1. The GSI anomaly: Theoretical interpretations Alexander Merle Max-Planck-Institute for Nuclear Physics Heidelberg Germany LAUNCH workshop, 9-12 November 2009

2. Contents: 1.Introduction 2.General problems for explanations 3.The ideas up to now 4.Conclusions

3. 1. Introduction

4. Litvinov et al: Phys. Lett. B664, 162 (2008) 1. Introduction

5. Periodic modula- tion of the expect- ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr- 140) Litvinov et al: Phys. Lett. B664, 162 (2008) 1. Introduction

6. Periodic modula- tion of the expect- ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr- 140) exponential law Litvinov et al: Phys. Lett. B664, 162 (2008) 1. Introduction

7. Periodic modula- tion of the expect- ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr- 140) exponential law periodic modulation Litvinov et al: Phys. Lett. B664, 162 (2008) 1. Introduction

8. Periodic modula- tion of the expect- ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr- 140) exponential law periodic modulation Litvinov et al: Phys. Lett. B664, 162 (2008) T~7s 1. Introduction

9. Literature on the GSI Anomaly (complete?): Lipkin, arXiv:0801.1465; Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079; Ivanov et al., arXiv:0801.2121; Giunti, arXiv:0801.4639; Ivanov et al., arXiv:0804.1311; Faber, arXiv:0801.3262; Walker, Nature 453N7197 (2008) 864–865; Ivanov et al., arXiv:0803.1289; Kleinert & Kienle, arXiv:0803.2938; Ivanov et al., Phys. Rev. Lett. 101 (2008) 182501; Burkhardt et al., arXiv:0804.1099; Peshkin, arXiv:0804.4891; Giunti, Phys. Lett. B665 (2008) 92– 94, arXiv:0805.0431; Lipkin, arXiv:0805.0435; Vetter et al., Phys. Lett. B670 (2008) 196–199, arXiv:0807.0649; Litvinov et al., arXiv:0807.2308; Ivanov et al., arXiv:0807.2750; Faestermann et al., arXiv:0807.3297; Giunti, arXiv:0807.3818; Kienert et al., J. Phys. Conf. Ser. 136 (2008) 022049, arXiv:0808.2389; Gal, arXiv:0809.1213; Pavlichenkov, Europhys. Lett. 85 (2009) 40008, arXiv:0810.2898; Cohen et al., arXiv:0810.4602; Peshkin, arXiv:0811.1765; Lambiase et al., arXiv:0811.2302; Giunti, Nucl. Phys. Proc. Suppl. 188 (2009) 43–45, arXiv:0812.1887; Lipkin, arXiv:0905.1216; Ivanov et al., arXiv:0905.1904; Giunti, arXiv:0905.4620; Faber et al., arXiv:0906.3617; Isakov, arXiv:0906.4219; Faestermann, arXiv:0907.1557; Winckler et al., arXiv:0907.2277; Merle, arXiv:0907.3554; Ivanov & Kienle, Phys. Rev. Lett. 103 (2009) 062502, arXiv:0908.0877; Flambaum, arXiv:0908.2039; Kienle & Ivanov, arXiv:0909.1285; Kienle & Ivanov, arXiv:0909.1287; Lipkin, arXiv:0910.5049

10. 2. General problems for explanations

11. HERE: Let us assume that the observation at GSI is a real effect.

12. 2. General problems for explanations HERE: Let us assume that the observation at GSI is a real effect. THIS MEANS: Any explanation has to meet several require- ments.

13. What do we have to explain?

14. trivial (?) requirement: there must be a mechanism that generates the oscillations there must be an explanation why this effect has not been seen in other experiments scaling: it seems that ω~1/M (or ω~Q), while Q/M≈const. (Ivanov et al., arXiv:0905.1904) How can the explanation be tested? Does it lead to further consequences?

