in-source photoionization spectroscopy: methods of data analysis

In-Source Photoionization Spectroscopy: Methods of data analysis

M.D. Seliverstov

20-22 February 2013 CERN

1st LA³NET Topical Workshop on Laser Based Particle Sources

[email protected]

Contents:

Resonant photoionization in-source spectroscopy: advantages and limitationsGeneral problems of data analysis (isotopes with I = 0)

Correction to the laser power Laser lineshape asymmetry

Isotopes with I > 0: hyperfine splitting Relative intensities of hfs lines Saturation hfs levels population redistribution

Conclusions and outlook

1st LA³NET Topical Workshop on Laser Based Particle Sources, 20-22 February 2013, CERN

3

Resonant photoionization in-source spectroscopy

Isotope shift dnA,A’

dnA,A’ = F lA,A’ + MS

Rms charge radius

lA,A’ = dr 2A,A’ + C2dr 4A,A’ + … = 0.93 dr2 A,A’

Relative line position hyperfine constants A & B mI, QS

For 208Pb at TLIS = 2000K:D = 2.4 GHz (FWHM) dnA,A+1 = 1 GHz

For Pb isotope chain:

Doppler limitation:

mkT

cD

2ln80


Laser linewidth about 1 GHz

4

-15 -10 -5 0 5 100

2000

Frequency detuning, GHz

188Pb

0

4000

8000

Co

un

ts

186Pb

0

400

800

1200

1600

184Pb

0

20

40

60

182Pb

11853.2 11853.4 11853.6 11853.8 11854.00

50

100

Wavenumber, cm-1

192Po

0.0

0.5

1.0

194Po

0

50000

196Po

0

2000

4000

198Po

0

2000

4000200Po

0

10000

20000

202Po

0

1000

2000204Po

0.0

0.2

0.4206Po

0.0

0.4

0.8208Po

0.00.20.40.6

210Po

0

400

800216Po

0500

10001500

218Po

io

n cu

rrent

Spectra of even-A isotopes of Pb and Po


Resonant photoionization in-source spectroscopy

5

Fitting function


001 ''')( CdvvvIvNCvN LGi

The simplest case:

General form:

(Voigt profile)

0'

01 ''')( CdvvvIPvNCvN Li

Gi

'' '' vvIkvvIP LLi

'' vvI L

Saturation is possible

Laser lineshape can be an asymmetrical function

6

Asymmetry of the fitting function

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.50.0

0.2

0.4

0.6

0.8

1.0

Lorentzian fit Deformed-Lorentzian fit, k

A = 0.13

Am

litu

de,

a.u

.

Frequency detuning , GHz


220 )2/()(

2/)(

vv

vL

“standard” Lorentzian:

“deformed” Lorentzian:

0

0

'),1('

'),1('),'()(

vvkvv

vvkvvvLvL

a

a

7

Additional correction to asymmetry of the lineshape

0 1000 2000 3000 4000 5000 6000-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

"standard" fitting fitting with CG-correction

dri

ft o

f m

easu

red

0 (

20

8 Pb

), G

Hz

Time, min


8

Correction to the laser power

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.0

0.1

0.2

0.3

0.4

0.5

0.6

208 P

b io

n c

urr

en

t., a

.u.

first step laser power (UV), a.u.

Working area


Optical transition saturation

9

Saturation broadening

-10 -5 0 5 100.0

0.5

1.0

208 P

b io

n c

urr

en

t, n

orm

aliz

ed

1st step frequency (UV), GHz

full power reduced power (~5%)


10

Saturation + desynchronization of the laser pulses

0.0 0.5 1.0 1.50.0

0.1

0.2

0.3

0.4

0.5

208 P

b io

n c

ur.

, a.u

.

first step laser power (UV), a.u.


Dye lasers withCVL pumping

Dye lasers withNd:YAG pumping:No timing problems

Ti:Sa – timingproblems again

Corrections for desynchronization

0

5000

10000

15000

20000

-

cou

nts

186Pb

0011 0021 0031 0041 0051 0061 --0.0

0.5

1.0

1.5

lase

r p

ow

er ,

a.u

.

