ASACUSA Overview Ryugo S. Hayano (UTokyo) ASACUSA Spokesperson - - PowerPoint PPT Presentation

ASACUSA Overview

Ryugo S. Hayano (UTokyo)

ASACUSA Spokesperson

LEAP 2013: June 11, 2013

7-Oct-97 CERN/SPSC 97-19 CERN/SPSC P-307

ATOMIC SPECTROSCOPY AND COLLISIONS USING SLOW ANTIPROTONS

ASACUSA Collaboration

ASACUSA

Jun 11, 2013, R.S. Hayano

ASACUSA

Atomic Spectroscopy And Collisions Using Slow Antiprotons

100 keV p̅s (RFQD) 100 eV p̅s (“MUSASHI” trap)

Aghai Khozani, H.1, Barna, D.2,6, Caradonna, P.3, Corradini, M.4, Dax, A.2, Diermaier, M.3, Federmann, S.3, Friedreich, S.3, Hayano, RS.2, Higaki, H.5, Hori, M.1, Horvath, D.6, Kanai, Y.5, Knudsen, H.7, Kobayashi, T.2, Kuroda, N.5, Leali, M.4, Lodi-Rizzini, E.4, Malbrunot, C.3, Mascagna, V.4, Massiczek, O.3, Matsuda, Y.5, Michishio, K.5, Mizutani, T.5, Murakami, Y.2, Murtagh, D.5, Nagahama, H.5, Nagata, Y.5, Otsuka, M.5, Sauerzopf, C.3, Soter, A.1, Suzuki, K.3, Tajima, M.5, Todoroki, K.2, Torii, H.5, Uggerhoj, U.7, Ulmer, S.5, Van Gorp, S.5, Venturelli, L.4, Widmann, E.3, Wunscheck, B.3, Yamada, H.2, Yamazaki, Y.5, Zmeskal, J.3, Zurlo, N.4

• 1. Max-Planck-Institut f¨

ur Quantenoptik (DE), 2. The University of Tokyo (JP), 3. Stefan Meyer Institute (AT),

• 4. Universita’ di Brescia, and INFN, Gruppo Collegato di Brescia, (IT),
• 5. RIKEN, and The University of Tokyo, Komaba (JP), 6. KFKI (HU), 7. University of Aarhus (DK)

3

ASACUSA

Jun 11, 2013, R.S. Hayano

RFQD - inverse linac

Antiproton pulse from AD (5.3 MeV ~ 10% of c) Antiproton Decelerator (100 keV ~ 1% of c, ~25% efficiency, 100πmm•mrad) 2 x 1 MW 200 MHz amplifiers

4

ASACUSA

Jun 11, 2013, R.S. Hayano

Cooling and extraction

5

ASACUSA

Jun 11, 2013, R.S. Hayano

ASACUSA

Atomic Spectroscopy And Collisions Using Slow Antiprotons

p̅He & H̅ spectroscopy →CPT, fundamental const.

Aghai Khozani, H.1, Barna, D.2,6, Caradonna, P.3, Corradini, M.4, Dax, A.2, Diermaier, M.3, Federmann, S.3, Friedreich, S.3, Hayano, RS.2, Higaki, H.5, Hori, M.1, Horvath, D.6, Kanai, Y.5, Knudsen, H.7, Kobayashi, T.2, Kuroda, N.5, Leali, M.4, Lodi-Rizzini, E.4, Malbrunot, C.3, Mascagna, V.4, Massiczek, O.3, Matsuda, Y.5, Michishio, K.5, Mizutani, T.5, Murakami, Y.2, Murtagh, D.5, Nagahama, H.5, Nagata, Y.5, Otsuka, M.5, Sauerzopf, C.3, Soter, A.1, Suzuki, K.3, Tajima, M.5, Todoroki, K.2, Torii, H.5, Uggerhoj, U.7, Ulmer, S.5, Van Gorp, S.5, Venturelli, L.4, Widmann, E.3, Wunscheck, B.3, Yamada, H.2, Yamazaki, Y.5, Zmeskal, J.3, Zurlo, N.4

