Laser spectroscopic investigations of atoms with open 3d and 4f shells – elements with high nuclear spins Ewa Stachowska Chair of Atomic Physics Poznan University of Technology ul. Nieszawska 13b PL 60-965 Poznan, Poland
High resolution laser spectroscopy, combined with extensive theoretical analysis, allows the investigation of: ● electronic levels, ● configuration interaction effects, ● hfs interactions in atoms with a complex structure in stable and unstable isotopes, ● higher order nuclear moments − apart from magnetic-dipole and electric-quadrupole nuclear moments, which are accessible to some other methods as well, also magnetic-octupole and electric- hexadecapole nuclear moments, ● hyperfine anomaly in an isotopic series, ● isotope shifts.
High resolution laser spectroscopy of free atoms and ions LIF Laser – rf resonance method double resonance triple resonance atomic beam Paul or Penning trap Penning trap ABMR-LIRF combined ion trap atoms, ions neutral atoms till now-singly ionised atoms only typical amount g g <<g → single ion spectroscopy used ⇒ short lived isotopes (pg) typical value MHz – GHz GHz of hfs - intervals determined by: investigated laser line width (min) laser scan width (max) experimental errors min a few MHz >0.3 kHz Hz of hfs – interval measurements (time of flight) kind of levels no restriction ground level ground level and untill now investigated and low lying very low lying ground level metastable levels metastable levels external magnetic no control mainly strict strict field control (except for Zeeman compensation studies)
Laser induced fluorescence F 4 ’ J’ F 1 ’ J” F 4 ” F 1 ” J F 4 F 1 Frequency intervals between the hyperfine components in the spectral line yield the ● hyperfine splittings of both fine structure levels involved in the transition. Optical pumping causes depopulation of the lower sublevels F. ● Induced fluorescence causes population of the sublevels F”. ●
Laser-rf double resonance J’ F 1 ’ J F 2 F 1 Observation of resonance with rf radiation yields the value of the interval ● F 1 ↔ F 2 . The atom is in resonance with both rf and laser radiation. ● The method allows determination of the values of hyperfine intervals with an accuracy ● typical for rf frequency measurements.
r z U 0 + V 0 cos Ω t Paul trap setup
Experimental setup Computer control and data acquisition system Argon Tunable Dye laser pump laser dye laser control system Paul trap Wavemeter Rf λ generator Laser frequency marker Photon counting Laser system power meter Electronic Hollow cathode Monochromator detection with system photomultiplier
Atomic Data for Europium (Eu) Atomic Number = 63 Atomic Weight = 151.965 Isotope Mass Abundance Spin Mag. Moment 151 Eu 150.919847 47.8% 5\2 +3.464 153 Eu 152.921225 52.2% 5\2 +1.530 ● Eu I Ground State (1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 3 d 10 4 s 2 4 p 6 4 d 10 5 s 2 5 p 6 ) 4 f 7 6 s 2 8 S° 7/2 Ionization energy 45734.74 cm -1 (5.67038 eV) ● Eu II Ground State (1 s 2 2 s 2 2 p 6 3 s 2 3 p 6 3 d 10 4 s 2 4 p 6 4 d 10 5 s 2 5 p 6 ) 4 f 7 6 s 9 S° 4 Ionization energy 90700 cm -1 (11.25 eV)
Hyperfine anomaly A ( ) g ( ) 1 2 ∆ = − I 1 2 1 A ( ) g ( ) 2 1 I A – magnetic dipole hfs interaction constant ● g I – nuclear g-factor ● Eu large number of long living isotopes with non-zero nuclear spin ● strong variation in nuclear shape single particle model, ● one-proton hole in 5d subshell experiment outside the protection area ● Experimental methods laser-microwave double resonance technique in a Paul trap ● laser-microwave double resonance technique in a Pennig trap ●
