Laser spectroscopic investigations of atoms with open 3d and 4f - - PowerPoint PPT Presentation

Laser spectroscopic investigations

• f 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 ABMR-LIRF Paul or Penning trap Penning trap combined ion trap

atoms, ions neutral atoms till now-singly ionised atoms only

typical amount used

g g

(pg)

<<g → single ion spectroscopy

⇒ short lived isotopes

typical value

• f hfs - intervals

investigated

MHz – GHz GHz

determined by: laser line width (min) laser scan width (max)

experimental errors

• f hfs – interval

measurements

min a few MHz >0.3 kHz

(time of flight)

Hz

kind of levels investigated no restriction ground level and low lying metastable levels ground level and very low lying metastable levels untill now ground level external magnetic field control no control

(except for Zeeman studies)

mainly compensation strict strict

Laser induced fluorescence

F4 F1 J J’ J” F4’ F1’ F4” F1”

• 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

F2 F1 J J’ F1’

• Observation of resonance with rf radiation yields the value of the interval

F1 ↔ F2.

• 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.

Paul trap setup

U0 + V0 cos Ω t

r z

Experimental setup

Rf generator Dye laser control system Computer control and data acquisition system Tunable dye laser Argon pump laser Photon counting system Electronic detection system Monochromator with photomultiplier

Hollow cathode Laser power meter Laser frequency marker Wavemeter

λ

Paul trap

Atomic Data for Europium (Eu) Atomic Number = 63 Atomic Weight = 151.965

Isotope Mass Abundance Spin

• Mag. Moment

151Eu

150.919847 47.8% 5\2 +3.464

153Eu

152.921225 52.2% 5\2 +1.530

• Eu I Ground State (1s22s22p63s23p63d104s24p64d105s25p6) 4f76s2 8S°7/2

Ionization energy 45734.74 cm-1 (5.67038 eV)

• Eu II Ground State (1s22s22p63s23p63d104s24p64d105s25p6) 4f76s 9S°4

Ionization energy 90700 cm-1 (11.25 eV)

Hyperfine anomaly 1 1 2 2 1

2 1

− = ∆ ) ( g ) ( A ) ( g ) ( A

I I

• A – magnetic dipole hfs interaction constant
• gI – nuclear g-factor

Eu

• large number of long living isotopes with non-zero nuclear spin
• strong variation in nuclear shape single particle model,
• ne-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(8S) 6s 9S4 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 Hz Exp. error Hz Second order hfs

• corr. Hz

(Exp)-(fit) Hz

151Eu+

13/2-11/2 11/2-9/2 9/2-7/2 7/2-5/2 5/2-3/2 10 017 442 828 8 473 144 121 6 930 424 679 5 388 995 721 3 848 568 018 22 105 57 183 150

• 5 831 871
• 1 547 373

1 040 890 2 243 683 2 370 252 26

• 20

249

• 84

153Eu+

13/2-11/2 11/2-9/2 9/2-7/2 7/2-5/2 5/2-3/2 4 449 976 109 3 765 315 459 3 080 679 446 2 396 063 741 1 711 463 310 70 101 111 187 210

• 1 151 697
• 305 715

205 486 443 128 468 221 5

• 17

59

• 37

Determination of the hyperfine structure constants

first order perturbation theorie: ... D ) I , J , F ( g C ) I , J , F ( f B ) 1 J 2 ( J 2 ) 1 I 2 ( I 2 ) 1 J ( J ) 1 I ( I 2 ) 1 K ( K A 2 K E ... 4 E ˆ 3 M ˆ 2 E ˆ 1 M ˆ ... 4 E ˆ 3 M ˆ 2 E ˆ 1 M ˆ H ˆ E

4 3 hfs ) I ( hfs hfs ) I (

+ ⋅ + ⋅ + ⋅ − − + + − + + ⋅ = ∆ + ψ ψ + ψ ψ + ψ ψ + ψ ψ = ψ + + + + ψ = ψ ψ = ∆

∠ ∠

A B C D A- B- C- and D- hfs constants second order perturbation theorie: E E 2 E ˆ ' ' 1 M ˆ E E ' H ˆ E

