Proton radius and Rydberg constant from electronic and muonic atoms - PowerPoint PPT Presentation

Proton radius and Rydberg constant from electronic and muonic atoms Randolf Pohl Johannes Gutenberg-Universität Mainz Institut für Physik, QUANTUM und PRISMA before: Max-Planck Institute of Quantum Optics Bormio, 25. Jan. 2018

Outline ● Muonic atoms as a probe of nuclear physics ( charge radii , magnetization radii, polarizabilities, …) ● The “Proton Radius Puzzle” ● Rydberg constant key parameter to check atomic physics part of the discrepancy ● Muonic helium, later Li, Be, T?

The “Proton Radius Puzzle” Measuring R p using electrons: 0.88 fm ( +- 0.7%) using muons: 0.84 fm ( +- 0.05%) 0.84 fm 0.88 fm μ d 2 0 1 6 C O D A T A - 2 0 1 4 5.6 σ μ p 2 0 1 3 e - p s c a t t . μ p 2 0 1 0 H s p e c t r o s c o p y 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] ch μd 2016: RP et al (CREMA Coll.) Science 353, 669 (2016) μp 2013: A. Antognini, RP et al (CREMA Coll.) Science 339, 417 (2013)

A “Proton Radius Puzzle ” ?? H o r b a t s c h , H e s s e l s , P i n e d a 2 0 1 6 H i g i n b o t h a m e t a l . 2 0 1 6 G r i ffjo e n , C a r l s o n , M a d d o x 2 0 1 6 L e e , A r r i n g t o n , H i l l 2 0 1 5 H o r b a t s c h , H e s s e l s 2 0 1 5 S i c k 2 0 1 2 P e s e t , P i n e d a 2 0 1 5 H i l l , P a z 2 0 1 0 5.6 σ ?? μ d 2 0 1 6 C O D A T A - 2 0 1 4 μ p 2 0 1 3 L o r e n z e t a l . 2 0 1 2 e - p s c a t t . μ p 2 0 1 0 B e l u s h k i n e t a l . 2 0 0 7 H s p e c t r o s c o p y 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] ch

Energy levels of hydrogen ∞ E n ≈− R ∞ 2 n Bohr formula

Energy levels of hydrogen ∞ Rydberg constant E n ≈− R ∞ 2 n Bohr formula

Energy levels of hydrogen ∞ E n =− R ∞ 2 + 1.2 MHz δ l 0 + Δ( n,l, j ) 2 ⟩ n ⟨ r

Energy levels of hydrogen ∞ E n =− R ∞ 2 + 1.2 MHz δ l 0 + Δ( n,l, j ) 2 ⟩ n ⟨ r finite size effect

Energy levels of hydrogen ∞ 2S-2P Lamb shift E n =− R ∞ 2 + 1.2 MHz δ l 0 + Δ( n,l, j ) 2 ⟩ n ⟨ r finite size effect

Part 1: Muonic atoms A nucleus, orbited by one negative muon Muon mass = 200 x electron mass muonic Bohr radius = 1/200 electronic Bohr radius wave function overlap = 200 3 = 10 million times larger muon = very sensitive probe of nuclear properties

Muonic Hydrogen ΔE [meV] = 209.998 – 5.226 R p 2 2P state: μ not inside proton. State insensitive. 2S-2P Lamb shift 2S state: μ spends some time inside the proton! State is sensitive to the proton size.

