The analysis of the spark spectrum of gadolinium (Gd II)

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The analysis of the spark spectrum of gadolinium (Gd II)

J. Blaise, Th. A. M. van Kleef, J.F. Wyart

To cite this version:

J. Blaise, Th. A. M. van Kleef, J.F. Wyart. The analysis of the spark spectrum of gadolinium (Gd

II). Journal de Physique, 1971, 32 (8-9), pp.617-626. �10.1051/jphys:01971003208-9061700�. �jpa-

00207118�

617

THE ANALYSIS OF THE SPARK SPECTRUM OF GADOLINIUM (Gd II)

by

^J.

BLAISE,

^{Th. A. M. van KLEEF}

(*)

^{and J. F. WYART}

Laboratoire Aimé

Cotton,

C. R. N. S.

II, Orsay,

^{France and}

Amsterdam,

The Netherlands

(Reçu

^{le 29}

janvier 1971)

Résumé. ²⁰¹⁴ L’analyse ^du spectre d’émission de Gd II a permis de découvrir 108 niveaux impairs

et 70 niveaux pairs. Les 2 200 raies actuellement classées correspondent ^{à 2 300} transitions entre 162 niveaux impairs ^et 150 niveaux pairs. ^Les longueurs ^d’onde de 18 500 raies de Gd I et Gd II ont été mesurées dans le domaine 2 468-8 752 A. On a observé la structure Zeeman de plus ^de

900 raies de Gd II entre 2 700 et 11400 A et le facteur de Landé de chaque ^{niveau est maintenant}

connu. Les termes impairs appartiennent à 4 f7 5 d 6 _s, 4 f7 6 s2, ^{4 f7 5 d2 et} à la nouvelle confi-

guration ⁴ f8 6 p ; les ^termes pairs ^sont attribués à 4 f7 6 s 6 _p, 4 f7 5 d 6 _{p et} aux nouvelles confi-

gurations ^{4 f8 6 s et} 4 f8 5 d. On donne une interprétation paramétrique ^des configurations ^{4 f8 6} s, 4 f8 5 d et 4 f8 6 p.

Abstract. ²⁰¹⁴ The analysis ^of wavelength data of the Gd II spectrum has resulted in the detection of 108 odd and 70 even levels in addition to those reported by previous investigators. ^{The total}

number of classified lines is now 2 200, belonging ^to 2 300 transitions between 162 odd and 150 even

levels. The wavelength list, including ^{the Gd I} lines, ^{contains over} 18 500 lines in the wavelength region ^{2 468-8 752 Å.} The Zeeman effect has been investigated ^{in the} wavelength region ^{2 700-}

11400 A. Of about 900 lines belonging ^{to Gd} II transitions the splitting has been observed. The

g-values of all levels could be determined. The odd terms belong ^to the electron configurations

4 f7 5 d 6 _s, 4 f7 6 s2, 4f7 5 d2 and the newly established 4 f8 6 p ; ^{the even terms have been associated} with the configurations ^{4 f8 6} s and 4 f8 5 d (see ^{4 f8 6} p), ^{4 f7 6 s 6} p and 4 f7 5 d 6 _p. Calculations have been carried out in the 4 f8(7F) ⁶ s, 5 d and 6 _p subconfigurations. The values of the electro- static and spin-orbit interaction parameters give ^a good least-squares ^{fit to the} experimental levels.

LE JOURNAL DE PHYSIQUE TOME 32, AOUT-SEPTEMBRE 1971,

Classification Physics Abstracts :

13.20

1. Historical

Survey.

^{- An}

analysis

of the Gado- linium II

spectrum

^was

given

^{in 1950}

by

^Russell

[1].

His

analysis

^{was based on the} temperature ^classi- fication of Gd lines

published

^{in 1943}

by King [2].

Russell

only

established terms of

configurations belonging

^{to the 4 f’-core}

(system A) :

^the

expected

4

f8-configurations

remained undetected

(system B).

He classified 1 177 out of the 2 627 Gd II lines of

King’s

^list.

Isotope

^shift measurements of Brix

[3]

a few _years

later,

confirmed Russell’s

analysis

^for

the lowest levels of the

4 f’

5 d 6 s and

4 f’ 5 d 6 p configurations. Only

^a few Zeeman effect measurements were available to

Russell, by

Albertson’s work

[4].

