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

SLIDE 1

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

SLIDE 2

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?

SLIDE 3

The “Proton Radius Puzzle”

[fm]

ch

Proton charge radius R

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

C O D A T A

2

1 4 H s p e c t r

s

c

p

y e

p

s c a t t . p 2 1 μ p 2 1 3 μ d 2 1 6 μ

σ 5.6

μd 2016: RP et al (CREMA Coll.) Science 353, 669 (2016) μp 2013: A. Antognini, RP et al (CREMA Coll.) Science 339, 417 (2013)

0.84 fm 0.88 fm Measuring Rp using electrons: 0.88 fm ( +- 0.7%) using muons: 0.84 fm ( +- 0.05%)

SLIDE 4

A “Proton Radius Puzzle” ??

[fm]

ch

Proton charge radius R

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

C O D A T A

2

1 4 H s p e c t r

s

c

p

y e

p

s c a t t . B e l u s h k i n e t a l . 2 7 L

r

e n z e t a l . 2 1 2 p 2 1 μ p 2 1 3 μ d 2 1 6 μ H i l l , P a z 2 1 L e e , A r r i n g t

n

, H i l l 2 1 5 S i c k 2 1 2 P e s e t , P i n e d a 2 1 5 H

r

b a t s c h , H e s s e l s 2 1 5 G r i ffjo e n , C a r l s

n

, M a d d

x

2 1 6 H i g i n b

t

h a m e t a l . 2 1 6 H

r

b a t s c h , H e s s e l s , P i n e d a 2 1 6

?? σ 5.6

SLIDE 5

Energy levels of hydrogen

∞

En≈− R∞ n

2

Bohr formula

SLIDE 6

Energy levels of hydrogen

∞

En≈− R∞ n

2

Bohr formula

Rydberg constant

SLIDE 7

Energy levels of hydrogen

∞

En=− R∞ n

2 +1.2 MHz

⟨r

2⟩

δl0 + Δ(n,l, j)

SLIDE 8

Energy levels of hydrogen

∞

En=− R∞ n

2 +1.2 MHz

⟨r

2⟩

δl0 + Δ(n,l, j)

finite size effect

SLIDE 9

Energy levels of hydrogen

∞

En=− R∞ n

2 +1.2 MHz

⟨r

2⟩

δl0 + Δ(n,l, j)

2S-2P Lamb shift finite size effect

SLIDE 10

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 = 2003 = 10 million times larger muon = very sensitive probe of nuclear properties

SLIDE 11

Muonic Hydrogen

2S-2P Lamb shift 2S state: μ spends some time inside the proton! State is sensitive to the proton size. 2P state: μ not inside proton. State insensitive.

ΔE [meV] = 209.998 – 5.226 Rp

2

SLIDE 12

The accelerator at PSI

Villigen, AG

SLIDE 13

The muon beam line in πE5

SLIDE 14

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 (H2)

SLIDE 15

The hydrogen target

SLIDE 16

Time Spectra

13 hours of data

SLIDE 17

Time Spectra

13 hours of data prompt (t=0)

SLIDE 18

Time Spectra

prompt (t=0) “delayed” (t = 1 μs)

SLIDE 19

Time Spectra

prompt (t=0) “delayed” (t = 1 μs)

resonance curve

SLIDE 20

Muonic Hydrogen

muonic hydrogen: 0.8409 ± 0.0004 fm electronic hydrogen: 0.876 ± 0.008 fm electron scattering 0.879 ± 0.011 fm 0.84 fm 0.88 fm 20x more accurate

[fm]

ch

Proton charge radius R

0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

C O D A T A

2

1 4 H s p e c t r

s

c

p

y e

p

s c a t t . p 2 1 μ p 2 1 3 μ d 2 1 6 μ

σ 5.6

SLIDE 21

Muonic Deuterium

PRELIMINARY

μD: 2.12562 (13)exp (77)theo fm (nucl. polarizability) μH + H/D(1S-2S): 2.12771 (22) fm CODATA-2014: 2.14130 (250) fm

RP et al. (CREMA Coll.), Science 353, 559 (2016)

6 σ

SLIDE 22

Deuteron radius

Pohl et al. (CREMA), Science 353, 669 (2016)

Deuteron is CONSISTENTLY smaller!

Rd

2 = R2 struct + Rp 2 + Rn 2 (+ DF)

SLIDE 23

Muonic Helium-4

PRELIMINARY

prel. accuracy: exp +- 0.00019 fm, theo +- 0.00058 fm (nucl. polarizability)

Theory: see Diepold et al. arxiv 1606.05231

SLIDE 24

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]

SLIDE 25

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]

SLIDE 26

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!!!