' ' , ' 2 hfs hfs ) II (

≡ − ψ ψ ψ ψ − ψ ψ = ∆

ψ ψ ψ ψ ψ ψ

∑

Hfs constants of the ground state 4f 76s 9S4 before correction and after correction for second order hfs

• interactions. I: ∆E = f(Ψ,J) and II: ∆E = f(Ψ,J,F).

hfs constant

151Eu+ Hz 153Eu+ Hz

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(Z1X) / Q(Z2X) = B(Z1X) / B(Z1X)

first order approximation

B(151Eu+) / B(153Eu+) ≈ 65 [1]

muonic x-ray measurements

Q(151Eu+) / Q(153Eu+) = 0.3744 (53) [2]

second order hfs effects taken into account

Bcorr(151Eu+) / Bcorr(153Eu+) = 0.37702 (2) [1]

[1] C. Becker, D. Enders, G. Werth, J. Dembczyński, 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

• f the unstable europium isotopes (in barn)

Isotope Paul trap Measurements [3] Other work

148Eu+

0.392(10) 0.35(6) [4]

149Eu+

0.716(17) 0.75(2) [4] 0.74 [5]

150Eu+

1.125(27) 1.13(5) [4]

B(151Eu+)= - 600 612 (70) Hz [1] Q(151Eu+)=0.903(10) b [2] B(153Eu+)= - 1 759 520 (180) Hz [1] Q(151Eu+)=2.412(21) b[2]

[1] C. Becker, D. Enders, G. Werth, J. Dembczyński, 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. Dembczyński, 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 151,153Eu+ observed in the ground and excited states

ground states 4f 7 6s

A(151Eu+, 9S4)/A(153Eu+, 9S4)=2.25003493(4) [1] A(151Eu+, 9S4)/A(153Eu+, 9S4)=2.2500338(3) [2]

in the excited states 4f 7 6s

A(151Eu+, 7S3)/A(153Eu+, 7S3)=2.2503957(4) [3]

[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. Dembczyński,

• G. Werth; Z. Phys. D 42, 171-175, (1997).

Zeeman splittings

• f the hyperfine structure sublevels
• Simplified estimation

( )

I z B ` I J z B J J I J I z

M B g M B g M M A M M E µ µ + + =

B N I I

g g µ µ =

`

Results of measurements – 151Eu

tra n sitio n ∆ m J= 0, ∆ m I= 1 ν [k H z] ∆ ν [k H z] F W H M [k H z] ∆ ν /ν m J= 4 ; m I= -5/2 → -3 /2 6 5 5 8 2 4 8 .1 0 .3 7 7 .6 8 5.6 ⋅1 0 -8 m J= 4 ; m I= -3/2 → -1 /2 6 2 9 1 4 1 1 .5 1 .0 2 11 .0 2 1.6 ⋅1 0 -7 m J= 4 ; m I= -1 /2→ 1/2 5 9 7 5 5 2 5 .7 0 .4 8 11 .9 4 1.3 ⋅1 0 -7 m J= 4 ; m I= 1/2 → 3 /2 5 7 4 5 2 3 7 .0 0 .9 4 16 .7 4 1.5 ⋅1 0 -7 m J= 3 ; m I= 3/2 → 5 /2 5 6 4 2 4 8 5 .1 0 .6 5 11 .0 9 1.2 ⋅1 0 -7

|4f7(8S)6s; 9S4〉 = + 0.984145 |4f7(8S)6s; 9S4〉 + 0.175147 |4f7(6P)6s; 7P

4〉

• 0.003930 |4f7(6D)6s; 5D4〉 - 0.014394 |4f7(6D)6s; 7D4〉

+ 0.000559 |4f7(6F)6s; 5F4〉 + 0.001220 |4f7(6F)6s; 7F4〉 + ...