• 1. Max-Planck-Institut f¨

ur Quantenoptik (DE), 2. The University of Tokyo (JP), 3. Stefan Meyer Institute (AT),

• 4. Universita’ di Brescia, and INFN, Gruppo Collegato di Brescia, (IT),
• 5. RIKEN, and The University of Tokyo, Komaba (JP), 6. KFKI (HU), 7. University of Aarhus (DK)

6

ASACUSA

Jun 11, 2013, R.S. Hayano

• N. Zurlo, Tue 10:05 σ(p̅A)
• D. Barna, Tue 11:25 pHe expt.
• V. Korobov, Tue 12:00 pHe theory
• C. Malbrunot, Thu 09:35 H
• N. Kuroda, Thu 10:00 H

7

Related talks

ASACUSA

Jun 11, 2013, R.S. Hayano

Continuation

• f the
• riginal

Spectroscopy (CPT & fundamental constant) Antiprotonic helium atoms antiproton mass << 10-9 magnetic moment < 10-3

• riginal

ASACUSA programme Collision atomic collision cross section Use ultra-slow antiprotons extracted from the trap Extending ASACUSA programme Spectroscopy (CPT) Antihydrogen ground-state hyperfine splitting Sensitivity to CPTV higher than the K0 system programme approved 2005 Collision antiproton-nucleus cross section Extend the LEAR measurements to much lower energies

8

ASACUSA

Jun 11, 2013, R.S. Hayano

Continuation

• f the
• riginal

Spectroscopy (CPT & fundamental constant) Antiprotonic helium atoms & ions antiproton mass << 10-9 magnetic moment < 10-3

• riginal

ASACUSA programme Collision atomic collision cross section Use ultra-slow antiprotons extracted from the trap Extending ASACUSA programme Spectroscopy (CPT) Antihydrogen ground-state hyperfine splitting Sensitivity to CPTV higher than the K0 system programme approved 2005 Collision antiproton-nucleus cross section Extend the LEAR measurements to much lower energies

9

ASACUSA

Jun 11, 2013, R.S. Hayano

Continuation

• f the
• riginal

Spectroscopy (CPT & fundamental constant) Antiprotonic helium atoms & ions antiproton mass << 10-9 magnetic moment < 10-3

• riginal

ASACUSA programme Collision atomic collision cross section Use ultra-slow antiprotons extracted from the trap Extending ASACUSA programme Spectroscopy (CPT) Antihydrogen ground-state hyperfine splitting Sensitivity to CPTV higher than the K0 system programme approved 2005 Collision antiproton-nucleus cross section Extend the LEAR measurements to much lower energies

① ②

③ ③

10

• 1. p̅He laser spectroscopy

CPT & fundamental const.

More by Barna & Korobov

ASACUSA

Jun 11, 2013, R.S. Hayano

p _ e-

++

He

n~40 p̅He laser spectroscopy contributes to mp/me

12

ASACUSA

Jun 11, 2013, R.S. Hayano

p _ e-

++

He

laser pulse changes the p̅ orbit resonance detection via p̅ annihilation n~40 p̅He laser spectroscopy contributes to mp/me

13

ASACUSA

Jun 11, 2013, R.S. Hayano

p _ e-

++

He

laser pulse changes the p̅ orbit resonance detection via p̅ annihilation

νn,⇥⇥n,⇥ = Rcm

¯ p

me Z2

eff

1 n⇤2 − 1 n2 ⇥

p̅ (p) - e mass ratio Theory Frequency

+QED

Korobov

n~40 p̅He laser spectroscopy contributes to mp/me

14

CODATA recommended values of the fundamental physical constants: 2010*

Peter J. Mohr,† Barry N. Taylor,‡ and David B. Newell§

National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8420, USA (published 13 November 2012) This paper gives the 2010 self-consistent set of values of the basic constants and conversion factors

• f physics and chemistry recommended by the Committee on Data for Science and Technology

(CODATA) for international use. The 2010 adjustment takes into account the data considered in the 2006 adjustment as well as the data that became available from 1 January 2007, after the closing date of that adjustment, until 31 December 2010, the closing date of the new adjustment. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2010 set replaces the previously recommended 2006 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.