SLIDE 27

The 3He – 4He isotope shift

3He / 4He (squared) charge radius difference

]

2

[fm

2 α

r

2 h

r 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 **: with recent theory

PRELIMINARY

muonic He (preliminary) Cancio Pastor, PRL 2012 ** Shiner, PRL 1995 ** van Rooij, Science 2011 ** Zheng, PRL 2017

1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09

SLIDE 28

]

2

[fm

2 α

r

2 h

r 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 **: with recent theory

PRELIMINARY

muonic He (preliminary) Cancio Pastor, PRL 2012 ** Shiner, PRL 1995 ** van Rooij, Science 2011 ** Zheng, PRL 2017

1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09

The 3He – 4He isotope shift

Another >5σ discrepancy?!

3He / 4He (squared) charge radius difference

superseded by Zheng?

SLIDE 29

Part 2: The Rydberg constant

R∞=α

2mec

2h

most accurately determined fundamental constant ur = 5.9 * 10-12
corner stone of the CODATA LSA of fundamental constants

links fine structure constant α, electron mass me, 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)

SLIDE 30

Energy levels of hydrogen

∞

En=− R∞ n

2 +1.2 MHz

⟨r

2⟩

δl0 + Δ(n,l, j)

proton radius Rydberg constant

SLIDE 31

Energy levels of hydrogen

∞

En=− R∞ n

2 +1.2 MHz

⟨r

2⟩

δl0 + Δ(n,l, j)

proton radius Rydberg constant measure between different n 2 unknowns → measure 2 transitions: 1S-2S + any other → correlated Rydberg/radius pairs 1S - 2S 2S - nl

SLIDE 32

Rp from H spectroscopy

[fm]

p

proton charge radius r

0.82 0.84 0.86 0.88 0.9 0.92

5 1 1 5 2 2 5

1/2

2P → 2S

1/2

2P → 2S

3/2

2P → 2S

1/2

4S → 2S

5/2

4D → 2S

1/2

4P → 2S

3/2

4P → 2S

1/2

6S → 2S

5/2

6D → 2S

1/2

8S → 2S

3/2

8D → 2S

5/2

8D → 2S

3/2

12D → 2S

5/2

12D → 2S

1/2

3S → 1S

H μ H a v g . C O D A T A

2

1 4

D + i s

μ

SLIDE 33

Garching H(2S-4P)

Beyer, Maisenbacher, RP et al, Science 358, 79 (2017)

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

1st order Doppler cancellation 90° 88°

SLIDE 34

Rp from H spectroscopy

[fm]

p

proton charge radius r

0.82 0.84 0.86 0.88 0.9 0.92

5 1 1 5 2 2 5

1/2

2P → 2S

1/2

2P → 2S

3/2

2P → 2S

1/2

4S → 2S

5/2

4D → 2S

1/2

4P → 2S

3/2

4P → 2S

1/2

6S → 2S

5/2

6D → 2S

1/2

8S → 2S

3/2

8D → 2S

5/2

8D → 2S

3/2

12D → 2S

5/2

12D → 2S

1/2

3S → 1S

H μ H a v g . C O D A T A

2

1 4

D + i s

μ

SLIDE 35

Rp from H spectroscopy

[fm]

p

proton charge radius r

0.82 0.84 0.86 0.88 0.9 0.92

5 1 1 5 2 2 5

1/2

2P → 2S

1/2

2P → 2S

3/2

2P → 2S

1/2

4S → 2S

5/2

4D → 2S

1/2

4P → 2S

3/2

4P → 2S

1/2

6S → 2S

5/2

6D → 2S

1/2

8S → 2S

3/2

8D → 2S

5/2

8D → 2S

3/2

12D → 2S

5/2

12D → 2S

1/2

3S → 1S

1/2

4P → 2S

3/2

4P → 2S

H μ H a v g . C O D A T A

2

1 4

D + i s

μ

NEW MPQ 2017

Beyer, Maisenbacher, RP et al, Science 358, 79 (2017)

SLIDE 36

[fm]

p

proton charge radius r

0.82 0.84 0.86 0.88 0.9 0.92

5 1 1 5 2 2 5

1/2

2P → 2S

1/2

2P → 2S

3/2

2P → 2S

1/2

4S → 2S

5/2

4D → 2S

1/2

4P → 2S

3/2

4P → 2S

1/2

6S → 2S

5/2

6D → 2S

1/2

8S → 2S

3/2

8D → 2S

5/2

8D → 2S

3/2

12D → 2S

5/2

12D → 2S

1/2

3S → 1S

1/2

4P → 2S

3/2

4P → 2S

1/2

3S → 1S

H μ H a v g . C O D A T A

2

1 4

D + i s

μ

Rp from H spectroscopy

MPQ 2017

Beyer, Maisenbacher, RP et al, Science 358, 79 (2017) Fleurbaey , PhD thesis (2017)

