Electronic Structure of the Actinide Elements - Advances in Chemistry

14 Electronic Structure of the Actinide Elements MARK FRED

Downloaded by UNIV OF ARIZONA on November 12, 2012 | http://pubs.acs.org Publication Date: June 1, 1967 | doi: 10.1021/ba-1967-0071.ch014

Argonne National Laboratory, Argonne, Ill.

The 5f, 6d, and 7s electrons of the elements from actinium to curium, all having about the same energy, produce many low levels. The spectra are complex, and analysis is complicated by the existence of two sets of low parent terms built on f and f d, having opposite parities and responsible for two almost independent sets of transitions. Within the past several years considerable progress has been made in the analysis with the aid of new data, especially Zeeman data, and the further help of theoretical predictions. It is now possible to describe the variation of binding energies of different types of electrons as a function of atomic number and degree of ionization, which can be correlated with chemical behavior. N

N-1

T n t e r e s t i n the e l e c t r o n i c structure of t h e actinides existed before t h e * ·* t r a n s u r a n i c elements b e c a m e a v a i l a b l e . T h i s w a s s t i m u l a t e d b y the h o p e that k n o w l e d g e of t h e structure c o u l d l e a d to p r e d i c t i o n s chemical behavior.

about

S i n c e the s t r u c t u r e w a s difficult to e s t a b l i s h , t h e

c h e m i c a l b e h a v i o r w a s e s t a b l i s h e d first a n d d e d u c t i o n s w e r e t h e n m a d e a b o u t t h e structure. T h e s e d e d u c t i o n s about a c t i n i d e atoms w e r e v a g u e because c h e m i c a l b e h a v i o r

is also i n f l u e n c e d b y n e i g h b o r i n g

atoms.

F i r s t , i t w o u l d b e d e s i r a b l e to k n o w t h e s t r u c t u r e of i s o l a t e d atoms. T h e m o s t precise i n f o r m a t i o n a b o u t this comes f r o m a t o m i c

spectroscopy.

H o w e v e r , a c t i n i d e spectra are v e r y c o m p l e x , a n d e a c h element c a n p r o d u c e tens of thosands of different lines. H e n c e , i t is difficult b o t h to d e t e r m i n e the e n e r g y levels w h i c h cause t h e transitions a n d to i d e n t i f y the levels i n terms of q u a n t u m n u m b e r s a n d e l e c t r o n configurations. A f t e r 20 years of effort w e h a v e b e e n able to a n a l y z e m a n y of these spect r a a n d extract definite i n f o r m a t i o n a b o u t t h e r e l a t i v e b i n d i n g energies of the v a l e n c e electrons. 180 In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

14.

F R E D

Electronic

Structure

181

Energy Levels L e v e l s are i d e n t i f i e d f r o m the f o l l o w i n g considerations.

Each kind

of e l e c t r o n c o n f i g u r a t i o n gives rise to a c e r t a i n n u m b e r of levels for e a c h v a l u e of J , the t o t a l a n g u l a r m o m e n t u m . T h e v a l u e of the energy for e a c h l e v e l is g i v e n i n p r i n c i p l e b y the s o l u t i o n of Schrôdinger's e q u a t i o n , expressed as a c o m b i n a t i o n of p o w e r s of r i n t e g r a t e d over the e l e c t r o n d e n s i t y . Since a n exact s o l u t i o n is i m p o s s i b l e i n p r a c t i c e , it is c u s t o m a r y to fit the levels e m p i r i c a l l y u s i n g the a n g u l a r parts of the integrals ( w h i c h Downloaded by UNIV OF ARIZONA on November 12, 2012 | http://pubs.acs.org Publication Date: June 1, 1967 | doi: 10.1021/ba-1967-0071.ch014

c a n b e d e t e r m i n e d e x a c t l y ) as coefficients for the r a d i a l integrals w h i c h are t r e a t e d as parameters.

T h e parameters c a n be d i v i d e d i n t o electro-

static interactions ( e l e c t r o n - n u c l e u s a n d e l e c t r o n - e l e c t r o n )

and spin-orbit

interactions, w h i c h are m a g n e t i c . T h e L S l e v e l scheme corresponds to t h e case i n w h i c h t h e electrostatic parameters are large c o m p a r e d w i t h the s p i n - o r b i t parameters. elements.

