Ab initio MCDHF calculations of electron-nucleus interactions

Size: px

Start display at page:

Download "Ab initio MCDHF calculations of electron-nucleus interactions"

Emery Bailey
5 years ago
Views:

1 Ab initio MCDHF calculations of electron-nucleus interactions Jacek Bieroń Universitas Iagellonica Cracoviensis Zakład Optyki Atomowej Institute of Physics 1364 Trento 25 Aug 2015

2 Complete Active Space in Dirac-Hartee-Fock theory Zakład Optyki Jacek Bieroń Atomowej Uniwersytet Jagielloński Instytut Fizyki

3 Hartree-Fock theory in 10 minutes ( r 1, r 2,, r N ) ( r 1 ) ( r 2 ) ( r N )

4 Hyperfine structure in 10 minutes E ( atom) ( nucl ) B(el ) magnetic dipole hyperfine structure electric 2 quadrupolev (el ) E Q ( nucl ) z 2

5 CPT invariance by M. C. Escher P start C matter mirror image anti-particle e+ anti-matter time identical to start time exotic physics in 10 minutes Courtesy H.W. Wilschut particle e- T

6 Hartree-Fock theory in 10 minutes Hyperfine structure in 10 minutes exotic physics in 10 minutes

7 Central Field Approximation ( r 1 ) ( r 2 ) ( r N ) radial function ( r ) R( r ) Y (, ) spherical function

8 Double substitutions describe pair correlations Correlated fluctuations of 2 electrons In general, they are quartic in number. Empty levels Occupied levels Correlations decay (somewhat) rapidly with separation. Exponentially between functions of the same electron Algebraically (R-3) between the 2 electrons ( dispersion)

9 Hartree-Fock Approximation ( r 1 ) ( r 2 ) ( r N ) radial function ( r ) R( r ) Y (, ) spherical function wikipedia.org/wiki/fourier_series

10 Multi-Configuration Variational WaveFunction for the ground state of Carbon reference configuration 1s 2 s 2 p valence correlation core polarization targeting specific region single substitution double substitution triple substitution 1s 2 2s 2 2 p 2 1s 2 2 s 2 2 p3 p 1s 2 2 s 2 2 p 2 1s 2s 2 2 p 2 3s 1s 2 2s 2 2 p 2 1s 2 2s 2 p 2 3d s 2s 2 p 1s 2 s 2 p3s3 s3 p 1s 2 2s 2 2 p 2 1s 2 2s 2 2 p nl 1s 2 2 s 2 2 p 2 1s 2 s 2 2 p nln'l' 1s 2 2 s 2 2 p 2 1s 2 2s nln'l'n "l" spectroscopic orbitals virtual set active orbital set nl = all possible combinations of: n1l1, n2l2 ni li with ni n and li l

11 MultiConfiguration Hartree-Fock theory ( ) ( ( ( ) ) ( cn n ( N n N ) ) ( ) ) n Complete Active Space

12 Hartree-Fock Approximation ( r 1 ) ( r 2 ) ( r N ) radial function ( r ) R( r ) Y (, ) spherical function

13 systematic step by step n by n increase of active set

14 accuracy ~ 0.01% (10) (8)

15 Relativistic effects V c m m0 NR r rnr 1 for U 91 r rnr 0.75 Z

16 Aufbau Non-Rel. Rel. 1s

17 orthogonal radial orbitals

18 Relativistic aufbau 4f 4d Rel. Non-Rel. f - ekspansion d - ekspansion... s - contraction Non-Rel. Rel. 7s 3s 2s 1s

19 Complete Active Space in Dirac-Fock theory Relativistic wave equation: 2 (c p m c V ) Multiconfiguration wavefunction: ( ) ( c n ( N n n N n ) ( ) ) Complete Active Space

20 Aufbau: radium vs lithium Ra 1s s 2 Li 1s 2 2 s

21 multire fer lowest n quantum number of opened occupied shells systematic ence number of substitutions (SDTQ ) 5D-systematic ual set t r i v f o umbers n m u t n q ua angular highest n quantum number of virtual set

22 5 dimensions: size of virtual orbital set angular symmetry of virtual set: spdfgh number of opened core shells substitution number: SDTQ multireference set

23 nuclear Quadrupole moment of gold DF values: Q( 2 D5 2 ) Q( 2 D3 2 ) accuracy ~ 1%

24 2-3 virtual sets, oscillations, uncertainties

25 2-3 virtual sets, oscillations, uncertainties

27 discrete symmetry violation

Time reversal violation and the Electric Dipole Moment Why is EDM a TRV observable J d time time QM: J//d any particle will do dn 0.6 10-27 em de < 1.

28 Time reversal violation and the Electric Dipole Moment Why is EDM a TRV observable J d time time QM: J//d any particle will do dn em de < em de (SM) < em find suitable object Schiff need amplifier atomic (Z3) nuclear suitable structure Consider all nuclides EDM violates parity and time reversal Courtesy Klaus Jungmann

29 particle EDM within SM E Standard Model prediction of EDM of: electron ~ 10^-38 e.cm neutron ~ 10^-32 e.cm muon ~ 10^-26 e.cm tau ~ 10^-23 e.cm

30 EDM Now and in the Future The more Winnie the Pooh looked inside the more Piglet wasn t there. NUPECC list 199 Hg Radium potential Start TRI P de (SM) < Courtesy Klaus Jungmann

31 EDM Limits as of summer 2004 spring 2011 Particle e (Tl) n Tl (odd p) Hg (odd n) summer 2009 Possible Exp. Limit SM New Physics [10-27 e cm] [factor to go] [factor to go] < < 1.05 * < 3.1 * < < < various ~ 1 order of magnitude / decade if the electron were magnified to the size of the solar system, its EDM would be no bigger than the width of a human hair. Courtesy Klaus Jungmann

32 d-p amplitude p-s amplitude (14) from: Dzuba et al., Phys. Rev. A 61 (2000)

33 Tensor-pseudotensor contributions to EDM of: 225-Ra, 199-Hg, 171-Yb DF vs MCDHF

34 EDM of Copernicium

35 coffee time?