Using this wave function the gJ for the ground state is given by:

. g ) ( g

n 1 i ) i ( J 2 i J

∑

=

α = ψ

The value which we obtain is: gJ = 1.991169. Substituting this value into the energy matrix, gI the only free parameter remaining, is varied to minimize the difference between the calculated and observed Zeeman intervals for a given ∆mJ = 0, ∆mI = 1 transition. We obtain a weighted average of: gI = 1.37734(6).

• S. Trapp, G. Tommaseo, G.Revalde, E. Stachowska, G. Szawioła and G. Werth, Eur. Phys. J. D. 26, 237-244 (2003)

Atomic Data for Neodymium (Nd) Atomic Number = 60 Atomic Weight = 144.24

Isotope Mass Abundance Spin

• Mag. Moment

142Nd

141.907719 27.13%

143Nd

142.909810 12.18% 7\2

• 1.08

144Nd

143.910083 23.80%

145Nd

144.912570 8.30% 7\2

• 0.66

146Nd

145.913113 17.19%

148Nd

147.916889 5.76%

150Nd

149.920889 5.64%

• Nd I Ground State (1s22s22p63s23p63d104s24p64d105s25p6) 4f46s2 5I4

Ionization energy 44562 cm-1 (5.5250 eV)

• Nd II Ground State (1s22s22p63s23p63d104s24p64d105s25p6) 4f46s 6I7/2

Ionization energy 86500 cm-1 (10.72 eV)

2 4 6 8 10 12 14

U0 ≅ 7-11 V

900 300 500 400 600 700 800

Amplitude of resonance circuit [mV] Time [s]

C A B

Amplitude of resonance circuit [a.u.]

↓

↓

↓

↓

↓

↓

↓

9,5 10,0 10,5 11,0 11,5 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0

Amplitude of resonance circuit [a.u.] Direct voltage [V]

DC voltage U0 [a.u.]

A- p=10-4 mbar B- p=3·10-5 mbar C- p=7·10-7 mbar

Observed electronic detection signal in Paul trap – mixed samples (Pr+Nd)

λ IS IS IS IS nm

142Nd – 144Nd 144Nd – 146Nd 146Nd – 148Nd 148Nd – 150Nd

1 422.772

• 678 (72)
• 680(100)
• 720 (170)
• 850 (150)

2 423.315

• 2640 (40)
• 2380 (40)
• 2840 (100)
• 4010 (150)

3 423.985

• 2619 (21)
• 2352 (23)
• 2732 (52)
• 3850 (100)

4 426.184

• 1025 (70)
• 955 (80)
• 990 (120)
• 1200 (120)

5 428.451

• 1443 (17)
• 1352 (21)
• 1440 (30)
• 1946 (63)

6 430.443

• 1957 (35)
• 1828 (45)
• 2050 (50)

7 431.334

• 1220 (80)
• 1122 (72)
• 1160 (120)
• 1862 (170)

8 431.436

• 1428 (26)
• 1374 (33)
• 1439 (50)
• 2022 (80)

9 432.793

• 817 (80)
• 740 (70)
• 800 (300)
• 900 (400)

10 445.639

• 1390 (40)
• 1306 (34)
• 1512 (52)
• 1619 (44)

11 450.658

• 745 (52)
• 748 (60)
• 761 (80)
• 780(100)

Values of isotope shifts between even isotopes

• f Nd II for the investigated spectral lines (all values in MHz).

0,25 0,30 0,35 0,40 0,45

• 4200
• 4000
• 3800
• 3600
• 3400
• 3200
• 3000
• 2800
• 2600
• 2400
• 2200

MRIS [MHz]

δ <r

2>M

King plot for the line λ 423.985 nm.

