Atomic Physics with Stored and Cooled Ions

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1 Lecture #7 Atomic Physics with Stored and Cooled Ions Klaus Blaum Gesellschaft für Schwerionenforschung, GSI, Darmstadt and CERN, Physics Department, Geneva, Switzerland Summer School, Lanzhou, China, 9 17 August Lecture: The importance of atomic masses and Penning trap mass spectrometry 1. The importance of atomic masses 2. Methods and evaluation 3. Penning trap mass spectrometers 4. Some recent highlights

2 Energy Mass equivalence Mass and Energy Einstein 1905: = N + Z + Z binding energy High-precision mass measurements convey information on nuclear and atomic binding energies

3 The Importance of Atomic Masses Physics & Chemistry basic information required General Physics fundam. constants test of CPT δm/m Atomic Physics binding energy, QED in HCI δm/m δm/m Nuclear Physics mass formula, models, halo δm/m Weighing Astro- physics atomic masses nuclear synthesis, r-, rp-process δm/m < Weak Interactions symmetry tests, CVC hypothsis δm/m <

4 The Importance of Atomic Masses e + /e -, e + /p, p - /p +, : fundamental mass ratios, CPT tests 28 Si for Atomically Defined Kilogram Mass Standard 133 Cs, 85,87 Rb and 23 Na for Accurate Determinations of the Fine Structure Constant α and Molar Planck Constant N a h 76 Ge for constraints on neutrino-less double beta decay Seattle Harvard-CERN MIT / Boston SMILETRAP / Stockholm 34 Ar, 62 Ga, 74 Rb and other superallowed β emitters for CVC tests in the weak interaction ISOLTRAP / ISOLDE, CERN Geneva a relative mass accuracy of δm/m = is required

5 Methods of mass determination Early techniques magnetic & electric sector fields Q-values from β +, β - and α decay Q- values from nuclear reactions Limitations stable isotopes mass difference, complex level schemes stable isotopes as target Novel techniques in the eighties time-of flight mass spectrometry in the nineties Limitations resolving power, accuracy FREQUENCY MEASUREMENTS Penning traps Half life > 65 ms in the seventies on-line Mattauch- Herzog mass spectrometer resolving power storage rings Smith RF spectrometer Half life > 50 ms (TOF) Half life > 65 ms

6 The net of mass values Q-values of β -decays direct mass measurements Q-values of reactions Q-values of α-decays absolute mass measurements: relative to 12 C G. Audi et al., Nucl. Phys. A 729, 3 (2003)

7 Mass spectrometry techniques at FRS/ESR Measurement of * revolution frequency (~ 2MHz) or * revolution time (~ 500ns) Schottky spectrometry: cooling v 0 T ½ > 1s isochronous spectrom.: transition energy γ=γ t df/de = 0 T ½ > 10 µs

8 Time-resolved Schottky Mass Spectrometry (SMS)

9 Schottky spectroscopy - achievements Cs Dy m,g 65+ Eu Tb Sm 143m,g 62+ Pr Gd I Nd Dy Tb Gd Tm Pt Er Ta Ho Dy Tb Ta Re Yb Lu Er Ho Hf Tm Lu Os Yb Er Hf W W Tm Lu Hf Re Hf Ta W Intensity / arb. units 2 1 mass known mass unknown m kev Sm (1 particle) 143 g 62+ Sm Intensity / arb. units m/ m ~ (1 particle) Frequency / Hz Frequency / Hz resolving power m/ m 10 6 ; precision kev sensitivity: 1 ion (Z > 40) T ½ : 1s... years 280 new masses

10 Observation of dynamic effects decays of single ions Noise power density / arb. u. Time after injection / s Ho height of 1 particle nuclear - e capture Dy Noise power density / arb. u Frequency / khz

11 Isochronous mass spectra - achievements Revolution time / ns particles Zn Cu Br Rb 25 Na Al Ne Mg Cl As P Si 57 Fe Kr Ni 53 53m Ar Se S Ca Br Se Co Mn Cr V Ti Sc Ca K 41 Ge Ge Sc Ga Zn 65 Cu As Ga V 46 Ti 62 Zn Cu Cr Mn 58 Ni 54 Fe 56 Co resolving power m/ m: 3 x 10 5 ; precision: kev; sensitivity: 1 ion T ½ > 10 µs

12 Bound state β decay of highly charged ions first observation in ESR (Dy, Re, Tl) p process Er Ho Dy s process r process enhancing stellar β decay rates altering β chronometers modifying s-process branching points

13 Penning traps for mass measurements Type of reaction ISOL- TRAP CPT JYFL- SHIP- TRAP TRAP LEBIT MAFF- TRAP TITAN SMILE- TRAP HITRAP ISOL x x fusion x x IGISOL x fragmentation x x neutronfission x highlycharged x x x stable x x There is a high degree of complementarity!