15. What do we have to explain? trivial (?) requirement: there must be a mechanism that generates the oscillations there must be an explanation why this effect has not been seen in other experiments scaling: it seems that ω~1/M (or ω~Q), while Q/M≈const. (Ivanov et al., arXiv:0905.1904) How can the explanation be tested? Does it lead to further consequences?

16. What do we have to explain? trivial (?) requirement: there must be a mechanism that generates the oscillations there must be an explanation why this effect has not been seen in other experiments scaling: it seems that ω~1/M (or ω~Q), while Q/M≈const. (Ivanov et al., arXiv:0905.1904) How can the explanation be tested? Does it lead to further consequences?

17. What do we have to explain? trivial (?) requirement: there must be a mechanism that generates the oscillations there must be an explanation why this effect has not been seen in other experiments scaling: it seems that ω~1/M (or ω~Q), while Q/M≈const. (Ivanov et al., arXiv:0905.1904) How can the explanation be tested? Does it lead to further consequences?

18. We know 2 types of explanations:

19. 1. Explanations that do not work for principal reasons.

20. We know 2 types of explanations: 1. Explanations that do not work for principal reasons. 2. Explanations that do work in principle but yield a wrong order of magnitude or some other wrong behavior.

21. We know 2 types of explanations: 1. Explanations that do not work for principal reasons. 2. Explanations that do work in principle but yield a wrong order of magnitude or some other wrong behavior. It would be nice to also have:

22. We know 2 types of explanations: 1. Explanations that do not work for principal reasons. 2. Explanations that do work in principle but yield a wrong order of magnitude or some other wrong behavior. It would be nice to also have: 3. Explanations that do work and are correct.

23. We know 2 types of explanations: 1. Explanations that do not work for principal reasons. 2. Explanations that do work in principle but yield a wrong order of magnitude or some other wrong behavior. It would be nice to also have: 3. Explanations that do work and are correct. → not so easy to find…

24. 3. The ideas up to now

25. CAUTION!!! I only discuss several ideas that have appeared. This DOES NOT mean that I agree with all of them!!!

26. 3. The ideas up to now CAUTION!!! I only discuss several ideas I came across. This DOES NOT mean that I agree with all of them!!!

27. 3. The ideas up to now CAUTION!!! I only discuss several ideas I came across. This DOES NOT mean that I agree with all of them!!!

28. 3. The ideas up to now CAUTION!!! I only discuss several ideas I came across. This DOES NOT mean that I agree with all of them!!! Please keep that in mind!

29. 3. The ideas up to now Neutrino oscillations:

30. 3. The ideas up to now Neutrino oscillations: Lipkin, arXiv:0801.1465 Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0804.1311 Faber, arXiv:0801.3262 Walker, Nature 453N7197 (2008) 864–865 Ivanov et al., arXiv:0803.1289 Lipkin, arXiv:0805.0435 Ivanov et al., arXiv:0807.2750 Lipkin, arXiv:0905.1216 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Ivanov & Kienle, Phys. Rev. Lett. 103 (2009) 062502, arXiv:0908.0877 Kienle & Ivanov, arXiv:0909.1285 Kienle & Ivanov, arXiv:0909.1287

31. 3. The ideas up to now Neutrino oscillations: Lipkin, arXiv:0801.1465 Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0804.1311 Faber, arXiv:0801.3262 Walker, Nature 453N7197 (2008) 864–865 Ivanov et al., arXiv:0803.1289 Lipkin, arXiv:0805.0435 Ivanov et al., arXiv:0807.2750 Lipkin, arXiv:0905.1216 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Ivanov & Kienle, Phys. Rev. Lett. 103 (2009) 062502, arXiv:0908.0877 Kienle & Ivanov, arXiv:0909.1285 Kienle & Ivanov, arXiv:0909.1287 Problem:

32. 3. The ideas up to now Neutrino oscillations: Lipkin, arXiv:0801.1465 Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0804.1311 Faber, arXiv:0801.3262 Walker, Nature 453N7197 (2008) 864–865 Ivanov et al., arXiv:0803.1289 Lipkin, arXiv:0805.0435 Ivanov et al., arXiv:0807.2750 Lipkin, arXiv:0905.1216 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Ivanov & Kienle, Phys. Rev. Lett. 103 (2009) 062502, arXiv:0908.0877 Kienle & Ivanov, arXiv:0909.1285 Kienle & Ivanov, arXiv:0909.1287 Problem:

33. 3. The ideas up to now Neutrino oscillations: Lipkin, arXiv:0801.1465 Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0804.1311 Faber, arXiv:0801.3262 Walker, Nature 453N7197 (2008) 864–865 Ivanov et al., arXiv:0803.1289 Lipkin, arXiv:0805.0435 Ivanov et al., arXiv:0807.2750 Lipkin, arXiv:0905.1216 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Ivanov & Kienle, Phys. Rev. Lett. 103 (2009) 062502, arXiv:0908.0877 Kienle & Ivanov, arXiv:0909.1285 Kienle & Ivanov, arXiv:0909.1287 Problem: neutrino not detected ‹ν i |ν k ›=δ ik incoherent summation

34. 3. The ideas up to now Neutrino oscillations: Lipkin, arXiv:0801.1465 Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0804.1311 Faber, arXiv:0801.3262 Walker, Nature 453N7197 (2008) 864–865 Ivanov et al., arXiv:0803.1289 Lipkin, arXiv:0805.0435 Ivanov et al., arXiv:0807.2750 Lipkin, arXiv:0905.1216 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Ivanov & Kienle, Phys. Rev. Lett. 103 (2009) 062502, arXiv:0908.0877 Kienle & Ivanov, arXiv:0909.1285 Kienle & Ivanov, arXiv:0909.1287 Problem: neutrino not detected ‹ν i |ν k ›=δ ik incoherent summation

35. 3. The ideas up to now Neutrino oscillations: Lipkin, arXiv:0801.1465 Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0804.1311 Faber, arXiv:0801.3262 Walker, Nature 453N7197 (2008) 864–865 Ivanov et al., arXiv:0803.1289 Lipkin, arXiv:0805.0435 Ivanov et al., arXiv:0807.2750 Lipkin, arXiv:0905.1216 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Ivanov & Kienle, Phys. Rev. Lett. 103 (2009) 062502, arXiv:0908.0877 Kienle & Ivanov, arXiv:0909.1285 Kienle & Ivanov, arXiv:0909.1287 Problem: neutrino not detected ‹ν i |ν k ›=δ ik incoherent summation

36. 3. The ideas up to now Neutrino oscillations: Lipkin, arXiv:0801.1465 Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0804.1311 Faber, arXiv:0801.3262 Walker, Nature 453N7197 (2008) 864–865 Ivanov et al., arXiv:0803.1289 Lipkin, arXiv:0805.0435 Ivanov et al., arXiv:0807.2750 Lipkin, arXiv:0905.1216 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Ivanov & Kienle, Phys. Rev. Lett. 103 (2009) 062502, arXiv:0908.0877 Kienle & Ivanov, arXiv:0909.1285 Kienle & Ivanov, arXiv:0909.1287 Problem: neutrino not detected ‹ν i |ν k ›=δ ik incoherent summation

37. Interference of the final states:

38. Isakov, arXiv:0906.4219

39. Interference of the final states: Isakov, arXiv:0906.4219 General idea:

40. Interference of the final states: Isakov, arXiv:0906.4219 General idea: The competing process to EC is β + decay. → Assumption of the author: The final states |EC› and |β + › might interfere like |ν e › and |ν μ ›.

41. Interference of the final states: Isakov, arXiv:0906.4219 General idea: The competing process to EC is β + decay. → Assumption of the author: The final states |EC› and |β + › might interfere like |ν e › and |ν μ ›.

