Ground state hyperfine structures of 43K and 44K measured by atomic beam magnetic resonance coupled with laser optical pumping

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Submitted on 1 Jan 1982

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Ground state hyperfine structures of 43K and 44K

measured by atomic beam magnetic resonance coupled

with laser optical pumping

H.T. Duong, P. Juncar, S. Liberman, J. Pinard, J.L. Vialle, S. Büttgenbach,

P. Guimbal, M. de Saint Simon, J.M. Serre, C. Thibault, et al.

To cite this version:

Ground

state

_hyperfine

structures

of

43K

and

44K

measured

by

atomic

beam

_magnetic

resonance

_coupled

with laser

_optical

_pumping

H. T.

_Duong,

P.

_Juncar,

S.

_Liberman,

J.

Pinard,

J. L. Vialle

Laboratoire Aimé-Cotton _(*), C.N.R.S. II, Bât. 505, 91405 _Orsay, France

S.

_{Büttgenbach (**),}

P.

_Guimbal,

M. de Saint

_Simon,

J. M.

_Serre,

C.

_Thibault,

F. Touchard and R.

Klapisch

Laboratoire René-Bernas du Centre de _{Spectrométrie} Nucléaire et de

_{Spectrométrie}

de _Masse, 91406 _Orsay, France

(Reçu le 12 novembre 1981, accepté le 24 novembre 1981)

Résumé. 2014 Les structures

hyperfines

de l’état fondamental de 43K et 44K ont _{été mesurées par} une méthode de

résonance

_magnétique

sur

_{jet atomique}

dans

_laquelle

les

_spins

_atomiques

sont orientés par pompage

optique

laser. Les résultats

_{spectroscopiques}

sont les suivants :

039403BD43(2S1/2)

= 192,648 4 (30) MHz _et

0394v44(2S1/2) = -

946,718 (3) MHz.

La sensibilité de notre méthode est _comparée à celle obtenue avec un

_{appareil correspondant}

au

_dispositif

_classique

de Rabi.

Abstract. 2014 The

ground

state

_hyperfine

structures of 43 K and 44K have been measured

_by

an _{atomic beam}

magne-tic resonance method in which the atoms are

spin-polarized by

laser

optical

pumping. The

spectroscopic

results are :

0394v43(2S1/2)

= 192.648 4 (30) MHz and

039403BD44(2S1/2) = -

946.718 (3) MHz. The

sensitivity

of _our method is

compared

to the one achieved in classical ABMR apparatus.

Classification

Physics Abstracts 32.20B - 35.IOF

1. Introduction. -

High

resolution laser

spectros-copy on

_long

series of

_isotopes

has shown to be a _very

fruitful method for the

_{investigation}

of nuclei proper-ties

_[1-3].

A wealth of data has been obtained in this way

for Na

_[4],

Rb

_[5],

Cs

_[6],

Fr

_[7]

and _very

_recently

for K

isotopes [8]. Isotope

shifts

_(I.S.),

nuclear

_spins

_(7),

hyperfine

constants of the

_ground

state

_[A(2S,,2)]

as well as of the excited states

_{[A(2P 1/2)’ A(2p 3/2)’}

B(2 P3/2)]

have been determined

_{by optical}

spectro-scopy, with an _accuracy of a few

_MHz,

even 1 MHz in the best cases.

In a recent

_{experiment [9]}

on the

_D1

and

_D2

lines

of

39,40,41K

_using

well collimated atomic beams and modulated laser

_light,

an _{accuracy and} a

repro-ducibility

of a few hundred kHz for the

frequency

intervals measurements have been obtained. This is

comparable

to the usual

_{precision given by}

radio-(*) Laboratoire associé a l’Universit& Paris-Sud.

(**) Permanent address : University of Bonn,

D-5300,

Bonn.

frequency

methods for the same excited states

_(optical

double resonance and level

_{crossing) [l0-12].}

On the other

_hand,

for the

_hyperfine

structure of the

ground

state, it is well known that the r.f.

_spectroscopy

[13]

leads to much more accurate measurements than the

_optical

_{spectroscopy :}

the levels involved in the r.f. transitions are

_hyperfine

sublevels of the

_ground

state; the

_frequency

width of the resonances is then

only

limited

_by

the interaction time. With

_{sophisticated}

techniques, precisions

better than 1 Hz have been

reported [14,15]

and it is

_possible,

without

_special

_care,

to

_get

an _accuracy of a few kHz which is

_already

three

orders of

_magnitude

better than that obtained in

optical

laser

_{spectroscopy.}

In the

_present

_paper we _report on an r.f.

