Post on 07-Feb-2021
12/05/2014 De Renzi - ISIS Muon Training
Introduction to µSR
Roberto De Renzi DiFeST, Department of Physics and Earth Sciences University of ParmaItaly
1896 1987 2014
Setup of the first spectrometer at ISIS, MuSR
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Introduction to µSR
• Muon history– The charged particles– Anti-matter– The neutrinos– Parity violation
• How it works– Production– Spin polarization– Transport– Implantation– Detection
• Few examples• Summary
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J.J. Thomson: the electron
1896 1955 2014
B
Electrons orbit around BThomson measures the ratio :a light (lepton) q
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E. Rutherford: the nucleus
1911 1955 2014
particles througha gold foil scatter atlarge angles
An even better cake!
Bohr atom
E Rutherford
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E. Rutherford: the proton
1918 1955 2014
particles throughN2 scatter hydrogennuclei
Let's call them protons!
E Rutherford
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P.A.M. Dirac, C. Anderson: the positron
1928 1955 2014
From relativity, quadratic energy form
Dirac predicted the electron sea
E 2=p2 c 2+m2 c 4
E =√p2 c 2+m2 c 4 E =−√p2 c 2+m2 c 4e- ?
E
e-
e-
0
B
No, it's an anti-electron
1932
PAM Dirac
CD Anderson
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Antimatter
1932 1955 2014
B
p ⇔ p̄p + p -
e ⇔ ēe - e +
proton
electron
antiproton
antielectron = positron
Dirac's E
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The name is my idea, yo!Nuclear massdidn't add up!
J. Chadwick: the neutron
1932 1955 2014
particles from Po on Boproduce unknown radiation
Po
N2
N
n
Neutral particle with mass mnc2
= 938 MeV = 1.0014 mpc
2
= 1800 mec2
heavy (baryon) J Chadwick
E Rutherford
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Pauli suggested a neutralparticle for β decays
1930 1955 2014
Beta decay at rest, if it were a 2-body decayproducts would have fixed energies
614 C → 7
14 N +e−
e−714 N
There must bean additional
neutralparticle,
the neutron!
Instead they have an energy spectrum 3-body decay!
?
W Pauli
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Pauli suggested a neutrino
1930 1955 2014
After Chadwick'sdiscovery of theneutron let's call
it neutrino
1932614 C → 7
14 N +e−+ν̄ e
There must bean additional
neutralparticle,
the neutron!
Instead they have an energy spectrum
Beta decay at rest, if it were a 2-body decayproducts would have fixed energies
614 C → 7
14 N +e−
e−714 N
W Pauli
E Fermi
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H. Yukawa: the meson
1935 1955 2014
Nuclei are made of n and p+. What force binds them with finite range?Coulomb force = exchange of photons
In analogy
e- hν p+ mν = 0
n meson p+ mc2 ~ 150 MeV
V (r )∝1r
V (q )∝ 1q2
V (r )∝1r
e− h r
√2mc V (q )∝ 1
q 2+2m2 c 2
h2
Mass justifies screening, finite range
0.5 140 980 Mev leptons mesons baryons
H Yukawa
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C. Anderson, S Neddermayer: mesotron
1936 1955 2014
Within two years a new particle with that mass (~) is found. C.D. Anderson calls it mesotron
100 < mc2 < 150 MeV
withcosmic ray balloons
τ ~ 2 μs I measured itin 1941
However its decay is a bit slow
and it has spin S=1/2
But I don't know that yet
CD AndersonBB Rossi
VF Hess
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M. Conversi: not Yukawa's meson?
1946 1955 2014
Furthermore the mesotron does not interactstrongly enough with matter.
μ ⇔ μ̄μ- μ+
Fe C
µ+ 0.67 ± 0.07 0.36 ± 0.05
µ- 0.03 ± 0.03 0.27 ± 0.03
μ- + p+ → n + νμ
M Conversi
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π
e
μ
μ
C. Powell G. Occhialini: Two particles, pion and muon
1947 1955 2014
Three tracks in a photographic emulsions at Mt Chacaltaya (5600 m).
