文部科学省科学研究費新学術領域 「コンピューティクスによる物質デザイン：複合相関と非平衡ダイナミクス」
平成23年度第１回研究会

東京大学工学部6号館セミナー室A/D
10月7日（金）－10月8日（土）ミューオン・水素がみる金属表面・サブ表面
Quantum states of the muon and hydrogen on metal surfaces and in subsurfaces

大阪大学大学院工学研究科
精密科学・応用物理学専攻

中西 寛、笠井秀明

Particles in the system

Surface, Subsurface, Bulk, Interface

Solid state physics
Condensed Matter Physics

mass・electron

9.10×10-31kg

Two kinds of particles
× 2000～200000

・nucleus(atom core)ma ×1.67×10-27 kg
ma : atomic mass

4678

Pt
195.078

Pd106.4229Cu63.536

Particles in the system

Surface, Subsurface, Bulk, Interface

electrone-(Anti)Muon μ＋
1.9×10-28 kg

9.1093897×10-31kg

X 206.7

X 8.882
P＋

protonD+H+T+

1.672210x10-27kg

X 50～200
4679Pt195.078Pd
106.4229

Cu
63.536

(Anti) muon μ＋
Particle statistics

Fermionic

Mass:

105.658369(9) MeV/c2

mμElectric charge:

eSpin:

1⁄

Mean lifetime : τ2.19703(4)×10−6 sec

Antimuon catches an electron, and forms
the hydrogen like atom.
μ+＋e−
Muonium
Its reduced mass and magnetic
moment is different from ahydrogen atom.

2Isotope of hydrogenmμ ～0.113mp～206.7me

μ＋ Antimuon -------> positron ＋ Antimuon neutrino ＋ electron neutrinoLife time:τ～2.2μsec

Muon spin spectroscopy：μSR

Spin:1⁄positron emission------->
2

The primary decay mode of a pion is a purely
leptonic decay into a muon and a muon neutrino.
And the muon is 100% spin polarized

Gyromagnetic ratio ：135.53 MHz/T

precession movement in
the magnetic moment
sensitive magnetic measurement

μSR time spectrum.
e+ detector

e+Fouriertransformation

In the material
Muon plays as the small-mass proton with acommunication function.
We can detect the quantum behaviors ofHydrogen-like particles in material.

K. Shimomura et al., Phys. Rev. Lett. 89 (2002) 255051.

Particles in the system

Surface, Subsurface, Bulk, Interface

electrone-(Anti)Muon μ＋
1.9×10-28 kg

9.1093897×10-31kg

X 206.7

X 8.882
P＋

protonD+H+T+

1.672210x10-27kg

X 50～200
4679

Pt
195.078Pd
106.42

29Cu63.536

Naniwa codes
 NANIWA is the first principles quantum mechanicalcalculation code for atomic motions near and/or in thematerials.

パラメータフリーの現実物質の第一原理量子シミュレーション

Our quantum simulation scheme: Naniwa
Interactions between nucleus is calculated
by DFT based first principle calculations

Potential energy
for nucleus motions: U n (R)Solve the Schrödinger
equation for nucleus
motionWave function for
nucleus motion

Derive thevarious
physicalquantities-Parameters are only
atomic number of elements-No fitting and no artificial procedureNaniwa-Static

Comparison between our simulationand experimental results

Calculate the Eigen states
for the atomic motions

3D-potential energy surface :V(x,y,z)Surface-normal vibrationenergy of Hydrogen atom
adsorbed on Cu(111) surface
Our simulation
result *135 meV

Experimental
data **129 meV

5% error*K. Nobuhara et al., J. Appl. Phys. 96 (2004) 5020.

for Excited stateElectron energy loss spectroscopy (EELS)**G. Lee, et al., Surf. Sci. 498 (2002) 229.

No fitting parameters !

Naniwa-Static

Comparison between our simulationand experimental results

Calculate the Eigen states
for the atomic motions

Surface-normal vibrationenergy of Hydrogen atom
adsorbed on Cu(111) surface
Our simulation
result *135 meV

Experimental
data **

129 meV

5% error*K. Nobuhara et al., J. Appl. Phys. 96 (2004) 5020.

for Excited stateElectron energy loss spectroscopy (EELS)**G. Lee, et al., Surf. Sci. 498 (2002) 229.

