Relativistic Shifts of gμ in Muonic Atoms

Jess H. Brewer

UBC Physics & Astronomy

The discovery of an M9B tune giving substantial transverse muon spin polarization allows convenient µ– SR experiments in high transverse magnetic field. This new capability has made possible precise measurements of the magnetogyric ratios of negative muons in the ground states of muonic atoms of 12C, 16O, 24Mg, 28Si, 32S, 40Ca, natTi, natZn, natCd and natPb. The precision for 12C µ– is ± 23 ppm, of which only 6 ppm is statistical; for natZn µ– the precision is ± 269 ppm and for natPb µ– it is ± 0.23%. Such experiments may eventually provide a new testing ground for QED in very strong Coulomb fields; today they offer a new way of measuring finite nuclear size effects. I will discuss a little of the history of TRIUMF Experiment 932 and explain how these measurements emerged “accidentally” from an attempt to improve the performance of µ– SR experiments in general.

Phys. Rev. A Brief Report, in press (2005)

People:

Jess H. Brewer	UBC (Physics & Astronomy)

Khashayar Ghandi	TRIUMF  Mt. Allison U. (Chem)

Aaron M. Froese	UBC  U. Sask. (Physics)

Bruce A. Fryer	Chatelech Secondary School

Donald Arseneau	TRIUMF (CMMS)

Visit http://musr.org

[and “Fundamental” Physics]

Facility & Method used:

“Themes” in µ±SR

Muonium as light Hydrogen

(Mu = µ+e-) (H = p+e-)

Mu vs. H atom Chemistry:

- gases, liquids & solids

- Best test of reaction rate theories.

- Study “unobservable” H atom rxns.

- Discover new radical species.

Mu vs. H in Semiconductors:

- Until recently, µ +SR → only data on

metastable H states in semiconductors!

The Muon as a Probe

Quantum Diffusion: µ + in metals (compare H+); Mu in nonmetals (compare H).

Ultra-Heavy Hydrogen: neutral muonic helium (α++μ-e-) has m ≈ 4.11 mH

Muonic Atoms: HF transitions with nucleus; relativistic shifts of gµ

Probing Magnetism: unequalled sensitivity

- Local fields: electronic structure; ordering

- Dynamics: electronic, nuclear spins

Probing Superconductivity: (esp. HTcSC)

- Coexistence of SC & Magnetism

- Magnetic Penetration Depth λ

- Coherence Length ξ

μ+ only (?)

μ+ or μ –

Transverse Field (TF) µ+SR

Typical time spectrum (histogram)

Typical time spectrum (histogram)

µ+SR vs. µ-SR

Asymmetry spectrum

Single lifetime

μ = 2.197 μs

Multiple lifetimes

(some very short!)

Large amplitudes

Small amplitudes

TRIUMF Experiment # 932 :

Improving Performance

Initial proposal (Dec 2001) to M.S. EEC:

M9B at LOW priority(!)

We take only beam no one else wants.

:

It is easy to get the impression that only

positive muons are employed in .

Although most is , it is often desirable to use

negative muons in the same way, albeit with more difficulty.

It is the goal of E932 to reduce that difficulty.

Drawbacks of

Proposed Mitigations

Nuclear Muon Capture:

short lifetimes, few decay e-

LS Depolarization in

the atomic cascade

Giant Hyperfine Int. with

nonzero-spin nuclei

Look for neutron asymmetries

in heavier elements

"Tag" events with specific

muonic X-rays

Observe characteristic F

precession signals



?

??

Suzuki, 1980

µ–p n µin a nucleus:

rate comparable to that of

µ– e– µe for Z 

–

Possible Help: Many times a fast neutron is emitted from nuclear muon capture. Very few measurements have been made of the correlation of that neutron with the muon's spin direction. If cases are found where this neutron asymmetry is sizeable, we may be able to do neutron-triggered , for which the event rate can be higher than in .

PROBLEM

Nuclear µ– Capture

μ–SR Histograms from E932 (M9B, 2004)

View along µ-

momentum

Large impact parameters are more probable

 initial orbits tend to be fairly circular.

Atomic Capture & LS Depolarization of µ–

LS couplings Depolarize µ– Spin unless fast Auger!

μ+ C

μ– C

Initial Depolarization of Negative Muons in 1 kG TF

For positive “surface muons”

E×B velocity selector

("DC Separator" or Wien filter)

Removes beam positrons

Allows TF-µ+SR in high field

(otherwise B┴ deflects beam)

But not available for negative muons!

