Accurate determination of ground state hyperfine structures of some radioactive alkali isotopes by r. f. magnetic resonance and laser optical pumping

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Accurate determination of ground state hyperfine

structures of some radioactive alkali isotopes by r. f.

magnetic resonance and laser optical pumping

H.T. Duong, S. Liberman, J. Pinard, A. Coc, C. Thibault, F. Touchard, M.

Carré, J. Lermé, J.L. Vialle, P. Juncar, et al.

To cite this version:

Accurate determination of

_ground

state

_hyperfine

structures

of

some

radioactive alkali

_{isotopes by}

r. f.

_magnetic

resonance

and laser

optical

pumping

H. T.

_Duong,

S.

Liberman,

J.

_Pinard,

A. Coc

_(*),

C. Thibault

_{(*), F.}

Touchard

_(*),

M. Carré

_(**),

J. Lermé

_(**),

J. L. Vialle

_(**),

P. Juncar

_(°),

S.

_Büttgenbach

_{(..) ,}

_{(°°), A.}

Pesnelle

_(+),

and the ISOLDE Collaboration

_(++).

Laboratoire Aimé Cotton

_{(.) ,}

CNRS II, Bâtiment _505, F-91405

Orsay

Cedex, France

(*)

Laboratoire René-Bernas du

_CSNSM,

B.P. 1, F-91406

Orsay

Cedex, France

(**)

Laboratoire de

_{Spectrométrie Ionique}

et _{Moléculaire,} Université de

_Lyon

I,

F-69622 Villeurbanne Cedex, France

(°)

Institut National de

_Métrologie

du CNAM, 292, rue _{St-Martin, F-75141,} Paris Cedex 03, France

(°°)

Institut für

_{Angewandte Physik,}

Universität Bonn, D-5300 Bonn, F.R.G.

(+ )

Service de

_Physique

des Atomes et des Surfaces, CEN

_Saclay,

F-91191 Gif-sur-Yvette Cedex, France

(+ + )

CERN, CH-1211 Genève _23, Switzerland

(Requ

le 27 mai _1986,

_accept6

le 21

_{juillet 1986)}

Résumé. - Les structures

hyperfines

de l’ état fondamental de

_{76,17 ,82,84mRb,}

140Cs et 226Fr

ont été mesurées avec

précision

par une méthode associant la résonance

_magnétique

et _{le pompage}

_optique

laser. Par _rapport aux

techniques

purement

optiques

la

_précision

des mesures est _{améliorée par trois ordres de}

_grandeur.

Les _spectres obtenus pour

l’isotope

le moins

_{abondant ( 76 Rb)}

donnent une bonne idée de la sensibilité du _montage. La

comparaison

en terme de _{sensibilité,} avec le

_{dispositif classique}

de Rabi est en faveur de la méthode

_présente.

Abstract. - The

ground

state

_hyperfine

structures of

76,77,82,84mRb,

140Cs

and

226Fr

have been

_accurately

measured

_by

an atomic beam

magnetic

resonance method associated with laser

_{optical pumping.}

In

comparison

with the

_{purely optical}

methods a

_gain

_{in accuracy of three orders of}

_magnitude

is achieved.

Spectra

obtained for the least abundant

_isotope

_(76Rb)

_give

a

_good

estimate of the

_sensitivity

of the set _up,

which is

favourably

compared

to the one obtained with classical ABMR

_Apparatus.

Classification

Physics

Abstracts 32.30-35.10

1. Introduction.

Since the first

_experiment

in 1975

_[1]

_high

resolution laser

_spectroscopy

on thermal beams associated with a _{very sensitive}

_magnetic

detection has

proved

to be a fruitful method for the

_{investigation}

of nuclear

properties

on

_long

series of radioactive alkali isoto-pes.

_Isotope

shifts

(I.S.)

and

hyperfine

constants been measured

_{by optical}

_spectroscopy

with an accuracy of a few

MHz,

even 1 MHz in the best

cases, for

Na, K, Rb,

Cs and Fr

_{[2-6] isotopic}

sequences.

