Very high resolution study of high Rydberg levels of the configurations 4f$^{14}$ 6$sn$d of Yb I

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Very high resolution study of high Rydberg levels of the

configurations 4f

14

_{6snd of Yb I}

Luc Barbier, René-Jean Champeau

To cite this version:

Luc Barbier, René-Jean Champeau.

Very high resolution study of high Rydberg levels of the

configurations 4f

14

_{6snd of Yb I. Journal de Physique France, 1980, 41 (9), pp.947 - 955.}

Very

high

resolution

_study

of

_high

_Rydberg

levels

of the

_{configurations}

4f14

6snd of Yb I

L. Barbier and R.-J.

_Champeau

Laboratoire Aimé Cotton, C.N.R.S. II _(*), Batiment 505, F 91405 _Orsay Cedex, France

(Reçu le 17 mars _{1980, accepté} le 8 mai 1980)

Résumé. 2014 Les niveaux de

Rydberg élevés de l’ytterbium ont été étudiés sur un _jet d’atomes métastables. Les niveaux de la série 4f14 6snd ont été _peuplés à

_partir

du niveau métastable 4f14 6s _6p

_3P0

grâce à la lumière ultra-violette d’ùn laser à colorant monomode double en

_fréquence

et détectés par la méthode d’ionisation par un

_champ

électrique. Les _{champs critiques} d’ionisation _Fc des niveaux 4f14 6snd

3D1

(24 ~ n ~ 57) ont été mesures; ils obéissent à la loi du

_{col(Fc =}

₍₁₆

_n*4)-1).

Les structures

_hyperfines

des _{isotopes impairs} ont été _analysées; comme

l’interaction

_hyperfine

est du même ordre de _grandeur que les interactions électrostatiques et

_spin-orbite

_(ou même pour les valeurs de n les plus élevées

_{plus importantes}

_que ces _dernières), ces structures ont un _aspect très

_particulier.

Les structures observées ont été _{interprétées théoriquement par la méthode paramétrique} de Slater-Condon. Les influences _respectives de l’électron _optique excité (nd) et de l’électron

_optique

non excité (6s) ont _{ainsi pu être}

étudiées. De

_{plus, l’influence}

d’un niveau de valence _perturbant seulement les composantes des _{isotopes impairs}

a été mise en _{évidence pour le nombre quantique n} = 26.

Abstract. 2014

High Rydberg levels of _ytterbium were studied in a beam of metastable atoms. Levels of the series 4f14 6snd were _populated from the metastable 4f14 6s

_6p

_3Po

level _by means of the U.V. _light of a

frequency-doubled _{single-mode dye} laser and detected _using the field ionization _technique. The critical ionization fields _Fc

of the levels 4f14 6snd

_3D1

_{(24 ~} n ~ 57) were measured and found to obey the _{saddle point} law

_{(Fc =}

₍₁₆

_n*4)-1).

The

_hyperfine

structures of the odd

_isotopes

were _{investigated. They} are _{very peculiar} due to the fact that the

hyperfine

interaction is of the same order of _magnitude as _(or even for the _{highest n} values, much more

_important

than) the _spin-orbit and electrostatic interactions. A theoretical account of the observed structures _using the Slater-Condon _parametric method is _given. The relative influence of the excited _(nd) and of the non-excited (6s) optical electron could thus be studied. Furthermore the influence of a valence level

_perturbing

_only the odd

_isotopes

components for n = 26 _was demonstrated.

Classification Physics Abstracts 32.20J - 32.60

1. Introduction. -

During

the last few _years, the

study of high lying Rydberg

levels of atoms has become

a field of

_increasing

interest in atomic _{spectroscopy.}

The _spectra of one-electron atoms have been the

subject

of a _very

_large

amount of

_experimental

and theoretical work.

_{Comparatively,}

rather few _very

high-resolution

studies have been

_performed

on

many-electron atoms. Technical as well as theoretical difficulties

_easily

_explain

this fact. However the

_study

of

_{high Rydberg}

levels of

_{many-electron}

atoms is

particularly

interesting

because of the

_specific

cha-racteristics

_they

_{possess :}

(i)

their

_properties

are influenced

_by

the _presence

of the non-excited

_optical

electrons ;

(ii)

in the energy range where

high

Rydberg

levels

are located there can also exist levels

_belonging

to

(*) Laboratoire associé à 1Université Paris-Sud.

doubly

excited electronic

_{configurations}

that interact with the usual

_Rydberg

series,

thus

_leading

to the

so-called

_perturbed

series.