LKB 2018

SLIDE 37

[fm]

p

proton charge radius r

0.82 0.84 0.86 0.88 0.9 0.92

5 1 1 5 2 2 5

1/2

2P → 2S

1/2

2P → 2S

3/2

2P → 2S

1/2

4S → 2S

5/2

4D → 2S

1/2

4P → 2S

3/2

4P → 2S

1/2

6S → 2S

5/2

6D → 2S

1/2

8S → 2S

3/2

8D → 2S

5/2

8D → 2S

3/2

12D → 2S

5/2

12D → 2S

1/2

3S → 1S

1/2

4P → 2S

3/2

4P → 2S

1/2

3S → 1S

H μ H a v g . C O D A T A

2

1 4

D + i s

μ

Rp from H spectroscopy

MPQ 2017 LKB 2018

Proton Radius Puzzle is NOT “solved” !! We have a “Rydberg problem” now → need more data!

Beyer, Maisenbacher, RP et al, Science 358, 79 (2017) Fleurbaey , PhD thesis (2017), paper submitted

SLIDE 38

Conclusions

smaller radii from muonic hydrogen and deuterium imply a smaller Rydberg constant
new H(2S-4P) gives small Rydberg constant in agreement with muonic values
new H(2S-4P) gives thus a smaller proton radius, too
new H(1S-3S) however confirms large proton radius
H(2S – 6P, 8P, 9P, …) and D(2S-nl) underway in Garching and Colorado
H(1S – 3S, 4S, ..) underway in Paris and Garching
H(2S-2P) in Toronto (Hessels)
Muonium
Positronium (Cassidy, Crivelli)
He+(1S-2S) underway in Garching (Udem) and Amsterdam (Eikema)
HD+, H2, etc.
new low-Q2 electron scattering at MAMI, JLab, MESA
muon scattering: MUSE @ PSI, COMPASS @ CERN

More data needed:

SLIDE 39

Up next: Hyperfine structure in μp

The 21 cm line in hydrogen (1S hyperfine splitting) has been measured to 12 digits (0.001 Hz) in 1971:

νexp = 1 420 405. 751 766 7 ± 0.000 001 kHz

Essen et al., Nature 229, 110 (1971)

QED test is limited to 6 digits (800 Hz) because of proton structure effects:

νtheo = 1 420 403. 1 ± 0.6proton size ± 0.4polarizability kHz

Eides et al., Springer Tracts 222, 217 (2007)

SLIDE 40

Proton Zemach radius

HFS depends on “Zemach” radius: Form factors and momentum space

Δ E=8(Z α)m πn

3

EF∫

∞ dk

k

2 [

GE(−k

2)G M(−k 2)

1+κ

]

Δ E=−2(Z α)m⟨r⟩(2)EF ⟨r⟩(2)=∫d

3r d 3r 'ρE(r)ρM(r')|r−r'|

Zemach, Phys. Rev. 104, 1771 (1956)

SLIDE 41

Proton Zemach radius from μp

SLIDE 42

Proton Zemach radius from μp

12

12

0.8751 (61) 2.1413 (25) 1.9730 (160) 1.6810 ( 40) 2.0680 (110) 1.7550 (860) 1.9290 (260) 2.5890 (390) 2.4440 (420) 2.3390 (440) 2.2450 (460) 2.4820 (430) 2.6460 (150) 2.5190 (120) 2.3600 (140) 2.4650 (150) 2.5020 (150) 0.8409 ( 4) 2.1277 ( 2) 1.6783 ( 5) 1.9686 ( 13) 2.0695 ( 80) * * * * * = preliminary 1.9307 (246)

μBe in Be+ ion trap target: 5x better μLi in Li vapour (heatpipe target): 10x better T(1S-2S) using trapped T atoms: 400x better