The accelerator at PSI Villigen, AG

The muon beam line in πE5

The laser system Yb:YAG Disk laser → fast response on μ Frequency doubling (SHG) → green light to pump Ti:sapphire laser Ti:sapphire cw laser → determines laser frequency Ti:sapphire MOPA → high pulse energy (15 mJ) Raman cell → 3 sequential stimulated Raman Stokes shifts Laser wave length → 6 μm Target Cavity → Mirror system to fill the muon stop volume (H 2 )

The hydrogen target

Time Spectra 13 hours of data

Time Spectra 13 hours of data prompt (t=0)

Time Spectra prompt (t=0) “delayed” (t = 1 μs)

Time Spectra prompt (t=0) “delayed” (t = 1 μs) resonance curve

Muonic Hydrogen 0.84 fm 0.88 fm μ d 2 0 1 6 C O D A T A - 2 0 1 4 5.6 σ μ p 2 0 1 3 e - p s c a t t . μ p 2 0 1 0 H s p e c t r o s c o p y 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] ch muonic hydrogen: 0.8409 ± 0.0004 fm 20x more accurate electronic hydrogen: 0.876 ± 0.008 fm electron scattering 0.879 ± 0.011 fm

Muonic Deuterium 6 σ PRELIMINARY μD: 2.12562 (13) exp (77) theo fm (nucl. polarizability) μH + H/D(1S-2S): 2.12771 (22) fm CODATA-2014: 2.1 4 130 (250) fm RP et al. (CREMA Coll.), Science 353, 559 (2016)

Deuteron radius Deuteron is CONSISTENTLY smaller! R d 2 = R 2 + R p 2 + R n 2 (+ DF) struct Pohl et al. (CREMA), Science 353, 669 (2016)

Muonic Helium-4 PRELIMINARY prel. accuracy: exp +- 0.00019 fm, theo +- 0.00058 fm (nucl. polarizability) Theory: see Diepold et al. arxiv 1606.05231

Muonic Helium-3 PRELIMINARY prel. accuracy: exp +- 0.00012 fm, theo +- 0.00128 fm (nucl. polarizability) Theory: see Franke et al. EPJ D 71, 341 (2017) [1705.00352]

Muonic Helium-3 PRELIMINARY prel. accuracy: exp +- 0.00012 fm, theo +- 0.00128 fm (nucl. polarizability) Theory: see Franke et al. EPJ D 71, 341 (2017) [1705.00352]

Muonic conclusions ● The proton radius is 0.84087 (26) exp (29) theo fm ● The deuteron radius is 2.12771 (22) fm ● both are >5σ smaller than CODATA values ● No discrepancy for the absolute radii of the helion and alpha particle (limited by e-scattering accuracy) ● BUT: The helium isotope shift!!!

The 3 He – 4 He isotope shift 3 He / 4 He (squared) charge radius difference Zheng, PRL 2017 PRELIMINARY muonic He (preliminary) Cancio Pastor, PRL 2012 ** van Rooij, Science 2011 ** Shiner, PRL 1995 ** **: with recent theory 1.02 1.02 1.03 1.03 1.04 1.04 1.05 1.05 1.06 1.06 1.07 1.07 1.08 1.08 1.09 1.09 2 r 2 - r 2 [fm ] α h

The 3 He – 4 He isotope shift 3 He / 4 He (squared) charge radius difference Zheng, PRL 2017 PRELIMINARY muonic He (preliminary) Cancio Pastor, PRL 2012 ** van Rooij, Science 2011 ** superseded by Zheng? Shiner, PRL 1995 ** **: with recent theory 1.02 1.02 1.03 1.03 1.04 1.04 1.05 1.05 1.06 1.06 1.07 1.07 1.08 1.08 1.09 1.09 2 r 2 - r 2 [fm ] α h Another >5σ discrepancy?!

Part 2: The Rydberg constant 2 m e c R ∞ =α 2 h ● most accurately determined fundamental constant u r = 5.9 * 10 -12 ● corner stone of the CODATA LSA of fundamental constants links fine structure constant α, electron mass m e , velocity of light c and Planck’s constant h ● correlation coefficient with proton radius: 0.9891 → The “proton radius puzzle” could be a “Rydberg puzzle” ● R ∞ is a “unit converter”: atomic units → SI (Hertz)

Energy levels of hydrogen ∞ Rydberg constant E n =− R ∞ 2 + 1.2 MHz δ l 0 + Δ( n,l, j ) 2 ⟩ n ⟨ r proton radius

