med en atom i vågskålen eller Hur man väger atomer och ... - Fysikum
med en atom i vågskålen eller Hur man väger atomer och ... - Fysikum
med en atom i vågskålen eller Hur man väger atomer och ... - Fysikum
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Precisionsmassbestämning -<br />
<strong>med</strong> <strong>en</strong> <strong>atom</strong> i vågskål<strong>en</strong><br />
<strong>eller</strong><br />
<strong>Hur</strong> <strong>man</strong> <strong>väger</strong> <strong>atom</strong>er <strong>och</strong> varför?<br />
Från vikt<strong>en</strong> av ett kilogram till massan av <strong>en</strong> neutrino<br />
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Reinhold Schuch, FYSIKUM, Stockholm Universitet
En historia om(av) vikt<br />
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<strong>och</strong>(om) massa
För mätning av massa användar<br />
<strong>man</strong> (ofta o<strong>med</strong>vetet)<br />
materi<strong>en</strong>s tunga massa<br />
(gravitation) <strong>och</strong> bestämmer<br />
mängd, dvs d<strong>en</strong> tröga massan<br />
gravitationskraft = trög massa x acceleration<br />
Newtons andra lag: G Q E Q i /R 2 E = m i g<br />
EP: Q i /m i = g (R 2 /Q E G) =konstant,<br />
obero<strong>en</strong>de av i<br />
Ekvival<strong>en</strong>s-Princip<strong>en</strong>: Ekvival<strong>en</strong>s mellan<br />
tung <strong>och</strong> trög massa<br />
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m 2<br />
m 1<br />
?
En historia om vikt <strong>och</strong> massa<br />
1 kg ⇔ 1Ltr vatt<strong>en</strong> vid 3,98grad...<br />
Ur-Kilogram" i Labor des "Bureau International<br />
des Poids et Mesures" i Sèvres vid Paris<br />
Kilogram <strong>en</strong>da dim. i SI måttsystem som inte<br />
har någon <strong>atom</strong>istisk definition.<br />
James Clerk Maxwell var först <strong>med</strong> förslag....<br />
Eg<strong>en</strong>tlig<strong>en</strong> finns def.: <strong>en</strong> Mol 12C har massan<br />
12 g.<br />
M<strong>en</strong> fortfarande inte användbar. Dock om <strong>man</strong><br />
kunde räkna antal (N A=6,022.. · 10 23 ) C<strong>atom</strong>er<br />
noggrant...<br />
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Vad <strong>väger</strong> ett kilo?<br />
Idag Framtid<strong>en</strong>?<br />
Kilogram prototype<br />
Bureau International des Poids et Mesures<br />
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Boll gjord av <strong>en</strong> <strong>en</strong>da silikonkristall<br />
Krav: δm/m ≤ 1 10 -8
Atomär definition av ett kilo<br />
“Recept“<br />
Tillverka <strong>en</strong> <strong>en</strong> perfekt perfekt Si Si kristall kristall<br />
Gör Gör <strong>en</strong> <strong>en</strong> boll boll av av d<strong>en</strong> d<strong>en</strong><br />
Mät Mät diametern<br />
Bestäm gitterparametern<br />
Mät Mätr<strong>en</strong>het<strong>en</strong> r<strong>en</strong>het<strong>en</strong><br />
Beräkna antalet antalet Si Si <strong>atom</strong>er <strong>atom</strong>er<br />
The Avogadro Project:<br />
“The kilogram is the mass of N 28 Si-<strong>atom</strong>s.”<br />
§ 1nm<br />