In 1965 Smith and

Wybourne [5]

made calculations in the

subconfigurations

- neglecting

^{the 4}

f7 (8S0) 6 S2 8S7/2

^{level -, and}

in

4 f7 (8S0) 6 s 6 p

^{and 4}

f7 (8S0)

^{5 d 6 p.}

Though they

^{made a} wrong

supposition

^{about the}

coupling

scheme in the 4

f7 (8S0)

^{5 d 6 s}

configuration

^{as we}

shall discuss later

(see § IV), they

gave

predicted

g-

values of all levels

belonging

^{to the}

subconfigurations

mentioned

above,

^{which turned out to} be useful.

Furthermore

they predicted

^the

positions

^{of the}

unknown levels of 4

f7 (8S0)

⁵

d2,

^{which viere not}

detected

by

^Russell. In 1967 Desmarais and

Pinning-

ton

[6] published

measurements of 120 resolved Zeeman patterns

belonging

^{to 86}

wavelenghts

^and

determined the

g-values

of 26 odd and 41 even known levels. The agreement between the observed

g-values

and the

predictions

^{of Smith and}

Wybourne [5]

^was

satisfactory

^{for most of the levels. In the same} year Noorman made two series of spectrograms

of 158Gd

at the

Paschen-Runge mounting equipped

^{with the}

« G5 »

grating

^{of the}

Argonne

^National

Laboratory

with an electrodeless

discharge

^{tube in the}

region

2 468-8 752

A.

Each

plate

contained three

images

^of

the

gadolinium

spectrum

exposed

^{for different}

lengths

of

time,

^{and a}

superposed

^thorium spectrum ^for purposes of calibration. This series has been measu-

red

by

^{Slooten and Hoekstra}

[7] by

^{means of an auto-}

matic comparator ^{« Zelacom »}

[8]

^{built at the Zeeman}

laboratory.

The second series contains Zeeman spec- trograms ^{which we used for}

deriving

^the

g-values.

In 1969 an additional series was taken

by

^{M. Fred}

in the

region

6 000-11400

A.

Our first results of the

analysis

of the Gd II spec- (*) Zeeman-Laboratorium der Universiteit van Amsterdam.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01971003208-9061700

trum were

published

in March 1969

[9].

^We gave the

positions

of the unknown levels

along

^{with the} g- values of 4

f7 (8S0)

⁵

d2 levels,

^the

complete 4 f8(7P) 6 s

multiplets,

^{over 40} levels of the 4

fl(7 F)

⁵

^d,

^many

levels of the 4

f8(7F)

6 p

subconfigurations

and many unidentified odd levels.

Independently

^{and at the}

same

time, Spector [10]

^{at the San}

Diego Meeting

of the

Optical Society (March 1969) presented

^{11 levels}

of the 4

f8(7F)

^{6 s}

multiplets (the

^{two levels with}

J =

1/2

^{were not}

given).

^{The same author}

[11] ]

ⁱⁿ

March 1970

published

^a list of 966 Gd lines in the

region

^{7 300-12 300}

A ;

^he

assigned

602 of them to the Gd 1 and 309 to the Gd II spectrum. ^{In the sche-}

mes of Gd I and Gd

II,

^we classified 491 of these lines as transitions between Gd 1 levels and 243 as

transitions between Gd II

levels ;

³⁶ of the classified lines had a wrong

assigment.

In 1970

Spector [12]

gave ^more results : 17 even

levels of the 4

fl(7 F)

^{5 d}

subconfiguration (all

pre-

viously published by

^{us in}

1969)

which levels

belong

to the octets and 61 odd

levels,

^{31 of} which he inter-

preted

^{as levels}

belonging

^{to the 4}

f8(8F)

⁶

po

^suc-

configurations.

^{Seven levels of the} group of odd

levels have incorrect

J-values,

^{three of these levels}

were

already given

^{in our article}

[9]

^{and at least four}

levels,

^not

belonging

^{to the 4}

f ’(’F)

⁶

p° subconfigu-

ration are fortuitous

(see also § II).

Furthermore he gave 300 classified lines as transitions on the

newly

detected levels. In connection with the incorrect

interpretations

^{of the J-values and} the fact that several levels which

Spector

^{ascribed to the 4}

f8(7F)

6 p

subconfiguration

^{must be}

interpreted differently (see § IV),

^his calculations of the

predicted positions,

percentage

compositions

^and calculated values for this

subconfiguration

^is erroneous.

Recently Spector [13] ]

^{made a} calculation in the 4

f8(7F)

^{5 d subcon-}

figuration, using

^{45 of our level}

values,

^{and a}

good

fit was obtained

(see §

^{V and}

VI).