The _purpose of this work on the

_ytterbium

atom

was to

_investigate

the two

_foregoing

_phenomena

and more

_precisely

to

_investigate

their influence on the

critical ionization fields and on the

hyperfine

struc-tures of the

_Rydberg

levels.

2.

_Energy

_spectrum

of

_ytterbium

I. - The atomic

number of

_ytterbium

is 70. Ytterbium _possesses seven

stable

_isotopes

with mass numbers

_ranging

from 168

to

_{176 ;}

the

_{corresponding}

natural relative abundances

are

_given

in table I. The nuclear

_spins

of "’ Yb

and of

"3Yb

are

_1/2

and

_{5/2 respectively.}

A _part of the level scheme of Yb 1 is

_given

in

_figure

1.

For some of the levels of Yb 1 located below the first ionization limit

_and,

in

_particular,

for the

_Rydberg

series

_converging

towards this

limit,

the 4f shell is

948

Table 1. -

Isotopic composition

of

natural

_ytterbium.

Fig. 1. - Part of the level-scheme of Yb 1

showing the levels of interest for the _{present experiment.} The metastable 4f " 6s _6p

_3Po

level is populated inside the atomic beam _by means of a _discharge.

High Rydberg levels belonging to the configurations 4f 14 6snd are

excited from this level by the U.V. light of a _{frequency-doubled}

dye-laser. Atoms in the other, higher lying, metastable levels are

directly photoionized by the U.V. beam.

closed : these levels can be considered as

_being

those

of a two-electron atom. The other levels below the first ionization limit are those of a four-electron

spectrum

(in

fact one hole in the 4f shell and three

electrons in other _open

_shells).

3.

_{Expérimental}

_set-up.

- The

_{experimental set-up}

we used for

_{studying high Rydberg}

levels of

_ytterbium

is

_quite

_analogous

to that described

_by

H. T.

_Duong,

S. Liberman and J. Pinard in their work on

rubi-dium

_[1].

The atoms of a beam are excited

_by

a

fre-quency-doubled

single-mode dye

laser

_{[2] (this}

laser is

basically

a CW

_dye

laser but it is

_pumped

simulta-neously by

a CW

_argon-ion

laser and

_by

a

_pulsed

Nd

Yag laser)

providing

U.V.

_pulses

of 50 W

_peak

_power

and 50 ns duration with a

_repetition

rate of

approxi-mately

50 Hz. Atomic - and laser - beams

cross at

right

angle

so as to _get rid of the

_{Doppler broadening}

of the lines.

_By

those means, both very

high

resolution and

_{good efficiency}

can be achieved.

In

fact,

due to the rather

_high

value of the ionization

energy of

ytterbium,

the atoms cannot be excited

directly

from the

_ground

level

_by

the

frequency-doubled laser beam as was done in the rubidium

experiment

[1].

We therefore had to take

_advantage

of the existence of metastable levels

_(Fig.

_1).

These levels can be

efficiently

_populated

inside the atomic

beam itself

_by

means of a

discharge

produced

at the

exit _aperture of the oven

_[3].

The _energy difference

between the

_Rydberg

levels under

_study

and the

metastable level 4f 14 6s

_6p

_3pO

is about 33 000 cm-l.

The

_{corresponding wavelength}

close to 600 nm, before

frequency doubling,

is in the

_spectral

range of Rhoda-mine 6 G

_dye

lasers ;

single-mode

CW

_dye

lasers are

particularly

easy to _operate in this

_{spectral region.}

Table II. - Critical ionization

fields

in the series

4f146snd

_3D

1

of

Yb 1. The values

of

the critical

ionization

_fields

_(Fc)

are

_given

as a

function

of

the

principal

quantum number

(n)

or

_of

the

_effective

princi-pal

quantum number

_(n*).

The relative

_uncertainty

on the measured

_Fc

values is about 2

%.