Measured transition frequencies in the 4f 7 ( 8 S) 6s 9 S 4 ground-state hyperfine structure of Eu + corrected by second-order Zeeman shift (column 3). Column 5 gives the final second-order hfs. The last column gives the differences between experimental frequencies and the calculated ones using the fitted parameters. Isotope Transition Frequency Exp. Second order hfs (Exp)-(fit) corr. Hz Hz error Hz Hz 13/2-11/2 10 017 442 828 22 - 5 831 871 0 11/2-9/2 8 473 144 121 105 - 1 547 373 26 9/2-7/2 6 930 424 679 57 1 040 890 -20 151 Eu + 7/2-5/2 5 388 995 721 183 2 243 683 249 3 848 568 018 150 2 370 252 -84 5/2-3/2 13/2-11/2 4 449 976 109 70 - 1 151 697 0 11/2-9/2 3 765 315 459 101 - 305 715 5 153 Eu + 9/2-7/2 3 080 679 446 111 205 486 -17 7/2-5/2 2 396 063 741 187 443 128 59 5/2-3/2 1 711 463 310 210 468 221 -37
Determination of the hyperfine structure constants first order perturbation theorie: ˆ ∆ hfs = ψ ψ E H ( I ) hfs ˆ ˆ ˆ ˆ = ψ + + + + ψ M 1 E 2 M 3 E 4 ... ˆ ˆ ˆ ˆ = ψ ψ + ψ ψ + ψ ψ + ψ ψ + M 1 E 2 M 3 E 4 ... + − + + K K ( K 1 ) 2 I ( I 1 ) J ( J 1 ) 3 ∆ hfs = ⋅ + ⋅ + ⋅ + ⋅ + 4 E A B f ( F , J , I ) C g ( F , J , I ) D ... A B C D ∠ ∠ ( I ) − − 2 2 I ( 2 I 1 ) 2 J ( 2 J 1 ) A - B - C - and D - hfs constants second order perturbation theorie: 2 ˆ ˆ ˆ ψ ψ ψ ψ ψ ψ H ' M 1 ' ' E 2 ∑ hfs ∆ = ≡ hfs E 0 ( II ) − − E E E E ψ ψ , ' ψ ψ ψ ψ ' '
Hfs constants of the ground state 4f 7 6s 9 S 4 before correction and after correction for second order hfs interactions. I: ∆ E = f ( Ψ ,J) and II: ∆ E = f ( Ψ ,J,F). 151 Eu + Hz 153 Eu + Hz hfs constant before correction A 1 540 476 486(12) 684 601 369(5) B 8 910 554(231) 137 400(86) C 466(22) 66(8) D -6(5) -5(2) after correction I A 1 540 297 161(12) 684 565 948(5) B - 653 445(231) -1 751 726(86) C 466(22) 66(8) D -6(5) -5(2) after correction II A 1 540 297 394(13) 684 565 993(9) B - 660 862(231) 137 400(84) C 26(23) 3(7) D -6(5) -5(2)
The spectroscopic nuclear electric quadrupole moment Q Q( Z1 X) / Q( Z2 X) = B( Z1 X) / B( Z1 X) first order approximation B( 151 Eu + ) / B( 153 Eu + ) ≈ 65 [1] muonic x-ray measurements [2] Q( 151 Eu + ) / Q( 153 Eu + ) = 0.3744 (53) second order hfs effects taken into account [1] B corr ( 151 Eu + ) / B corr ( 153 Eu + ) = 0.37702 (2) [1] C. Becker, D. Enders, G. Werth, J. Dembczy ń ski, Phys. Rev. A 48 , 3546 (1993) [2] Y. Tanaka, R. M. Steffen, E. B. Scherer, W. Reuter, M.V.Hoelm, J.D. Zumbro, Phys. Rev.Lett. 51 , 1633 (1983)
The spectroscopic nuclear electric quadrupole moments of the unstable europium isotopes (in barn) Isotope Paul trap Measurements [3] Other work 148 Eu + 0.392(10) 0.35(6) [4] 149 Eu + 0.716(17) 0.75(2) [4] 0.74 [5] 150 Eu + 1.125(27) 1.13(5) [4] [1] [2] B( 151 Eu + )= - 600 612 (70) Hz Q( 151 Eu + )=0.903(10) b B( 153 Eu + )= - 1 759 520 (180) Hz [1] Q( 151 Eu + )=2.412(21) b [2] [1] C. Becker, D. Enders, G. Werth, J. Dembczy ń ski, Phys. Rev. A. 48 , 3546 (1993). [2] Y. Tanaka, R. M. Steffen, E. B. Scherer, W. Reuter, M.V.Hoelm, J.D. Zumbro, Phys. Rev.Lett., 51 1633 (1983). [3] K. Enders, E. Stachowska, G. Marx, Ch. Zölch, G. Revalde, J. Dembczy ń ski, G. Werth; Z. Phys. D 42 , 171 (1997). [4] S.A. Ahmad, W. Klempt, C. Ekström, R. Neugart, W. Wendt,Z.Phys., A 321 , 35 (1985). [5] K. Dörschel, W. Heddrich, H. Hühnermann, E.W. Peau, H. Wagner, Z.Phys.A 317 , 233 (1984).