36 Co-Producers (in alphabetical order) Jacek Bieroń Charlotte Froese Fischer Stephan Fritzsche Gediminas Gaigalas Michel Godefroid Ian Grant Paul Indelicato Per Jönsson Pekka Pyykkö Uniwersytet Jagielloński Vanderbilt University & NIST Universität Jena Vilniaus Universitetas Université Libre Bruxelles University of Oxford l Université Paris VI Malmö Högskola Helsingin Yliopisto Thank you for your attention

37 Large Numbers Hypothesis as always, history goes back to Dirac (who was influenced by Weyl, Eddington, Milne, Lemaitre) P.A.M. Dirac "The Cosmological Constants Nature 139: 323 (1937) According to current cosmological theories, the universe had a beginning about 2 x 10^9 years ago, when all the spiral nebulae were shot out from a small region of space, or perhaps from a point. If we express this time, 2 x 10^9 years, in units provided by the atomic constants, say the unit e^2/mc^3, we obtain a number about 10^39. This suggests that the above-mentioned large numbers are to be regarded, not as constants, but as simple functions of our present epoch, expressed in atomic units.

38 Large Numbers Hypothesis ct T is the age of the universe re is the classical electron radius re 2 Fe e Fg 4 0 GM p me LNH hypothesis 1 G T

39 why alpha and not G? G (67) m3kg 1s CODATA G (30) m 3kg 1s 2 International Astronomical Union

40 e g L 2m s e B g 2 Ls mc electron gyromagnetic ratio g e s s ( s 1) mc Ls s( s 1) Dirac Schwinger Bohr magneton g C2 C4 ( ) C6 ( ) C8 ( ) C10 ( ) a ahadr aweak 2 C2, C4,C6 exact C (35) PRL 99, (2007) g = (15) PRL 100, (2008) 139 ((33 31) (39)CODATA

41 Foils with white background thanks to Victor Flambaum and Vladimir Dzuba Variation of Fundamental Constants from Big Bang to Atomic Clocks V.V. Flambaum School of Physics, UNSW, Sydney, Australia Co-authors: Atomic calculations V.Dzuba,M.Kozlov,E.Angstmann,J.Berengut,M.Marchenko,Cheng Chin,S.Karshenboim,A.Nevsky Nuclear and QCD calculations E.Shuryak,V.Dmitriev,D.Leinweber,A.Thomas,R.Young,A.Hoell, P.Jaikumar,C.Roberts,S.Wright,A.Tedesco,W.Wiringa Cosmology J.Barrow Quasar data analysis J.Webb,M.Murphy,M.Drinkwater,W.Walsh,P.Tsanavaris,S.Curran Quasar observations C.Churchill,J.Prochazka,A.Wolfe, thanks to W.Sargent,R.Simcoe

42 Search for variation of fundamental constants Big Bang Nucleosynthesis Oklo natural nuclear reactor Quasar Absorption Spectra 1 Atomic clocks 1 Enhanced effects in atoms 1, molecules1 and nuclei Dependence on gravity 1 Based on atomic and molecular calculations Courtesy Victor Flambaum and Vladimir Dzuba

43 Quasar absorption spectra Gas cloud Earth Quasar Light One needs to know E( 2) for each line to do the fitting Courtesy Victor Flambaum and Vladimir Dzuba

44 energy of a one electron atom E mc Z 2 QED ( n 2 2Z 2 ) mc Z mc Z n 3 Z 2 k 2 E mc ck ( ) QED n 2 n 4 k 3 n rest energy Balmer energy Sommerfeld energy Schrödinger equation Pauli equation Dirac equation Feynman diagrams

45 Results of calculations (in cm-1) Negative shifters Anchor lines Atom Atom q q Mg I Ni II Mg II Ni II Mg II Cr II Si II Cr II Si II Cr II Al II Fe II Al III Al III Ni II Also, many transitions in Mn II, Ti II, Si IV, C II, C IV, N V, O I, Ca I, Ca II, Ge II, O II, Pb II Different signs and magnitudes of q provides opportunity to study systematic errors! Positive shifters Atom q Fe II Fe II Fe II Fe II Fe II Fe II Zn II Zn II Courtesy Victor Flambaum and Vladimir Dzuba

46 Co-Producers (in alphabetical order) Jacek Bieroń Charlotte Froese Fischer Stephan Fritzsche Gediminas Gaigalas Michel Godefroid Ian Grant Paul Indelicato Per Jönsson Pekka Pyykkö Uniwersytet Jagielloński Vanderbilt University & NIST Universität Jena Vilniaus Universitetas Université Libre Bruxelles University of Oxford l Université Paris VI Malmö Högskola Helsingin Yliopisto Thank you for your attention

Tests of fundamental symmetries with atoms and molecules

Tests of fundamental symmetries with atoms and molecules 1 Listening to an atom q Coulomb forces + Quantum Electro-Dynamics => a relatively simple interpretation q Unprecedented control over internal and