14 Principle of mass measurements in Penning traps Confinement of ions in a strong magnetic field of known strength B Mass measurement via determination of cyclotron frequency ν c = (q/m) (B/2π) from characteristic motion of stored ions ION SOURCE: stable isotopes radioactive isotopes highly charged ions antiprotons Example: B = 6 T, A = 100 ν c = 1 MHz T obs = 1 s ν c = 1 Hz R = 10 6

TOF Resonance Mass Spectrometry Time-of-flight resonance technique MCP Detector Scan of excitation frequency Dipolar radial excitation at f - increase of r - Quadrupolar radial excitation

15 TOF Resonance Mass Spectrometry Time-of-flight resonance technique MCP Detector Scan of excitation frequency Dipolar radial excitation at f - increase of r - Quadrupolar radial excitation near f c coupling of radial motions, conv. Ejection along the magnetic field lines radial energy converted to axial energy Time-of-flight (TOF) measurement 1.2 m Resolving power: R = f T exc exc

16 TOF Cyclotron Resonance Curve (Stable Nuclide) Mean time of flight / µs TOF as a function of the excitation frequency 85 Rb Centroid: f c = 1 2π T 1/2 = q m B Measurement Theoretical Fit Excitation frequency f rf / Hz Determine Determine atomic atomic mass mass from from frequency frequency ratio ratio with with a well-known well-known reference reference mass mass

17 TOF Cyclotron Resonance Curve (Radionuclide) 390 TOF as a function of the excitation frequency Mean time of flight / µs Centroid: f c = 1 2π q m B 63 Ga T 1/2 = 32.4 s Excitation frequency ν RF / Hz f rf Determine Determine atomic atomic mass mass from from frequency frequency ratio ratio with with a well-known well-known reference reference mass mass

18 y Magnetron Phase Locking Mechanism K. Blaum et al., JP B 36, 921 (2003) U d φ x E d +U d U d E d U d +U d +Ud + + φ = φ m,rf φ - φ m,rf = π, φ - = -π/2 φ = 3π/2 φ m,rf = 0, φ - = -π/2 φ = π/2 TOF [µs] free φ ν c [Hz] TOF [µs] φ= 3π/ ν c [Hz] TOF [µs] φ= π/ ν c [Hz] The (δν/ν) stat is reduced by almost a factor of two!

19 Non-Destructive Single Ion FT-ICR Detection z magnetic field Penning Trap (cross section) Voltage/Current Amplifier low noise Amp. FFT Fourier-Transformspectral analyser excited ion I ion current signal dp/df FFT mass spectrum slit radially split electrode time-domain time frequency-domain frequency Applications Mass measurements on superheavy rare elements Ultra high-precision mass measurements on stable ions

Triple-Trap Mass Spectrometer ISOLTRAP Mean TOF (µs) 220 32 Ar 200 180 160 140 120 100 10 cm 10 cm 80-40 -30-20 -10 0 10 20 30 ν RF 2842679 (Hz) precision Penning trap B = 5.9 T 1.

20 Triple-Trap Mass Spectrometer ISOLTRAP Mean TOF (µs) Ar cm 10 cm ν RF (Hz) precision Penning trap B = 5.9 T 1.2 m MCP 5 MCP 3 precision Penning trap determination of cyclotron frequency (R = 10 7 ) preparation Penning trap stable alkali ion reference source stable alkali ion reference source cooling Penning trap B = 4.7 T MCP 1 removal of contaminant ions (R = 10 5 ) ISOLDE beam (DC) 60 kev RFQ structure 2.8-keV ion bunches F. Herfurth, et al., NIM A 469, 264 (2001) K. Blaum et al., NIM B 204, 478 (2003) HV platform ion beam cooler and buncher carbon cluster ion source C 60 pellet laser beam Nd:YAG 532 nm cluster ion source K. Blaum et al., EPJ A 15, 245 (2002)