Concerning

the

_hyperfine

constants, it is well known that

_{radiofrequency techniques}

may lead to

(’ )

Laboratoire associd a l’Université Paris Sud.

( )

Present address :

_{Forschungsinstitft}

_FFMU, Breit-scheidstratie 2b, D-7000

_Stuttgart

1.

more accurate determinations than

_optical

spectros-copy. For the excited state

hyperfine

constants, the

natural lifetime limits the

_gain

_{in accuracy but for the}

hyperfine

structure of the

_ground

state the

_frequency

width of the resonances is

_only

_governed

_by

the interaction time. Precisions better than 1 Hz have been

_reported

_{[7, 8]}

and an _{accuracy of} a few kHz is

easily

achievable.

_Therefore,

we can

_get

a

gain

in accuracy

by

three orders of

_magnitude

for the determination of the A

_2Sln

_hyperfine

constants

by

performing

an additional r.f.

_magnetic

resonance

experiment.

This has been demonstrated on the

43K

and

44K

_isotopes

_[9].

We

_report

here on a similar

experiment

performed

on

_Rb,

Cs and Fr

_isotopes

in

parallel

with laser

_optical

_spectroscopy

_experiments

[10], [6].

Due to the

_frequency

limitation of the available

_r.’f.

excitation

_{(« 2}

GHz in our

case)

_only

six

_isotopes

have been studied. The least abundant

one

(76Rb )

provides

a

_good

test of the

_sensitivity

of the method.

1904

2.

_Principle

of the

_experiment.

The

_principle

of the laser r.f.

_spectroscopy

experi-ment has been

_{extensively explained}

in a

_previous

paper

[9]

and we shall recall it

_{only briefly.}

A thermal atomic beam of the studied

_isotope

interacts at a

_{right angle}

with the

_light

beam

delivered

_by

a c.w. tunable

_single

mode

_dye

laser in the _{presence of} a weak static

_magnetic

field

Ho (see Fig. 1).

At _resonance,

_{optical hyperfine}

pumping

modifies the relative

_populations

of the

ground

state

_magnetic

substates

_{(F, mp ).}

These

population

changes

are

_analysed

_by

a

_sixpole

_magnet

which focusses the atoms with _mJ = ₊ 1/2 and defo-cusses those with _mJ = - 1/2. The focussed atoms are

_ionized,

mass

_separated

and counted

(see Figs. 1

and 2 in Ref.

_[4]).

When the laser

_frequency

is

scanned,

the

_optical

resonances _appear as

_negative

or

_positive

_peaks

on a mean ion beam

_intensity

according

to whether the

_{optical pumping}

_process

increases or decreases the number of focussed atoms. One can

_get,

this way, a first determination of the

_{hyperfine ground}

state

_splitting

with an accuracy of a few MHz

_owing

to the residual

Doppler

width of the observed

_optical

transitions

(typically 30 MHz)

and to the

_precision

and

the

reliability

of the laser

_frequency

control ensured

_by

the

_sigmameter

_[11].

The laser

_frequency

_is

then locked on an atomic transition

_{corresponding}

to a

_{negative peak}

and the

laser

_light

is u -

_polarized

with

_respect

to

_Ho

in order to maximize the

_amplitude

of this

_peak.

Downstream

from the laser interaction

_region

and before

_they

enter the

_sixpole

_magnet,

the

_{optically pumped}

atoms interact with a r.f.

_magnetic

field. When its

frequency

is resonant with an allowed

_magnetic

transition between two Zeeman

_sublevels,

the inte-raction tends to

_equalize

the

_population

of the two involved sublevels and the detected ion

_signal

increa-ses

_again.

It is then

_possible

to observe the

_following

high-frequency

magnetic

transitions

with

_AmF

= _± 1 if

Ho

and the r.f. field are

perpendi-cular,

AmF

= 0 if

they

_are

parallel.

Finally

the

hyperfine splitting

in zero field

is

_easily

deduced from the measured

_frequencies

of the observed transitions.

Fig.

1. -

Experimental

set-up.

Table I. -

Measured ground

state

_hyperfine

constants.