Experimental values of NMS, SMS and FS for selected lines

λ nm Isotope pair NMS MHz SMS MHz FS MHz 142,144 38.02

• 120
• 2540

144,146 36.99

• 100
• 2280

146,148 36.00

• 100
• 2700

423.985 148,150 35.04

• 110
• 3800

142,144 37.62

• 390
• 1090

144,146 36.61

• 380
• 1010

146,148 35.63

• 370
• 1120

428.451 148,150 34.68

• 360
• 1620

142,144 36.17

• 830
• 590

144,146 35.20

• 810
• 530

146,148 34.25

• 780
• 780

445.639 148,150 33.34

• 770
• 890

Atomic Data for Praseodymium (Pr) Atomic Number = 59 Atomic Weight = 140.90765

Isotope Mass Abundance Spin

• Mag. Moment

141Pr

140.907647 100% 5\2 +4.3

• Pr I Ground State (1s22s22p63s23p63d104s24p64d105s25p6) 4f36s2 4I°9/2

Ionization energy 44140 cm-1 (5.473 eV)

• Pr II Ground State

(1s22s22p63s23p63d104s24p64d105s25p6) 4f3 6s 4I°4 Ionization energy 85100 cm-1 (10.55 eV)

Transitions in Pr II investigated

Energy

1743.72 cm-1 22675.44 cm-1 22571.46 cm-1 22885.56 cm-1 23261.36 cm-1 24716.04 cm-1 0.00 cm-1

Even configurations Odd configurations

441.95 cm-1 1649.01 cm-1 2998.36 cm-1 23660.08 cm-1 23977.83 cm-1 24115.48 cm-1 25569.19 cm-1 3403.21 cm-1

Population of metastable levels in a Paul trap

100 % 0.00 cm-1 68 % 441.95 cm-1 11 % 1649.01 cm-1 1743.72 cm-1 9 % Level energy Relative population compared to the ground level

Coincidence of components belonging to two different spectral lines

20000 40000 60000

Intensity [a.u.]

127_276sr 124_276sr

W W µ µ 4 55

10000 20000 30000 40000 50000 Laser frequency detuning [GHz]

449.6456 nm 449.6329 nm P1 P5 P6

Signal intensity for selected components

20000 40000 60000 20 40 60 80 100 120 140

Laser power [µW] Intensity [a.u.]

P1 P5 P6

Partial transition scheme of Pr II

1743.72 cm-1 23977.83 cm-1 22675.44 cm-1 441.95 cm-1

3893.46 cm-1 4097.58 cm-1 7446.43 cm-1 0.00 cm-1

476.4127 nm

5226.52 cm-1 5108.40 cm-1 2998.36 cm-1 3403.21 cm-1 1649.01 cm-1 8489.87 cm-1

424.7631 nm 449.6456 nm 449.6329 nm

Coincidence of components belonging to two different spectral lines

442.9254 nm

10000 20000 30000 40000 Laser frequency detuning [GHz]

5000 10000 15000 20000 Intensity [a.u.]

55miW 4miw

W W µ µ 4 55

442.9128 nm P1 P3 P6

Partial transition scheme of Pr II

25569.19 cm-1 (J = 7) 22571.46 cm-1 (J = 5) 2998.36 cm-1 (J = 7) 0.00 cm-1 (J = 4)

3893.46 cm-1 4097.58 cm-1

442.9128 nm

5108.40 cm-1

442.9254 nm

3403.21 cm-1 441.95 cm-1 5079.34 cm-1 9646.62 cm-1 6413.93 cm-1 6417.83 cm-1

∆J

Chair of Atomic Physics, Poznań University of Technology - staff

• prof. E. Stachowska (E) (C)
• prof. J. Dembczyński (C)
• prof. B. Arcimowicz (E)

dr D. Stefańska (E) dr G. Szawioła (E)(C)

• Ms. M. Andrzejewska (E)
• Ms. Wł. Kowalkiewicz (E)
• Ms. K. Potocki (E)
• Ms. A. Walaszyk (E)

(E) – experiment (C) – semi-empirical calculation

dr A. Buczek (E) dr M. Elantkowska (C) dr B. Furmann (E) dr A. Jarosz (E) dr W. Koczorowski (E) dr A. Krzykowski (E) dr J. Ruczkowski (C)

Berlin