DOI: 10.1103/RevModPhys.84.1527 PACS numbers: 06.20.Jr, 12.20.m

CONTENTS

• I. Introduction

1528

• A. Background

1528

• B. Brief overview of CODATA 2010 adjustment

1529

• 1. Fine-structure constant

1529

• 2. Planck constant h

1529

• 3. Molar gas constant R

1530

• 4. Newtonian constant of gravitation G

1530

• 5. Rydberg constant R1 and proton radius rp

1530

• C. Outline of the paper

1530

• II. Special Quantities and Units

1530

• A. Hydrogen and deuterium transition frequencies,

the Rydberg constant R1, and the proton and deuteron charge radii rp, rd

• 1. Theory of hydrogen and deuterium

energy levels

• a. Dirac eigenvalue
• b. Relativistic recoil
• c. Nuclear polarizability
• d. Self energy
• e. Vacuum polarization
• f. Two-photon corrections

REVIEWS OF MODERN PHYSICS, VOLUME 84, OCTOBER–DECEMBER 2012

• IV. ATOMIC TRANSITION FREQUENCIES

Measurements and theory of transition frequencies in hy- drogen, deuterium, antiprotonic helium, and muonic hydro- gen provide information on the Rydberg constant, the proton and deuteron charge radii, and the relative atomic mass of the

• electron. These topics as well as hyperfine and fine-structure

splittings are considered in this section.

ASACUSA

Jun 11, 2013, R.S. Hayano PR10.11 28.07.2011 The ASACUSA experiment. More photos: 1 - 2.

CERN experiment weighs antimatter with unprecedented accuracy

Geneva, 28 July 2011. In a paper published today in the journal Nature, the Japanese-European ASACUSA experiment at CERN1 reported a new measurement of the antiproton’s mass accurate to about one part in a billion. Precision measurements of the antiproton mass provide an important way to investigate nature’s apparent preference for matter over antimatter. “This is a very satisfying result,” said Masaki Hori, a project leader in the ASACUSA collaboration. “It means that our measurement of the antiproton’s mass relative to the electron is now almost as accurate as that of the proton.” Ordinary protons constitute about half of the world around us,

• urselves included. With so many protons around it would be natural

to assume that the proton mass should be measurable to greater accuracy than that of antiprotons. After today’s result, this remains true but only just. In future experiments, ASACUSA expects to improve the accuracy of the antiproton mass measurement to far better than that for the proton. Any difference between the mass of protons and antiprotons would be a signal for new physics, indicating that the laws of nature could be different for matter and antimatter. To make these measurements antiprotons are first trapped inside helium atoms, where they can be ‘tickled’ with a laser beam. The laser frequency is then tuned until it causes the antiprotons to make a quantum jump within the atoms, and from this frequency the antiproton mass can be calculated. However, an important

• M. Hori et al., Nature 475, 484 (2011).

16

This ↓ contributed to CODATA

ASACUSA

Jun 11, 2013, R.S. Hayano

p̅He sub-Doppler 2-photon spectroscopy

Heterodyne spectrometer F r e q u e n c y c

• m

b CW seed laser Ti:S oscillator Pulsed laser ULE cavity RF quadrupole decelerator

p

Cherenkov counter

L a s e r 2 Laser 1 Virtual state Δνd (35, 33) (34, 32) (n, l) = (36, 34)

c b a

Identical laser system 0.0

Elapsed time ( μs) ν1 laser ν2 laser

2.0 2.5 3.0 –0.1 –0.2

Average PMT signal (V)

Achromatic beam transport

p

SHG/THG crystal

He2+ e–

T~15K

• M. Hori et al., Nature 475, 484 (2011).

17

ASACUSA

Jun 11, 2013, R.S. Hayano

1 2 3 1 2 3 –1 1 –1 1 Two-photon signal intensity (a.u.) Laser frequency offset (GHz)

c a d b

1 photon (36,34)→(35,33) of p̅4He+ 2 photon (36,34)→(34,32) of p̅4He+ 2 photon (33, 32)→(31, 30) of p̅4He+ 2 photon (35, 33)→(33, 31) of p̅3He+

T~15K

• M. Hori et al., Nature 475, 484 (2011).