The

_quantity

in the last column

₍₁₆

n*4

_Fe)

is

_expressed

in atomic

units ;

according

to the classical

_{(saddle-point) formula,}

this

_quantity

should be

_equal

to 1.

The excited atoms are detected

_by

the field ioni-zation

_{technique [1, 4].}

The

_positive

ions

_resulting

from the field ionization _process are accelerated

_by

the

_ionizing

field and collected

_by

the first

_dynode

of

an electron

multiplier.

The

_pulses

_provided

_by

the

multiplier

are counted

_during

the _aperture time of a

gate, the

_delay

and duration of which are

_adjusted

so that the ions of interest are all counted whereas the

parasitic

counts are

_rejected

as

_thoroughly

as

_possible.

The excitation _spectrum we have

_investigated

corresponds

to the line series :

4f 14

6s

_6p

3Po-4f14

6snd

F,

F

_being

the total

_angular

momentum of

the atom

_(electrons

+

_nucleus).

4. Critical ionization fields. - The critical

ioniza-tion fields of all levels with n

_ranging

from 24 to 57

have been measured. The results are

_given

in table II.

As is well

known,

in a classical

_picture

the value of

the critical ionization

field,

Fc,

corresponding

to a level with effective

_principal

quantum number n* is

_given

in atomic units

_by

the formula :

_Fc

=

1/16

n*4.

This limit

_corresponds

to the value of the

_potential

energy at the saddle

_point

of the

_potential

_energy

surface of the atom submitted to a static electric

field F.

To check the saddle

_point

formula,

the n* values are

needed. For the lowest n values

_{(24 n 33), they}

were deduced from the measurement of the

wave-length

of the laser in resonance with the transition under

_{study ;}

for

_{higher n}

values

_(n

>

₃₃₎

we used n*

values derived from the work of P.

_Camus,

A. Débarre

and C. Morillon

_[5].

According

to the saddle

_point

formula,

the

_quantity

a =

Fe X 16

n*4

should

equal

1 for

every level.

This was verified

by

plotting

the measured a values versus n in

_figure

2. As can be seen the law is

_obeyed

Fig. 2. - Check of the

saddle-point formula _relating the critical ionization _{field F,} to the effective _{principal quantum} number n* of the level of interest. For every investigated level, the _quantity

16(n*)4 Fc which should _{equal 1 (in} atomic _{units) according} to the classical theory has been plotted versus n.

within the

_experimental

uncertainties for all

investi-gated

levels. This is not too

_surprising

since none of

these levels turned out to be

_perturbed.

In

fact,

as we shall see in

_paragraph

11,

the levels n = 26 _are

slightly perturbed

but

_only

for the odd

_isotopes.

However,

critical field measurements

_performed

on these _components do not _{show any} noticeable

diffe-rence with the values measured on the

_unperturbed

even

isotope

levels

corresponding

to the same value

of n. But it must be

_kept

in mind that first the pertur-bation is

_only

weak and second critical field

measu-rements made on the odd

isotopes

are not _very

_precise

due to the weak

_intensity

of the

_{signal (cf.}

_§"5).

5.

_Hyperfine

structure measurements. -

By

scann-ing continuously

the

_frequency

of the

laser,

one can

record the structure of the transition under

_study.

Figure

3

_{gives typical}

_{recordings corresponding}

to the levels n = 30 and n = 38.

The most intense _components near the centre of

each

_recording

are due to the even

_{isotopes ;}

in the direction of

_increasing

wavenumbers,

one

successively

finds

_17°Yb,

_172Yb,

174Yb

and

176Yb.

The linewidth of a

_single

_component is

_{approximately}

60 MHz due

to the

_spectral

width of the laser

_light

and to the

residual

_Doppler

_{broadening corresponding}

to the

divergence

of the atomic beam. The

_remaining,

less

intense,

components make _{up the} structure of the odd

isotopes.

The

_intensity

of the weakest recorded

component

is less than 1

_%

of the total

_intensity

of the

line.

For

_measuring

the distances between _the compo-nents of the structure, the wavenumber scale of the

recordings

was calibrated

_{by simultaneously}

_recording

the

_fringes

of a

_spherical

_Fabry-Pérot

interferometer

providing

frequency

markers with an interval of

1.5 GHz

_(Fig.

