Edmund G. Myers, Florida State University, Department of Physics

Penning Trap Mass Measurements at the Highest Levels of Precision

Outline

1) Motivations for very high mass precision:

For “unlimited precision”

For < 1ppb (10-9)

2) Techniques: How to measure atomic mass

to ~0.01 ppb (10-11) - (mainly the MIT/FSU way)

3) FSU results since TCP2006

Motivations for “unlimited precision”

(10-11 → 1eV/100u)

-  Anti-proton/proton to test CPT (also anti-deuteron/d…)

-  Atomic and molecular binding energies

-  Neutron binding energies for gamma-ray calibration

(also called “E=mc2” test)

Anti-proton/proton (H-) to test CPT G. Gabrielse et al, PRL (1999)

With H- polarizability: |(q/m)p-bar/(q/m)p| = 1 - 1.6(0.9) x 10-10

But Antihydrogen Spectroscopy will measure…

H(1s1/2 – 2s1/2) already at 1.4 x 10-14

Electronic Binding Energies

Highly Charged Ion: e.g. H-like U91+/U92+ to test QED

But: x-ray spectroscopy at GSI:

1s Lamb Shift = 460.2(4.6)eV ≡ σm/m = 2 x 10-11

Molecular ions: “Molecular binding energies (Heats of Formation) are half of Chemistry…”

But: for 0.01 eV at mass = 100, need σm/m = 10-13 !!

Neutron binding energies

[M(AZ)+M(n) - M(A+1Z)] c2 /NA = Δmc2 = hc/λ Penning trap Gamma Spectroscopy

MIT/NIST/ILL: 28Si → 29Si, 32S → 33S “E = mc2” to 1.4(4.4) x 10-7

Limited by gamma precision, Rainville et al, Nature 2005

35Cl → 36Cl (M. Jentschel, ILL) Needs 10-11 mass measurement!

n + AZ → A+1Z + γ

Motivations for σ(m)/m <10-9

(10-10 → 0.1 eV/1u, 10 eV/100u)

-  3T/3He for neutrino mass

-  M(atom) for α obtained from photon-recoil h/M(atom)

-  Q-values for neutrino-less double-beta-decay and electron

capture

-  Contributing to the AME: Other applications to nuclear

physics, astrophysics, molecular spectroscopy, etc.

KATRIN will measure beta-decay spectrum of tritium…

Beta-decay spectrum of 3T near endpoint

10-10 ⇒ 0.3 eV

Q = m(3H) - m(3He) = Eemax + m(ν)

E2 = P2 + M(ν)2

and must use counts with (Q-E) >> M(ν), so KATRIN also determines Q, not Q –Ee

max !

Van Dyck: 18 590.1(1.7) eV, PRL (1993) SMILETRAP: 18 589.8(1.2) eV , EuroPhys L (2006)

3T → 3He + e– + ν for Neutrino Mass

Determinations of α

Electron g-factor measurements + QED Theory

0.37 ppb

α from photon-recoil h/m(atom) α2 = (2R/c)(h/me)

h/me = (h/matom) (Matom /Me)

[electron atomic mass: Me at 0.4ppb (12C5+, 16O7+ g-factor)]

h/m(133Cs): S. Chu (Stanford), H. Mueller (Berkeley) h/m(87Rb): F. Biraben (Paris)

other h/m(atom) interferometry work in progress…

Atom recoil velocity gives h/m(atom)

Neutrinoless ββ-decay: Several large-scale 0ν2β experiments

•  76Ge – 76Se GERDA, MAJORANA •  130Te– 130Xe CUORICINO/CUORE •  136Xe– 136Ba EXO •  …… Gran Sasso underground lab

Sensitive to mββ < 0.1eV (If neutrinos are Majorana particles)