The Helios μSR spectrometer of the TRIUMF CMMS facility.

Helios

H = 2 T

The negative muon beam of M9B at TRIUMF has nearly 50% transverse spin polarization, allowing injection into a strong magnetic field parallel to the beam momentum but (partially) transverse to the spins. Strong TF allows high precision measurements of the muon Larmor frequency and thus of gµ.

The Helios μSR spectrometer of the TRIUMF CMMS facility enables TF-μSR at fields up to 2 T, using 4 e detectors in a cylindrical array around the target sample.

Helios on M9B

Deeply Bound Hydrogenic States

µ-



e-

(t ≈ 0)

Muonic orbitals are 207 times smaller than electronic.

For high Z, the muon is well inside even core electronic orbitals.

Relativistic shift of lepton's magnetogyric ratio (Breit, 1924):

for pointlike nuclei,

Theory (Ford et al.) vs. Expt. (Hutchinson et al.) in 1961

(4 years after the discovery of P violation in π-µ-e decay)

μ–SR Histograms from E932 (M9B, 2004)

μ– precession signals from E932 (M9B, 2004)

μ– precession signals from E932 (M9B, 2004)

μ– Pb

μ– Mg

μ+ C

μ– Z frequency spectra from E932 (M9B, 2004)

μ– Mg

μ– S

μ– Ca

μ– Ti

μ– Zn

μ– Pb

Only statistical uncertainties are shown, to emphasize the potential accuracy of such measurements.

In this experiment, systematic uncertainties were dominant for the light elements.

Raw Data

Fractional shifts (in %) of the negative muon's g factor due to relativistic effects in the deeply bound ground state of the muonic atom.

(In Pb, most of the muon's orbital lies inside the nucleus!)

Results

So what does it mean?

For pointlike nuclei (Breit, 1928):

Improved by Margeneau (1940) and later by Ford et al. (1962) in response to first μ-SR measurements by Hutchinson et al. (1961) in light elements. First high-Z measurements by Yamazaki et al. (1974) challenged by Mamedov et al. (2003). Meanwhile electronic spectroscopy of high Z hydrogenlike ions has become possible [e.g. Häffner et al. (2000)].

Relativistic Shift of µ - Frequency

Pb

Cd

Dramatic effect of finite nuclear size

Breit Eq.

Zn

Ti

Ca

S

Relativistic Shift of µ - Frequency

Not yet corrected for diamagnetic or paramagnetic shifts

(Z-1) in Z

Relativistic Shift of µ - Frequency

Si

Mg

O

C

Need NMR data on

B in C

N in O

Na in Mg

Al in Si

etc.

E932 vs. Ford & Hutchinson

E932 vs. Yamazaki et al. (1974)

Phil Anderson:

(at a High Tc Superconductivity conference)

“Experimentalists should not attempt to

interpret their own data.”

[paraphrased]

Darth Vader:

“Leave that to me.”

Finis
(for now)

μ ±

M

Ui

Uo

Di

Do

e U

e D

n U

n D

E932 on M9B, July 2005: 1st look at Neutrons

B

E932 on M9B, July 2005: Neutron counters in Omni'

• µ− beam

target

Uo

Ui

Do

Di

nU

nD

copper

collimator

View

from

downstream

μ+ in graphite at 53 G

μ- in silicon at 300 G

μ- in graphite at 300 G

μ- in graphite at 300 G

eU

eD

nU

nD

eU

eU

eU

eD

eD

eD

nU

nU

nU

nD

nD

nD

(RF)

M9B data 2-4 July 2005: Raw Histograms

An ≈ 0.25(3) Ae

An ≈ 0.06(4) Ae

An ≈

0.15(6)

Ae

An ≈

0.15(6)

Ae

μ+ in graphite at 53 G

μ- in silicon at 300 G

μ- in graphite at 300 G

μ- in graphite at 300 G

e+

“n”

nU

M9B data 2-4 July 2005: (U-D)/(U+D) Asymmetries

An ≈ 0.25(3) Ae

An ≈ 0.06(4) Ae

An ≈ 0.15(6) Ae

e–

n

n

e–

An ≈ 0.15(6) Ae

Negative muon spin precession measurement

of the hyperfine states of muonic sodium

Jess H. Brewer, Khashayar Ghandi,

Aaron M. Froese & Bruce A. Fryer

CIAR, UBC, TRIUMF & Chatelech Secondary School

Both hyperfine states of muonic 23Na and the rate RHF of conversion between them have been observed directly in a high field negative muon spin precession experiment using a backward muon beam with transverse spin polarization. The result in metallic sodium, R = 13.7 ± 2.2 µs-1, is consistent with Winston's prediction in 1963 based on Auger emission of core electrons, and with the measurements of Gorringe et al. in Na metal, but not with their smaller result in NaF. In NaOH we find R = 23.5 ± 8 µs-1, leaving medium-dependent effects ambiguous.