II. The

wavelength

^{list and the} classifications. ^- Our list contains over 18 500 lines in the

region

2 468-8 752

A,

^{with all} information on a

magnetic

tape. ^{In the table 1 we}

give

^the computer-output ^of

a part ^{of the list. In} the first column the number of the line is

given, starting

^with

1, 6, 11,

^{etc. In the case}

of a

doubly

^or

trebly

classified

line,

^{it has 2 or 3 num-}

TABLE 1

Gadolinium

wavelengths, wavenumbers,

transitions and Zeeman

effects

bers

(see

2 370 and 2

371).

^{In the} second column is the

intensity ;

lines with an asterisk have been measu-

red in the track of the lowest _exposure

[8].

^{The num-}

bers in the third column refer to the character of the line under consideration. The code is the

following :

0 means the line is

symmetrical, 1

^{and 2 are used for}

asymmetrical lines (1

for shaded to shorter

wavelength,

2 for shaded to

longer wavelength,

^{and 3} is used for lines which are

strongly perturbed ; 5, 6, 7,

^{and 8 have} the same

meaning

^as

0, 1,

^{2 and 3 for broadened} lines. In the columns 4 and 5 the

wavelengths

^and

wavenumbers have been recorded. In column 4 the

wavelength

^is

given

ⁱⁿ

^A

^x

¹⁰⁺⁴

^{and the wavenumber}

in column 5 in mK

(1

^{K is 1}

cm-1).

^{In the next column}

we

give

^the

assignment

^of the classified lines to Gd 1

or Gd II. The columns

7, 8,

^{9 and} 10 contain the level values in 0.1 K

(the

first level is

always

^{the odd}

one)

and the J-values

(omitting

^{the decimal}

point).

^In

column

11,

^{Au = 6} observed-a calculated

(in mK).

Owing

^{to the} accuracy of the measurements

only

values

of 1 Au 1

^{30 mK are}

printed. Only

ⁱⁿ

special

cases, for instance

doubly

classified

lines,

^{has a}

bigger discrepancy

^been

accepted.

^{The next 5} columns refer to the results of the Zeeman effect measurements, in columns 12 and 14 the

g-values

^{of the} levels times

10+ 3,

mentioned in the columns 7 and

9,

in the columns 13 and 15 the J-values

(identical

with the columns 8 and

10).

^{When the}

pattern

^was

unresolved,

^we calculated the

g-values

^if the transition was known

(see

for instance the lines Il 326 and

11 332) (1).

^In

the cases of unclassified lines

(2

^{399 and 2}

401),

^when

J1 =1= J2,

^{we list in column 12 the}

position

^{of the}

strongest a-component ^{f on one} side of the pattern and in column 14 the value of the width of the x-

pattern ^{Je on the same}

side ;

^{in column 16 the cha-}

racter of the

pattern :

^{SO means shade-out}

(1)

^{See note on next page.}

619

SI means shade-in

(Jl > J2

^and 91 >

g2).

^When

J1

⁼

J2,

^we put ^{in column 12} the values of the center

of gravity

^{in the} a-pattern and in column 14 the value of the strongest Tr-component ^{on one} side of the pattern ; ^{in column 16 the}

symbol

^{S stands for} sym- metrical. In cases of the _presence of Paschen-Back effect

(over

¹⁰

%

of the measured

patterns)

^column

16 is needed for the abbreviation PB.

In column 17

King’s

classification is

given.

^{If it}

is necessary ^to

give

^more information about the

wavelength,

^{the Zeeman}

effect,

etc., ^{we add our}

comments under that

wavelength.

^{It is not}

possible

to

publish

^{the whole}

wavelength

^list.

People

^{who are}

interested in it can receive a copy of the list _upon request

(1).

Since we do not want to repeat ourselves in both articles about the

Gd-spectrum,

^we

give

information for both

spectra.

We have classified over 2 200 lines as Gd II tran- sitions and over 5 300 lines as Gd 1 transitions. This is about

42 %

of the total number of the lines.

Nearly

400 lines have been

doubly

classified

(in

^{Gd 1 and Gd}

II) ;

in many ^cases the double classifications could be deter- mined

by

^{Zeeman effect} measurements

(see

^numbers

2 370 and 2 381 in Table

I).

^We measured about 2 700 Zeeman patterns, ^{of which} about 300 have not

yet ^{been used in the}

analysis.

^{It must be mentioned}

that for a

large

^number of unclassified

lines,

^{we have}

not yet ^measured the Zeeman patterns.