21 ISOLTRAP Setup 1 m

22 ISOLTRAP Highlights and Status In 2002/ masses measured ( / ) rel. accuracy δm/m mean improvement: factor 40 K. Blaum et al., Nucl. Phys. A, in print (2004) Bi Bi Ra Ra Cs Cs Kr Kr Rb Rb Highlights 2002 / 2003 Nuclide Half-life Uncertainty Yield Ar Ar Cu Cu 18 Ne 32 Ar 1.67 s 98 ms 360 ev 1.8 kev ~3E6/ s ~100/s Ne Ne Ar Ar 72 Kr 74 Rb 17.2 s 65 ms 8.0 kev 4.5 kev ~1000/s ~500/s K. Blaum et al., Phys. Rev. Lett. 91, (2003) J. Van Rooesbroeck et al., Phys. Rev. Lett. 92, (2004) K. Blaum et al., Europhys. Lett., submitted (2004)

23 Superallowed β Decay and the Standard Model Conserved-vector-current hypothesis: Vector part of weak interaction not influenced by strong interaction Intensity of β decays (ft value) only a function of the vector coupling constant and the matrix element: ft = G 2 V K M V 2 K Product of fund. constants G V Vector coupling constant M V - Nuclear matrix element Corrections: to the statistical rate function f δ C isospin symmetry breaking correction (Coulomb force, strong force) to the nuclear matrix element M V : δ R radiative correction (bremsstrahlung etc.)

24 Experimental Access to Ft Value Q T 1/2 b P EC δ R δ C Ft = Ft ( Q 5,T, b, P, δ 1/ 2 EC R Decay energy mass m Half-life Branching ratio Electron capture fraction Radiative correction Isospin symmetry breaking correction, δ C ) Weak Interaction symmetry tests, CVC hypothesis δm/m < Unitarity of the CKM matrix d' s' b' Vud Vus Vub d 2 2 G V = Vcd Vcs Vcb s V ud = 2 b G A Vtd Vts Vtb Mean Ft value of all decay pairs contributes to V ud via G V Can check unitarity via sum of squares of elements of the first row

25 Previous Status Ft Value Existing data for 9 light nuclides from 10 C to 54 Co 46 V 42 Sc 38m K 26m Al 34 Cl 50 Mn 54 Co Ft value: Ft = (1.4) s 10 C 14 O Ft (s) C 14 O 26m Al 34 Cl 38m K 42 Sc 46 V 50 Mn 54 Co CVC hypothesis confirmed in this mass region Measurements in heavier nuclides required to substantiate results u (Ft ) (s) Q t Proposed decay: 74 Rb(β + ) 74 Kr 0 10 C 14 O 26m Al 34 Cl 38m K 42 Sc 46 V 50 Mn 54 Co mother nuclide

26 Results FT Value 74 Kr: T 1/2 = 11.5 min δm = 2.1 kev (previously 720 kev) 74 Rb: T 1/2 = 65 ms δm = 4.0 kev Ft value from ISOLTRAP data: Ft (s) u (Ft ) = 15 s 74 Rb Uncertainty budget: rel. unc. contribution Q % T 1/ % R % P EC % δ R % δ C % Z of daughter nuclide Ft ( 74 Rb) in 1.3-σ disagreement with data from lighter nuclides Uncertainty too large for clear statement on CVC

27 Status CKM Matrix Check unitarity via elements of the first row: V ud V us and V ub from particle physics data (K and B meson decays) From nuclear β decay (world average 2003): V ud obtained from avg. Ft and G A from muon decay From neutron decay: 2 + V us 2 + V = 1 + V ud obtained from neutron β decay asymmetry A and lifetime τ ub 2 = (14) [I.S. Towner & J.C. Hardy, J. Phys. G 29 (2003) 197] = (27) (RPP world average 2002) = (28) [H. Abele et al., PRL 88 (2002) ]

28 Solution to the Non-Unitarity Problem Present status: V ud (nuclear β-decay) = (5) V us (kaon-decay) = (26) V ub (B meson decay) = (5) Contribution to the unitarity: V ub V us % 0.05% New measurement of V us from K e3+ decay V us = (23)(07)(18) = (16 ) [A. Sher et al., PRL 91 (2003) ] V ud 99.95% but : in disagreement with previous K e3+ decay data in disagreement with K e30 decay data [RPP 2002: V us = (26)]

Solving the Identification Puzzle in 70 Cu Isomerism in 70 Cu: Hyperfine structure of 70 Cu isomers (using laser ionization): I π E / kev T 1/2 / s (6-) 242.4(3) 6.