Point number

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00

2000

4000

6000

8000

10000

12000

14000

-co

un

ts

laser power (1st step)


Corrections for desynchronization

-6 -4 -2 0 2 40

2000

4000

6000

8000

10000

-co

un

ts


corrected raw data


13

Hyperfine splitting (hfs)

6p8p 3D2

IP = 59819.4 cm-1

6p2 3P0

Ground state

6p7s

Continuum

= 283.305 nm

= 600.186 nm

= 510.554 nm and 578.213 nm

Ip = 13/2+ I = 3/2-

F = 11/2

13/2

15/2

1/2

3/2

5/2

Hyperfine splitting

F = I + J

o

1

3P

Photoionization scheme for Pb



-20 -10 0 10 200

2000

4000

6000

cou

nts


189Pb I = 13/2 I = 3/2

0

500

1000

1500

187Pb I = 13/2 I = 3/2

0

500

1000

185Pb I = 13/2 I = 3/2

0

200

400

600

800

183Pb I = 13/2 I = 3/2




Photoionization scheme for Po


Position of the hfs lines:

Relative intensities (simplified form):



-20 -15 -10 -5 0 50

2000

0

20

40 193Po, I = (3/2)

0

10000

195Po, I = (3/2)

0

1000

197Po, I = (3/2)

0

500

1000

199Po, I =(3/2)

0.000.020.04

201Po, I = 3/2

0.00

0.02

Frequency detuning (GHz)

203Po, I = 5/2

0.0

0.3

0.6

209Po, I = 1/2

ion

cu

rre

nt

(a.u

.)

211Po, I = 9/2

0

10

20

0

300

0

10000

20000

0

10000

0

5000

0.00

0.05

-20 -15 -10 -5 0 50.00

0.02

191Po, I = (11/2)

ion

cu

rren

t (a

.u.)

193Po, I = (13/2)

195Po, I = (13/2)

197Po, I = (13/2)

201Po, I = 13/2

199Po, I = (13/2)

203Po, I = 13/2

Frequency detuning (GHz)


Rate equations

To take into account the saturation of transitions, pumping processes between hyperfine structure (hfs) components and a population redistribution of the hfs levels the number of photoions Nion for each frequency step was calculated by solving the rate equations for the given photoionization scheme:

0'

01 ''')( CdvvvIPvNCvN Li

Gi

)12/(),'(~ '*

''*

'' FSSvvvISW FFFFFF

FFFF

At t = 0:


Rate equations

ionizationNion

F1

F2

F0

F’1

F’2

F’0

F’’1

F’’2

F’’0

NF

N’F’

N’’F’’

.... dtNWdN Fionion""

W F’F’’ W F’’ F’

W ion

W FF’ W F’F

...

...)(

''''

'"

dtWN

dtWWNdN

FFF

FFionFF

'

""

""

dtWNWN

dtWWNdN

FFFFFF

FFFFFF

...)(

...)(

''"''

''''

''

''

''

dtWN

dtWNdN

FFF

FFFF

...)(

...)(

''

'

'

12

1'2

'

'

F

F

W

W

FF

FF


King plot for Po isotopes

King plot for Po atomic transitions 843 nm (our data) and 255 nm.

200–210Po

0 20000 40000 60000 800000

-10000

-20000

-30000

-40000

Mo

dif

ied

iso

top

e sh

ift

A,A'

843

Modified isotope shift A,A'255


Charge radii of Po isotopes


Rate equations for the polarized light

MF’ -3/2 -1/2 1/2 3/2

F = 1/2 F’ = 3/2

MF -1/2 1/2


Q = MF – M’F

Rate equations for the polarized light

MF’ -3/2 -1/2 1/2 3/2

F = 1/2 F’ = 3/2

MF -1/2 1/2


Q = MF – M’F

Linear polarization

Universal fitting program


Conclusions

The laser ion source is not only a very effective in its normal use as an element-selective tool for producing intense ion beams, but it can be used as a very powerful atomic-spectroscopy tool due to the resonance character of the photoionization (In-Source Laser Resonant Photoionization Spectroscopy). In contrast to other laser spectroscopic techniques, in that case the laser frequency scanning procedure is applied directly within the mass-separator ion source. The main advantage of this technique is its very high sensitivity, nevertheless its spectral resolution is Doppler-limited, therefore the accurate data analysis is of great importance.

Thanks for your attention!


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