Progress

^{can be}

expected

^{in the}

analysis, especially

for

detecting

^{levels of}

high

energy which ^{are not} based

on the 4

f7 (8S0)

^{- and 4}

f8(7F)

^terms.

However,

the location of these levels will be

difficult,

^because

in most cases the lines are weak. The total

intensity

of the unclassified lines is about

10 %

of the total

integrated intensity

^{in the} spectrum. ^{From the Gd-}

lines

given

^{in the}

NBS’monograph 32-part

^{1 : Tables}

of

spectral-line

intensities

[14]

^we classified 1 402 lines out of the total number of

1413,

^{that is}

99 % ;

^{5 lines}

assigned

^{to Gd II and 6 lines to Gd I remained un-}

classified. In respect ^to

King’s

^list

[2],

^{we remarked}

that many of his

assigments

^{to Gd 1 or Gd II lines}

were

incorrect,

^some in the lowest

wavelength region

and many in the

highest region.

^In the lowest

region

a number of lines which he

assigned

^{as Gd II lines}

belong

^{to Gd 1} transitions and in the

highest region

vice versa. Out of 2 627 Gd II lines

given by him,

about 800 remained

unclassified,

^{most of them in}

the

wavelength region

^{less than 3 000}

^Á.

^{This confirms}

the above mentioned

proposition

^that many

high expected

^{levels can be found.}

III. The levels of Gd II. ^- In Table II we

give

all known odd levels of Gd II in the order

of increasing

energy and in Table III the even ones

(2).

^We

give

in column 1 the term value in

cm-1,

^{column 2 the}

J-value and in column 3 the

g-value

^{rounded off}

at 0.005. If the level has a Paschen-Back

effect,

^{it is}

given

^{in column 4. In} the fifth column we

give

^the

configuration

^{to which the level}

belongs

^{and in the}

last column the

multiplet.

^{Here it must be mentioned}

that the level values differ somewhat from the values

given

^{in reference 9. The reason for this difference}

has been described

by

Hoekstra and Slooten

[7],

^so

we can omit a discussion here. In the same article the reader can find the method for

determining

^the

level values to three decimal

places.

The J-values

are without doubt well

established,

because for all levels we determined the

g-value

^{at least twice.}

A more accurate

listing

^{of the}

g-values

^{than ± 0.005}

is without

meaning

^{because many of} the measured patterns ^are unresolved. In Table IV we

give

^the computer output of all transitions of the odd level

TABLE IV

Transitions

of

^{the level 37}

^569.5310

^{J =}

11/2

37

596.5310 cm-’

J ⁼

11/2

^{of the 4}

f8(7F)

6 p confi-

guration.

The columns have the same

meaning

^as

given

^{in Table 1}

(the

^{number in the} list of the lines

has been

omitted)

except ^{that in the} last column

we have

accepted

^a

discrepancy of Ao- 1

⁵⁰

mK,

to include transitions which we had not

accepted

ⁱⁿ

our

list ;

in many ^{cases a} line has 2

classifications,

and this is the case with the

wavelength 5 212.2104Â

(the

^{line is broadened}

(character 5),

^the

discrepancy

^is

- 31 mK in this

transition,

^{and in the other one}

it is ^- 6

mK). Furthermore, King’s

classification

[2]

(1) ^{Th. A. M. van} Kleef, ^Zeeman Laboratorium.

(2) ^{The tables II and III are available} to anyone interested at the address : Rédaction du Journal de Physique, 33, ^rue Croulebarbe, ^Paris.

and the measured Zeeman pattern indicate that the line

belongs

^{to Gd} I. We measured two Zeeman patterns ^at 3 510. 5984

A ;

^{the first one is in} agreement with the transition

given,

^{the second one}

belongs

^to

an unknown

transition, probably

^a

6p 1/2 - 8G,/2

(accepting negative g-values).

A level is attributed to a

configuration only

^when

we are

absolutely

convinced of its

reality.

^{The same}

assumption

is made for the

multiplet assignment.

Of the 11 new odd levels

given by Spector [12], only

two could be confirmed

by

^{means of Zeeman effect}

measurements and

they

^{are included in Table III.}

We remarked that in addition to our

previous publi-

cation

[9],

^{we located 12 even} levels of the 4

f8(7P)

^{5 d}

subconfiguration

^{and 24} odd levels. The 4

f8(7 F)

^{5 d}

configuration

^is

complete.

IV.

Interprétations

^{of the odd levels. - The lowest}

odd levels of Gd II can be derived from the

ground-

state of the

Gd3 + -ion

4

f7 (8S7/2) by adding

^{a combi-}

nation of two

(d

⁺

s)-electrons.