Energy levels of hydrogen ∞ measure between different n 2 unknowns → measure 2 transitions: 2S - nl 1S-2S + any other → correlated Rydberg/radius pairs Rydberg constant 1S - 2S E n =− R ∞ 2 + 1.2 MHz δ l 0 + Δ( n,l, j ) 2 ⟩ n ⟨ r proton radius

Rp from H spectroscopy 5 2 μ 2 0 D + i s o C O D A T A - 2 0 1 4 μ H H a v g . 1S → 3S 1/2 5 1 2S → 12D 5/2 2S → 12D 3/2 2S → 8D 5/2 2S → 8D 3/2 2S → 8S 1/2 0 1 2S → 6D 5/2 2S → 6S 1/2 2S → 4P 3/2 2S → 4P 1/2 2S → 4D 5/2 5 2S → 4S 1/2 2S → 2P 3/2 2S → 2P 1/2 2S → 2P 1/2 0 0.82 0.84 0.86 0.88 0.9 0.92 proton charge radius r [fm] p

Garching H(2S-4P) 1 st order Doppler cancellation 90° 88° ● cryogenic H beam (6 K) ● optical 1S-2S excitation (2S, F=0) ● 2S-4P transition is 1-photon: retroreflector ● split line to 10 -4 !!! ● 2.3 kHz vs. 9 kHz PRP ● large systematics Beyer, Maisenbacher, RP et al, Science 358, 79 (2017)

Rp from H spectroscopy 5 2 μ 2 0 D + i s o C O D A T A - 2 0 1 4 μ H H a v g . 1S → 3S 1/2 5 1 2S → 12D 5/2 2S → 12D 3/2 2S → 8D 5/2 2S → 8D 3/2 2S → 8S 1/2 0 1 2S → 6D 5/2 2S → 6S 1/2 2S → 4P 3/2 2S → 4P 1/2 2S → 4D 5/2 5 2S → 4S 1/2 2S → 2P 3/2 2S → 2P 1/2 2S → 2P 1/2 0 0.82 0.84 0.86 0.88 0.9 0.92 proton charge radius r [fm] p

Rp from H spectroscopy 5 2 2S → 4P 3/2 2S → 4P 1/2 NEW MPQ 2017 μ 0 2 D + i s o C O D A T A - 2 0 1 4 μ H H a v g . 1S → 3S 1/2 5 1 2S → 12D 5/2 2S → 12D 3/2 2S → 8D 5/2 2S → 8D 3/2 2S → 8S 1/2 0 1 2S → 6D 5/2 2S → 6S 1/2 2S → 4P 3/2 2S → 4P 1/2 2S → 4D 5/2 5 2S → 4S 1/2 2S → 2P 3/2 2S → 2P 1/2 2S → 2P 1/2 0 0.82 0.84 0.86 0.88 0.9 0.92 proton charge radius r [fm] p Beyer, Maisenbacher, RP et al, Science 358, 79 (2017)

Rp from H spectroscopy LKB 2018 1S → 3S 2 5 1/2 2S → 4P MPQ 2017 3/2 2S → 4P 1/2 2 0 μ D + i s o C O D A T A - 2 0 1 4 μ H H a v g . 1S → 3S 1/2 5 1 2S → 12D 5/2 2S → 12D 3/2 2S → 8D 5/2 2S → 8D 3/2 2S → 8S 1/2 1 0 2S → 6D 5/2 2S → 6S 1/2 2S → 4P 3/2 2S → 4P 1/2 2S → 4D 5/2 5 2S → 4S 1/2 2S → 2P 3/2 2S → 2P 1/2 2S → 2P 1/2 0 0.82 0.84 0.86 0.88 0.9 0.92 proton charge radius r [fm] p Beyer, Maisenbacher, RP et al, Science 358, 79 (2017) Fleurbaey , PhD thesis (2017)