Mät masskvot<strong>en</strong> 28 Si/ 12 C<br />
Allt måste göras <strong>med</strong> <strong>en</strong> osäkerhet av 10 -9 <strong>eller</strong> bättre!<br />
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Bestämma lattice parametern:<br />
Röntg<strong>en</strong>diffraktion <strong>med</strong> Si kristall<br />
Braggvillkor<br />
Int<strong>en</strong>sitetsmax. för !<br />
n " = 2dsin!<br />
•Braggvillkoret kopplar d <strong>och</strong> " <strong>med</strong><br />
Braggvinkeln !.<br />
•Röntg<strong>en</strong> – Laser-interferometer kopplar<br />
" <strong>med</strong> meter<strong>en</strong>het<strong>en</strong>: Δ = 6057.80211Å<br />
gul 86Kr linje.<br />
Mätosäkerhet 12 Attometer (10 -18 m)<br />
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!<br />
A<br />
E<br />
B<br />
C<br />
d<br />
(R. Deslattes)
Atomär definition av ett kilo<br />
“Recept“<br />
Tillverka <strong>en</strong> <strong>en</strong> perfekt perfekt Si Si kristall kristall<br />
Gör Gör <strong>en</strong> <strong>en</strong> boll boll av av d<strong>en</strong> d<strong>en</strong><br />
Mät Mät diametern<br />
Bestäm gitterparametern<br />
Mät Mätr<strong>en</strong>het<strong>en</strong> r<strong>en</strong>het<strong>en</strong><br />
The Avogadro Project:<br />
“The kilogram is the mass of N 28 Si-<strong>atom</strong>s.”<br />
§ 1nm<br />
Beräkna antalet Si <strong>atom</strong>er<br />
Mät masskvot<strong>en</strong> 28Si/ 12 Beräkna antalet Si <strong>atom</strong>er<br />
Mät masskvot<strong>en</strong> C<br />
28Si/ 12 Mäta masskvot<strong>en</strong> C<br />
28Si/ 12C GJORT VID SMILETRAP i Stockholm<br />
Dock, Kg framställt så här var inte tillräkligt noggrant !<br />
Mät isotopsam<strong>man</strong>sättning<strong>en</strong> !!<br />
28Si, 29Si, 30Si <strong>och</strong> deras massa<br />
Allt måste göras <strong>med</strong> <strong>en</strong> osäkerhet av 10 -9 <strong>eller</strong> bättre!<br />
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<strong>Hur</strong> kan <strong>man</strong> ’väga’ <strong>en</strong> <strong>atom</strong> (jon)?<br />
Traditionell<br />
massbestämning<br />
Gravitationskraft<br />
F = m ⋅<br />
g<br />
q/m<br />
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I <strong>en</strong> P<strong>en</strong>ningfälla<br />
Magnetisk kraft<br />
F = q(<br />
v × B)<br />
1 q<br />
Cyclotronfrekv<strong>en</strong>s: fc = ⋅ ⋅ B<br />
2π<br />
m<br />
jon<br />
B<br />
q/m<br />
q/m<br />
mät f c i <strong>en</strong> P<strong>en</strong>ningfälla !
1cm<br />
Exitation of an ion in a P<strong>en</strong>ning trap<br />
+<br />
B r<br />
ν - ≈ 800 Hz, ν + ≈ 36 MHz, ν z ≈ 240 kHz<br />
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-<br />
-<br />
+<br />
+<br />
-<br />
∼<br />
ν<br />
c<br />
ν<br />
+ ν<br />
= + −<br />
=<br />
1<br />
2π<br />
qeB<br />
m
SMILETRAP<br />
Cyclotron Frequ<strong>en</strong>cy Detection<br />
F = −µ<br />
⋅∇B<br />
radial ⇒ axial <strong>en</strong>ergy<br />
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B<br />
Number of ions<br />
100<br />
80<br />
60<br />
40<br />
20<br />
0<br />
νºν c<br />
ν>ν c<br />