42. Interference of the final states: Isakov, arXiv:0906.4219 General idea: The competing process to EC is β + decay. → Assumption of the author: The final states |EC› and |β + › might interfere like |ν e › and |ν μ ›. Problem: The EC and the β + mode are distinct. → How should they interfere at all???

43. Interference of the final states: Isakov, arXiv:0906.4219 General idea: The competing process to EC is β + decay. → Assumption of the author: The final states |EC› and |β + › might interfere like |ν e › and |ν μ ›. Problem: The EC and the β + mode are distinct. → How should they interfere at all??? The author seems to be aware of this problem:

44. Interference of the final states: Isakov, arXiv:0906.4219 General idea: The competing process to EC is β + decay. → Assumption of the author: The final states |EC› and |β + › might interfere like |ν e › and |ν μ ›. Problem: The EC and the β + mode are distinct. → How should they interfere at all??? The author seems to be aware of this problem:

45. The pulsating vacuum:

46. Kleinert & Kienle, arXiv:0803.2938

47. The pulsating vacuum: Kleinert & Kienle, arXiv:0803.2938 Idea:

48. The pulsating vacuum: Kleinert & Kienle, arXiv:0803.2938 Idea: emission of a ν e with E>0 ≡ absorption of an anti-ν e with E<0 (from the vacuum) that oscillates

49. The pulsating vacuum: Kleinert & Kienle, arXiv:0803.2938 Idea: emission of a ν e with E>0 ≡ absorption of an anti-ν e with E<0 (from the vacuum) that oscillates Problems:

50. The pulsating vacuum: Kleinert & Kienle, arXiv:0803.2938 Idea: emission of a ν e with E>0 ≡ absorption of an anti-ν e with E<0 (from the vacuum) that oscillates Problems: first, this is just a different way of drawing the decay diagram → What should that change? even if a vacuum-neutrino oscillates, the vacuum contains all sorts of neutrinos → effect killed due to unitarity Why should the oscillation in the vacuum have any correlation to the injection time of the ions?

51. The pulsating vacuum: Kleinert & Kienle, arXiv:0803.2938 Idea: emission of a ν e with E>0 ≡ absorption of an anti-ν e with E<0 (from the vacuum) that oscillates Problems: first, this is just a different way of drawing the decay diagram → What should that change? even if a vacuum-neutrino oscillates, the vacuum contains all sorts of neutrinos → effect killed due to unitarity Why should the oscillation in the vacuum have any correlation to the injection time of the ions?

52. The pulsating vacuum: Kleinert & Kienle, arXiv:0803.2938 Idea: emission of a ν e with E>0 ≡ absorption of an anti-ν e with E<0 (from the vacuum) that oscillates Problems: first, this is just a different way of drawing the decay diagram → What should that change? even if a vacuum-neutrino oscillates, the vacuum contains all sorts of neutrinos → effect killed due to unitarity Why should the oscillation in the vacuum have any correlation to the injection time of the ions?

53. Quantum Beats:

54. Giunti, arXiv:0801.4639 Peshkin, arXiv:0804.4891 Giunti, Phys. Lett. B665 (2008) 92– 94, arXiv:0805.0431 Kienert et al., J. Phys. Conf. Ser. 136 (2008) 022049, arXiv:0808.2389 Splitting in the initial state:

55. Quantum Beats: Giunti, arXiv:0801.4639 Peshkin, arXiv:0804.4891 Giunti, Phys. Lett. B665 (2008) 92– 94, arXiv:0805.0431 Kienert et al., J. Phys. Conf. Ser. 136 (2008) 022049, arXiv:0808.2389 Splitting in the initial state:

56. Quantum Beats: Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Giunti, arXiv:0801.4639 Peshkin, arXiv:0804.4891 Giunti, Phys. Lett. B665 (2008) 92– 94, arXiv:0805.0431 Kienert et al., J. Phys. Conf. Ser. 136 (2008) 022049, arXiv:0808.2389 Splitting in the initial state: Splitting in the final state:

57. Quantum Beats: Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Giunti, arXiv:0801.4639 Peshkin, arXiv:0804.4891 Giunti, Phys. Lett. B665 (2008) 92– 94, arXiv:0805.0431 Kienert et al., J. Phys. Conf. Ser. 136 (2008) 022049, arXiv:0808.2389 Splitting in the initial state: Splitting in the final state:

58. Quantum Beats: Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079 Ivanov et al., arXiv:0801.2121 Ivanov et al., arXiv:0905.1904 Faber et al., arXiv:0906.3617 Giunti, arXiv:0801.4639 Peshkin, arXiv:0804.4891 Giunti, Phys. Lett. B665 (2008) 92– 94, arXiv:0805.0431 Kienert et al., J. Phys. Conf. Ser. 136 (2008) 022049, arXiv:0808.2389 Splitting in the initial state: Splitting in the final state: → Both ideas have their problems!

59. Splitting in the initial state:

61. the only surviving “explanation” up to now required splitting: ΔE≈10 -15 eV → tiny problem: there is no explanation for this ΔE preliminary data on β + decays shows no oscillation (Ivanov et al., arXiv:0905.1904) → splitting can only be in the electron level

62. Splitting in the initial state: the only surviving “explanation” up to now required splitting: ΔE≈10 -15 eV → tiny problem: there is no explanation for this ΔE preliminary data on β + decays shows no oscillation (Ivanov et al., arXiv:0905.1904) → splitting can only be in the electron level

63. Splitting in the initial state: the only surviving “explanation” up to now required splitting: ΔE≈10 -15 eV → tiny problem: there is no explanation for this ΔE preliminary data on β + decays shows no oscillation (Ivanov et al., arXiv:0905.1904) → splitting can only be in the electron level

64. Splitting in the initial state: the only surviving “explanation” up to now required splitting: ΔE≈10 -15 eV → tiny problem: there is no explanation for this ΔE preliminary data on β + decays shows no oscillation (Ivanov et al., arXiv:0905.1904) → splitting can only be in the electron level

65. Splitting in the initial state: the only surviving “explanation” up to now required splitting: ΔE≈10 -15 eV → tiny problem: there is no explanation for this ΔE preliminary data on β + decays shows no oscillation (Ivanov et al., arXiv:0905.1904) → splitting can only be in the electron level

66. Splitting in the final state:

68. average distance between ions: ~100 m (Steck et al., Phys. Rev. Lett. 77, 3803) → excluded in the GSI case (Merle, arXiv:0907.3554) Splitting in the final state: only one ion: does NOT beat! (Chow et al., Phys. Rev. A11 (1975) 1380) interaction between different ions: might be HOWEVER: ions must be within λ de-Broglie ≈10 -12 m

69. average distance between ions: ~100 m (Steck et al., Phys. Rev. Lett. 77, 3803) → excluded in the GSI case (Merle, arXiv:0907.3554) Splitting in the final state: only one ion: does NOT beat! (Chow et al., Phys. Rev. A11 (1975) 1380) interaction between different ions: might be HOWEVER: ions must be within λ de-Broglie ≈10 -12 m

70. average distance between ions: ~100 m (Steck et al., Phys. Rev. Lett. 77, 3803) → excluded in the GSI case (Merle, arXiv:0907.3554) Splitting in the final state: only one ion: does NOT beat! (Chow et al., Phys. Rev. A11 (1975) 1380) interaction between different ions: might be HOWEVER: ions must be within λ de-Broglie ≈10 -12 m

71. average distance between ions: ~100 m (Steck et al., Phys. Rev. Lett. 77, 3803) → excluded in the GSI case (Merle, arXiv:0907.3554) Splitting in the final state: only one ion: does NOT beat! (Chow et al., Phys. Rev. A11 (1975) 1380) interaction between different ions: might be HOWEVER: ions must be within λ de-Broglie ≈10 -12 m