_3).

The

_position

of a

_given

_component

is obtained

_by

a linear

_{interpolation}

between the two

adjacent

reference

_fringes.

The

_position

of all

_compo

nents are referred to the _component of the

_isotope

176Yb

.

The uncertainties in the

_position

measurements

have two

_{origins :}

the noise and other fluctuations

(of

the atomic and

_laser-beams)

and the

_{non-linearity}

of the

_scanning

of the laser

_frequency.

For the odd

isotopes

components the

_uncertainty

is estimated to

be

_{approximately}

3

mK ;

for the _components of the

even

_isotopes

which are more intense and less distant

from one

_another,

the

uncertainty

is

only

1 mK.

The final results are

given

in table III and a

plot

of

the structures of all recorded transitions is

_given

on

figure

4. The structures of the four even

isotopes

remain

_{remarkably unchanged}

as n

_{varies ;}

in contrast, one observes that those of the odd

_isotopes

_change

considerably

as n is

_{increasing ;}

in

_particular,

the

structures become much

_simpler

for the

_{highest n}

values,

as will be

_explained

in the next section. One should also notice that the structures

_change

_smoothly

950

Table III. - Structures

of Rydberg

levels

_belonging

to the

_{configurations}

4f"

6snd. The

_positions

_of

the recorded components

referred

to

the 176Yb

_component are

_expressed

in GHz. Each line

_of

the table

_corresponds

to a

_given

value

_of

the

_principal

quantum number n. Each column in the table

_corresponds

to a _group

of

_components as it

appears in the

recording (see

Figs.

3 and

4).

The

experimental

uncertainty

is

_{approximately}

0.03 GHz

_for

the even

isotopes

components and 0.1 GHz

for

the odd ones.

Fig. 3. - Recordings of the structures of the transitions 4f14 6s 6p

3Po-4f14

6s 30d and 4fi4 6s 6p

3Po-4f14 bs

38d F. In the region of the

even _isotopes, the ordinates have been divided by 10 in the first _{recording, by} 5 in the second one. In the former _recording the components

Fig. 4. - Plot of the recorded

structures. For the perturbed n-26

level, triangles are used instead of circles for representing the

components of the structure.

this is due to _{the presence} of a

_perturbing

level

_(cf.

§ 11).

6. Interactions

_responsible

for the level structure.

-For the considered

transitions,

4f 14 6s

_6p

3Po-4f 14 6snd,

the structure is

_entirely

due to the _upper

level ; the lower level

_having

J = 0 is

simple

_even in

the case of the odd

_isotopes.

In order to understand the observed structures, it is first _necessary to list the relevant interactions. There are three main

_perturbing

terms in the hamil-tonian :

_(i)

the electrostatic interaction between the

two

_optical

electrons G =

e2/r 12,

where e is the

electron

_charge

and rl2 the relative distance of the

two

_electrons,

_(ii)

the

_spin-orbit

interaction

where

li

and s, are the orbital and

_spin

_angular

momenta of electron i and

_ç(ri)

a scalar function of

the

_{distance r;}

of electron i from the

_origin,

_(iii)

the

magnetic

hyperfine

interaction

_(Fermi

contact

_term)

which can be accounted for

_by

the effective _operator

H.

=

as I.

_ss, where

as is a constant

_{(hyperfine splitting}

factor of the 6s

_electron),

1 the nuclear

_spin

and _ss the

spin

angular

momentum of the 6s electron.

Other

interactions,

e.g. the

magnetic

dipole

and electric

_quadrupole

_hyperfine

interactions associated with the nd electron as well as the

_spin-spin

and

spin-other-orbit interactions are

_supposedly

_negligible.

For each of the

_important

_operators,

_only

one

radial

_integral

_plays

a role in the level structure of the

configuration

4f14 6snd : the Slater

_{integral G2(6s,}

_nd)

for _operator

_G,

the

_spin-orbit

interval

factor

of the nd

electron,

(nd,

for _operator A and the constant _as for

operator

Hm.

The radial function of the nd electron is involved in the first two _{parameters, G2} and

_(,,d,

but not, of

course, in the third one, as. In a

hydrogenic

picture,

it is well known that

(nd

varies as

(n*) - 3

with

_increasing

n ; it can be shown that

G2

also

_obeys

the same law.