0 25 50 75 100 125 150 175<br />
Time-of-flight [us]<br />
M<br />
A<br />
ν<br />
R=ν<br />
c =<br />
cREF<br />
qmREF<br />
q m<br />
REF<br />
1 q<br />
q+<br />
mREF+<br />
qm −EB(<br />
A )<br />
e<br />
RqREF<br />
mc2 =EB = −
Precisionsmassbestämning<br />
SMILETRAP<br />
A q+ kg<br />
• Vi använder högt laddade joner:<br />
Stockholm Mainz Ion LEvitation TRAP<br />
m ν c 1 q<br />
precision<strong>en</strong>: = = ⋅ ⋅ B växer lineärt <strong>med</strong> ladning<strong>en</strong>!<br />
Δm<br />
Δν<br />
2πΔν<br />
m<br />
• Vi behöver kalibrera B fältet, <strong>med</strong> refer<strong>en</strong>smassan 12 C<br />
• Använder C 6+ för att kalibrera Si 14+<br />
c<br />
ν<br />
R=ν<br />
c =<br />
cREF<br />
⇒ nästan samma q/M dvs. nästan samma frekv<strong>en</strong>s!!<br />
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c<br />
qmREF<br />
q m<br />
REF<br />
M<br />
A<br />
1 q<br />
q+<br />
mREF+<br />
qm −EB(<br />
A )<br />
e<br />
Rq<br />
= −<br />
REF
Ion Pulse Int<strong>en</strong>sity [pC]<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
0<br />
Charge-and Isotope-selected Highly Charged Ions :<br />
198Hg 2s 4He only<br />
9.5 9.7 9.9 10.1 10.3<br />
Magnet Curr<strong>en</strong>t [A]<br />
CRYSIS<br />
Production of highly charged ions<br />
by electron bombardm<strong>en</strong>t<br />
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CHORDIS<br />
Production of singly charged<br />
isotope separated ions
Ion transport to SMILETRAP and evaporative cooling<br />
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precision trap<br />
evaporative cooling<br />
-5V<br />
Finally: 0 or 1 or 2 cold<br />
ions in precision trap !
~4m<br />
SMILETRAP<br />
Stockholm-Mainz-Ion LEvitation-TRAP<br />
10 cm<br />
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Fällan 10 -12 mbar<br />
Elektronik-rack<br />
Supraledande<br />
magnet inuti <strong>en</strong> tank<br />
<strong>med</strong> flytande helium<br />
Jontransportsystem<br />
vid ultrahögt vakuum<br />
−9<br />
−7<br />
( 10 mbar = 10 Pa)<br />
Datoriserat<br />
kontrollsystem
esonanskurva<br />
ν-ν c<br />
n c #3.510 7 Hz<br />
⇒ uplösning<strong>en</strong> är 0,4 Hz/ 3.5 10<br />
precision<strong>en</strong> vi kan få <strong>med</strong> SMILETRAP:<br />
7 Hz # 10-8 m<br />
Δm<br />
Fourier limit?<br />
ν c<br />
Δν<br />
Tänkvärt: Att mäta <strong>med</strong> <strong>en</strong> noggrannhet på 10 -9 motsvarar tex:<br />
Att räkna befolkning<strong>en</strong> i Kina på <strong>en</strong> person när.<br />
Att mäta avståndet mellan Stockholm <strong>och</strong> Kiruna på 1 mm när.<br />
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=<br />
Δν<br />
c<br />
c<br />
1.<br />
0<br />
[ Hz]<br />
≈<br />
T [ s]<br />
=<br />
10 10<br />
exc
Systematical uncertainties<br />
•Uncertainty of the refer<strong>en</strong>ce mass<br />
12 C q+ or H2 + as mass refer<strong>en</strong>ces! 0 or 0.14 ppb<br />
•Field errors, geometrical imperfections and magnetic field fluctuations<br />
large trap dim<strong>en</strong>sions, strong magnetic field, small<br />
motion amplitudes,a large number of ions,<br />
