1. Accurate analytic potentials for HeH +, HeD +, HeT +, including finite-mass, relativistic and 4 th order QED Staszek Welsh, Mariusz Puchalski, Grzegorz Lach, Wei-Cheng Tung, Ludwik Adamowicz, Nike Dattani 2014 年 6 月 20 日

2. Accurate analytic potentials for HeH +, HeD +, HeT +, including finite-mass, relativistic and 4 th order QED Staszek Welsh, Mariusz Puchalski, Grzegorz Lach, Wei-Cheng Tung, Ludwik Adamowicz, Nike Dattani Oxford University 2014 年 6 月 20 日

3. Accurate analytic potentials for HeH +, HeD +, HeT +, including finite-mass, relativistic and 4 th order QED Staszek Welsh, Mariusz Puchalski, Grzegorz Lach, Wei-Cheng Tung, Ludwik Adamowicz, Nike Dattani Oxford University 2014 年 6 月 20 日 Adam Mickiewicz University

4. Accurate analytic potentials for HeH +, HeD +, HeT +, including finite-mass, relativistic and 4 th order QED Staszek Welsh, Mariusz Puchalski, Grzegorz Lach, Wei-Cheng Tung, Ludwik Adamowicz, Nike Dattani Oxford University 2014 年 6 月 20 日 Adam Mickiewicz University University of Arizona

5. Accurate analytic potentials for HeH +, HeD +, HeT +, including finite-mass, relativistic and 4 th order QED Staszek Welsh, Mariusz Puchalski, Grzegorz Lach, Wei-Cheng Tung, Ludwik Adamowicz, Nike Dattani Oxford University 2014 年 6 月 20 日 Adam Mickiewicz University IIMCB University of Arizona

6. Accurate analytic potentials for HeH +, HeD +, HeT +, including finite-mass, relativistic and 4 th order QED Staszek Welsh, Mariusz Puchalski, Grzegorz Lach, Wei-Cheng Tung, Ludwik Adamowicz, Nike Dattani Oxford University 京都大学 （ Kyoto University) 2014 年 6 月 20 日 Adam Mickiewicz University IIMCB University of Arizona

7. At what number of electrons, do you think agreement between experiment and theory collapses?

8. 1e - : H Hyperfine structure 142040575768(1) mHz (present best experiment) 1420452 (theory – QED) What’s missing is the effect of the nuclear structure

9. 1e - : Mu (p + in H is replaced by μ + ) Hyperfine structure 4463302780(50) Hz (experiment) 4463302880(550) Hz (theory – QED) 2e - : He Hyperfine structure 6739701177(16) Hz (experiment) 6739699930(1700) Hz (theory, QED + nuclear structure) Agreement possible because Hz precision, not mHz

11. 2e - : H 2 1975: Kolos & Wolniewicz (numerical soln to Schroedinger Eqn) More recently: E v = 1 – E v = 0 4161.16632(18) cm -1 ( experiment ) 4161.16612(9) ( best theory )

12. 3e - : Li 2S2S 2P2P

13. Experiment: 14903.632061014 +/- 0.0000005003 cm -1 Theory: 14903.631765 +/- 0.000667 cm -1

14. Experiment: Theory:

15. 3e - : Li Energy (for lowest transition) Radiative lifetime ? V(r) = - C 3 / r 3 – C 6 / r 6 – C 8 / r 8 … Radiative lifetime : τ = ( 3ħ / 2C 3 ) ( λ / 2 π ) 3

16. Oldest experimental value ? Guess !

17. 1931 Loomis F.W. and Nusbaum R.E. Phys. Rev. 38 pg. 1447

18. University of Illinois Urbana-Champaign physics department: “Loomis Laboratory of Physics” Loomis was challenged in bringing top-notch physics talent to a university in the rural Midwest. When he approached Isaac Rabi, Rabi said "I love subways and I hate cows." Isaac Rabi While building the department, Loomis attracted John Bardeen (2 Nobel prizes) to join the staff, and had Polykarp Kusch (1 Nobel Prize) as his graduate student.John BardeenPolykarp Kusch YearNameNobel Prize 1923Du VigneaudNobel Prize in Chemistry 1929StanleyNobel Prize in Chemistry 1933KuschNobel Prize in Physics 1947KilbyNobel Prize in Physics 1957SchriefferNobel Prize in Physics 1969SharpNobel Prize in Chemistry ???? Ben McCall

