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below Charge radii of medium-mass nuclei using the atomic physics input Magdalena Kowalska CERN, PH-Dept. [email protected] Outline Laser spectroscopy on radioactive nuclei Optical isotope shifts A long way from isotope shifts to charge radii Take-home message 2 Charge radii from optical transitions A, A' ( K NMS K SMS ) m A' m A F r 2 m A' m A Atomic factors: (normal and specific mass shift, F-factor (main source of uncertainties) Cocolios et al, Phys. Rev. Lett, 106, 052503 (2011) 3 A, A ' Laser spectroscopy on radionuclides Blue – since 1995 4 Collinear laser spectroscopy Why collinear? Ions at RIB facilities come out as a beam, so laser-ion interaction is longest in (anti) collinear geometry Laser beam, Laser on fixed frequency Charge exchange region (if needed) Ion beam Retardation zone Excitation / Observation region Electrostatic deflection Detection method depends on chemical element or even isotope => optimised for best S/N ratio: - photon detection: all nuclei - beta asymmetry: short-lived nuclei 5 - collision reionisation: noble gases Review: B Cheal and K T Flanagan 2010 J. Phys. G: Nucl. Part. Phys. 37 113101 Optical isotope shifts What is measured? (independently for each isotopes) Laser frequency of resonance (including HFS) in laboratory frame (often: moving ions/atoms) Or accelerating high voltage at which ion/atom beam is in resonance with laser What is needed to extract differences in charge radii? Frequency difference (HFS centroid) for 2 isotopes at rest Conversion for ion beams (Collinear laser spectroscopy): Uncertainty in all input values contributes Statistical – collected statistics, quality of fit (especially for HFS) Systematic: precision and accuracy of atomic masses and measuring devices (laser frequency and accelerating voltage) set laser frequency (Wavemeter or frequency comb) Accelerating voltage (voltage divider + voltmeter) 6 atomic masses Optical isotope shifts - uncertainties Uncertainties: Statistical – collected statistics, quality of fit (especially for HFS) Systematic: precision and accuracy of atomic masses and measuring devices set laser frequency (Wavemeter or frequency comb) Accelerating voltage (usually voltage divider + voltmeter) atomic masses Mg+, 2006 data Systematic uncertainties much larger than statistical 7 From isotope shifts to charge radii A, A' ( K NMS K SMS ) Due to reduced mass of nucleus-e- system and correlations between e-’s. m A' m A F r 2 m A' m A A, A ' Proportional to (change in) e- density at nucleus. Semi-empirical or ab initio methods. Ab initio methods or “King plot”. From HFS: all inner e’s are paired off in alkali-like atom and make no contribution to magnetic HFS. HFS directly proportional to density of ns e- at point nucleus A: HFS constant for ns e: correction for finite size of nucleus e – HFS anomaly g’ – reduced g factor of nucleus Goudsmit-Fermi-Segre formula: ns electron density at nucleus is related to effective quantum number of ns level Screening effects: 8 K_MS: Modified King plot When data for at least 3 isotopes exists (i.e stable isotopes) partial help is there! Combine absolute radii (transitions in muonic atoms or electron scattering) and isotope shifts in optical transition Usually resulting uncertainties too large -> so use F from semi-empirical or ab ignition approaches e.g. for Ne A good side effect: offset in accelerating voltage Scales with mass like mass shift -> can incorporate it in K_MS Result: Determine K_MS and F usually too large uncertainties So: use calculated F Modified isotope shift Offset: K_MS Slope: F A, A’ A, A’’ 0 9 Modified difference in charge radii From isotope shifts to charge radii It is not that easy: Many correlated systematic effects In IS – accelerating voltage In King-plot: Muonic data Inconsistent values from ab initio atomic theory and other approaches Large uncertainties in F and K_MS, whichever approach taken Which F and K_MS to use? Resulting radii trend must be the final judge: Consistent with radii trends of neighbouring chains Consistent with nuclear structure known from other observables 10 Some examples Below medium-mass nuclei The lucky cases with at least 3 stable nuclei + K with 2 stable isotopes 11 Laser spectroscopy on Mg isotopes Mg+: Detection via: HFS structure of 21Mg observed in b-decay asymmetry (D1 line) Fluorescence photos Or beta-decay asymmetry 12 From Mg isotope shifts to charge radii F factor F [MHz/ fm2] Semi-empirical Ab initio GFS HFS [Tor85] [Saf01] [Ber03] [Sah12] s->p1/2 -158 -148 -117 -125.81 -127 -126.221 s->p3/2 -158 -148 -117 -126.821 -127 -126.324 20% difference, seen also in other elements 10% error assumed Specific mass shift K_SMS [GHz/u] Ab initio [Saf01] [Ber03] [Sah12] [Sah12] s->p1/2 -362 -379 -390.1 -398.8 s->p3/2 -361 -373 -386.1 -389.9 [Tor85] G. Torbohm, B. Fricke, A. Rosen, PRA 31, 2038 (‘85) [Saf01] M.S. Safronova & W.R. Johnson, PRA 64, 052501 (‘01) [Ber03] J.C. Berengut, V.A. Dzuba, V.V. Flambaum, PRA 68, 022502 (‘03) [Sah12] B.K. Sahoo, J. Phys. B 43 231001 (’10) Large differences or uncertainties -> let’s try a King plot (need Muonic data) 13 Mg charge radii from muonic transitions Large corrections and many systematic uncertainties Fricke et al, PRC 45, 81 (’92) 14 Can they be determined more accurately nowadays? Mg modified King plot Differences in radii from Muonic data vs electron scattering Uncertainties: from transition energy + 10% of larger nucl. polarization uncert. d Too large uncertainties to be used syst error 1: uncertainty in nuclear polarisation correction (30% of total nuclear polarization) Syst error 2: due to choice of skin thickness t of Fermi distribution Mg+, 24,25,26Mg Syst error in IS would lead to additional 5 GHz u uncertainty in KMS K_NMS = 365 GHz u 15 Resulting charge radii King plot d<r2> (fm2) Uncertainties in atomic factors are equally important as central values [Saf01] Which atomic factors should I use? The resulting nuclear physics interpretation will tell me … King plot [Ber03] [Sah10] 16 Best nuclear physics description from King plot: In general radii increase Minimum radii for 24,26Mg (new sub-shell closures) Radii around N=20 larger than around N=8 Charge radius (fm) Mg charge radii and nuclear structure Uncertainty of the slope due to atomic F factor uncertainty not included N=14 N=20 Atomic number, A Smallest radius at N=14, not N=20: Migration of the shell closure 17 D. Yordanov et al, Phys. Rev. Lett. 108, 042504 (2012) Laser spectroscopy of Ne isotopes Ne atoms Special type of setup: Excitation to a meta-stable level (neutralization) Laser excitation from this state Detection after reionization – ions or beta counts Acceleration-voltage calibration: Use of (anti-) collinear laser 18 Charge radii of Ne isotopes A, A' ( K NMS K SMS ) m A' m A F r 2 m A' m A A, A ' 1 GHz 10 MHz F determined from semi-empirical approaches: Goudsmit-Fermi-Segre: F=-40(4) MHz/fm2 (assuming 10% uncertainty) HSF: F= -38 (4) MHz/fm2 (also, assuming 10% uncertainty) Any ab initio calculations existing for this transition? Mass shift from modified King plot Muonic radii for 20,21,22Ne With fixed F 19 Ne charge radii and nuclear structure Determined trend in radii can be explained by nuclear models Wealth of structures revealed: Presence and disappearance of shells, clustering, onset of halo formation Intrinsic density distributions of dominant proton FMD configurations 20 Geithner et al, PRL 101, 252502 (‘08) Marinova et al, PRC 84, 034313 (‘11) 20 Laser spectroscopy of Ar isotopes Ar atom Technique: the same as later used for Ne (including energy calibration) Determination of F – semi-empirical approach: F= - 104(10) MHZ/fm2 Determination of mass shift constant: modified King plot With fixed F Any ab initio calculations? Muonic data Talmi – Zamick formula HF calculation, A. Klein et al, Nucl. Phys. A 607 (1996) 1. K. Blaum et al, NPA 799, 30 (2008) 21 Laser spectroscopy of K isotopes Collinear laser spectroscopy on atoms Detection via fluorescence photons Bunched ion beam (to lower laser background) K_SMS and F determined from ab initio calculations (only 2 data points from muonic atoms) A.-M. Martensson-Pendrill, et al., JPB 23, 1749 (‘90) – reliable results for Ca K_SMS = −15.4(3.8) GHz u F =−110(3) MHz/fm2 N=28 shell closure well visible 22 Charge radii of Ar and K isotopes Resulting trends in radii make sense from nuclear structure point of view N=28 shell closure visible (but not N=20) Rather consistent with radii trends in neighbouring chains – although strong Z dependence is clearly visible Systematic errors in trends due to F uncertainty not shown K Ar K. Kreim et al, PLB 731, 97 (‘14) 23 Take-away message Optical isotope shifts are sensitive to small changes in nuclear charge radii The art lies in determining the proportionality (atomic) factors with both enough precision and enough accuracy to provide a quantitative relation and to provide nuclear radii