Virtual state Δνd (35, 33) (34, 32) (n, l) = (36, 34)

a

ν1 laser ν2 laser p He2+ e–

18

ASACUSA

Jun 11, 2013, R.S. Hayano

mp (mp̅) / me

}

p̅ ASACUSA 2006} CODATA 2006

19

ASACUSA

Jun 11, 2013, R.S. Hayano

mp (mp̅) / me

}

}

CODATA 2010

20

ASACUSA

Jun 11, 2013, R.S. Hayano

mp (mp̅) / me

}

}

CODATA 2010

1836.15267245(75) 1836.1526736(23)

Nature 475, 484

21

ASACUSA

Jun 11, 2013, R.S. Hayano

↓ this was the problem in 2006

4He+

p

(40,35)⇒(39,34) (39,35)⇒(38,34) (37,35)⇒(38,34) (37,34)⇒(36,33) (36,34)⇒(35,33) (35,33)⇒(34,32) (32,31)⇒(31,30)

( ν − ν ) / ν (ppb)

th exp exp

• 50

50

3He+

p

(38,34)⇒(37,33) (36,34)⇒(37,33) (36,33)⇒(35,32) (34,32)⇒(33,31) (32,31)⇒(31,30)

( ν − ν ) / ν (ppb)

th exp exp

• 50

50

10-30 ppb differences

• M. Hori et al., Phys. Rev. Lett. 96, 243401 (2006).

22

ASACUSA

Jun 11, 2013, R.S. Hayano

• “cold” p̅He :

(1) less Doppler (2) improve S/N (3) less collisional broadening

• Improvements

(1) laser (2) p̅ beam (electrostatic quad) (3) detector (Cherenkov) (4) collisional shift corrections (5) AC stark shift corrections

Thermal baffle 6 K 1.5 K heat exchanger (coil type) Thermal baffle 77 K To 2000 m3 roots blower 0.5 Torr 3He or 4He inlet line 1.5 K needle valve 4 K needle valve To flow controller for 4.2 K cooling

cool p̅He+ to T = 1.5 K

measurements at different target densities, and with various laser powers (time consuming)

T~15K→T=1.5K

23

ASACUSA

Jun 11, 2013, R.S. Hayano

example (36,34)→(37,33) in p̅3He+ (wavelength ~ 723 nm)

First RFQD (2003)

Comb (2006)

2

Annihilation sig. (a.u.) Laser frequency (GHz)

1 2 3

• 2

1 3

• 2
• 2

414.146 414.148 2 4 6 8

Laser frequency (GHz)

Laser frequency (GHz)

2

2

T~1.5 K (NEW)

414146 414148

νth-νexp difference 10-30 ppb → <3~6 ppb

PRELIMINARY

24

ASACUSA

Jun 11, 2013, R.S. Hayano

next: 2-photon of “cold” p̅He

H e t e r

• d

y n e s p e c t r

• m

e t e r Freq uency comb CW seed laser T i : S

• s

c i l l a t

• r

P u l s e d l a s e r ULE cavity R F q u a d r u p

• l

e d e c e l e r a t

• r

p

Cherenkov counter

Laser 2 Laser 1 Virtual state Δνd (35, 33) (34, 32) (n, l) = (36, 34)

c b a

Identical laser system 0.0

Elapsed time ( μs) ν1 laser ν2 laser

2.0 2.5 3.0 –0.1 –0.2

Average PMT signal (V)

Achromatic beam transport

p

SHG/THG crystal

He2+ e–

2011 (Nature 475, 484 )

T~15K ↓ “Cold (T=1.5)” p̅He+ in 2012

25

ASACUSA

Jun 11, 2013, R.S. Hayano

“warm” vs “cold” 2-photon

1 2 3 ‒1

• 0.4
• 0.2

0.1 0.2 0.3 0.4 0.5

6 . 4 . 6 .

