4. III. The status of π - K + and π + K ‒ atoms 4 A. Benelli, V. Yazkov Run 2008-2010, statistics with low and medium background (⅔ of all statistics). Point-like production of all particles. The e + e ‒ background was not subtracted. Q – relative momentum in the πK c.m.s. Coulomb pairs Atomic pairs non-Coulomb pairs

5. IV Status π + π ‒ -atoms 5 Run 2008-2010, statistics with low and medium background (⅔ of all statistics). Point-like production of all particles. The e + e ‒ background was not subtracted. Coulomb pairs Atomic pairs non-Coulomb pairs A. Benelli, V. Yazkov Coulomb pairs Atomic pairs non-Coulomb pairs

6. V Status of 2011 run 6 Neodymium magnetic piece=70x60x5mm 3 : Gap=60mm; BL=0.01Tm Time of delivery to CERN: before 4 May 2011 y z x 150mm 90mm 60mm Tokyo Metropolitan University & Kyoto University

7. Simulation of long-lived A 2π observation V. Yazkov Without magnetWith magnet after Be target 7

8. Coulomb peak of π + π ‒ 8 Shift because of magnet degradation !

9. Shift of Q y (June-August) π + π ‒ data 9

10. Q x distribution (B x =0) 10 F. Takeutchi, V. Yazkov

11. Shift of Q y (June-August) e + e ‒ data 11 12 Pairs generated after magnet Pairs generated on Be target before magnet F. Takeutchi, V. Yazkov 12

12. Shift of Q y (June-August) e + e ‒ data without central peak 12 e + e ‒ generated on Be target before magnet F. Takeutchi, V. Yazkov

13. Shift of Q y (August-September) e + e ‒ data without central peak 13 F. Takeutchi, V. Yazkov

14. VI STATUS OF THE FUTURE MAGNET Halbach configuration NdBFe or SmCo 60 x 60 bore B = 0.89 T The magnets cost about 17000 $. The fabrication time is about 65 days. Y. Iwashita 14 flat

15. Y. Iwashita By along z-axis 15

16. V. Brekhovskikh Current Magnet Holder 16

17. The New Magnet Holder Y. Iwashita 17

18. A 2π Energy Levels J. Schweizer (P. L. 2oo4) For Coulomb potential E depends on n only. CONCLUSION: one parameter (2a 0 +a 2 ) allows to calculate all Δ ns-np values. VII ENERGY SPLITTING MEASUREMENT 18

19. Coulomb bound state and strong & electromagnetic perturbation DGBT *) formula & numerical values: A) Energy shift contributions: ______ *) Deser, Goldberger, Baumann, Thirring, PR 96 (1954) 774. B) Decay width: with Remark S-wave scattering lengths are amplitudes at threshold: em shiftstrong shift vacuum polarization 19 and

20. A 2π level scheme and 2s – 2p energy splitting n=1 n=2 n=3 -0.21 -0.47 -1.86 E n (keV) ε 1s Γ 1s ε 2s Γ 2s Stark mixing J. Schacher 20 ΔE 2s-2p

21. Values for energy shifts and lifetimes of π + π − atom [J. Schweizer, PL B587 (2004) 33] *) J. Schacher 21

22. CERN, Geneva - Monday 26, September, 2011 M. Pentia nHnH τ H 10 8 sτ 2π 10 11 s Decay length A 2π in L.S. cm for γ=16.1 2p0.161.175.7 3p0.543.9419 4p1.249.0544 5p2.4017.584.5 6p4.129.9144 7p 46.8 * 226 8p 69.3 * 335 A 2π lifetime, τ, in np states * - extrapolated values 22

23. L. Afanasev; O. Gorchakov (DIPGEN) Atomic pairs from A 2π long-lived states breakup in 2μm Pt. Long-lived A 2π yield and quantum numbers 23