_magnetic

resonance

_experiment

on radioactive

_potassium

iso-topes

performed during

the laser

_optical

_spectroscopy

experiment quoted

above and

_using

the same

appa-ratus. As a test of the _accuracy obtained with this

experimental

set-up,

the well known h.f.s. of

45K

and

2°Na

have been measured. Then the h.t:s. of

43K

and

44K

have been determined The h.t:s. of other

510

isotopes

have not been studied in this _way because of the

_frequency

limitation of the r.f.

_{amplifier (1}

_GHz).

2.

_Principle

of the

_experiment.

- The

principle

of the laser

_spectroscopy

_experiment

has been

_extensively

explained

in

_previous

_papers

_[4,

_5,16].

In

_brief,

a ther-mal atomic beam of

_potassium

interacts at

_{right angle}

with the

_light

beam from a C.W. tunable

_single

mode

dye

laser

_{(see Fig.}

_la)

in the _presence of a weak static

magnetic

field

_Ho,

which defines the

_quantization

axis,

parallel

to the laser beam. At

_optical

resonance with one of the

hyperfine

_components

of the

_D1

line

the laser

_light

induces an

_optical

pumping

which

changes

the

_population

distribution between the

magnetic

substates

_{(F, mF)}

of the

_ground

state. These

population changes

are

_{analysed by}

a

sixpole

_magnet,

which focusses the atoms

_{corresponding}

to _{mj =}

_{+ 1/2}

and defocusses those

_{corresponding}

to

_{mj = - 1/2 [16].}

After the

_sixpole

_magnet,

the focussed atoms of the beam are

ionized,

mass

separated

and counted. When the laser

_frequency

is

scanned,

the

_optical

resonances

appear as

positive

or

negative peaks

on a baseline ion

_signal.

One can obtain in this _way a first

deter-mination of the

_{hyperfine ground}

state

_splitting

with an _accuracy of a few MHz.

Moreover,

the

sign

of the

nuclear

_magnetic

moment can be deduced from the relative intensities of the four components of the

hyperfine

structure.

Fig.

1. -

a)

Principle

of the

_experiment;

b) Schematic view of the interaction

_region.

Let us now _{suppose that the laser}

frequency

is

locked on the

frequency

of the atomic transition

giving

the

_strongest

negative peak,

i.e. for an

_isotope

with

_positive

nuclear

_magnetic

moment

or in the case of

_negative

nuclear

_magnetic

moment

The laser

_light

beam is 6-

_polarized

with _respect to

Ho.

Under these

_conditions,

the detected atomic beam

_intensity

is

_strongly

reduced

_since,

_{by optical}

pumping,

the atoms are transferred from the focussed

F = I ₊

1/f

(or

F = I -

1/2

for

III

0)

state to the

defocussed state F = I -

1/2 (or

F = I ₊

1/2

for

,ul

0).

Between the interaction

region

with the laser

light

and the

_sixpole

_magnet,

a r.f

_magnetic

field

_given

by

a r.£

loop

is

applied

to the

_{optically pumped}

atoms

(Fig. la).

When the r.f

_frequency

is set

_equal

to the

frequency

of an allowed

magnetic

transition between

two Zeeman sublevels of the two

_ground

state

hyper-fine

levels,

the r.f.

_magnetic

field tends to

_equalize

the

_populations

of the involved

sublevels,

so that the observed

_signal

increases

_again.

Since

_Ho

is

_known,

the

_hyperfine

interval in zero field can be deduced from the

_frequencies

of the observed

_magnetic

transi-tions F = I -

1/2,

MF +-+ F = I ₊

1/2,

MF +

_AMF

where :

AMF

= ₊ 1 if the r.f. field is

perpendicular

_to

Ho.

AMF

= 0 if the r.f. field is

_parallel

to

_Ho.

The

_only

difference between the method described above and the ABMR method introduced

_by

Rabi

_[13]

is that the atoms are

_{spin-polarized by}

laser interaction instead of

_magnetic

deflection in the A

_magnet.

Such a

possibility

of

_{replacing deflecting inhomogeneous}

magnetic

field

_{by optical pumping}

had been

_pointed

out _{several years ago}

_[17-19].

Moreover,

just

as in the

flop-in

geometry

in classical ABMR

_method,

_positive

signals

on a zero

background

could be

achieved,

provided

that the

_hyperfine

component

to be matched with the laser

_frequency

is

_suitably

chosen.

3.

_Apparatus.

- The

apparatus is almost the same

as the one used for

_previous

measurements on sodium

isotopes

and a detailed

_description

can be found in reference

_[4].

We

_report

here

_only

the

_specific

modi-fications introduced for this

_experiment.

A carbon and iridium

_powder

_target

is

_placed

inside

a

_high

_temperature

oven. When bombarded

by

the 20 GeV

_proton

beam from the

_proton

_synchrotron

(P.S.)

at

_C.E.R.N.,

_{the many}

_produced

_nuclei,

once

thermalized,

effuse from the oven and form an atomic beam

_(see

_Fig.