Discrepancies in the A-ratios for the isotopes 151,153 Eu + observed in the ground and excited states 4f 7 6s ground states [1] A( 151 Eu + , 9 S 4 )/A( 153 Eu + , 9 S 4 )= 2.25003 493(4) [2] A( 151 Eu + , 9 S 4 )/A( 153 Eu + , 9 S 4 )= 2.25003 38(3) 4f 7 6s in the excited states [3] A( 151 Eu + , 7 S 3 )/A( 153 Eu + , 7 S 3 )= 2.2503 957(4) [1] O. Becker,K. Enders and G. Werth; Phys. Rev. A 48 , 3546-3554 (1993). [2] K. Enders; doctor thesis,Mainz 1996. [3] K. Enders, E. Stachowska, G. Marx, Ch. Zölch, G. Revalde, J. Dembczy ń ski, G. Werth; Z. Phys. D 42 , 171-175, (1997).
Zeeman splittings of the hyperfine structure sublevels ● Simplified estimation ( ) = + µ E M M A M M g B M z I J I J J B z J + µ ` g B M I B z I µ ` = N g g µ I I B
Results of measurements – 151 Eu tra n sitio n ∆ m J = 0, ∆ m I = 1 ν [k H z] ∆ ν [k H z] ∆ ν / ν F W H M [k H z] m J = 4 ; m I = -5/2 → -3 /2 5.6 ⋅ 1 0 -8 6 5 5 8 2 4 8 .1 0 .3 7 7 .6 8 m J = 4 ; m I = -3/2 → -1 /2 1.6 ⋅ 1 0 -7 6 2 9 1 4 1 1 .5 1 .0 2 11 .0 2 m J = 4 ; m I = -1 /2 → 1/2 1.3 ⋅ 1 0 -7 5 9 7 5 5 2 5 .7 0 .4 8 11 .9 4 m J = 4 ; m I = 1/2 → 3 /2 1.5 ⋅ 1 0 -7 5 7 4 5 2 3 7 .0 0 .9 4 16 .7 4 m J = 3 ; m I = 3/2 → 5 /2 1.2 ⋅ 1 0 -7 5 6 4 2 4 8 5 .1 0 .6 5 11 .0 9
| 4f 7 ( 8 S)6s; 9 S 4 〉 = + 0.984145 | 4f 7 ( 8 S)6s; 9 S 4 〉 + 0.175147 | 4f 7 ( 6P )6s; 7P 4 〉 - 0.003930 | 4f 7 ( 6 D)6s; 5 D 4 〉 - 0.014394 | 4f 7 ( 6 D)6s; 7 D 4 〉 + 0.000559 | 4f 7 ( 6 F)6s; 5 F 4 〉 + 0.001220 | 4f 7 ( 6 F)6s; 7 F 4 〉 + ... Using this wave function the g J for the ground state is given by: n ∑ 2 ψ = α ( i ) g ( ) g . J i J = i 1 The value which we obtain is: g J = 1.991169. Substituting this value into the energy matrix, g I the only free parameter remaining, is varied to minimize the difference between the calculated and observed Zeeman intervals for a given ∆ m J = 0, ∆ m I = 1 transition. We obtain a weighted average of: g I = 1.37734(6). S. Trapp, G. Tommaseo, G.Revalde, E. Stachowska, G. Szawio ł a and G. Werth, Eur. Phys. J. D. 26 , 237-244 (2003)
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