24. 24 Impact on atomic beam by external magnetic field B lab and Lorentz factor γ ++  See: L. Nemenov, V. Ovsiannikov, Physics Letters B 514 (2001) 247. …. relative distance between  + and   in A 2  system …. laboratory magnetic field …electric field in A 2  system Lamb shift measurement with external magnetic field

25. L. Nemenov, V. Ovsiannikov [PL B514 (2oo1) 247] F … strength of electric field in A 2π c.m.s. → m must be 0 B L  B lab in lab system CONCLUSION: the lifetimes for long-lived states can be calculated using only one parameter → E 2s -E 2p. The lifetime of A 2π in electric field 25

26. A 2π * (2p-state) lifetime versus electric field Atom-field interaction: with J. Schacher 26 …will change => [weak-field limit]

27.  0.411.6 H=0.4 T328317302 111513 H=0.6 T325304279 212523 H=0.8 T322290258 32 H=1.0 T317276241 413538 H=1.2 T312263227 493646 H=1.4 T307251215 563646 H=1.6 T302241206 613548 H=0.0 T  =1 N A =330 ± 40 H=0.1 T  =1 N A =330 (1-0.7%) 27 V. Brekhovskikh

28. Magnetic Field - 1.0 T 28 2p3p4p5p6p7p8p∑ n,% 0.420.270.150.0790.0460.0250.0121.002  ∙10 -11,s 1.173.949.0517.529.946.869.3177.66 L,cm 5.6419.0243.6884.47144.32225.89334.49857.50  n 0.00750.02540.06030.11770.20340.32310.48221.2197  eff ∙10 -11,s 1.1623.6566.3026.5715.0113.4612.39728.561 L eff,cm 5.60917.64730.41831.71524.18816.70311.572137.85 NaNa 0.07140.15950.11930.07010.04290.02390.01160.499 N a eff 0.07100.15570.11240.06240.03490.01710.00700.4605 Magnetic Field 1.0 T  = 40%317.273 2p3p4p5p6p7p8p∑ n,% 0.420.270.150.0790.0460.0250.0121.002  ∙10 -11,s 1.173.949.0517.529.946.869.3177.66 L,cm 5.6419.0243.6884.47144.32225.89334.49857.50  n 0.01880.06360.15070.29430.50860.80761.20563.0492  eff ∙10 -11,s 1.1222.6532.4291.5350.9330.5900.3959.659 L eff,cm 5.41612.80611.7267.4124.5042.8491.90746.622 NaNa 0.07140.15950.11930.07010.04290.02390.01160.499 N a eff 0.06830.13690.08210.03350.01180.00300.00050.3362 Magnetic Field 1.0 T  = 100%276.147 2p3p4p5p6p7p8p∑ n,% 0.420.270.150.0790.0460.0250.0121.002  ∙10 -11,s 1.173.949.0517.529.946.869.3177.66 L,cm 5.6419.0243.6884.47144.32225.89334.49857.50  n 0.03010.10170.24110.47090.81371.29221.92894.8788  eff ∙10 -11,s 1.0551.7571.1350.6340.3720.2330.1555.339 L eff,cm 5.0928.4835.4763.0591.7931.1220.74725.774 NaNa 0.07140.15950.11930.07010.04290.02390.01160.499 N a eff 0.06370.10790.04580.01060.00160.00013.87∙10 -6 0.2296 Magnetic Field 1.0 T  = 160%240.908 CERN, Geneva - Monday 26, September, 2011 V. Brekhovskikh

29. 29

30. Reserve: 30

31. External magnetic and electric fields Atoms in a beam are influenced by external magnetic field and the relativistic Lorentz factor. 31

32. L. Nemenov, V. Ovsiannikov (P. L. 2oo1) F – strength of electric field in A 2π c.m.s. → m must be 0 B L in lab. syst. CONCLUSION: the lifetimes for long-lived states can be calculated using only one parameter → E 2s -E 2p. The lifetime of A 2π in electric field 32 mmmmmmmmmm m