29 Solving the Identification Puzzle in 70 Cu Isomerism in 70 Cu: Hyperfine structure of 70 Cu isomers (using laser ionization): I π E / kev T 1/2 / s (6-) 242.4(3) 6.6(2) Intensity ratio: IT 5% β 95% 16% 80% 4% (3-) 101.1(3) 33(2) IT 50% β 50% (1+) (2) normalized to the area Mass excess Lit: (15) kev β =100% J. Van Roosbroeck et al., Phys. Rev. Lett. 92, (2004).

30 Identification of Triple Isomerism in 70 Cu Intensity ratio: 16% 80% 4% Mean TOF / µs (6 ) state = gs q ω c = m B normalized to the area Unambiguous state assignment! ME of ground state is 240 kev higher than literature value! Preparation of isomerically pure beams. R , δm/m For the first time: Nuclear spectroscopy by mass spectrometry! Mean TOF / µs Mean TOF / µs (3 ) state = 1.is 242(3) kev ν c / Hz 101(3) kev with cleaning of 6 state 1 + state = 2.is

31 rp-process above Z = 32 Masses are the most critical nuclear physics parameters for reliable calculations in astrophysics! D. Rodriguez., Phys. Rev. Lett., submitted (2004) Nuclide Half-life Accuracy 72 Kr 17.3 s 1x10-7 Proton drip-line 34 As63 35 Se65 As64 36 Br67 Se66 As65 37 Kr69 Br68 Se67 As66 38 Rb71 Kr70 Br69 Se68 As67 Sr73 Rb72 Kr71 Br70 Se69 As68 Sr74 Rb73 Kr72 Br71 Se70 As69 Z = 39 Sr75 Rb74 Kr73 Br72 Se71 As70 Y77 Sr76 Rb75 Kr74 Br73 Se72 As71 Y78 Sr77 Rb76 Kr75 Br74 Se73 As72 N=Z Y79 Sr78 Rb77 Kr76 Br75 Se74 P As73 Y80 Sr79 Rb78 Kr77 Br76 Se75 As74 Kr78 P Y81 Sr80 Rb79 Br77 Se76 Se77 Se78 As75 Y82 Sr81 Rb80 Kr79 Br78 As76 Y83 Y84 Y85 Sr82 Rb81 Kr80 Br79 As77 Sr83 Rb82 Kr81 Br80 Se79 As78 Sr84 P Rb83 Kr82 Br81 Se80 As79 Ge62 Ge63 Ge64 Ge65 Ge66 Ge67 Ge68 Ge69 Ge70 Ge71 Ge72 Ge73 Ge74 Ge75 Ge76 Ge77 Ge78 possible rp - process main path (H. Schatz et al. Phys. Rep. 294 (1998) 167) possible waiting points mass excess not yet measured (AME95) ISOLTRAP measurements before 2000

32 Masses and their relevance for nuclear astrophysics Mass measurements in the vicinity of doubly magic 78 Ni, 132 Sn, and 208 Pb will provide important data for a better understanding of the r-process!

33 Isobaric Multiplet Mass Equation A = 33, T = 3/2 quartet: Mass formula for multiplets of nuclear states with same mass and isospin T=3/2 M = a + bt z + ct z 2 + dt z 3 M e T=3/2 T=3/2 T=3/2 Commonly used quadratic form? d coefficients for all 18 complete ground state quartets d / δd A=9 A=33 (incl. ISOLTRAP) d = -2.95(90) kev A T=1/2 T=1/2 T z -3/2-1/2 1/2 3/2 33 Ar 33 Cl 33 S 33 P 2001: Breakdown of IMME F. Herfurth et al. PRL 87 (2001) : Revalidation of IMME T=3/2 state in 33 Cl wrong M.C. Pyle et al. PRL 88 (2002)

34 Recently: Most Stringent Test of IMME (with 32,33 Ar) Ground state quartets Excited state quartets Ground state quintets d / kev A ISOLTRAP measurements 2002: 33 Ar with u (m ) = 0.44 kev 32 Ar with u (m ) = 1.8 kev New status: A = 33, T = 3/2 quartet: A = 32, T = 2 quintet: K. Blaum et al., Phys. Rev. Lett. 91, (2003). d = 0.13(45) kev d = -0.11(30) kev