3. The

_experimental

set-up.

The

_apparatus

is

_{approximately}

the same as the one used for

_optical

laser

_spectroscopy

and we will go into more details

_only

for the

_particular

modifica-tions introduced for this r.f.

_spectroscopy

experi-ment. The studied radioactive

_isotopes

are

_produced

and

_separated

in mass

_by

the ISOLDE on line

facility

at CERN.

A detailed

_description

_{of the atomic beam} appara-tus and of the data

_acquisition

system

is

_given

in

references

_[4]

and

_[12].

Informations

_concerning

the

production

yields

of the radioactive

_isotopes

and the

dye

laser

_system

to be used for each element can be found in references

_[4-6]

for

_respectively

the

rubi-dium,

caesium and francium

_isotopes.

The interaction

_region

has been

_slightly

modified since the first r.f.

_experiment

on

_{potassium isotopes}

[9].

It is shown

_{schematically}

in

_figure

2a. The r.f.

electromagnetic

wave

_propagates

in a 50 fl coaxial

line,

the section of which

_{changes progressively}

from

a circular

_shape

(usual

r.f.

cable)

to a

_rectangular

one and

_again

to a circular one

(see

_{Fig. 2b).}

The atomic beam intersects this r.f. line at a

_right

_angle

in its central

_part

where the external conductor

_presents

a

_rectangular

section and the internal one is a flat metallic

_plate.

The sizes of these conductors are

calculated so that the

impedance

of the line remains

everywhere approximately

50 SI. At the end of the coaxial

line,

a 50 fl load absorbs the r.f. wave. Therefore the r.f. wave

_interacting

with the atoms is a

_travelling

one and the r.f.

_magnetic

field

_strength

seen

_by

the atoms

_depends

_only

on the r.f. power delivered

_by

the

_generator

_(no

resonance effects due to the

_length

of the coaxial

_line).

Moreover,

since the r.f.

_travelling

wave

_propagates

_{perpendicularly}

to the atomic

beam,

any

Doppler

shift of the resonances is avoided.

The r.f. wave is

produced by

a commercial r.f.

0.4-Fig.

2. - Schematic view of the interaction

region

(a)

and

of the r.f. line

_(b).

1 040

_MHz)

followed

_by

a

_frequency

doubler and a linear wide band

_{amplifier (2}

_W,

0.4-2

_GHz).

A 2 W r.f. power,

continuously

tunable up to 2

_GHz,

is then available.

Two Helmholtz coils

_produce

a static

_magnetic

field

_Hc

_parallel

to the x’x direction of the laser beam.

_Hc

is

_roughly

_homogeneous

over the interac-tion zones with the laser field and the r.f. field.

A

_magnetic

shield of Armco iron and

_mu-metal.

sheets surrounds the whole interaction zone. In order to avoid non adiabatic transitions for the

optically pumped

atoms one has to _preserve a weak

magnetic

stray

field from the

_sixpole

_magnet

_[12].

For this reason, a

sufficiently large

hole is bored

through

the

_magnetic

shield in front of the entrance of the

_sixpole

_magnet.

This

_stray

field

_{Hs points}

approximately parallel

to the atomic beam

_(y’y

direction) ;

its

_amplitude

over the r.f. coaxial line is

relatively

weak

_(typically

0.4

_G)

and

_strongly

inho-mogeneous.

4. Observed resonances and line

_shapes.

The observable resonances

_depend

on the rela1ive orientation of the static and r.f.

_magnetic

fields seen

by

the atoms. The total static

_magnetic

field is

Ho

=

Hc

₊

H,.

When the d.c. current in the Helm-holtz coils is

_{high enough}

to

_get

_{Hc > Hs}

the static field is

_{roughly homogeneous}

and

_parallel

to the

x’x direction

_{(case a).}

When the coils are not

energi-zed the total static field is

_{strongly inhomogeneous}

and

_parallel

to the

_y’y

direction

_{(case b).}

Let H’ be the r.f.