72. average distance between ions: ~100 m (Steck et al., Phys. Rev. Lett. 77, 3803) → excluded in the GSI case (Merle, acc. Phys. Rev. C) Splitting in the final state: only one ion: does NOT beat! (Chow et al., Phys. Rev. A11 (1975) 1380) interaction between different ions: might be HOWEVER: ions must be within λ de-Broglie ≈10 -12 m

73. Hyperfine splittings:

74. Discussion: J. Kopp, M. Lindner, A. Merle

75. Hyperfine splittings: Discussion: J. Kopp, M. Lindner, A. Merle hyperfine splittings might be the first thought BUT: there are two problems… (1) order of magnitude for getting ΔE≈10 -15 eV: μ N =3.2∙10 -8 eV/T → B required =3.2∙10 -8 T μ B =5.8∙10 -5 eV/T → B required =1.7∙10 -11 T → Where should such a field come from? (2) scaling: a magnetic moment always scales with Q/M, but never with Q or 1/M → problems if indeed ω~1/M

76. Hyperfine splittings: Discussion: J. Kopp, M. Lindner, A. Merle hyperfine splittings might be the first thought BUT: there are two problems… (1) order of magnitude for getting ΔE≈10 -15 eV: μ N =3.2∙10 -8 eV/T → B required =3.2∙10 -8 T μ B =5.8∙10 -5 eV/T → B required =1.7∙10 -11 T → Where should such a field come from? (2) scaling: a magnetic moment always scales with Q/M, but never with Q or 1/M → problems if indeed ω~1/M

77. Hyperfine splittings: Discussion: J. Kopp, M. Lindner, A. Merle hyperfine splittings might be the first thought BUT: there are two problems… (1) order of magnitude for getting ΔE≈10 -15 eV: μ N =3.2∙10 -8 eV/T → B required =3.2∙10 -8 T μ B =5.8∙10 -5 eV/T → B required =1.7∙10 -11 T → Where should such a field come from? (2) scaling: a magnetic moment always scales with Q/M, but never with Q or 1/M → problems if indeed ω~1/M

78. Hyperfine splittings: Discussion: J. Kopp, M. Lindner, A. Merle hyperfine splittings might be the first thought BUT: there are two problems… (1) order of magnitude for getting ΔE≈10 -15 eV: μ N =3.2∙10 -8 eV/T → B required =3.2∙10 -8 T μ B =5.8∙10 -5 eV/T → B required =1.7∙10 -11 T → Where should such a field come from? (2) scaling: a magnetic moment always scales with Q/M, but never with Q or 1/M → problems if indeed ω~1/M

79. Hyperfine splittings: Discussion: J. Kopp, M. Lindner, A. Merle hyperfine splittings might be the first thought BUT: there are two problems… (1) order of magnitude for getting ΔE≈10 -15 eV: μ N =3.2∙10 -8 eV/T → B required =3.2∙10 -8 T μ B =5.8∙10 -5 eV/T → B required =1.7∙10 -11 T → Where should such a field come from? (2) scaling: a magnetic moment always scales with Q/M, but never with Q or 1/M → problems if indeed ω~1/M

80. Hyperfine splittings: Discussion: J. Kopp, M. Lindner, A. Merle hyperfine splittings might be the first thought BUT: there are two problems… (1) order of magnitude for getting ΔE≈10 -15 eV: μ N =3.2∙10 -8 eV/T → B required =3.2∙10 -8 T μ B =5.8∙10 -5 eV/T → B required =1.7∙10 -11 T → Where should such a field come from? (2) scaling: a magnetic moment always scales with Q/M, but never with Q or 1/M → problems if indeed ω~1/M