• 0.2

Signal intensity (arb.u.)

1

Laser frequency offset (GHz)

ASACUSA 2011 ASACUSA 2012 (“cold” p̅He) p̅4He (36,34)→(34,32) ↓ spectral resolution x 3 ↓

data taking in 2014

26

1.5 p̅He microwave spectroscopy

OPEN ACCESS IOP PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS

• J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 125003 (9pp)

doi:10.1088/0953-4075/46/12/125003

Microwave spectroscopic study of the hyperfine structure of antiprotonic 3He

S Friedreich1, D Barna2,3, F Caspers4, A Dax2, R S Hayano2, M Hori2,5, D Horv´ ath3,6, B Juh´ asz1,7, T Kobayashi2, O Massiczek1, A S´

• t´

er5, K Todoroki2, E Widmann1 and J Zmeskal1

ASACUSA

Jun 11, 2013, R.S. Hayano

hyperfine structure of p̅3He

Agreement th-exp <5x10−5 (~theory error)

Microwave Frequency [GHz] 11.154 11.156 11.158 11.160 11.162 Peak-to-total ratio 0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10 1.12 Microwave Frequency [GHz] 11.120 11.122 11.124 11.126 11.128 11.130 Peak-to-total ratio 0.95 1.00 1.05 1.10 1.15 νHF−−

νHF−+

28

ASACUSA

Jun 11, 2013, R.S. Hayano

Comparison theory-experiment 3He

Kor: Ki: E10: E10/11:

• V. Korobov, Phys. Rev. A 73 (2006) 022509.
• Y. Kino, et al., Hyperfine Interactions 146–147 (2003) 331.
• S. Friedreich et al., Physics Letters B 700 (2011) 1–6
• S. Friedreich et al., J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 125003.
• exp. error: 13 ppm 16 ppm 0.7%

theory error 50 ppm 50 ppm 50 ppm

Microwave Frequency [GHz] 11.1244 11.1248 11.1252 11.1256 11.1575 11.158 11.1585 0.0322 0.0324 0.0326 0.0328 0.033 Ki Kor

’10

E

’10/’11

E Ki Kor

’10

E

’10/’11

E Kor

’10

E

’10/’11

E

• HF
• HF
• HF
• Ki
• 29

• 2. “CUSP” experiment for

H̅ Spectroscopy

Synthesis of Cold Antihydrogen in a Cusp Trap

• Y. Enomoto,1 N. Kuroda,2 K. Michishio,3 C. H. Kim,2 H. Higaki,4 Y. Nagata,1 Y. Kanai,1 H. A. Torii,2 M. Corradini,5
• M. Leali,5 E. Lodi-Rizzini,5 V. Mascagna,5 L. Venturelli,5 N. Zurlo,5 K. Fujii,2 M. Ohtsuka,2 K. Tanaka,2 H. Imao,6
• Y. Nagashima,3 Y. Matsuda,2 B. Juha

´sz,7 A. Mohri,1 and Y. Yamazaki1,2 PRL 105, 243401 (2010) P H Y S I C A L R E V I E W L E T T E R S

week ending 10 DECEMBER 2010

H̅ production demonstrated in 2010 H̅ beam development started in 2011 H̅ production rate optimization & full setup development in 2012

More by Malbrunot & Kuroda

ASACUSA

Jun 11, 2013, R.S. Hayano

• ASACUSA

1420405751768(1)

1015 1012 109 106 103 100 10-3 TRANSITION FREQUENCY (Hz)

CPT( p) HFS

100 10-3 10-6 10-9

CPT( e)

current precision experimental errors experimental values for hydrogen theoretical uncertainty ()

31

ASACUSA

Jun 11, 2013, R.S. Hayano

Method

B (T)

0.00 0.02 0.04 0.06 0.08 0.10

(GHz)

• 2.0
• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0

(F,M)=(1,1) (F,M)=(1,0) (F,M)=(1,-1) (F,M)=(0,0)