^{As the} lowest level in Gd IV

(8S°7/2)

^{is about 32 500 cm-1 below the}

next

multiplet (6P° ^[15], [16]),

^{we also can expect that}

in Gd II the odd levels not based on the

’S07/2

^will

be about 32 500 cm-1 above the lowest

multiplet

4 f7(IISO) 5 d 6 s ’OD5/2, 0

We have also identified the

configuration

⁴

^f8

6 p. The lowest

multiplets

^{in this}

configuration

^{are based on the 4}

f8(7F).

^In

comparison

with other

spectra

^{in the} lanthanides

[17], [18], [19], [20],

^the transitions between

4 f8(7P)

^{6 s and the}

4

f8(7F)

⁶

p-levels

^{must be found at} about 24 500

cm-1 (4 000 A).

^{As the lowest state of the 4}

f8(7F)

^{6 s}

8F13/2

has been located at 7 992. 268 cm-1

(see § V)

^above

the

groundstate

⁴

f’(8S°)

^{5 d 6 s}

10D5/2’

^{the lowest}

levels of the 4

fl(7 F)

6 p

subconfiguration

^{can be}

expected

about 32 500 cm-1 above the

groundstate, independently

^{of the}

coupling

^{scheme in the 4 f8} 6 p

configuration.

^{These two} facts indicate that many levels will _appear at the same energy. This ^means that

only intensity

rules and not the

g-values give

information about the

assignment

^{of the}

levels,

because both

configurations

contain the same multi-

plets.

^{In Table V we}

give

^{the lowest}

multiplets

^{of the}

lowest odd

configurations

in Gd II. The underlined

multiplets

^{in the 4}

^f7

^{5 d 6 s}

configuration

^are

expected

TABLE V

« Low

»-expected

^odd

multiplets

^{in Gd II}

at the same

height,

^{as the lowest}

multiplets

ⁱⁿ

4 f8(7F)

6 p. The

multiplets

derived from the

can be

expected

^{3 000 cm-1}

higher [15], [16].

The

subconfigurations

^{based on the 4}

f 7 8SO)-core.

^-

We have determined all levels based on 4

f7(8 S’)

^{5 d 6 s,}

4

f7(8S0) 6 ^s2

^{and 4}

f7(8S0)

⁵

^d2

and have confirmed the

analysis

^{of Russell}

[1].

^{All his levels} except 1 ° J ⁼

5/2

^have been confirmed

by means

^{of Zeeman}

effect measurements. His

20,

^{3° and 40 levels were} identified as 4 f7 5

d2 8P07/2, 8P9/2

^and

6F9/2

^respec-

tively.

^The other levels

belonging

^{to the 4}

f7 (8S)

^{5 d2}

subconfiguration

^were

easily

^found

by

^us

including

the

high

^{level 4}

^f7

⁵

^d2 8S07/2.

^{The one remarkable}

thing

^{about the 4}

f’(8S°)

⁵

^{d 2} subconfiguration

^{is the}

large discrepancy

^{in the}

g-values

^{of the 4 f7 5}

^d2 ’Do .5/2

and

8G5/2-values,

^{which are 1.690 and} 1.720 respec-

tively.

^{As the} theoretical

g-values

^{of these levels}

predicted

ⁱⁿ

LS-coupling

^are 2.057 and 1.257 respec-

tively,

^{and since} the calculation in the

coupling

^scheme

mentioned elsewhere

[12] gives approximately

^these

same results

(a

similar calculation was made in

1969) (see § VI)

^{- there must be an} interaction with

higher

levels of the

multiplets

^{with the same}

L-values,

^which

have not yet ^{been detected.}

The difference in the sum between the

experimen- tally

determined

g-values

^{and the} theoretical ones

is 0.096

(see

^Table

II).

^{Moreover when we take the}

g-sum of all levels with J ⁼

5/2

^{in the}

configurations

4 f’ 5 d 6 s and

4 f7 5 d2

we find

in LS-coupling experimentally

21.086 and 21.050

respectively,

^the

difference

being

^{within our limits of error.}

Only

^the

fact that the levels

18.00103/2,

¹⁸

09505/2

^and

18 15007/2

have P. B.

effects,

^{allows us to maintain the}

given interpretations

ⁱⁿ

spite

^{of the}

g-values

^which suggest the alternative identification.