81. Hyperfine splittings: Discussion: J. Kopp, M. Lindner, A. Merle hyperfine splittings might be the first thought BUT: there are two problems… (1) order of magnitude for getting ΔE≈10 -15 eV: μ N =3.2∙10 -8 eV/T → B required =3.2∙10 -8 T μ B =5.8∙10 -5 eV/T → B required =1.7∙10 -11 T → Where should such a field come from? (2) scaling: a magnetic moment always scales with Q/M, but never with Q or 1/M → problems if indeed ω~1/M

82. Response fields:

83. Discussion: D. Jenkins, A. Merle

84. Response fields: Discussion: D. Jenkins, A. Merle Is there a way around the scaling problem???

85. Response fields: Discussion: D. Jenkins, A. Merle Is there a way around the scaling problem??? YES!!! The field that causes the splitting might be induced by the charged ion itself!

86. Response fields: Discussion: D. Jenkins, A. Merle Is there a way around the scaling problem??? YES!!! The field that causes the splitting might be induced by the charged ion itself! The propagating ion induces field in the Schottky pickups that is proportional to Q! → Would lead to a scaling Q 2 /M≈const.∙Q BUT: Any levels that could be split by the image field will be split by stronger fields, too!

87. Response fields: Discussion: D. Jenkins, A. Merle Is there a way around the scaling problem??? YES!!! The field that causes the splitting might be induced by the charged ion itself! The propagating ion induces field in the Schottky pickups that is proportional to Q! → Would lead to a scaling Q 2 /M≈const.∙Q BUT: Any levels that could be split by the image field will be split by stronger fields, too!

88. Response fields: Discussion: D. Jenkins, A. Merle Is there a way around the scaling problem??? YES!!! The field that causes the splitting might be induced by the charged ion itself! The propagating ion induces field in the Schottky pickups that is proportional to Q! → Would lead to a scaling Q 2 /M≈const.∙Q BUT: Any levels that could be split by the image field will be split by stronger fields, too!

89. Spin precession in the magnetic field:

90. Pavlichenkov, Europhys. Lett. 85 (2009) 40008, arXiv:0810.2898 Lambiase et al., arXiv:0811.2302

91. Spin precession in the magnetic field: Pavlichenkov, Europhys. Lett. 85 (2009) 40008, arXiv:0810.2898 Lambiase et al., arXiv:0811.2302 Idea: spin precession in the gravitational field (Pavlichenkov) or magnetic field (Lambiase et al.)

92. Spin precession in the magnetic field: Pavlichenkov, Europhys. Lett. 85 (2009) 40008, arXiv:0810.2898 Lambiase et al., arXiv:0811.2302 Idea: spin precession in the gravitational field (Pavlichenkov) or magnetic field (Lambiase et al.) → periodic population of the F=3/2-level, which does NOT decay via EC → periodic modu- lation of the decay rate

93. Spin precession in the magnetic field: Pavlichenkov, Europhys. Lett. 85 (2009) 40008, arXiv:0810.2898 Lambiase et al., arXiv:0811.2302 Idea: spin precession in the gravitational field (Pavlichenkov) or magnetic field (Lambiase et al.) → periodic population of the F=3/2-level, which does NOT decay via EC → periodic modu- lation of the decay rate BUT: There seems to be a tuning problem! According to (Faestermann, arXiv:0907.1557), fine- tuning of the order of 10 -11 is required to match the numbers…

94. Z´-exchange:

95. Discussion: J. Kopp, A. Merle

96. Z´-exchange: Discussion: J. Kopp, A. Merle Idea: Could a new interaction (like a Z´-boson) have an effect that leads to oscillations?