_magnetic

field seen

_by

the atoms. In a first

approximation

we can consider that H’ is

_parallel

to the

_y’y

direction and the induced r.f.

_magnetic

transitions are the

_OmF

= _± 1

(respectively

I1mF

=

0)

for _{case a}

(respectively

case

_b).

If we enter into more

details,

since the r.f.

magnetic

field lines turn around the internal conduc-tor, the r.f. field H’ seen

_by

the atoms exhibits two

components

_Hy’

and

_H’

which are different from zero

(see Fig. 3).

The first one is an even function of the

position

of the atoms, the second one an odd

function.

As

_explained

above

_Hy

will induce some

_magnetic

transitions

_(AmF

= ± 1 in case a or

_I1mF

= 0 in case

_b)

but

_Hx

will induce the other ones

_(AMF

= 0 in case a and

_OmF

= _± 1 in _case

b) ;

this

requires,

of

course, a

_higher

_{r.f. power due} to the low

_amplitude

of

_Hx

_compared

to

_Hy.

Moreover,

it is clear in

_figure

3 that

_Hx

is confined

in two

_separated

zones at the entrance and the exit of the r.f. line on the atomic

_path.

The atoms of the beam interact

_successively

with the r.f.

_magnetic

field of these two zones : this

geometry

is similar to the one used in

_Ramsey

fringes

technique [13].

But one has to notice that in our case the

_sign

of

_H’

_changes

between the two zones

_{corresponding}

to a difference in

_phase

of w for the two r.f. fields

_successively

seen

_by

the atoms. For this reason one

_expects

that the resonance curve will

present

a minimum at the exact resonance

_frequency.

Fig.

3. -

1906

Fig.

4. - Zeeman

splitting

of the AF = 1

_hyperfine

transition for

14OCs.

_Recordings

a and b have been

obtained for

_{H, .> H.,}

_{(case a)}

and

_He

= 0

_{(case b) (see}

text).

For both

_recordings

the

_frequency

scale is 10

_kHz/step.

Fig.

5. -

High

resolution

_recordings

_(frequency

_{step :}

2

_kHz)

of the central resonance curve

_{corresponding}

to the first order field

_independent

unresolved doublet for

14OCs.

As in

_{figure 3}

_recordings

a and b

_correspond

respectively

to case a and b for the static field

_{(see text).}

Notice, in the b

_recording,

the _strong

_dip

at the center of

the resonance.

Figures

4 and 5

_present

the

_experimental

curves

obtained for

14OCs

_{(I = 1)}

with a static field

corres-ponding

either to cases a or b. The

expected

structures have been observed. The whole Zeeman

splitting

of the AF = 1

_hyperfine

transition has been first recorded at

_relatively

low resolution with a

frequency

step

of 10 kHz

_{(Figs. 4a}

and

_b):

The relative intensities of the

_AmF

= 0 and

_AmF=±’

components

are coherent with the

_explanations

given

above. The resonances the

_frequency

of which are first order field

_dependent

are broadened due to the

_{inhomogeneities}

of the static field

_particularly

in case b. For these transitions the line

_shapes

are linked in a

_complicated

_way to the field

inhomoge-neities

_[13],

and no

_attempt

has been done to

_analyse

them

_precisely.

On the other

_hand,

one resonance is

_only

second order field

_dependent.

For the case of

’4oCs

_(even

isotope),

it is an unresolved doublet of two

AMF

= _± 1 transitions

and

For this resonance,

recordings

obtained at

_high

resolution with a

_frequency

_step

of 2 kHz are

displayed

in the

_figure

5a and b. The

_frequency

width of the first

_recording

_{(30 kHz)}

is not far from the limit value deduced from the interaction time

(-

20

_kHz).

The second

_recording,

obtained in case

b,

exhibits a

_strong

_dip,

as

_{expected, just}

at the center of the resonance.

Finally

an

_important

_{remark may be made} on the

geometry

of the

_{set-up :}

the r.f. field H’ seen

_by

the atoms does not turn around the static field

_Ho,

it remains in the xy

plane

(see

Fig.

3).