The

subconfiguration

⁴

f8(7F)

6 p. This subconfi-

guration

^{contains 37}

^{levels ;}

^among the levels

arising

above 32 500

cm-1,

^we have ascribed 30 to this

configuration by

^{means of their strong} transitions with the levels based on the 4

f8(7F)

^{6 s and}

4f8(7 F)

^{5 d}

subconfigurations.

^As

already

^mentioned

(§ II)

^the

p-d

transitions have been located in the red and infrared

region. Many

^{lines in}

King’s

^list

[2]

^which

he attributed to class

V, appeared

^{to be}

just

^these

p-d

transitions. This was confirmed

by

^{Zeeman effect}

measurements. Our first

attempt

^to

interpret

^the

4

f8(7F)

6 p ^was in the

LS-coupling

^scheme

[9],

^but

in the course of this work we concluded that the

J-j coupling agreed

^much better with

experimental

^data.

The

remaining levels,

^{those not}

belonging

^{to this}

configuration,

^{in the}

region

32 500-40 000

cm-1,

and the levels with

higher

energy, have ^not yet ^been ascribed to a definite

configuration.

621

V.

Interprétations

^{of the even levels. - The low}

even

subconfigurations

^{in Gd II are}

4 f8(7F) 6 sand

4

f8(7 F)

⁵

^d,

⁴

f7(8So)

^{6 s} 6 p and 4

f7(8S0)

⁵ d 6 p.

All levels of the last two

subconfigurations

^were

previously given by

^Russell

[1] ; they

^{were confirmed}

by

^{us and the}

experimental g-values

^{were in}

good

agreement with the calculated values

given by

^Smith

and

Wybourne [5].

^The

interpretation

^{needs no further}

discussion. The first two

subconfigurations

^{are new.}

In the

region

above 38 000 cm-1 there are some levels which do not

belong

^{to the 4}

f7 (8S0)

⁵ d 6 p

configu-

ration. One

of them,

^{40 888.843 J =}

11/2 g

⁼

1.310,

has been

interpreted

^as

4 f8(5D) 5 d 4G11/2;

^the

position

^of this level is in very

good

agreement ^with the calculated value.

THE SUBCONFIGURATION 4

fl(7 F)

^{6 s. - We have}

located the 13 levels

belonging

^{to the}

^8F

^{and 6p}

multiplets.

^The lowest level

8F 13/2

^{is 7 992.268}

^cm-1

above the

groundstate

⁴

f7(8SO)

^{5 d 6}

s ’ODOS/2.

^The

level intervals in both

multiplets

agree

quite

^well

with the Landé-interval

rule,

except ^{for the}

- and the

’F, 1/2 _ 6F9/2

intervals. In Table VI we

give

^the intervals in these

multiplets

^{and the ratio}

This ratio increases

slightly

^{when J} increases from

1/2

to

13/2

^{in both}

multiplets

except ^{for the}

13/2-11/2

interval in the

8p,

^but

strongly

increases from

9/2

^to

11/2

^{in both}

multiplets.

TABLE VI

Levels

of

^{the 4}

f8(7P)

^{6 s}

^{8F and 6F} multiplets

The

possible

^{reason for this}

jump

may be that there is a strong

perturbation

between the levels of these

multiplets

^{and the levels}

belonging

^{to the 4}

f8(5D)

^{6 s}

6,4D multiplets.

The lowest ones which have J ⁼

9/2

and J =

7/2,

^{were located at} 26 351. 767 cm-1 and 27 273.505 cm-1

respectively.

^The

experimental g-values

^{of the}

^8,6F

levels agree very well with the theoretical

gLs-values. Only

^for the levels

having

J ⁼

11/2

^{in both}

configurations

^is

Ag (=

gobS -

9cale.) large

ⁱⁿ

comparison

with the other

dg’s,

which indi- cates a strong

interaction,

^{as was} confirmed later

by

calculations

(see § VI).

^{We should}

point

^{out that the}

Ag-values

^are

negative

^{for all 8F} levels and

positive

for the 6p ones, which is in agreement ^{with the}

theory

that when there is an interaction between two levels with the same

J-value,

^the

highest g

^{decreases and the}

lowest g

^increases.

THE SUBCONFIGURATION 4

f8(7F)

^{5 d. -} This confi-

guration

^{contains ten}

multiplets : 8,"(HGFDP).

^All

57

expected

^{levels are known. In our}

previous publi-

cation

[9]

^{we have}

given

^a wrong

assignment

^{to the}

levels

belonging

^{to the 4}

f ’(’F)

^{5 d and 4}

f8(5D)

^{6 s}

multiplets respectively. Spector [12]

^has

given

^a

explanation

^{of this}

misunderstanding.