which make sense from the nuclear physics point of view Have to rely a lot on semi-empirical approaches and muonic data with large corrections calculated with limited computer power Hopefully ab initio approaches are catching up 24 Collinear-anticollinear 25 Modified King plot Isotope pair A, A’ slope Isotope pair A,A’’ 0 26 King plot for 2 optical transitions In Mg+ s->p1/2 (D1) and s->p3/2 (D2) 27 From optical isotope shifts to radii Mass shift in spectra of many-electron atoms Normal mass shift First order field shift Specific mass shift, Due to e- correlations 1st order perturbation theory (finite nucleus as perturb to point-like nucleus) 1st approach Then corrections For distribution nonrelativistic probability density of e- at point nucleus s-1 close to 1 for light isotopes, close to 0.1, 0.2 for heavy -> changes slowly with r, so can use 28 From optical isotope shifts to radii Electronic factor nonrelativistic probability density of e- at point nucleus, but it should be rather change in probability density Determination of density of ns electron at point-like nucleus Ab initio atomic calculations Semi-empirical approaches: From HFS: all inner e’s are paired off in alkali-like atom and make no contribution to magnetic HFS. HFS directly proportional to density of ns e- at point nucleus A: HFS constant for ns e: correction for finite size of nucleus e – HFS anomaly g’ – reduced g factor of nucleus Goudsmit-Fermi-Segre formula: ns electron density at nucleus is related to effective quantum number of ns level Screening effects: F for Mg+ from GFS 30 F for Mg+ from HFS 31 Field shift according to Seltzer Seltzer A, A' ( K NMS K SMS ) m A' m A F r 2 m A' m A A, A ' 32 2nd order field shifts Due to 2nd-order contributions and from relativistic effects 33 Nuclear radii Which radius? Depends on the used probe Charge radius – studied via Coulomb interaction of a charged particle with nucleus Matter radius – studied via strong interaction of nuclei and particles Nuclei don’t have abrupt boundaries - useful two parameters: Mean radius – where density is 50% of maximum Diffuseness/“skin thickness” – distance where density drops from near max to near min Mean square radius of charge distribution 34 Modified King plot When data for at least 3 isotopes exists (i.e stable isotopes) partial help is there! Combine absolute radii (transitions in muonic atoms or electron scattering) and isotope shifts in optical transitions A A A A A A A Isotope pair A, A’ A A slope A A A A A A Isotope pair A,A’’ A 0 A A 35 But if there are fewer stable isotopes … See Na, Mn, Cu, Ga … Lasers + ion traps: n-def Hg & Au isotopes RILIS, Windmill, ISOLTRAP teams Bonn et al., PLB38 (1972) 308 Ulm et al., Z Physik A 325 (1986) 247 Several techniques combined RILIS lasers to probe the hyperfine structure of Hg & Au isotopes Detection: Alpha spectroscopy with Windmill Selective ion counting in MR-ToF Au 36 Resulting charge radii King plot King plot only K_MS + error K_MS - error Too large uncertainties d<r2> (fm2) Middle values [Saf01] King plot [Ber03] [Sah10] 37 Zamick 38 Electron scattering Diffraction with radiation of wavelength smaller than the object – high-energy eLambda < 10 fm -> p> 100 MeV (e.g 100 MeV to 1 GeV e-) Result: rms radius: <r2>1/2 Diffraction minima 39 Electron transitions Nuclei are not point-like particles -> atoms electrons can penetrate inside and probe the nuclear distribution (K X-ray transitions, especially 1s electrons) Biggest penetration into nucleus for 1s eMuch easier to compare distibutions of two neighbouring isotopes (than determine size of 1 radius absolutely) K X-ray isotope shifts – relatively large Optical isotope shifts in valence e-: much smaller penetration and thus smaller shift Both are still very small effects – due to a small size of nucleus compared to e- orbits optical transition 1e-7 effect X-ray transition 1e-6 effect J. Bonn et al, Z. Phys. A 276, 203 (1976) P. Lee et al Phys Rev C 17, 1859 (1978) 40 Muonic atoms Muon’s mass = 200 e- mass -> Bohr (atomic) radius 200 smaller E.g. in 208Pb: muon’s mean radius is inside the nucleus Isotope shifts – factor 1-2 (vs 1e-4 – 1e-6 for e-) Technique: Muons produced at accelerators (in decay of pi mesons), e.g at PSI-Zurich Bombard target made of isotope(s) of interest Muons are captured in high-n orbits and cascade down to 1s orbits Emitted photons (of MeV energy) are detected Obtain directly charge-distribution parameters (although analysis is complex) 41