97. Z´-exchange: Discussion: J. Kopp, A. Merle Idea: Could a new interaction (like a Z´-boson) have an effect that leads to oscillations? 2 Problems: (1) like the exchange of an ordinary Z’ in addition to photon exchange, the levels are only shifted but not split (2) if quarks couple to the Z’ (as they should) more nucleons should lead to a higher probability of exchange → ω~M

98. Z´-exchange: Discussion: J. Kopp, A. Merle Idea: Could a new interaction (like a Z´-boson) have an effect that leads to oscillations? 2 Problems: (1) like for the exchange of an ordinary Z 0 in addition to photon exchange, the levels are only shifted but not split (2) if quarks couple to the Z’ (as they should) more nucleons should lead to a higher probability of exchange → ω~M

99. Z´-exchange: Discussion: J. Kopp, A. Merle Idea: Could a new interaction (like a Z´-boson) have an effect that leads to oscillations? 2 Problems: (1) like for the exchange of an ordinary Z 0 in addition to photon exchange, the levels are only shifted but not split (2) if quarks couple to the Z´ (as they should) more nucleons should lead to a higher probability of exchange → ω~M

100. Deformed nuclei:

101. Discussion: M. Krivoruchenko, A. Merle, F. Simkovic

102. Deformed nuclei: Discussion: M. Krivoruchenko, A. Merle, F. Simkovic Idea: a deformed nucleus might be able to split certain energy levels → QB type I

103. Deformed nuclei: Discussion: M. Krivoruchenko, A. Merle, F. Simkovic Idea: a deformed nucleus might be able to split certain energy levels → QB type I Although this might work in principle, also this idea has difficulties: triaxial deformation needed (only rotational deformation only causes a shift) main effect: splitting of L x, L y, and L z orbitals, which do, however, not undergo EC

104. Deformed nuclei: Discussion: M. Krivoruchenko, A. Merle, F. Simkovic Idea: a deformed nucleus might be able to split certain energy levels → QB type I Although this might work in principle, also this idea has difficulties: triaxial deformation needed (only rotational deformation only causes a shift) main effect: splitting of L x, L y, and L z orbitals, which do, however, not undergo EC

105. Deformed nuclei: Discussion: M. Krivoruchenko, A. Merle, F. Simkovic Idea: a deformed nucleus might be able to split certain energy levels → QB type I Although this might work in principle, also this idea has difficulties: triaxial deformation needed (only rotational deformation only causes a shift) main effect: splitting of L x, L y, and L z orbitals, which do, however, not undergo EC

106. 4. Conclusions

107. the observation at GSI is still puzzling… categories of ideas: (1) do not work physically: ν-oscillations, … (2) yield wrong order: spin precession,… actually, there is one more: (3) not sufficiently discussed yet: Deformed nuclei? Response fields? Gravitational field? Something completely different???

108. 4. Conclusions the observation at GSI is still puzzling… categories of ideas: (1) do not work physically: ν-oscillations, … (2) yield wrong order: spin precession,… actually, there is one more: (3) not sufficiently discussed yet: Deformed nuclei? Response fields? Gravitational field? Something completely different???

109. 4. Conclusions the observation at GSI is still puzzling… categories of ideas: (1) do not work physically: ν-oscillations, … (2) yield wrong order: spin precession,… actually, there is one more: (3) not sufficiently discussed yet: Deformed nuclei? Response fields? Gravitational field? Something completely different???

110. 4. Conclusions the observation at GSI is still puzzling… categories of ideas: (1) do not work physically: ν-oscillations, … (2) yield wrong order: spin precession,… actually, there is one more: (3) not sufficiently discussed yet: Deformed nuclei? Response fields? Gravitational field? Something completely different???

111. 4. Conclusions the observation at GSI is still puzzling… categories of ideas: (1) do not work physically: ν-oscillations, … (2) yield wrong order: spin precession,… actually, there is one more: (3) not sufficiently discussed yet: Deformed nuclei? Response fields? Gravitational field? Something completely different???

112. 4. Conclusions the observation at GSI is still puzzling… categories of ideas: (1) do not work physically: ν-oscillations, … (2) yield wrong order: spin precession,… actually, there is one more: (3) not sufficiently discussed yet: Deformed nuclei? Response fields? Gravitational field? Something completely different???

113. So…

114. Let’s discuss!!!!

115. So… THANK YOU!!!! Let’s discuss!!!!