In contrast, the parameter a.

only depends

on the

wavefunction of the 6s

electron,

more

_precisely

as is

proportional

to the

_probability

_density

of this electron

at the nucleus. For the values of n that have been

investigated,

the

_probability

_density

of the nd electron near the nucleus is _very

small ;

as a _consequence the

screening

effect

_produced

_by

the nd electron on the 6s

electron is

_{negligible ;}

therefore with _very

_good

accu-racy as has the same value for all

_{investigated high}

Rydberg

lévels and also for the

_ground

level

4f 14 6s

_{2S 1/2}

of Yb II.

7.

_Qualitative

_{interprétation}

of the structures of the

highest

levels. - The

previous

considerations enable

the structures encountered for the

_{highest n}

values

to be understood. For these cases the interactions G and A can be

_neglected

as a first

approximation.

For

each odd

_isotope,

the

_{configuration}

4f14

6snd is thus

split

into two levels whose interval should be

_equal

to as

x

_(I

+

_1/2)

as the

ground configuration

4f14

6s of Yb II, whose

_hyperfine

structure was measured

_by

Chaiko

_[6].

These values are

_compared

in table IV with the

_{corresponding}

values that we have measured

Table IV. -

Comparison

of

the structures

_of

the

Rydberg

levels

4f14

6s 53d and

4f14

6s 48d with the

hyperfine

structure

_of

the

_ground

level

4f14

6s

_2S1/2

of

Yb II. All values are

_given

in GHz.

Hyperfine splitting

(GHz)

in the

_{configurations}

4f14 6s 48d and 4f14 6s 53d.

For each

_isotope,

the values are rather close to one

another,

thus

_giving

a _{strong support} to the

952

8. Theoretical

_{interprétation}

of the

_experimental

results

_by

the

_parametric

method. - To

give

a

quanti-tative theoretical account of all the measurements

we have made use of the

semi-empirical

Slater-Condon

parametric

method.

It must be first recalled that the

_hyperfine

_operator

Hm

does not commute with the total

_angular

momen-tum J of the electrons.

As,

furthermore

Hm

is not

small

_compared

to G and A, none of the usual

_coupling

schemes

_(e.g.

_{Russell-Saunders, jj}

and also J - I

for the

_coupling

between electrons and

nucleus)

corresponds

to the

_physical

_{situation ;}

for the odd

isotopes,

even J is not a

good

_quantum number.

Except

for the

_{highest n}

values

_{(see § 7),}

none of the three

_perturbing

hamiltonians

_G,

A and

_Hm

can be considered as much more

_important

than the other two ; we have therefore to consider the entire

confi-guration

4f14

6snd as the

unperturbed

level and to

handle the total

_perturbation

H’ =

H.

₊ G ₊ A

as a whole.

To

_apply

the

_parametric

method,

the matrix of the hamiltonian H’ is built

_using

the basis set

14f14

6snd(SLJ,

I) FMF >. By diagonalizing

this

matrix,

one obtains the

_perturbed

_{energy levels} that

depends

on

_parameters

_(d,

_G2,

_{as(171), as(173)}

and one additional constant

_(ADD(171)

or

_ADD(173))

for

each odd

_{isotope. Physically}

each of the last two constants determines the

_position

of the structure

of one odd

_isotope

with _respect to the

_{corresponding}

level of

116 Yb

taken as reference.

The

_parameters

are fitted to the

_experimental

values

_by

_comparing

the theoretical and

_experimental

values of the _{energy. In}

_{fact, only G2(6s, nd), ’ncb}

ADD(171)

and

_ADD(173)

were

_free;

the two para-meters

_as(171)

and

_as(173)

were fixed to the values

_they

assume in the

_ground

level of Yb

II,

respectively

12.7 GHz and 3.51 GHz. In the

_{fitting procedure,}

the levels of the two odd

_isotopes

were treated

simul-taneously

so as to avoid that the _parameters

_G2

and

,,d

which have no

_{isotopic dependence}

take different values for the two

_isotopes.