This eliminates the

_possibility

of a

_systematic

error in the determina-tion of the resonance

_frequency

due to the Millmann effect

_{[13, 14].}

5.

_Experimental

_procedure.

In order to determine the

_hyperfine

_splitting

of the

ground

state with a

_high

_{accuracy the}

_following

_steps

have been

_successively

_performed.

An

_approximate

value of the

_hyperfine

structure is first

_{given by}

laser

_spectroscopy

to within an _accuracy of a few MHz. Then the static field is set to

Ho

=

H,

(no

current in the

_coils)

and the r.f.

experiment

is

_performed.

Since the resonance are broadened

_by

the field

_{inhomogeneities}

the r.f.

frequency

increment may be chosen

relatively large

(typically

20

_kHz)

which is time

_saving.

When this low resolution

spectrum

of the Zeeman

splitting

is

_obtained,

the field

_independent

compo-nent is searched in the center of this

_splitting.

_High

resolution

_spectra

_(typically

1 kHz

_increment)

of this

resonance are recorded for one or several values of

Ho.

One has to choose

_Ho

=

Hs (case b)

for odd

isotopes

since the involved transition is a

_AmF

= 0

one, and

_{Ho > H, (case a)}

for even

_isotopes

OmF

= _± 1

doublet .

In order to

_get

the

_hyperfine

structure in zero field from the measured

_frequency

of the transition one has to take into account the second order correction calculated from the usual Breit-Rabi formula

_[13].

The static field

_Ho

is known either from the current in the coils

_owing

to a

whole Zeeman

_splitting

in the same field

_{Ho [9].}

In any case this correction is

_always

small

_(less

than 20

_kHz).

6. Rdsults and discussion.

According

to the

_frequency

limitation of our r.f. set up the

experiment

has been carried out

only

for

76Rb, 77Rb, 82Rb, 84Rbm,

14OCs

and

_22,6Fr,

for which the

_hyperfine

structures are smaller than 2 GHz.

Taking

into account the second order

_correction,

the deduced values of the

_hyperfine

structures are

gathered

in table I. For

_14OCs,

84Rbm

two

_independent

measurements have been done with different static fields and the results differ

_by

less than 1 kHz. We

therefore

_adopted

a 2 kHz error bar. For

76Rb, 77Rb,

82Rb

and

_{226Fr only}

one

_high

resolution

spectrum

has been recorded. The

_{quoted uncertainty}

is _{increased up} to 3 kHz in the case of

82 Rb

and

226Fr

and up to 4 kHz in the case of

76 Rb

and

77Rb

for which the resonances are

_slightly

broader

(-

50

kHz)

and noisier.

Previous results obtained

_by

laser

_spectroscopy

are also collected in table I. The very

precise

values

obtained here are

always

coherent with these results from

_optical

_{spectroscopy.}

This is a

convincing

test of the

_reliability

of the error bars

_quoted

in our

previous

laser

_spectroscopy

_experiments

_[4-6].

An estimate of the

_sensitivity

of the

_set-up

has been

_given

in a

previous

_paper

[9].

The results obtained here allow us to be more

_explicit

about this

point.

A

_recording

of the resonance curve obtained for

76 Rb

is

_displayed

in

_figure

6. We are

_clearly

far above the limit of

_sensitivity.

The

_{production yield}

Fig.

6. -

High

resolution

_recording

of the central reso-nance obtained for the least abundant

_isotope

_studied,

76 Rb,

(frequency

scale : 4

_kHz/step).

for this

_{isotope being}

2 x

106

atoms

S-1

_[4]

the limit of

_sensitivity

is

_certainly

below

106

atoms

s- 1.

The

sensitivity

of the

_{present set-up}

is therefore

_higher

than the best one obtained in classical ABMR

technique [15].

In

_conclusion,

it is

_important

to

emphasize

that as far as nuclear

_magnetic

moments could be very

precisely

determined in the future for

long

radioactive _sequences, the

_present

_method,

owing

to its extreme _{accuracy and}

_sensitivity,

would be

_{fully adapted}

in

_determining

_hyperfine

anomalies.

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[2]

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