19. 1931 Loomis F.W. and Nusbaum R.E. Phys. Rev. 38 pg. 1447

20. More recently: (Le Roy & Dattani) 2009: C 3 = 357829(8) “most accurate C 3 value for any molecule ever determined, by an order of magnitude” “landmark in diatomic spectral analysis” (2011 Mitroy et al.) Theory: 2009: C 3 = 357810.89(7) (finite-mass corrections) 2010: C 3 = 357773 (relativistic corrections) 2011: C 3 = 357773 (third order perturbation theory) Experiment: 2011: C 3 = 357557(78) 2013: C 3 = 357682.8(44) 2013: C 3 = 357835.2

21. 1e - : Mu : H 2e - : He : H 2 3e - : Li 2e - : HeH +  

22. Li 2 V(r) = - C 3 / r 3 – C 6 / r 6 – C 8 / r 8 … Radiative lifetime of Li (2p) : τ = ( 3ħ / 2C 3 ) ( λ / 2 π ) 3 HeH + V(r) = - C 4 / r 3 – C 6 / r 6 – C 7 / r 7 … Dipole polarizability of He : α = 2C 4

23. New definition of k B, more rigorous temperature scale Current SI units: SI units will soon change: 25 th General Conference on Weights and Measures (18-20 November 2014)

24. New definition of k B, more rigorous temperature scale pressure (held fixed) vaccuum permitivity (defined) refractive index (measured accurately) Avagadro constant (known accurately)

25. Li 2 V(r) = - C 3 / r 3 – C 6 / r 6 – C 8 / r 8 … Radiative lifetime of Li (2p) : τ = ( 3ħ / 2C 3 ) ( λ / 2 π ) 3 HeH + V(r) = - C 4 / r 3 – C 6 / r 6 – C 7 / r 7 … Dipole polarizability of He : α = 2C 4

27. Recent experiments needed +/- 0.01 cm -1 predictions  Experiment would take several years, need better than ab initio

29. Experiment successful BECAUSE, MLR’s predicted energies were much better than ab initio

31. for large r, we should have for HeH + : V(r) = D e – C 4 / r 4 – C 6 / r 6 – C 7 / r 7 – C 8 / r 8 … So u(r) = C 4 / r 4 + C 6 / r 6 + C 7 / r 7 + C 8 / r 8 …

32. V(r) = D e – C 4 / r 4 – C 6 / r 6 – C 7 / r 7 – C 8 / r 8 … C 4 : dipole polarizability C 6 : quadrupole polarizability, non-adiabatic dipole polarizability C 7 : mixed dipole-dipole-quadrupole polarizability (3 rd order) C 8 : hyperpolarizability (4 th order), octupole polarizability, & non-adiabatic quadrupole polarizability

33. for large r, we should have: V(r) = D e – C 4 / r 4 – C 6 / r 6 – C 7 / r 7 – C 8 / r 8 … C 4 : dipole polarizability non-relativistic 1.383192174455(1)13 digits ! relativistic corrections -80.35(2) QED 3 rd order modulo Bethe ln QED 3 rd order with Bethe ln QED 4 th order, finite-mass 3 rd order 30.473(1) 0.193(2) 0.49(23) total dipole polarizability 1383760.79(23)

34. for large r, we should have: V(r) = D e – C 4 / r 4 – C 6 / r 6 – C 7 / r 7 – C 8 / r 8 … C 6 : quadrupole polarizability non-relativistic2.44508310433(5)12 digits !!! relativistic corrections-1.750786(2) x 10 -4 finite-mass corrections1.8749483(3) x 10 -3 total quadrupole polarizability 2.4467829742(4)

35. 1e - : Mu : H 2e - : He : H 2 3e - : Li 2e - : HeH +   In Progress

36. 1e - : Mu : H 2e - : He : H 2 3e - : Li 5e - : BeH  

37. 5e - : BeH Most accurate empirical potential: 2006 Le Roy et al. JMS 236, 178-188  C 6, C 8, C 10 not included  couldn’t determine leading BOB term (u 0 )  D e had uncertainty of +/- 200cm -1  single-state fit (excited states not included) V(r) = - C 6 / r 3 – C 8 / r 6 – C 10 / r 8 …

39. 5e - : BeH  C 6, C 8, C 10 not included  couldn’t determine leading BOB term (u 0 )  D e had uncertainty of +/- 200cm -1  single-state fit (excited states not included)  Next step!

40. 1e - : Mu 2e - : He : H 2 3e - : Li 5e - : BeH 5e - : LiHe in progress