_{1 a).}

The laser

_system

consists in a

commercial C.W.

_single

mode

_dye

laser

_(CR

₅₉₉₎

pumped by

a Kr+ laser

(CR

3 000

_K).

Its

_frequency

is scanned

_step

_by

_step and servocontrolled

_by

a

wavelength

of the

_{potassium D1}

line

_(A

= 770

nm)

,is oxazine 750. One watt r.f. _power,

_continuously

tunable in the _range 10 MHz-1 GHz is delivered

_by

a commercial r.f. _generator

_(Rohde

and Schwartz SMS 0.4-1040

_MHz)

followed

_by

a linear wide band

ampli-fier.

Special

care has been taken in the

_design

of the interaction

_{region, schematically}

shown in

_figure

1 b. Two Helmholtz coils

_produce

a

_homogeneous

static

magnetic

field

_{He parallel}

to the laser beam while the r.f.

_magnetic

field is

_{produced by}

a

single-turn

_copper

loop

centred on the atomic beam and

_{perpendicular}

to it. Therefore the r.f.

_magnetic

field seen

_by

the

atoms is

_parallel

to the atomic beam direction. The whole interaction

_region

is surrounded

_by

a

_magnetic

shield made of Armco iron and mu-metal sheet. In the direction of the

_sixpole

_magnet

a hole is bored in this

shield,

with such a diameter that the

_magnetic

_stray

field from the

_sixpole

_magnet

is sufficient to avoid nonadiabatic transitions. This

_{inhomogeneous}

_stray

field

_Hs,

is very weak at the r.f. coil

_(typically

0.1

_G)

and

_{pointing approximately parallel}

to the atomic beam. The total static

_magnetic

field is

_Ho

_{=He + Hs ;}

for

_{H,, >>}

_{Hs it is}

_{approximately perpendicular}

to the

Fig. 2. - Zeeman

splitting

of the AF = 1

hyperfine

tran-sition for 45K. The

_recording

shown in the lower _part of the

figure

has been obtained with a static field _parallel to the r.f. field _{(see text).} Therefore resonances are observed

_only

for

the

_AMF

= 0 _components. Note that the central _resonance

is narrower than the two other ones which are broadened

due to the _strong

_{inhomogeneity}

of the static _magnetic field

atomic beam and

_homogeneous;

for

_He

= 0 it is

quite parallel

to the atomic beam and

_strongly

inho-mogeneous.

Figure

2

_presents

a

_recording

of the Zeeman

com-ponents

of the AF = 1 r.f. transition for

45K.

It has

been obtained without d.c. current in the Helmholtz coils and therefore the static

_magnetic

field

_Ho

is the

stray

field

_H,.

Since the r.£ field and

_Ha

are then

parallel, only

the

_AMF

= 0 _{resonances occur.}

Moreo-ver, the central resonance is narrower than the two

other ones because it is field

_independent

to first order while the two others are broadened due to the

_strong

inhomogeneity

of the static

_magnetic

field.

4.

_Experimental

_procedure.

- Several

operations

are

successively

carried out for

_measuring

the

_hyperfine

splitting

of the

_ground

state. First an

_approximate

value of this

_{hyperfine splitting}

is obtained

_by

laser

spectroscopy

together

with the

sign

of the nuclear

magnetic

moment as

_explained

in

_paragraph

2. Then the static field

_Hc

is set to a value in the _range

0.5-1 _gauss so that the

_amplitude

of

_Ho

is

_roughly

known.

_Ho

is

_nearly,

but not

_exactly,

perpendicular

to the atomic

_beam,

i.e. the direction of the r.f.

_magnetic

field. Therefore the

_AMF

= ± 1

resonances are

_easily

excited with low r.f. _power while for the

_DmF

= 0 _{resonances more} r.f

power must be

applied

to the

_{loop. Figure}

3

_presents

all the Zeeman

components

of the AF = 1 transition in the _case of

43 K

_{(7 =}

_3/2,

,ul >

_0).

All the

_{components, except}

(1,

-

1)

H

_(2,

-

2),

correspond

to a

_change

in _mj

and are then observable.

_Moreover,

these resonances are

approximately equidistant

and the

frequency

spacing, essentially

related to

_Ho,

is

_roughly

known. Such a situation is

time-saving

in the search of a first resonance because it

_permits

to reduce the

_frequency

range to be scanned When one

_component

has been found it becomes easy to record the other ones. All the

components

of the Zeeman

_splitting

of

43K

have been recorded

_although

this

_procedure

was not _necessary

because the

_hyperfine

structure of the

ground

state

was

_already

known with an _accuracy of 50 kHz

[21].