The fact that the 4

f8(-5D)

^{6 d}

6D9/2

^{level is} lower than the

level

explains why

^{the total}

splitting

^{of the 4}

f8(7F)

^{6 s}

6D

multiplet

^is smaller than the

predicted

^one

[22],

because of a strong interaction between ^both multi-

plets [21].

^{This is contrary to}

Spector’s opinion [12].

In

figure

^{1 we}

give

^{the Grotrian}

diagram

^{for the}

even levels of Gd II in the

region

^{18 000-34 000}

^cm-1.

It can be seen, that the ⁴

f 8(’F)

^{5 d 6D}

multiplet

^is

FIG. 1.

irregular

^{for the interval}

6D9/2 - ’D7/2.

^The

^figure

shows the isolated

position

^{of the}

8(G, ^{F, D,} H)

^and

6F multiplets.

Most of the other

multiplets

^{of this}

subconfiguration

appear ^at the same energy ^as the levels of the 4

f ’(’S’)

^{6 s} 6 p and 4

f7(8S0)

^{5 d 6} p

configurations.

An interaction between these levels

can be

expected

^{and is} demonstrated

by finding

^com-

binations with reasonable

intensity

^for transitions between the levels of these

multiplets

^{and the lowest}

odd

multiplets

⁴

f7 (8S0)

^{5 d 6}

s 10,8,8,6D°

and

The

recently

^{detected 6H}

multiplet

^{is a}

good example.

The

6H15/2

^{and -}

6H13/2

levels which are isolated from the 4 f’

6 s 6 p

^and

^{4 f’} 5 d 6 p

levels with the

same

J-values,

^combine

only

with the levels derived from 4 f8 _{6 p in} the infrared

region. They

^{do not}

give

any transition with the levels of the low-odd multi-

plets

^{mentioned above. The}

6H5/2

^and

6H7/2

^levels

were determined

only

^on transitions with the levels of these low

multiplets,

^{while the}

6H9/2

^and

6Hll/2

give

^weak transitions both with the levels of the low odd

multiplets

^{and those of the 4}

^f8

6 p

configuration.

VI. The calculations. ^- We have

recently

^detected

12 levels of the 4

f ’(’F)

^{5 d}

subconfiguration

^{and have}

made a theoretical

study

^{of this}

configuration together

with the 4 f8

(three SD)

^{6 s terms. Their} interaction is _very strong ^{and one of us has}

recently published [21] ]

the 4

f7(8SO) (5

^{d + 6}

s)2 subconfiguration

^{in con-}

junction

^{with the 4}

f7(6pO) (5

^{d + 6}

s)’ subconfigu-

ration. The results are

given

^{in Table}

VII, together

with the parameters ^of

The parameters ^are

given

in the first column

(0153L(L+

1)

takes care of the effect of the operator

aL2) ;

^{in the}

last three

columns,

the values of the radial parameters and the associated standard errors are

given.

^When

a parameter ^{has been}

assigned

^{to a value} in the last

iteration,

the standard error is

replaced by

^{« fixed ».}

At the end of the table we

give

^{the mean}

coupling

percentage ^{for LS}

coupling.

Here :

where

Eo

^{is the observed term value and}

Ec

^{the cal-} culated value of the levels. N is the number of observed levels and _p is the number of free parameters ^{used in} the calculation. The main

part

of these calculations has been carried out

by

^{means of four} programs

[23]

with the use of the computer ^UNIVAC 1108 of the Faculté des Sciences

d’Orsay.

623

TABLE VII

Slater parameters ⁱⁿ the

configurations of

^{Gd II}

LE JOURNAL DE PHYSIQUE. ^{- T.} 32, ^N° 8-9, AOUT-SEPTEMBRE 1971

TABLE VII

(suite)

In

Spector’s

^{treatment of the 4}

f $(’F)

6 p subcon-

figuration

several levels were misidentified and some

of the J-values were wrong.

Consequently,

^{we made}

a new calculation of this

subconfiguration

^{both in}

LS - and

Jj-coupling.

^The

parameters

^are

given

ⁱⁿ

Table VIII. The calculated values for the 4

f8(7P)

6 p levels are

given

^{in Table IX}

along

^{with the}

predicted positions

^and percentage

compositions.

^{Most of the}

levels are

extremely

pure in

J-j coupling,

^whereas

only

22 levels have a main L-S component greater ^than 50

%.