T and p stabilization. 0.1~ppb<br />
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Cyclotron Frequ<strong>en</strong>cy Fluctuations<br />
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T stabilization system<br />
Fan<br />
Heater<br />
PID<br />
Regulator<br />
TRAP<br />
Control PC<br />
drift ΔT « 0.01 °C / 24 h<br />
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add. B-field<br />
correction
Systematical uncertainties<br />
•Uncertainty of the refer<strong>en</strong>ce mass<br />
12 C q+ or H2 + as mass refer<strong>en</strong>ces! 0 or 0.14 ppb<br />
•Field errors, geometrical imperfections and magnetic field fluctuations<br />
large trap dim<strong>en</strong>sions, strong magnetic field, small<br />
motion amplitudes,a large number of ions,<br />
T and p stabilization. 0.1~ppb<br />
•q/A dep<strong>en</strong>d<strong>en</strong>ce and number dep<strong>en</strong>d<strong>en</strong>ce<br />
take mass doublets and only one ion in the trap<br />
0 to 1 ppb,
Från jonmassa till <strong>atom</strong>massa:<br />
Noggranna massbestämningar av<br />
<strong>atom</strong>er ger information om bland annat<br />
<strong>atom</strong>ära <strong>och</strong> nukleära<br />
bindnings<strong>en</strong>ergier.<br />
ν<br />
R=ν<br />
= N ·<br />
c =<br />
cREF<br />
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mc 2<br />
+ Z · + Z ·<br />
– binding <strong>en</strong>ergy<br />
qmREF<br />
q m<br />
REF<br />
M<br />
A<br />
Einstein 1905:<br />
E = mc 2<br />
E<br />
1 q<br />
q+<br />
mREF+<br />
qm −EB(<br />
A )<br />
e<br />
Rq<br />
= −<br />
REF
The Importance of Atomic Masses<br />
Physics &<br />
Chemistry<br />
basic information<br />
required<br />
δm/m ≈ 1·10 -5<br />
Nuclear<br />
Physics<br />
mass formula,<br />
models, halo<br />
δm/m ≈ 1·10 -7<br />
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G<strong>en</strong>eral<br />
Physics<br />
fundam. constants<br />
test of CPT<br />
δm/m ≤ 1·10 -10<br />
= N ·<br />
Astro-<br />
physics<br />
+ Z · + Z ·<br />
– binding <strong>en</strong>ergy<br />
nuclear synthesis,<br />
r-, rp-process δm/m < 1·10 -7<br />
Atomic<br />
Physics<br />
binding <strong>en</strong>ergy,<br />
QED in HCI<br />
δm/m ≤ 1·10 -9<br />
Weak<br />
Interactions<br />
symmetry tests,<br />
CVC hypothsis<br />
δm/m < 3·10 -8
SMILETRAP<br />
Krav på Noggranhet<br />
G<strong>en</strong>eral physics and chemistry 10 -6<br />
Nuclear physics<br />
• Decay <strong>en</strong>ergies<br />
• Binding <strong>en</strong>ergies<br />
Nuclear structure, models and formulas<br />
• Shell closure, pairing, deformation, halos<br />
• Nucleosynthesis, IMME<br />
Fundam<strong>en</strong>tal studies with radionuclides<br />
• Symmetry tests<br />
• Weak interaction studies (CVC hypothesis)<br />
Fundam<strong>en</strong>tal studies with stable nuclides<br />
• Binding <strong>en</strong>ergies, QED in HCI<br />
• Fundam<strong>en</strong>tal constants, test of CPT<br />
Field Mass uncert. δm/m<br />
10 -7<br />
10 -7 - 10 -8<br />
10 -8 - 10 -9<br />
10 -9 - 10 -11<br />
(ppm)<br />
(ppb)<br />
SMILETRAP - Si-massa för ny Kilogram definition,<br />