Phys. Rev. C Brief Reports 71, 058501 (2005).

Characteristic

precession frequencies

of F± hyperfine states

in selected low-Z

muonic atoms

µ- Z

µ- Z

F +

F -

ΔEHF

µ-SR in Teflon [(CF2)n]:

High frequency signal: 12C μ-

Low frequency signal:

F+ (triplet) state of 19Fμ-

F- (singlet) state

HF transition rate

RHF = 5.2(5) μs-1

fF •f+•P+(0) = 0.08(1)

23Na µ-

F + state

f+•P+(0) = 0.064(8)

RHF = 14(3) µs-1

23Na µ-

F - state

f-•P-(0) = 0.0090(15)

T2-1 = 0.024(100) µs-1

µ-SR in Melamine (C3H6N6):

High frequency signal: 12C μ-

Low frequency signal: F+ state of 14N μ-

fN •f+•P+(0) = 0.050(3)

µ-SR in

Melamine

(C3H6N6)

fN •f+•P+(0) and Λ N

both decrease with B

and Λ N is much too large

to be caused by either

RHF or neighbouring

nuclear dipoles.

ΛC is also

anomalously fast.

“Coulomb Explosion” Leftovers

µ-Z

e-

R.

µ-

Auger

γ

e-

paramagnetic

ion or radical

free

electrons

muonic atom

Depolarization!

(later)

(t ≈ 0)

ONLY in NONMETALS!

Brewer's List of µSR Acronyms

Transverse

Field

Zero Field

Longitudinal

Field

Avoided

Level

Crossing

Resonance

Muon

Spin

Echo

Muon

Spin

Resonance

Fourier

Transform

µ SR

Verbally acknowledge Khashayar Ghandi and the staff of the TRIUMF µSR User Facility; except for their help, “I did it all by myself!” [½ min]

Verbally acknowledge Khashayar Ghandi and the staff of the TRIUMF µSR User Facility; except for their help, “I did it all by myself!” [½ min]

If anyone here doesn't know what µSR is, please go to this site to find out. There you will find everything I know, including this talk. [½ min]

[2 min]

A VERY quick review of the familiar µ+SR technique. Parity violation in the weak interaction gives us 100% polarized muons and the asymmetric decay that makes their polarization easy to follow as a function of time. See Web site for details.

[1 min]

Basic differences between µ+SR and µ-SR due to nuclear capture, depolarization during atomic capture, and giant HF coupling to nuclear spin (if any). [1 min]

Paramagnetic “junk” left over from ionization in initial cascade through muonic orbitals causes later relaxation of the muonic atom's spin. ONLY in insulators (and possibly semiconductors). [1 min]

Paramagnetic “junk” left over from ionization in initial cascade through muonic orbitals causes later relaxation of the muonic atom's spin. ONLY in insulators (and possibly semiconductors). [1 min]

Verbally acknowledge Khashayar Ghandi and the staff of the TRIUMF µSR User Facility; except for their help, “I did it all by myself!” [½ min]

Note keV (!) HF splittings deexciting via electronic Auger, rates predicted by Winston in 1963.

[1 ½ min]

[½ min]

[1 ½ min]

In a metal, initial ionization “heals” quickly; thus relaxation rate is due to HF transition via electronic Auger, as predicted by Winston in 1963. [1 min]

In a metal, initial ionization “heals” quickly; thus relaxation rate is due to HF transition via electronic Auger, as predicted by Winston in 1963. [1 min]

[1 ½ min]

Relaxation rates are much too fast to be due to HF transitions by electronic Auger. Best guess: initial “Coulomb explosion” of Auger electrons generates nearby paramagnetic species whose random local fields depolarize both 14Nµ- and 12Cµ-. [2 min]

Paramagnetic “junk” left over from ionization in initial cascade through muonic orbitals causes later relaxation of the muonic atom's spin. ONLY in insulators (and possibly semiconductors). [1 min]

A reminder of the wealth of techniques available in µ+SR thanks to its intrinsic simplicity and high sensitivity. [½ min]

2005-10-25T16:28:49