SLIDE 47

Thanks a lot for your attention

The Garching Hydrogen Team: Axel Beyer, Lothar Maisenbacher, Arthur Matveev, RP, Ksenia Khabarova, Alexey Grinin, Tobias Lamour, Dylan C. Yost, Theodor W. Hänsch, Nikolai Kolachevsky, Thomas Udem The CREMA Collaboration: Aldo Antognini, Fernando D. Amaro, François Biraben, João M. R. Cardoso, Daniel S. Covita, Andreas Dax, Satish Dhawan, Marc Diepold, Luis M. P. Fernandes, Adolf Giesen, Andrea L. Gouvea, Thomas Graf, Theodor W. Hänsch, Paul Indelicato, Lucile Julien, Paul Knowles,Franz Kottmann, Eric- Olivier Le Bigot, Yi-Wei Liu, José A. M. Lopes, Livia Ludhova, Cristina M. B. Monteiro, Françoise Mulhauser, Tobias Nebel, François Nez, Paul Rabinowitz, Joaquim M. F. dos Santos, Lukas A. Schaller, Karsten Schuhmann, Catherine Schwob, David Taqqu, João F. C. A. Veloso, RP My new Mainz group: Jan Haack, Julian J. Krauth, Stefan Schmidt, Marcel Willig, Rishi Horn

SLIDE 48

...

SLIDE 49

Correlation between R∞ and Rp / Rd

ν(1S−2S)≈ 3 4 R∞ − 7 8 ENS

The source of the 98.91% correlation of R∞ and Rp

10-15 = 10 Hz 10-12 = 20 kHz

SLIDE 50

Garching H(2S-4P)

Beyer, Maisenbacher, RP et al, Science 358, 79 (2017)

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

1st order Doppler cancellation 90° 88°

SLIDE 51

1st order Doppler shift

90° 88°

SLIDE 52

Quantum interference shifts

see Horbatsch, Hessels, PRA 82, 052519 (2010); PRA 84, 032508 (2011); PRA 86 040501 (2012) Sansonetti et al., PRL 107, 021001 (2011) Brown et al., PRA 87, 032504 (2013)

P(ω)∝| ( ⃗ d1 ⃗ E0) ⃗ d1 ω1−ωL+i γ1/2+ ( ⃗ d2 ⃗ E0) ⃗ d2e

i ΔΦ

ω2−ωL+i γ2/2|

2

= Lorentzian(1) + Lorentzian(2) + cross-term (QI)

SLIDE 53

Quantum interference shifts

P(ω)∝| ( ⃗ d1 ⃗ E0) ⃗ d1 ω1−ωL+i γ1/2+ ( ⃗ d2 ⃗ E0) ⃗ d2e

i ΔΦ

ω2−ωL+i γ2/2|

2

= Lorentzian(1) + Lorentzian(2) + cross-term (QI)

see Horbatsch, Hessels, PRA 82, 052519 (2010); PRA 84, 032508 (2011); PRA 86 040501 (2012) Sansonetti et al., PRL 107, 021001 (2011) Brown et al., PRA 87, 032504 (2013)

Fitting this with 2 Lorentzians creates

line shifts

SLIDE 54

Studying QI in 2S-4P

SLIDE 55

QI in hydrogen (Δ = 100 Γ)

Beyer, Maisenbacher, RP et al, Science 358, 79 (2017)

SLIDE 56

Systematics

SLIDE 57

CODATA “sub-adjustments”

Adj. 3: “The Adjustment” (all data) Rp = 0.8775(51) fm, Rd = 2.1424( 21) fm
Adj. 8: H spectroscopy only Rp = 0.8764(89) fm
Adj. 10: D spectroscopy only Rd = 2.1210(250) fm

SLIDE 58

Spectroscopy data in CODATA

H(1S-2S) D(1S-2S) – H(1S-2S) (iso shift)

SLIDE 59

Spectroscopy data: H

SLIDE 60

Rp from H spectroscopy

SLIDE 61

Rp from H spectroscopy

SLIDE 62

Spectroscopy data: D

Summary

Rp = 0.8775( 51) fm CODATA-2010

0.8747( 91) fm H(1S-2S) + 2S-nl (*) uncorrel. 0.8780(108) fm H(1S-3S) + 2S-nl 0.8764( 89) fm CODATA Adj. 8 0.8409( 4) fm muH 4.0 sigma

Rd = 2.1424( 21) fm CODATA-2010

2.1415( 45) fm Deuterium only (*) uncorrel. 2.1XXX( 8) fm muD → next talk

SLIDE 69

Rp and R∞ from H spectroscopy

2 unknowns: R∞ and Rp (ENS) → measure 2 transitions (1S-2S and 2S-nl) Bohr Finite size Dirac, fine struct., QED, ..

RP et al., Metrologia 54, L1 (2017) [1607.03165]

Sum of all terms from CODATA report (3 independent calculations, cross-checked with P. Mohr's code)

vs. 1S-2S accuracy 10 Hz (0.01 kHz)

Parthey, RP et al., PRL 107, 203001 (2011)

SLIDE 70

Combine transition frequencies

RP et al., Metrologia 54, L1 (2017) [1607.03165]