Exempel: - 3 H - 3 He massa för neutrinomassa från b sönderfall,<br />
- Cs massa för ny finstruktur-konstant,<br />
- Ca massa för elektron<strong>en</strong>s g-faktor<br />
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Tritiums beta sönderfall Q-värde<br />
3<br />
1<br />
H → He +<br />
3<br />
2<br />
Q=18,589 8(12) keV<br />
Skillnad<strong>en</strong> i massa mellan<br />
3 H 1+ - 3 He 1+<br />
−<br />
e<br />
+ ν<br />
Bestämd
3 He mass result-2005<br />
3 3 He 3,016,029,321 (26) u 0.8 ppb total<br />
H 3,016,049,278 (24) u 0.8 ppb total<br />
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Planck<br />
Einstein<br />
Heis<strong>en</strong>berg<br />
Finstrukturkonstant<strong>en</strong><br />
In classical electrodynamics interaction<br />
betwe<strong>en</strong> point charges Q 1 r Q 2<br />
described by F(r) = - gradV(r), V(r) =Q 1 Q 2 /4per<br />
(analog for charge moving in magnetic field)<br />
Maxwell<br />
quantization of fields "<br />
Charged particles " field quanta are photons<br />
electromagnetic interaction = exchange of virtual photons hn<br />
Q 1 hn Q 2<br />
hn has <strong>en</strong>ergy and mom<strong>en</strong>tum within conditions giv<strong>en</strong> by<br />
uncertainty relation ΔE Δ t = h, Δ p Δ x=h (virtual photons)<br />
One photon exchange dominant in Coulomb force ⇒<br />
(for mγ = 0) Δ p = E/c = h/c Δ t ; Δ t = r/c ⇒<br />
F(r) = Δ p/ Δ t ∼ h/c Δ t 2 = hc/ r 2<br />
by comparison with V(r) ⇒ proportionality constant<br />
Q 1 Q 2 /4pehc = n 1 n 2 e2/4pehc = ! fine structure constant ª<br />
1/137 (constant of el.magn. interaction, time dep<strong>en</strong>d<strong>en</strong>t?)<br />
consequ<strong>en</strong>t ⇒ Quantum Electro-Dynamics (QED).<br />
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Differ<strong>en</strong>t determinations of the Fine Structure Constant a<br />
α -1<br />
137.036010<br />
137.036005<br />
137.036000<br />
137.035995<br />
137.035990<br />
137.035985<br />
Γ 90<br />
Δν Mu<br />
Hans G.<br />
Dehmelt<br />
Nobelprize<br />
1989<br />
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g-2<br />
R k<br />
h/m n<br />
CODATA98<br />
h/m Cs
α -1<br />
133 Cs for Accurate Determinations of the Fine Structure Constant α<br />
α<br />
2<br />
137.036010<br />
137.036005<br />
137.036000<br />
137.035995<br />
137.035990<br />
137.035985<br />
=<br />
⎛<br />
⎜<br />
⎝<br />
2R<br />
c<br />
∞<br />
⎞⎛<br />
⎟⎜<br />
⎠⎝<br />
h<br />
m<br />
e<br />
⎞<br />
⎟<br />
⎠<br />
=<br />
< 2⋅10 -11<br />
(Hänsch<br />
Nobelp 05)<br />
Γ 90<br />
Δν Mu<br />
⎛<br />
⎜<br />
⎝<br />
2R<br />
c<br />
∞<br />
g-2<br />
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⎞⎛<br />
⎟⎜<br />
⎠⎝<br />
h<br />
m<br />
Cs<br />
R k<br />
⎞⎛<br />
⎜<br />
m<br />
⎟<br />
⎜<br />
⎠⎝<br />
m<br />
7.3 ppb<br />
(S.Chu<br />
Nobelp 98)<br />
Cs<br />
p<br />
h/m n<br />
⎞⎛<br />
m<br />
⎟<br />
⎜<br />
⎠⎝<br />
m<br />
p<br />
e<br />
CODATA98<br />
⎞<br />
⎟<br />
⎠<br />
h/m Cs<br />
In near future h/m(Cs)*<br />
3 ppb new setup 1 ppb<br />
*S. Chu, private communication (2003)<br />
2.2 ppb (vanDyck)<br />
SMILETRAP<br />
2 ppb<br />
Measured deviation [ppb]<br />