The result is shown on

figure

3. The same

_procedure

was

_repeated

for

44K.

It is well known in ABMR

technique

that one of the

components

is

_only

second order

_magnetic

field

dependent,

ie.

_(I

+

_{1/2, 0) +-+ (I - 1/2,}

0)

for the odd

isotopes

and the unresolved doublet

for the even

_{isotopes [22].}

The last

_step

of the

experi-mental

_procedure

is to

identify clearly

this _component and to

_precisely

measure its

frequency.

Since this

512

Fig. 3. - Zeeman

splitting

of the AF = 1 hyperfine transition in the _case of 43K (I = 3/2,

III > 0). All the Zeeman compo-nents, except (1, -

1) H _(2, -

2),

correspond

to a

_change

in _mf and are therefore observable. In the lower part of the

_figure

the

_frequency

scale is

_{strongly expanded}

for each recorded resonance.

5. Results and discussion. -

Figure

4

_presents

a

precise recording

of the first order field

_independent

doublet of

44K.

To

_get

the exact

_hyperfine

structure

in zero field one has to take into account the second order correction. An accurate value of the

_magnetic

field

amplitude

Ho

can be deduced

_by

a

_least-square

fit from the

_experimental

_frequency

_spacings

between the Zeeman

_components

of the r.f. transition. This fit

gives

Ho

= 0.704 G

(respectively

0.700

G)

for

43 K

(respectively

44K)

with an _accuracy better than 1

%.

Taking

into account this value of the

_magnetic

field

Ho

the second order correction is calculated for both

isotopes (-10

kHz for

43 K

and - 2 kHz for

_44K).

The deduced values of the

_ground

state

_hyperfine

structures are indicated in table I.

For

_43K,

our measurement is in _agreement with a

less

_precise

value

_quoted

in the literature

_[21].

Our 3 kHz error bar for

43 K

and

44K

is estimated from the

consistency

between several measurements of the same resonance. We have also measured the well known

hyperfine

structures of

45K

_[23]

and 2°

Na

_[24].

The 6 kHz error bar reflects the shorter time devoted to

these measurements. Our

_results,

_reported

in table

I,

are in _very

_good

_agreement with

_earlier,

more

_precise,

results.

As

_pointed

out, the _present method is

_comparable

to the classical ABMR method

_working

in the

_flop-in

arrangement.

Our _apparatus

_presents

the

_advantage

of

_simplicity

and its

_length

is

_greatly

reduced

_compared

to a classical ABMR

_{apparatus :}

the distance from the oven to the entrance of the

_sixpole

_magnet, which

corresponds

to the

_length

of the A and C

_regions

of an ABMR

_apparatus,

is

_only

seven centimeters

_(see

Never-Table I. - Measured

ground

state

hyperfine

structures.

Fig.

4. -

Typical recording

of the resonance curve

cor-responding

to the first order field

_independent

unresolved

doublet for 44K.

theless it is difficult to deduce from this

_experiment

our limit of

_sensitivity.

Production rates of

44K

and

4s K

were about 2.5 x

10’

atoms/proton

pulse (proton

pulse intensity:

1013

protons)

but

_they

do not

_represent

the lower limit

(see

the

_recording

of

4’K

on

figure 2).

Moreover the on-line

_{produced potassium isotopes}

were

unfavourable

cases for two reasons :

- For

43K

and

44K,

signals

were

_{perturbed by}

an

_{important background}

due to natural calcium isobars

_coming

from the heated ion source. This

background

has been subtracted on the

_recordings

but it contributes to the statistical noise.

- For

44K,

the nuclear

magnetic

moment is

negative;

this is unfavourable since it is then

_impossible

to

_optically

_pump all the atoms into defocussed states

and

_therefore,

the

_flop-in

resonances do not occur on a zero

background

One can

_get

an idea of the

_sensitivity

of our method

from the limit of

_sensitivity

obtained with the same

apparatus

in

_optical

laser

_spectroscopy

work.

_Optical

spectroscopy

has been

_performed

with

_production

rates as low as

104

_{atoms/proton pulse}

for sodium

at the

_proton

_synchrotron

of C.E.R.N.

_[25]

and

105

_atoms/s

for rubidium at the ISOLDE mass

sepa-rator

_{(C.E.R.N.) [5].}

In our

_method,

the r.f resonance

signals

are of course weaker than the

_optical

resonance

signals

because the Zeeman

_degeneracy

is removed but the loss in

_sensitivity

due to this fact

_is,

in all cases,

certainly

less than a factor of ten. Therefore our method can be used with

_{isotope production}

rates

higher

than

106

_atoms/s.

This limit

_corresponds

to

the one obtained with a _very efficient ABMR

appa-ratus

_{[26] especially designed}

to work with atomic beams of rare

_isotopes.

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