Need Q-value to identify energy of 2e- peak

Mass Measurement Techniques

Mainly discuss image current detection, mainly MIT/FSU

Reducing effects of magnetic field variation

The FSU/MIT Penning Trap

Developed by David Pritchard and collaborators at MIT ~1983 to 2003

MIT trap relocated to FSU by Myers and Redshaw May 2003

MIT

FSU, Tallahassee

Penning Trap

Penning Trap

V(ρ,z) ∝ (z2 - ρ2/2)

+

+

- -

Penning Trap

Uniform B-field Quadrupole E-field 3 Normal Modes

+ =

ωc2 = ωct

2 + ωz2 + ωm

2

Brown and Gabrielse, PRA 1982 exact in limit of small amplitudes!

Detecting Axial Motion

Superconducting self-resonant transformer (Q~30 000)

• Pulsed axial motion damps in a few sec (longer off resonance)

• Detect sinusoidal ring-down signal and measure its phase

Detecting Cyclotron Motion

Tilted-quadrupole rf electric field couples axial and cyclotron modes

Classical analog of Rabi Oscillations

Cyclotron-Axial coupling ”π-pulse”

“Transfers” cyclotron motion to axial motion phase coherently

tπ = π/ωRabi

Measuring Trap-Cyclotron Frequency

“cool” ion (10 s)

Cyc Drive Pulse (20 ms)

Phase Evolution (Tevol~ 0.1 to 60 s)

Cyc-Axial Coupling (200 ms)

Axial phase detection (8 s)

“MIT Pulse aNd Phase (PNP) Technique” Cornell et al. 1989

Precision of ~few x 10-10 in ~5-10 mins

Measuring Trap-Cyclotron Frequency

Measuring Mass Ratio: m(1)/m(2)

FSU 2004: “Make and remake”

How to minimize effect of dB/dt

0) Engineer stable B-field

1) Load, measure, reload…(quickly: TOF, HCI can help)

2) Two ions in one trap – “MIT technique”: simultaneously measure ions in a coupled magnetron orbit

3) Two ions in one trap – “Harvard technique”: swap between large and small cyclotron orbits (used extensively at FSU)

4) Double trap – alternate ions between traps (built at UW, now at MPIK)

THE Highest Precision Atomic Mass Measurements

Robert Van Dyck et al, U. Washington, proceedings of TCP2006:

16O 0.011 ppb from 16O6+/12C4+,6+ (HFI 2001)

4He 0.015 ppb from 4He2+/12C6+ (PRL 2004)

(also best 1H 0.1 ppb, 2D 0.071 ppb)

Sweep drive across ωct Make and remake – dB/dt ~10-11/hour

Double traps: MPIK 3He/3T Experiment relocated from Washington and PENTATRAP

Courtesy of Klaus Blaum, Sergey Eliseev

EBIT • up to q=81+

• 7 keV/q

UW-PTMS PENTATRAP

“Mag-Cyc Coupling and TOF Detection”

-Scan drive to find ωmc ≡ ωct + ωm ≅ ωc -Detect excitation of cyc. motion by change in TOF of ejected ion -Can use “Ramsey” (SOF) method to improve resolution

Penning traps designed for short-lived isotopes for Nuclear Physics

Measures ωct + ωm = ωc + Δωc(θ,ϕ,ε) (Gabrielse, PRL 2009)

SMILETRAP with TOF detection

3T/3He Q-value: 0.4 ppb of mass Europhys Lett. 2006

H2/D: 0.17 ppb PRA 2008

SMILETRAP II (EBIT/SUPER-EBIT, etc.) coming soon…

Both agree well with Van Dyck!

cyclotron axial magnetron

Δω/2π Scaling

2 kHz 40 Hz

2 mHz

m-1 m-1/2

m0

For m ~ 30 Δm/m ~10-3

Independent! Independent! Coupled by Coulomb interaction!

