Antiprotonic helium spectroscopy. Toward better than 10 digit precision
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Antiprotonic helium spectroscopy. Toward better than 10 digit precision V. I. Korobov
© Springer International Publishing Switzerland 2014
Abstract The recent progress in precision spectroscopy of the antiprotonic helium is outlined. It allows to claim that an accuracy achieved in the theoretical predictions for the ro-vibrational transition frequencies has relative uncertainty at a level of 10−10 . Keywords Antiprotonic helium · Atomic mass of electron · Precision spectroscopy
1 Introduction In March of 2012 I made a presentation of the state-of-art in precision spectroscopy of He+ p¯ at the annual Meeting of the Physical Society of Japan [1]. It was devoted to the 20th Anniversary of the antiprotonic helium discovery. Here are some major points of that talk: Status of the theory [2] may be characterized as follows (Table 1): As is seen from the Table the main uncertainty comes from the yet uncalculated contribution of order R∞ α 5 and the numerical inaccuracy in the nonrelativistic Bethe logarithm, which determines the leading order radiative contribution at order R∞ α 3 . In 2010 the two-photon experiment [3] brought new high precision spectroscopic results (Table 2): Comparison of theory and experiment yields the following inferred value of the electron relative atomic mass: Ar (e) = 0.000 548 579 909 1(7)[1.4×10−9].
(1)
This result provides a really competitive value for the electron mass, but, if we want to seriously improve this quantity, we have to be aimed at the 0.1 ppb precision.
Proceedings of the 11th International Conference on Low Energy Antiproton Physics (LEAP 2013) held in Uppsala, Sweden, 10-15 June, 2013 V. I. Korobov () Joint Institute for Nuclear Research, 141980 Dubna, Russia e-mail: [email protected]
V. I. Korobov Table 1 Various contributions in terms of the fine structure constant, α, expansion to the two-photon transition: (36, 34) → (34, 32) (in MHz). Theoretical uncertainties are from yet uncalculated QED terms (first) and numerical errors (last)
Enr
=
1 522 150 208.13
Eα 2
=
−50 320.63
Eα 3
=
Eα 4
=
Eα 5
=
Etotal
=
7 069.5(0.3) 113.1 −11.3(2.1) 1 522 107 058.8(2.1)(0.3)
Table 2 Transition frequencies (in MHz) of two-photon transitions. Experimental uncertainties indicate total, statistical, and systematic errors
4 He+ p¯ 3 He+ p¯
(n, l) → (n−2, l −2)
Theory
Experiment
(36, 34) → (34, 32)
1 522 107 058.8(2.1)(0.3)
1 522 107 062 (4)(3)(2)
(33, 32) → (31, 30)
2 145 054 857.9(1.6)(0.3)
2 145 054 858 (5)(5)(2)
(35, 33) → (33, 31)
1 553 643 100.7(2.2)(0.2)
1 553 643 100 (7)(7)(3)
From the above examination we may formulate the main theoretical problems, which should be solved in order to get spectroscopic precision of 10 digit level. • •
For the nonrelativistic Bethe logarithm (mα 5 order) the accuracy is limited by at most 5 significant digits due to limits of the Feshbach closed channel formalism. Direct numerical calculations of the mα 7 order one-loop self-energy contribution is required, it brings the largest theoretical uncertainty.
In
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