The π is Yukawa's meson
mπ = 140 MeV/c2
τπ = 26 ns S = 0
The μ is a lepton (a heavier electron)
mμ = 106 MeV/c2
τμ = 2200 ns S = ½
C Powell
G Occhialini
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π
e
μ
μ
C. Powell G. Occhialini: Two particles, pion and muon
1947 1955 2014
Three tracks in a photographic emulsions at Mt Chacaltaya (5600 m).
The π is Yukawa's meson
mπ = 140 MeV/c2
τπ = 26 ns S = 0
The μ is a lepton (a heavier electron)
mμ = 106 MeV/c2
τμ = 2200 ns S = ½
Hey, there's somethingmissing here
W Pauli
C Powell
G Occhialini
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So what is missing?
1947 1955 2014
Hey, there's somethingmissing there
Linear momentum conservation!
πe μμ
μμ
W Pauli
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π
eμ
μ
Pion and muon, bothweak decays
1947 1955 2014
π+ → μ++ νe
μ+ → e ++ν̄μ+νe
νe
νμ
νe
Matter Antimattere - ē=e+
p - p̄=p -
n n̄π- π0=π̄0 π̄=π
+
μ- μ̄=μ+
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Recognitions
Incidentally: Nobel prize for
● 1906 J.J. Thomson Physics● 1908 E. Rutherford Chemistry● 1933 P.A.M Dirac and E. Schrödinger Physics● 1935 J. Chadwick Physics● 1936 C.D. Anderson, V.F. Hess Physics● 1938 E. Fermi Physics● 1945 W. Pauli Physics● 1949 H. Yukawa Physics● 1950 C.F. Powell Physics
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uup
ccharm
ttop
ggluon
ddown
sstrange
bbottom
photon
e μ τ WW boson
νe
νμ
ντ
Z0Z
0 boson
What we know today
1955 2014
Three families
Qua
rks
Lep
tons
Un ifi
e d f o
r ces
BaryonsMesons
p=uud n=ddu
π=u d̄ π0=u ūd d̄
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So we now have everything
We can produce pions
and they produce muons
However μSR needs another ingredient to work....
p+ + n → n + n + π+
π+ → μ+ + νμ
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Lee and Yang: parity violation
In certain interactions (e.g. magnetic) parity is broken
Weak interactions violate parity
i.e. the mirror imagedoes not exist in nature
1957 2014
CN Yang
TD Lee
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Parity violation
weak interactions violate parity
1957 2014
Madame CB Wu demonstrated that
Only right-handed anti-neutrinosand left-handed neutrinosexist in nature
TD Lee and CN Yang gotthe 1957 Nobel prize
Anisotropicdecay
CB Wu
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Parity violation
weak interactions violate parity
1957 2014
Also Garwin Lederman & Weinrich showed that
μ+ → e+ + ν̄ μ + νe
Nµ
=- 1 Ne = -1 +1 = 0
Nµ = -1
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Let's sum up
Accelerate protons to Ek > 280 MeV ~ 2mπc2, to impinge on a target
p+ n
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Pion production
Accelerate protons to > 280 MeV and impinge them on a target
n
n
π
p++n → n + n + π+
Lots of pions
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Pion decay
Pions that decay at rest on the surface of the target
π
τπ=26 ns
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Parity violation
Remember! The pion is S=0 Two body decay
π+ → μ+ + νμ
Sµ=½Sν=½
100% spin polarized muon beamsthanks to parity violation
τπ=26 ns
π
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Energy and momentum
(c = 1)
mπ=√mμ2+p2+p
p=m π
2−mμ2
2m π= 29.8 MeV/c E μ=
mμ2+mπ
2
2m π= 109.8 MeV/c2
β=vc= p
E μ= 29.8
109.8≈0.271
√mπ2+p π2=√mμ2+pμ2+√mν2+pν2 Energy pμ=−p ν=p
pp π
and momentum
conservation
I.e.