δ MA' MA 2 A' A δ r nuclear charge radii r 2 A' A Mass uncertainty of δm /m <

35 Masses of light nuclides and halo candidates 11 Li Matter radius δν Isotope-shift measurements: A, A' IS = M M A' A ( KNMS + KSMS ) + Fel. δ MA' MA 2 A' A δ r nuclear charge radii r 2 A' A Mass uncertainty of δm /m < (~ 1 kev) required! Further important candidates: 11,12,14 Be, N, 17-19, Ne

Performance of ISOLTRAP: Summary Perfect description of line shape Two-parameter fit 133 Cs fit of theoretically expected line shape High resolving power (R = 6 10 6 ) Isomer separation 170

up to 10 7 Accuracy: 10-7... 2 10-8 Cycle time: 150 ms... 10 s Buncher effic.: 10% Overall efficieny: 10-2 Measuring time: 15 min... 4 h Absolute mass: carbon clusters K. Blaum et al., Nucl.

36 Performance of ISOLTRAP: Summary Perfect description of line shape Two-parameter fit 133 Cs fit of theoretically expected line shape High resolving power (R = ) Isomer separation High accuracy 33 Ar, T 1/2 = 174 ms IMME test Short half-live 74 Rb, T 1/2 = 65 ms Test of CVC hypothesis Performance Resolving power: up to 10 7 Accuracy: Cycle time: 150 ms s Buncher effic.: 10% Overall efficieny: 10-2 Measuring time: 15 min... 4 h Absolute mass: carbon clusters K. Blaum et al., Nucl. Instrum. Meth. B 204, 478 (2003). M e a n T O F (µs) Low yields 32 Ar, T 1/2 = 99 ms Test of Standard Model 370 ions 32 Ar ν RF (Hz)

37 Comparison of Direct Mass Measurement Techniques on RIB ACCURACY δ m/m SPEG TOFI ESR-TOF MISTRAL ESR Schottky ISOLTRAP HALF-LIFE RANGE [s]

38 Mass measurement programs worldwide Z stable indirect GANIL SPEG CSS2 ISOLDE MISTRAL ISOLTRAP GSI ESR-SMS ESR-IMS proton dripline (FRDM95) a possible r-process New (Penning trap) CPT (ANL) LEBIT (MSU) SHIPTRAP (GSI) JYFLTRAP MAFF (FRM II) TITAN (TRIUMF) neutron dripline (FRDM95) N Lunney, Pearson & Thibault, Rev. Mod. Phys. 75 (2003)

39 SMILETRAP: High-Precision Mass Measurements Principle: Using highly-charged stable ions Cyclotron frequency: f c 1 = 2π q m B TOF Ion Source EBIT Mass Analyzer Preparation Penning trap Precision Penning trap νc ν Time-of-flight detector Q Ion production Charge breeding q / A - selection Cooling process Mass measurement Detection I. Bergström et al., Eur. Phys. J. D 22, 41 (2003).

40 Manne Siegbahn Laboratory at Stockholm University Highly charged ions from EBIS ion source ω c = (q/m) B Measured masses p, 3 He, 4 He, 28 Si, 76 Ge, 133 Cs, 198 Hg, rel. mass accuracy δm/m FUTURE: Ramsey excitation for δm/m The SMILETRAP set-up C. Carlberg, et al., PRL 83, 4506 (1999) G. Douysset, et al., PRL 86, 4259 (2001)

41 Electron binding energy The observable is a frequency ratio: R = ν ν c = cref qm q REF REF m M A 1 q q m + ( + REF qm E e B A R qref = ) e.g. : 1 H + E B = ev = 8,3 ppb correction 40 Ar 18+ E B = kev = 360 ppb correction 208 Pb 72+ E B = kev = 889 ppb correction Z < 20: E B is known to 0.1 ppb or better Z > 20: only theoretical or semi-empirical values For heavy atoms calculations: few 100 ev (ppb) to few 10 ev (<ppb) for closed shells ±1 e -. One has to correct for the electron binding energy!