MIT: Simultaneous Cyclotron Measurement

Cornell, Boyce, Fygenson and Pritchard, PRA 1992

Consider mass dependence of mode frequencies:

Effect of ion-ion interaction for ρs ~ 1 mm Mode

MIT: Rainville, Thompson, Pritchard: 2002

-Coupled magnetron motion

-Ions follow the same path

-Simultaneous measurement of cyclotron frequency

⇒ Ions experience same B!

• Precision in the ratio of 0.07 ppb in 10 minutes

MIT Simultaneous Cyclotron Measurement

•  Final ratio to 0.007 ppb, limited by systematics

Effect of magnetic field noise reduced by Δm/m ~ 10-3

THE Highest Precision Atomic Mass Ratio Measurements

Rainville, Thompson and Pritchard, MIT:

14N2 /13CH2 0.007 ppb (Science 2004) 14N2 /12C16O 0.015 ppb (Nature 2004)

33S/32SH 0.009 ppb 29Si/28SiH 0.007 ppb (Nature 2005)

Two ions in trap: Swapping G. Gabrielse et al, PRL (1999)

Swap P-bar and H- between trap center and large cyclotron “parking orbit”

Swapping ions in the trap: Use large Cyclotron radius to park other ion

•  Move ion out using a single cyclotron pulse •  Move ion in using a series of cyclotron-axial coupling pulses

Measure cyclotron frequency of inner ion only

At FSU we:

FSU Two-ion Ratio Measurement

Statistical precision ~7 x 10-11 in 12 hours

Systematics…

Amplitude dependent shifts

Frequency pulling due to detection circuit

Image charges

Residual ion-ion interaction

“Technical imbalances”…

Suppressed for m1/m2 ≈1

Amplitude-dependent shifts

Special Relativity

Magnetic

Electrostatic

Δωz/ωz = (3C4/4d2) (az2 - 2ρc

2 - 2ρm2)… + (B2/4B0)[(ωct /ωm)ρc

2+ ρm2 )]…

Δωct/ωct = -(3C4/2d2) (ωm /ωct) (2az2 - ρc

2 - 2ρm2)… + (B2/2B0)(az

2 - ρc2- ρm

2 )…

Δωm/ωm = …

Effect of Ion-Ion Interaction Ring of Charge Model

Near trap center (r<<ρck)

Atomic mass of 28Si

Van Dyck 16O + MIT ratios → 14N, 13C (~0.015ppb)

+ FSU ratios → atomic mass of 28Si at 0.02ppb (PRL 2008)

Avogadro Project (measuring NA) Current definition of the kilogram: “The mass of the Pt-Ir prototype” (BIPM, Sèvres, France)

Atomic definition of the kilogram: (Avogadro project) “12 g is the mass of NA atoms of 12C”

d220 – lattice spacing ρ(Si) – macroscopic mass density m(28Si) – atomic mass of 28Si (Penning trap)

But d220 only at 26 ppb!… Mohr RMP (2008)

FSU Mass Table

Please see Poster by Brianna Mount!

Atom Mass (u) σm/m (ppb) Reference Why? 17O 16.999 131 756 6(9) 0.05 Mount et al, submitted Phys Rev A Molecular Spectroscopy 18O 19F

17.999 159 613 0(13) 18.998 403 162 9(11)

0.07 0.06

Redshaw et al, PRA 79, 012507 (2009) Molecular Spectroscopy Mass Reference

28Si 31P

27.976 926 535 0(6) 30.973 761 998 9(9)

0.02 0.03 Redshaw et al, PRL 100, 093002 (2008)

Avogadro Project Mass Reference

32S 31.972 071 173 5(16) 0.05 Shi et al, PRA 72, 022510 (2005) Mass Reference 84Kr 86Kr

129Xe 132Xe

83.911 497 731(8) 85.910 610 628(8)

128.904 780 859(11) 131.904 155 086(10)

0.10 0.09 0.09

0.08

Shi et al, PRA 72, 022510 (2005) Redshaw et al, PRA 79, 012506 (2009)