Hence
E μ ,k=√mμ2+p2−mμ= 4.12 MeV/c2And the muon kinetic energy is
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Muon beam transport
Quadrupole Dipole
Quadrupole pair
brings muonsto stop ina sample(mostly at aninterstitial site)
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Let's introduce Muonium
MuO
Mu = µ+ + e-
1s
Bound state, light isotope of H
Paramagnetic
In matter it most oftenbinds to other ions formingcovalent bonds
Diamagnetic
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Thermalization
4 MeV
Electron scattering(ionization) 10-10 s
2-3 keV
Muonium formation(e- capture/loss + collisions) 10-12 s200 eV few eV
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Muon decay
Average lifetime τμ = 2.2 μs
e+
μ+ → e+ + νe + ν̄μ
N e− tτμ
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Muon decay
Three body decay
e+
μ+ → e+ + νe + ν̄μTakes place like this:
μ+ν̄μνe
Emax ~ ½mµc2
~ 50 MeV
μ+
e+
ν̄μνe
(by parity violation this does not take place)
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Muon decay
Three body decay
e+
μ+ → e+ + νe + ν̄μ
ν̄μ
νe
Emin = 0
μ+
or like this:
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Energy distribution in the muon decay
Positron distribution
with asymmetry
and
probability of emission
P (x ,θ)=1+A (x )cosθ
E (x )= 2 x2
3−2 x
A (x )=2 x −13−2 x
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Asymmetry of the muon decay
E =E max
P (θ)∝1+cosθ
average over all energies
P (θ)∝1+ 13
cosθ
Probability of e+ emission
Sµ Sµ
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No spin dynamics
F B
Sµ
Asymmetry
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Spin dynamics: precession
m=γℏS
Magnetic moment
ℏ d Sdt
=m×B loc
ω m [−sinω t sinθcosω t sinθ0 ]=m (−γB loc )[−sinωt sinθcosω t sinθ
0 ]http://www.fis.unipr.it/~derenzi/dispense/pmwiki.php?n=NMR.SpinPrecession
Larmor
B = B ẑ
x̂
ẑŷ
θ
m(0)ẑ
x̂
Semiclassical dynamics
m (t )=m [cosωt sinθsinω t sinθcosθ ]
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Transverse field µSR
B
No spin dynamics ω=−γB loc
γ2π
=135.5 MHz/T
Spin precession at the Larmorfrequency
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e.g. in a magnetic material
B locα=∑
i
D iαβ m i
β
α ,β=x , y , z
Local field
ω=−γB locLarmor frequency
B loc
dipolar Fermi contact
+ Ac m1α
∝m magneticmoment
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MuSR nowadays
µ
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PSI GPS: another workhorse
µ
x
y
x
y
z
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Example: Antiferromagnetic YBa2Cu3O6+x
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The first magnet ever:Fe3O4
A spinel ferrimagnetwith the metal-insulator Verwey transition
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Examples
MnSi helimagnet
site determined by DFT
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Where?
J-PARC
TRIUMFISIS
PSI
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Summary
S γ m τ
½ 135.5 MHz/T 105.66 MeV 2.197 µs
γe/206.8 (*) 206.8 me
3.18 γp mp/9
* The anomalous electron g (QED corrections) is 2.0023193043615(5) cfr. the anomalous muon g 2.0023318414(1)
γ=g e2m
Muon properties
θ
Sμ
B
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Bibliography
Particle hystory survey● D. Griffith, John Wiley, New York, 1987, Ch. 1
μSR● A. Schenck, Adam Hilger, Bristol 1986
● A. Yaouanc, P. Dalmas de Reotier, Oxford Univ. Press, 2011. - 486 p
● S.J. Blundell Contemporary Physics 40, 175 (1999) http://arxiv.org/abs/cond-mat/0207699
● Some private notes athttp://www.fis.unipr.it/~derenzi/dispense/pmwiki.php?n=MuSR.MuSR
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