133 Cs<br />
Charge state<br />
PRL 83, 1999
QED (QuantumElectroDynamics)<br />
r<br />
µ<br />
=<br />
−<br />
g<br />
e<br />
2m<br />
e<br />
r<br />
J<br />
Enligt Diracs relativistiska kvantmekanik är g = 2<br />
för <strong>en</strong> fri elektron.<br />
QED-beräkningar ger i stället g = 2.0023...<br />
Används för definition av Finstrukturkonstant<strong>en</strong> a<br />
Tittar på bund<strong>en</strong> electron:<br />
G<strong>en</strong>om att experim<strong>en</strong>tellt bestämma g <strong>med</strong> stor<br />
noggrannhet kan QED testas.<br />
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µ= magnetiskt mom<strong>en</strong>t<br />
e, m e elektron<strong>en</strong>s laddning <strong>och</strong> massa<br />
J =rotationsmom<strong>en</strong>t<br />
g =g-faktorn
contribution to g-factor<br />
Test av QED: Bundna elektron<strong>en</strong>s g-faktor<br />
10 -1 - Dirac<br />
10 -2<br />
10 -3<br />
10 -4<br />
10 -5<br />
10 -6<br />
10 -7<br />
10 -8<br />
(Breit 1928)<br />
now<br />
gbound /gfree ≈ 1 – 1/3(Zα) 2 + α/4p(Zα) 2<br />
gbound /gfree ≈ 1 – 1/3(Zα)2 + α/4p(Zα) 2<br />
Yerokhin, Shabaev et al., 2002<br />
all orders in Zα<br />
Grotch et al.<br />
1970<br />
0 10 20 30 40 50 60 70 80 90<br />
nuclear charge Z<br />
relativistic effect<br />
(Dirac)<br />
future<br />
bound-state<br />
QED<br />
Precise g-Factor measurem<strong>en</strong>ts<br />
@ HITRAP(GSI) & SMILETRAP<br />
Larmor<br />
precesion<br />
Cyclotron<br />
motion<br />
h" L = g Jµ<br />
BB<br />
"<br />
c =<br />
g =<br />
J<br />
q<br />
2 # M<br />
2!<br />
!<br />
L<br />
ion<br />
c<br />
ion<br />
qm<br />
Framtid<strong>en</strong>: need mass of Ca 19+ $ U 91+ with
Nytt lab på AlbaNova<br />
Extremt högt laddade joner<br />
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Joner<br />
Elektron stråle<br />
40keV (250keV)<br />
Electron Beam Ion Trap<br />
SuperEBIT, Uranium 92+<br />
ion<br />
trap<br />
3T Magnet
Curr<strong>en</strong>t Masses knowledge measured of at <strong>atom</strong>ic SMILETRAP masses<br />
Protons<br />
28 Si<br />
20,22 24,26<br />
14 Ne Mg<br />
N<br />
16<br />
3,4 12 O<br />
He C<br />
1,2,3 H<br />
~200 isotopes
Previous SMILETRAP highlights<br />
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n
New masses of <strong>atom</strong>s and where it matters...<br />
• Si masses for Atomically Defined Kilogram Mass Standard<br />
• β-decay Q-value from 3 H - 3 He mass differ<strong>en</strong>ce ⇒ ν mass<br />
• Mass M N for bound-electron g factor determination in hydrog<strong>en</strong>-<br />
like ions ⇒ m e or theory test<br />
• 76 Ge- 76 Se for constraints on neutrino-less double beta decay<br />
• M(p)/M( 133 Cs), for new Fine Structure Constant $<br />
• Heavy M N to solve the ” 198-204 Hg problem in Audi & Wapstras<br />
mass table<br />
• Weighing <strong>atom</strong>ic binding <strong>en</strong>ergies ⇒ Ionization pot<strong>en</strong>tials of ions<br />
• Mass to <strong>en</strong>ergy conversion ⇒ Relativity Test E=mc 2<br />
…… … a relative mass accuracy of δm/m = 10 -11 is the goal!<br />
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