Mass Reference

136Xe 135.907 214 484(11) 0.08 Redshaw et al, PRL 98, 053003 (2007) Neutrinoless Double Beta Decay 130Xe 130Te

129.903 509 351(15) 129.906 222 744(16)

0.12

0.12 Redshaw et al, PRL 102, 212502 (2009) Neutrinoless Double Beta Decay

6Li 23Na

39K 41K

85Rb 87Rb 133Cs

6.015 122 887 4(31) 22.989 769 282 8(26) 38.963 706 485 6(52) 40.961 825 257 4(48)

84.911 789 738(9) 86.909 180 535(10) 132.905 451 960(13)

0.52 0.11 0.13 0.12 0.11

0.12

0.10

Mount et al, in preparation Photon Recoil, Mass Reference

74Se 74Ge 76Se

76Ge

73.922 475 938(15) 73.921 177 765(15) 75.919 213 707(19) 75.921 402 729(19)

0.20

0.20

0.25

0.25

Mount et al, Accepted by Phys Rev C Neutrinoless Double Electron Capture Neutrinoless Double Beta Decay

115Sn 115In

114.903 344 697(17) 114.903 878 774(16)

0.15

0.14 Mount et al, PRL 103, 122502 (2009) Lowest Q-Value Beta Decay

Alkali Mass 23Na, 85,87Rb, 133Cs

FSU: Mount et al, in preparation MIT: Bradley et al, PRL 1999

-10 -5 0 5

(M-M AME )/M

(pp

b)

ISOLTRAP FSU AME AME FSU 39 K 41 K

2008 2010 2003 2010 2003

Alkali Mass 6Li, 39,41K

6Li

39,41K

76Ge 0νββ Q-value Q(76Ge-76Se) = 2039.061(7) keV

c.f. GERDA/MAJORANA σ(E) ≈ 1.4 keV

[1] Ellis, et al, NPA 435, 34 (1985) [2] Hykawy, et al, PRL 67, 1708 (1991) [3] Douysset, et al, PRL 86, 4259 (2001) [4] Rahaman, et al, PLB 662, 111 (2008) [5] Mount, Redshaw, Myers, PRC-RC, in press.

⇐

⇐ FSU

FSU

FSU 0νββ Summary

The most precise Q-values for the three leading 0νββ experiments:

•  136Xe- 136Ba EXO •  130Te- 130Xe CUORE •  76Ge- 76Se GERDA/MAJORANA

And for 74Se-74Ge 0ν2EC (implying no close resonance!)

Lowest Q-value beta decay

Q[115In → 115Sn(1/2+)] = 497.489(10) keV

⇒ Q[115In → 115Sn(3/2+)] = 155(24) eV

c.f. JYFLTRAP: 350(170) eV

Mass of 17,18O for Molecular Spectroscopy

Ro-vibrational energy levels of a diatomic molecule, e.g. xCyO

Yij : Dunham parameters

Uij : Isotope-invariant parameters Δij : Born-Oppenheimer breakdown term µ = MCMO /(MC+MO)

Correlate data for all isotopic variants:

Molecular Ion Dipole Moments

motional electric field

Polarizability, αXX +

αXX(i) depends on the electric dipole moment and quantum state of the ion

HCO+ FSU 2009

µ (exp) = 1.52(3) ea0 µ(theory) = 1.530 ea0, Yamaguchi et al. JCP (1994)

Also PH+ (Redshaw, PRL 2008), and NH+ (in prep.)

Dipole Moment ⇒ Rotational Line Strengths ⇒ Relative Concentration HCO+/CO

Undergrad Students: Juliet Victoria Matt Wierman Elizabeth Wingfield Andrew Zarrella

Wei Shi (postdoc) Joseph McDaniel Matt Redshaw (now at MSU-NSCL) Brianna Mount

Funding: NSF, NIST, State of Florida

Acknowledgements