No fitting parameters !

Surface-normal vibration energy ofHydrogen atom adsorbed on Cu(111)
surfaceOur simulation
result *135 meV

Experimental
data **

129 meV

5% error*K. Nobuhara et al., J. Appl. Phys. 96 (2004) 5020.

for Excited state

Harmonic Potential Energy : V(Z)

Comparison between our simulation andexperimental results

normalvibrational excited Wave function

Our simulation results;

Simpleharmonic approximation

Excited state
Ground state
Distance from surface: Z

Electron energy loss spectroscopy (EELS)**G. Lee, et al., Surf. Sci. 498 (2002) 229.

No fitting parameters !

Pd surfaces
face center cubic (FCC)
lattice constant: 3.99Å (calc.) ,3.89Å (exp.)

Pd atom(111) surface(001) surface

First layer atom
2nd layer atomPd (111) surfaces
top(111) surface

Bridgehcp followfcc hollow

First layer atom
2nd layer atomμ＋, H on Pd (111) surfaces-1.8-1.9-2.0
Energy (eV)-2.1-2.2

Muon-2.3

H-2.4

D-2.5

T-2.6-2.7-2.80

102030quantum number: n40

H on Pd (111) surfaces
Ground state

1st excited state

2nd excited state 3rd excited state

4th excited state

5th excited state++Energy difference (excitation energy) is 114 meV(Experimental data: 124 meV)H. Conrad, et al, J. Vac. Sci. Technol. A5, 452 (1987).

H on Pd (111) surfaces
Ground state

1st excited state

2nd excited state 3rd excited state

4th excited state

5th excited stateμ＋ on Pd (111) surfaces
Ground state

1st excited state

2nd excited state 3rd excited state

4th excited stategap

5th excited statePd (001) surfaces(001) surface

First layer atom
2nd layer atomμ＋, H, D, T on Pd (001) surfaces-1.8-1.9-2.0
Energy (eV)-2.1-2.2

Muon-2.3

H-2.4

D-2.5

T-2.6-2.7-2.80102030
quantum number: n40μ＋ on Pd (001) surfaces
Ground state

1st excited state

2nd excited state 3rd excited state

4th excited state

5th excited stateH on Pd (001) surfaces
Ground state

1st excited state

2nd excited state 3rd excited state

4th excited state

5th excited stateD on Pd (001) surfaces
Ground state

1st excited state

2nd excited state 3rd excited state

4th excited state

5th excited stateT on Pd (001) surfaces
Ground state

1st excited state

2nd excited state 3rd excited state

4th excited state

5th excited stateElectron density distribution：  n , (r ) n, (r , R)   n; R (r )   ;n ( R) ,r  r1 , r2 , r3 ,  , ri ,  rne n , (r )    n;R (r )   ;n (R )  (r  r1 )dRdr
22   n;R (r )   ;n (R ) dR
2

From DFT based ab initio electron state calculation→ n ;R ( r ) ;R(r )occ.＊Even in the adiabatic approximation, isotope effects appear in the electron states.

2

 ;n (R )  broad, delocalizedD+⇒ H+ ⇒ μ ＋2

粒子の荷電状態 Pd（００１）<100>

Vacuum area
1st layer atom
2nd layer atom<001>

3rd layer atom

粒子の荷電状態 Pd（００１）
ミュオニウムH-0.2

H+ positivenegative<100>

Vacuum area
1st layer atom
2nd layer atom<001>

3rd layer atom

H0 neutralミューオンがみる固体表面・サブ表面
 物質環境下におけるプロトン・ミューオンの第一原理計算手法の開発： Naniwa codes
 Pd表面環境
Pd(111)、Pd(110)における μ＋、H、D、Tの量子状態
・ミューオンの同位体効果
著しい非局在化の効果により
 波動関数の結合様式に変化が見いだされる。
 縮重度、対称性にも影響が見られる。
 エネルギーの高いサブ表面内状態も低励起状態から見出されうる水素の代替粒子ではない “ミューオン量子ダイナミクス“↓・粒子の荷電状態：
水素では検出できない領域の観測