9. Results. - For all

_investigated

levels,

except

n = 26 and n

= 48,

_a

satisfactory

agreement between

experiment

and

_theory

has been achieved since the mean _square difference between

experimental

and theoretical values of the _energy levels is

_{approximately}

equal

to the

_{experimental uncertainty.}

We first comment on the

special

cases. For n =

48,

the

_{fitting procedure}

did not _{converge :} this _may be due to the fact that the values of

G2

and

_’nd

are not

large enough

in

_comparison

to the

_experimental

uncertainties. The case of n = 26 which is

perturbed

will be discussed in

_paragraph

11. For n =

53,

the

observed structure can be

_interpreted

_by

_putting

G2 = (d

= 0

(cf. § 6).

The final values of the _parameters

_G2

and

_’nd

obtained for all the other

investigated n

values are

listed in table V. These values are

_plotted

versus n

Table V. - Values

of

the parameters

G2

and

_’d

for

the

_{configurations}

4f14

6snd as a

function of

the

principal

quantum number n. These values are

_given

in

GHz.

in

_figure

5. As can be seen

_they

follow rather

accurately

an

(n*)-3

law,

in agreement with

_{theory (cf. §6).}

However,

a sudden decrease of the values

of (d

and

G2

is observed at n =

33 ;

this is

obviously

related to the

qualitative

change

in the recorded structures

_(in

particular

the

_components

for

173Yb

located on the

large

wavenumbers

_side)

which can be noticed in

Fig. 5. - Evolution with n of the

parameters G2 and ’do In a

hydro-genic scheme, the parameters G2 and ’d should vary like (n*)- 3. To check this, we have drawn on each diagram (dotted line) the

graph of the function (n*)- 3 multiplied by the factor a _{(resp. fui}

which _provides the best agreement with the values obtained for G2

figure

4 for the same value of n but no

_explanation

of

this

_phenomenon

could be found.

For a

given

n, the values obtained for

G2(6s,

nd)

and

₍₀₀

are

approximately

equal.

This is at first rather

surprising

because Hartree-Fock calculations of the ratio

_{(nd/G2 (which}

should be

_independent

of

n*,

as noticed

above)

performed

in the

configuration

4f14

6s 6d

_yield

the value 0.15.

_But,

on the one

_hand,

the

configuration

4f14

6s 6d may be not excited

enough

to fit in the normal characteristics of the

Rydberg

series

and,

on the other

hand,

for the n values we

consider,

the distance between two successive 6snd

_{configurations}

is not much

_larger

than _{the range}

occupied

by

each

_{configuration}

_(for

instance,

the distance between

_{configurations}

6s 38d and 6s 39d

is 5

cm-1,

the overall width of each structure

_being

0.6

_cm-1)

so that

configuration

interaction effects

may be

appreciable.

It is therefore most

_probable

that the values of the _parameters are

_effective

values

taking

into account at least

_partially

the effect of such

interactions. It would be more

appropriate

to treat

together

all

_{configurations}

6snd

_using

the Multi-channel

_{Quantum-Defect}

_{Theory. Unfortunately}

the

application

of the

_MQDT

method to

_hyperfine

sublevels is not

_{straightforward.}

10. Fine structure of the

_{configurations}

4f14

6snd.

-Once the values of the _parameters

_{G2 and (00}

have been obtained for a

_given

n, one can _compute the relative

_energies

of the four levels

_{’D2, 3D1, 3D2}

_and

3D3

without

_hyperfine

structure

_by

_putting

_as = 0

in the energy

matrix,

diagonalizing

it and

_taking

its

eigenvalues.

The

_energies

so obtained are

_plotted

in

_figure

6 with _respect to the _energy of the level

_3D

1

taken as

_origin.

Our measurements allow us to obtain the

_complete

level structure

_resulting

from the electrostatic and

spin-orbit

interactions for all

_investigated

4f " 6snd

Fig. 6. - Level scheme of the

configurations 4f 14 6snd. The relative positions of the four levels of each investigated configuration

4f 14 6snd (without hyperfine structure) have been obtained as a

result of the parametric analysis of the recorded structures (cf. § 10).