^In

comparison

^with

Spector’s

^treatment

[12]

we have

changed

⁸ level values out of 28. There is

now a

good

agreement between the calculated and the

experimental level

^values.

TABLE VIII

Parameter values

of

^{the 4}

^f8

6 p

configuration

Acknowledgements.

^{- The authors are}

grateful

to Dr. P. E. Noorman and Dr. M. Fred for

exposing

the

Gd-plates.

^We thank Dr. R. Hoekstra and Mr. Slooten for

measuring

^the

wavelengths

^{in zero}

magnetic

field. The CDC-3 200 computer ^was put ^at the

disposal

of the Zeeman

laboratory by

^{the « Stich-}

ting

^voor Fundamenteel Onderzoek der Materie ».

(*) Spector’s

^values

[12].

625

TABLE IX

Predicted

positions,

percentage

compositions

and calculated values

for

⁴

^f8

⁶ p

References

[1] ^RussELL (H. N.), ^J. Opt. ^Soc. Amer., 1950, 40, ^550.

[2] ^KING (A. S.), Astrophys. J., 1943, 97, ^323.

[3] ^BRIX (P.) and LINDENBERGER (K. H.), ^Z. Physik., 1955,141,1.

[4] ^ALBERTSON (W. E.), ^BRUYNES (H.) ^{and HANAU} (R.), Phys. Rev., 1940, 57, 292.

[5] ^SMITH (G.) and WYBOURNE (B. G.), J. Opt. ^Soc. Amer., 1965, 55, 1278.

[6] ^DESMARAIS (D.) and PINNINGTON (E. H.), ^J. Opt.

Soc. Amer., 1967, 57, 1245.

[7] ^HOEKSTRA

(R.)

and SLOOTEN (R.),

Spectrochim.

^Acta, 1971, ^26B.

[8] ^HOEKSTRA (R.), Thesis, Amsterdam, 1969.

[9] ^BLAISE

(J.)

and VAN KLEEF (Th. ^A. M.), C. R. Acad.

Sci., 1969, 268, ^792.

[10] ^SPECTOR (N.), ^J. Opt. ^Soc. Amer., 1969, 59, ^488A.

[11] ^SPECTOR (N.) ^{and HELD} (S.), Astrophys. J., 1970, 159, ^1079.

[12] ^SPECTOR

(N.),

^J. Opt. ^Soc. Amer., 1970, 60, ^763.

[13] ^SPECTOR (N.), ^J. Physique, 1970, 31, ^C4-173.

[14] ^MEGGERS (W.

F.),

^CORLISS (Ch. H.) and SCRIBNER

(B. F.), ^{N. B. S.} Monograph ^32-Part 1, ^1961.

[15] ^CARNALL (W. T.), ^FIELDS (P. R.) and RAJNAK (K.),

J. Chem. Phys, 1968, 49, ^{4412 and} 1968, 49,

4443.

[16] ^CASPERS (H. H.), ^MILLER (S. A.) ^{and RAST} (H. E.), Phys. Rev., 1969, 180, ^329.

[17] ^ROSEN (N.), ^HARRISON (G. R.) and MCNALLY (J. R.), Phys. Rev., 1941, 60, 722.

[18] ^RUSSELL (H. N.), ^ALBERTSON

(W.)

^{and DAVIS} (D. N.), Phys. Rev., 1941, 60, ^641.

[19] ^MCNALLY (J. R.) ^{and VAN DER SLUIS} (K. L.), ^J. Opt.

Soc. Amer., 1959, 49, ^200.

[20] ^BLAISE

(J.)

^{and CAMUS} (P.), ^{C. R. Acad.} Sci., 1965, 260, 4693.

[21] WYART (J. F.), C. R. Acad. Sci., 1970, 271, ^849.

[22] ^ELLIOTT (J. P.), ^JUDD (B. R.) and RUNCIMAN (W. A.),

Proc. Roy. Soc., 1957, 240, ^509.

[23] ^BORDARIER (Y.) ^{and CARLIER}

(A.),

Programme

AGENAC de calcul de formules suivant l’algèbre

de Racah ; ^BORDARIER (Y.), Programme ^ASSAC

de regroupement ^des résultats d’AGENAC.

BORDARIER

(Y.),

and DAGOURY

(P.),

Programme

DIAGAC de diagonalisation ^et de calcul de dérivées des énergies ^{et des} g, Orsay, 1968 ;

BORDARIER (Y.), Programme ^GRAMAC d’opti-

misation des paramètres par moindres carrés, Brochure en préparation.