42 The Kilogram Problem Present Future Single crystalline silicon ball Prerequisite: δm/m Kilogram prototype Bureau International des Poids et Mesures

43 Kilogram: The last basic unit defined by a prototype standard is unstable: cleaning prescription in definition Cleaning-washing 0-10 vor 1. nach 1. nach 2. Standard Date of previous cleaning-washing October 1982 m / µg K1 und 8(41) Sept./Oct und March Sept./Oct K 14 Sept T.J. Quinn, IEEE Instruments and Measurements, 40 (1991) 81

44 The solution to the kilogram problem Maxwell 1871: If, then, we wish to obtain standards of length, time, and mass which shall be absolutely permanent, we must seek them not in the dimensions, or the motion or the mass of our planet, but in the wavelength, the period of vibration, and the absolute mass of these imperishable and unalterable and perfectly similar molecules.

45 An Atomic Definition of the Kilogram The Avogadro Project: The kilogram is the mass of N kg 12 C-atoms. Recipe Produce a perfect Si Si crystal crystal Make Make a ball ball out out of of it it Measure the the diameter Determine the the lattice lattice parameter Measure the the contaminations Calculate the the number of of Si Si atoms atoms Measure the the isotopic abundance Measure the 28 Si/ 12 C mass ratio DONE with SMILETRAP and do all steps with an uncertainty of 10-9 or better!

46 Single ion mass spectrometry at MIT GOAL: Compare the mass of individual atoms and molecules with a precision of Confine SINGLE ions in a Penning Trap and directly detect their axial motion with a DC SQUID. T=4K DC SQUID Cool and measure the cyclotron mode by coupling it to the detected axial mode: Cyclotron Drive π-pulse phase is preserved! Cool ion Wait for time T In the dark Detect Phase

47 MIT results C 3 H 7 + f c Hz :00 85 Rb ++ C 3 H Þ Time of Measurement 2 nd Order Fit :00 04:00 05:00 06:00 (on 11/26/98) Rb ++ f c Hz Accuracy of ~ per run (4 hours) limited by magnetic field fluctuations. 13 neutral atomic masses measured with 1 m 133 Michael P. Bradley, et al., PRL 83, 4510 (1999) Frank DiFilippo, et al., PRL 73, 1481 (1994) FUTURE: Simultaneous cyclotron frequency measurements for a mass accuracy of δm/m

48 New determination of the fine structure constant α 2 α 2R h R = = 2 c m c e h m Cs m m Cs p m m p e cesium/proton mass ratio: 1.6 x 10-9 (statistical error) < 3 x10-9 (systematic error) (SMILETRAP, May 1998) 1 x (Pritchard et al. 1999) Rydberg constant H atom Biraben 99 9 x C. Schwob et al. PRL 82 (1999) 4960 Photon recoil Cs in MOT Chu 93 1 x 10-7 D.S. Weiss et al. PRL 70 (1993) 4960 Cs/p mass ratio new 99 2 x C. Carlberg et al. PRL 83 (1999) 4506 M.J. Bradley et al. PRL 83 (1999) 4510 T. Udem et al. PRL (1999) 3568 p/e-mass ratio Penning trap v. Dyck 95 3 x 10-9 D.L. Farnham et al. PRL 75 (1995) 3598 MEASURED DEVIATION [ppb] CHARGE STATE

49 The antiproton trap

50 No stringent test by hadrons CPT test with baryons

51 Results of the proton/antiproton mass comparison Results antiprotonic atoms: 5 x 10-5 cloud of antiprotons: 4 x 10-8 PRL 65 (1990) 1317 single antiproton/proton: 1 x 10-9 PRL 74 (1995) 3544 single antiproton/h - : 1 x PRL 82 (1999) 3198

52 High-Precision Mass Spectrometers Worldwide Experiment Mainz-Trap only one mass ( 4 He) Place University of Mainz Precision δm/m SMILETRAP MSL, University of Stockholm highly-charged ions, old trap system Seattle-TRAP University of Wachington light masses, systematic deviations MIT-TRAP MIT Cambridge only systematic uncertainty studies, moved to Florida

Lecture Series: Atomic Physics Tools in Nuclear Physics IV. High-Precision Penning Trap Mass Spectrometry

Euroschool on Physics with Exotic Beams, Mainz 005 Lecture Series: Atomic Physics Tools in Nuclear Physics IV. High-Precision Penning Trap Mass Spectrometry Klaus Blaum Johannes Gutenberg-University Mainz