1 1 2

H

• (anti)atomic beam
• measure σ1 at several B’s,

extrapolate to B = 0

• achievable precision ≲10–6

for T ≤ 100 K π1σ1

32

ASACUSA

Jun 11, 2013, R.S. Hayano

Method

Simulated T=5K, B=1G σ1

↓

π1

↓

• (anti)atomic beam
• measure σ1 at several B’s,

extrapolate to B = 0

• achievable precision ≲10–6

for T ≤ 100 K

33

ASACUSA

Jun 11, 2013, R.S. Hayano

2012

34

ASACUSA

Jun 11, 2013, R.S. Hayano

microwave cavity sextupole antihydrogen detector

efficiency ~10−4

Full setup (ready to be deployed in 2014)

4m

CUSP trap Cavity Sextupole CPT detector: Bmax =3.5T hodoscope + segmented scintillator array

35

ASACUSA

Jun 11, 2013, R.S. Hayano

4m

CUSP trap Cavity Sextupole CPT detector: Bmax =3.5T hodoscope + segmented scintillator array

Cavity

homogeneity : 10-2 relative precision : 10-4

• 1.4 GHz cavity surrounded by

Helmholtz coils

• 3 layers of mu-metal
• Highly sensitive flux gate sensors

monitor field inside the cavity

36

ASACUSA

Jun 11, 2013, R.S. Hayano

4m

CUSP trap Cavity Sextupole CPT detector: Bmax =3.5T hodoscope + segmented scintillator array

Sextupole

superconduting magnet Bmax=3.5T, Imax= 400A effective length: 22 cm

37

• 3. Collision experiments

ASACUSA

Jun 11, 2013, R.S. Hayano

AIA - Aarhus Ionization Apparatus

Transport Beamline MRT Extractor Superconducting Solenoid Cryohead Electrostatic lenses Foil 1.0 m MCP-PSD

RFQD

slow-extracted (~30s) 250 eV p̅ ➙ reaccelerated to ~10 keV (~7x105/AD shot) Ionization apparatus (not to scale)

Acceleration gap Electron gun Deflector plates Anti- protons Einzel lens Collision centre MCP for ion detection

Faraday cup for electrons MCP for projectile antiprotons Einzel lens

“MUSASHI” ultra slow beam

39

Knudsen et al PRL 105, 213201 (2010) Knudsen et al PRL 101, 043201 (08)

p̅ - He single ionization

Knudsen et al PRL 105, 213201 (2010) Knudsen et al PRL 101, 043201 (08)

p̅ - He single ionization

0.5 1.0 1.5 2.0 0.2 0.4 0.6 0.8 1.0 Velocity [a.u.] Cross Section [Å2]

σionization(H) σionization(H2)

Ep̅ = 2…………....11 keV

Naive expectation: σionization(H2) ~ 2 x σionization(H), but σionization(H2) < σionization(H), velocity linear behavior

p̅ - H2 single ionization

ASACUSA

Jun 11, 2013, R.S. Hayano

Nuclear collisions with antiprotons ?

ASACUSA PLB 2011

Aghai-Khozani et al.

• Eur. Phys. J. Plus

2012 42

Zurlo→

Summary

p̅He laser spectroscopy p̅He MW spectroscopy mp̅, (µp̅) CPT CODATA p̅ collisions H ground-state HFS H in cusp trap Paul trap

results development

H beamline

10-14 1920 1940 1960 1980 2000 2020 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

Relative Precision Year

laser comb

T.W. Hänsch, Nobel lecture

H 1s-2s

10-14 1920 1940 1960 1980 2000 2020 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

Relative Precision Year

p vs p̅ cyclotron freq.

10-14 1920 1940 1960 1980 2000 2020 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

Relative Precision Year

10-14 1920 1940 1960 1980 2000 2020 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

Relative Precision Year

mp/me codata

10-14 1920 1940 1960 1980 2000 2020 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

Relative Precision Year

10-14 1920 1940 1960 1980 2000 2020 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

Relative Precision Year

10-14 1920 1940 1960 1980 2000 2020 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

Relative Precision Year

mp̅/me ASCUSA

10-14 1920 1940 1960 1980 2000 2020 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3

Relative Precision Year

H̅