These _positions are _plotted versus n _(the level 3D2 is taken as a

reference).

configurations,

in

_spite

of the electric

_dipole

radiation selection rules that _prevent the levels

_{3D2, 3D3}

and

’D2

being

excited from the

_3Po

level. This is

_possible

because,

due to the

_hyperfine

structure

_operator,

the

eigenstates

of several

_hyperfine

levels of the odd

isotopes

contain a

significant

admixture of a state

corresponding

to

_{3D 1.}

Nevertheless,

as the

preceding

results

_rely

on

theoretical

_assumptions

_{(interactions}

have been

neglected),

it would be worthwhile to have a direct

experimental

check of the

_preceding

results

_{by exciting}

the even

_isotopes

levels

ID2,

3D2

and

3D3

and

measuring

their

_energies.

In order to

_perform

those

measurements, it would be

possible

to choose one of

the two metastable levels

_having

J = 2

(Fig. 1)

as

lower level instead of the 6s

_6p

_3Po

level.

11. Perturbation of the

_{configuration}

4f14

6s 26d.

-As was mentioned before

(cf. § 9),

it was not

_possible

to

_give

a theoretical

_{interpretation}

of the structure of

the

_{configuration}

4f14

6s 26d. As can

_clearly

be seen

on the

plot

of

figure

4,

this structure does not follow the normal evolution with n. This is due to _{the presence} of a

_perturbing

level with J = 2

belonging

to the

configuration

4f 13

5d 6s

_6p

_[7]

and located about

5

cm-1

above

the

_{configuration}

4f14

6s 26d. The even

isotopes

levels whose

_eigenstates

are

_purely

J = 1

states are not influenced

_by

this

_perturber,

but the odd ones can be

_perturbed

because their

_eigenstates

contain admixtures of

_3D2

or

1 D 2

states. As

_expected,

the odd levels are shifted

_(with

_respect to the

_unshifted

even

_levels)

towards lower

_frequencies

as a

conse-quence of the

repulsion

of the

perturbing

level. No

further

_analysis

of the

_phenomenon

was

_attempted.

As far as we know this is the first

_reported

evidence of the influence of a

_perturbing

level on the

_hyperfine

structure of a

high

Rydberg

level.

12.

_Isotope

shifts. - The shifts of the

even

_isotopes

are

_given

in table III. Those of the odd

isotopes

can be deduced from the theoretical

_study

of the structures

(cf. § 8)

as

_explained

in

_paragraph

10.

_{By definition,}

the _energy of the

_3Dl

level without

_hyperfine

structure obtained for each

_isotope,

_gives

the shift of that

isotope.

The shifts of both odd

_isotopes

referred to

176Yb

are

given

in table VI.

As can be seen the shift of a

_{given isotope}

does not

depend

on n, at least within the

_experimental

uncer-tainties. This is not

_surprising

because the field effect

as well as the mass effect must have

_{approximately}

constant values for all

_investigated

transitions. The

field effect is determined

_by

the

_probability

_density

at the nucleus of the electrons that should remain constant for all n values

_{(cf. § 5) ;}

the normal mass

effect

_(Bohr

_effect)

_proportional

to the wavenumber of

the considered lines varies

only

by

0.01 mK

_{(0.3 MHz),}

for an

_isotopic

_pair

whose mass numbers difference

is

2,

when n varies from 24 to

_{53 ;}

it is more difficult to

954

Table VI. -

Isotope

shifts

of

the odd

_isotopes

_of

ytterbium.

In this table are

_given

the _positions the levels

4f14 6snd

_3Dl

_of

the odd

_isotopes

_of

Yb _{would occupy}

if

the

_hyperfine

structure were _{zero ;} these values are

obtained as

explained

in

paragraph

10.

They

are

expressed

in GHz and

_referred

to the

_{corresponding}

component

of 176Yb.

The

uncertainty

is about 0.1 GHz.

but on a theoretical basis this effect is

_expected

to be

small and almost constant for all concerned transi-tions

_[8].

It is therefore

_justified

to take for each

_isotope

the

average values of the shifts of all transitions

(Table VII).

In table VII can also be found the so-called residual shift obtained

_by

_subtracting

the normal mass effect from the total measured shift.

Considering

that the

_isotope

shifts so obtained are dominated

_by

the field

shift,

it is

_interesting

to check if their values

can be

_interpreted

in terms of the

_{empirical screening}

factors well known in the

_analysis

of the field shift

_[8].

