Atomic Mass Evaluation

Transcription

1 Atomic Mass Evaluation Wenjia HUANG Centre de Sciences Nucléaires et de Sciences de la Matière May 10, 2016

2 Outline 1 Introduction Atomic Mass Mass Measurements 2 Evaluation technique History Input data Least-squares method Correlations W.J HUANG (CSNSM) AME May 10, / 18

3 Outline 1 Introduction Atomic Mass Mass Measurements 2 Evaluation technique History Input data Least-squares method Correlations W.J HUANG (CSNSM) AME May 10, / 18

4 Atomic Mass Mass Binding energy Interaction - Nuclear physics : shells, shapes, pairng, nuclear models... - Nuclear astrophysics : r,rp,νp-process - Atomic physics : QED - Metrology : Fundamental constants W.J HUANG (CSNSM) AME May 10, / 18

5 Atomic Mass Mass Binding energy Interaction - Nuclear physics : shells, shapes, pairng, nuclear models... - Nuclear astrophysics : r,rp,νp-process - Atomic physics : QED - Metrology : Fundamental constants Why Atomic mass? - Almost all measurements give the mass of the atom or of the single charge - easy to calculate Q-value... W.J HUANG (CSNSM) AME May 10, / 18

6 Mass Measurements Indirect methods: Energy Reaction Energies A(a, b)b: Qr = M A + M a M b M B (n, γ) and (p, γ) are the backbones close to stability Decay Energies: α, β, p decays far from stability W.J HUANG (CSNSM) AME May 10, / 18

7 Mass Measurements Indirect methods: Energy Reaction Energies A(a, b)b: Qr = M A + M a M b M B (n, γ) and (p, γ) are the backbones close to stability Decay Energies: α, β, p decays far from stability Direct Methods: Flight time or frequency TOF (MSU, GANIL et al) Penning Traps (ISOLDE, TRIUMF et al) Storage Rings (GSI, IMP) W.J HUANG (CSNSM) AME May 10, / 18

8 Storage Ring Theorem T T = 1 γ 2 t m q m q + (1 γ2 γt 2 ) V V W.J HUANG (CSNSM) AME May 10, / 18

9 Storage Ring Theorem T T = 1 γ 2 t m q m q + (1 γ2 γt 2 ) V V W.J HUANG (CSNSM) AME May 10, / 18

10 Penning Trap Cyclotron frequency ω c = q/mb The free cyclotron frequency is inversely proportional to the mass of the ions A = 100u, q = +1, B = 6T v c = ω c /2π 1 MHz W.J HUANG (CSNSM) AME May 10, / 18

11 60 years of mass evaluation In the early 1950 s, it was found that many relations (direct and indirect) overdetermined the mass value of many nuclides. W.J HUANG (CSNSM) AME May 10, / 18

12 60 years of mass evaluation In the early 1950 s, it was found that many relations (direct and indirect) overdetermined the mass value of many nuclides. Aaldert H. Wapstra established a procedure using a least-squares method to solve the problem of overdetermination. W.J HUANG (CSNSM) AME May 10, / 18

13 60 years of mass evaluation In the early 1950 s, it was found that many relations (direct and indirect) overdetermined the mass value of many nuclides. Aaldert H. Wapstra established a procedure using a least-squares method to solve the problem of overdetermination. Best values for the atomic masses and their associated uncertainties W.J HUANG (CSNSM) AME May 10, / 18

14 60 years of mass evaluation In the early 1950 s, it was found that many relations (direct and indirect) overdetermined the mass value of many nuclides. Aaldert H. Wapstra established a procedure using a least-squares method to solve the problem of overdetermination. Best values for the atomic masses and their associated uncertainties AME1955, AME1961, AME1964, AME1971, AME1977, AME1983, AME1993, AME2003, AME2012 W.J HUANG (CSNSM) AME May 10, / 18

15 AME masses = AME ground states = AME isomers(> 100ns) = AME AME2016 is coming... W.J HUANG (CSNSM) AME May 10, / 18

16 Input data for AME AME ESR-CSRe data Reaction Energies (ev) (p,n), (n,γ) Desintegration Energies (ev) β-decay(β, β + ) α-decay(α) Mass Spectrometry (u) Frequency correlations between all known and unknown W.J HUANG (CSNSM) AME May 10, / 18

17 Data Connections Schematic A k 2 B F H k 5 k 1 k 3 k 7 k 9 C k 4 D k 6 E k 8 G I Figure: Connections plot with primary, secondary and unconnected items. primary : A,B,C,D used in LSM secondary : E,F,G deduced from primaries unconnected : H, I systematic # W.J HUANG (CSNSM) AME May 10, / 18

18 Data Connections Real Figure: Diagram of connections for input data. W.J HUANG (CSNSM) AME May 10, / 18

19 Treatment of Data LSM-1 Q equations to N parameters (Q > N) N k ij m j = q i ± dq i i = 1,..., Q K m = q j=1 Simple construction t KW K m = t KW q A m = t KW q A: normal matrix, W : error matrix ω i = 1/(dq i dq i ) Parameters Masses m = A 1t KW q m = R q W.J HUANG (CSNSM) AME May 10, / 18

20 Treatment of Data LSM-2 Flow-of-information matrix F = t R K G.Audi(1986) The(i, j) element of F represents the influence of datum i on mass m j A column of F represents all the contribution brought by all data to a given mass m j A row of F represents the influences given by a single piece of data to each nuclide, their sum is the significance of the data Adjusted input data q = KR q W.J HUANG (CSNSM) AME May 10, / 18

21 Correlations Variance and Covariance (in nano-amu**2) n H D 4He 28Si 40Ar 107Ag 109Ag 133Cs Covariance matrix provided to Codata group as request now available on AMDC website W.J HUANG (CSNSM) AME May 10, / 18

22 Correlations in Storage rings Covariance matrix used in ESR and CSRe data? m q = a + bt + ct 2 W.J HUANG (CSNSM) AME May 10, / 18

23 Thank you! W.J HUANG (CSNSM) AME May 10, / 18