The field shift of each

_investigated

transition _is

pro-portional

to the difference of the 6s electron

_probability

densities at the nucleus for _{the upper and lower}

_{levels ;}

it therefore

_directly

reflects the

_screening

effect of the

6p

electron in the level 4f14 6s

_6p

_3Pl

since the nd electron has a

_{negligible screening}

effect. It is known from the

_analysis

of the field

_isotope

shifts in a

_large

variety

of atoms that the _presence of a _np electron decreases the

_{probability density}

at the nucleus of a ns

electron of about 10

_%.

If the residual shifts in table VII

were

_entirely

due to field

_{effects, they}

should thus be

equal

to

_1/10

of the field effect of a 6s electron that is to _say to - 0.10 times the field effect of the resonance lines

4f 14 6s-4f 14

_6p

of Yb II. The shifts of a transition of this _type were measured

_by

Chaiko

_[6]

and the values

can be found in table VII. As can be seen, the ratio of

the residual shifts of the

_Rydberg

lines and of the

resonance line of Yb II is in fact - 0.22 instead of

- 0.1. This

disagreement

should not be taken too

seriously

since we have

_neglected

the

_specific

mass

shifts in the

_Rydberg

as well as in the resonance Yb II

line,

and also because the 10

_{% screening}

factor is

only

an

_approximate

_empirical

_{value ;}

it is

_satisfactory

that the

_signs

and orders of

_magnitude

are in

agree-ment.

13. Conclusion. - The values of the critical

ioniza-tion fields we obtained in this work

_only

lead to the

expected

results that the classical saddle

_point

law is

valid also in the case

_{of many}

electron atoms. In fact

as was discussed

_above,

the series we

_investigated

is

only slightly

and

_indirectly

_perturbed;

the

_problem

of the influence of a

_perturber

on the critical ionization

fields remains therefore an _open one.

The

_analysis

of the structures is much more fruitful.

It

_gives

the

_possibility

of

_describing

the evolution of

the

_hyperfine

structures of

_high

_Rydberg

levels and of

_studying

the relative influence of the excited

_(nd)

and of the non-excited

(6s) optical

electrons on these

structures.

Furthermore,

the influence of a level

perturbing

only

the odd

_isotopes

via the

_hyperfine

interaction has been observed for the first time.

Table VII.

- Average

values

_of

the

_isotope

_{shifts of}

the transitions

4f14 6snd-4fl4

6s

_6p

_of

Yb 1. In the

_first

line

_of

the table are the _average values

_of

the

_{measured position of}

each

_isotope

referred

to l’6Yb

and in the second

line the

_{corresponding}

residual

_shifts.

For

_comparison,

the residual

_{shifts of}

the line  = 369 _nm

of

Yb II _are

_given

in the third line

and,

in the last

line,

the ratios

_for

the residual

_{shifts of}

the

_Rydberg

lines and

_of

the Yb II line. All

shifts

are given in GHz.

Measured shift

_{of Rydberg}

lines

Residual shift of

_Rydberg

lines Residual shift for Yb Il  = 369 _nm

For the

_{highest investigated n}

_values,

we were able

to

reach the limit where all interactions

_responsible

for the structure _except the

_hyperfine

interaction are

negligible.

It would be worthwhile to

_study

the

struc-tures for lower n values in order to reach another

limiting

situation _where, as is the more usual case, the

hyperfine

interaction becomes smaller than the other

interactions ;

in this _way the evolution of the observed

structure between the two

_limiting

_coupling

schemes could be followed

_completely.

Acknowledgments.

- It is

a

pleasure

for the authors

to thank Drs S. Liberman and J. Pinard who

_provided

continuous

_help

and advice

_during

the

_experiment

and Prof. J. Bauche who took a

_leading

_part in the

theo-retical

_analysis.

References

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[3] BRINKMANN, U., GOSCHLER, J., STEUDEL, A. and WALTHER, H.,

Z. _Phys. 228 ₍₁₉₆₉₎ 427.

CHILDS, W. J., POULSEN, O. and GOODMAN, L. S., Opt. Lett. 4 (1979) 35.

[4] DUCAS, T. W., LITTMAN, M. G., FREEMAN, R. R. and KLEPPNER,

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