T h i s scheme is a g o o d a p p r o x i m a t i o n for l i g h t

T h e s p i n - o r b i t i n t e r a c t i o n increases r a p i d l y w i t h a t o m i c n u m -

ber, a n d the actinides are m o r e a p p r o p r i a t e l y d e s c r i b e d b y the /; c o u p l i n g scheme, i n w h i c h the electrostatic i n t e r a c t i o n is s m a l l c o m p a r e d w i t h the spin-orbit. I n the g e n e r a l case ( i n t e r m e d i a t e c o u p l i n g ) the different parameters are c o m p a r a b l e .

L e v e l s w i t h the same / interact, a n d the w a v e f u n c t i o n s

m i x . T h e properties w h i c h d e p e n d o n the w a v e f u n c t i o n s are c o n s e q u e n t l y i n t e r m e d i a t e , p a r t i c u l a r l y the g-factors a n d the r e l a t i v e intensities of transitions to these levels. It is a n i m p o r t a n t p o i n t that the g's a n d i n t e n s i ties c a n b e c a l c u l a t e d f r o m the same parameters w h i c h d e t e r m i n e the energies, so no a d d i t i o n a l parameters are r e q u i r e d . Configuration. I f w e find e x p e r i m e n t a l l y a set of levels w h o s e e n ergies c a n b e d e s c r i b e d b y the r i g h t n u m b e r of parameters, a n d these parameters also give the r i g h t g-factors a n d r e l a t i v e intensities, w e c a n b e confident i n a s s i g n i n g t h e m to a g i v e n configuration. T h e assignment w o u l d be d o u b t f u l i f i t r e q u i r e d m o r e parameters for this c o n f i g u r a t i o n because w e c a n fit a n y set of levels w i t h e n o u g h parameters. W e

could

o b t a i n c o r r o b o r a t i o n i f the g's fit a n d the parameters are consistent w i t h the systematics of these configurations.

T h i s is v a l u a b l e b e c a u s e often

configurations are p e r t u r b e d b y other configurations ( c o n f i g u r a t i o n i n t e r a c t i o n ) a n d d o not g i v e a n exact fit b u t a close fit. Sometimes the fit is not close i f the c o n f i g u r a t i o n i n t e r a c t i o n is large, i n w h i c h case b o t h configurations m u s t b e c o n s i d e r e d

together.

E v e n t h o u g h a p r o p e r d e s c r i p t i o n of a c o n f i g u r a t i o n m u s t be

made

i n i n t e r m e d i a t e c o u p l i n g , i t is often u s e f u l e x p e r i m e n t a l l y to i d e n t i f y the levels a c c o r d i n g to the nearest p u r e c o u p l i n g s c h e m e because the l e v e l separations, g-values, a n d intensities a p p r o x i m a t e l y

correspond.

T h e levels of v a r i o u s configurations c a n b e i d e n t i f i e d f r o m the a p p r o p r i a t e secular equations.

T h i s i d e n t i f i c a t i o n was m a d e i n the e a r l y

In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

182

LANTHANIDE/ACTINIDE CHEMISTRY

Table I.

Conf.

Spectrum

%

1%

21/2

3y

A c III Pal P u II Ami Pal Pull Pal Paï Ami

2 10 17 8 184 61 88 825

6 21 31 15 342 110 160 1548

1 7 28 42 19 457 141 203 2085

0

1

2 8 21 6 14 48 14 825

1 23 40 7 36 136 19 2373

f fV fs fs fd£ fds fdïs fdsp fdp l

2


2

/%

Pall Pa II UI UI UI Pu I Pu I Cm I

2

fds /V fds fds

2 2

/%

2

fdsp

N u m b e r of L e v e l s of E a c h

4V2

51/2

6V2

1 7 30 50 19 516 149 212 2386

7 29 46 17 517 139 192 2443

5 26 42 13 466 113 154 2285

3 20 35 9 390 83 109 1971

305 52 66 1576

2

3

4

5

6

7

3 34 70 17 50 206 37 3633

1 38 71 13 59 251 37 4471

3 36 78 19 60 265 46 4829

1 30 61 14 54 252 37 4728

2 22 52 13 44 220 38 4256

14 31 7 31 176 24 3547

2

71/2 3 16 26

5

days of s p e c t r o s c o p y o n a n e m p i r i c a l basis w i t h o u t e x p l i c i t k n o w l e d g e of the e n e r g y equations, i n m u c h the same w a y that the e a r l y chemists e s t a b l i s h e d m o l e c u l a r structure a p p a r e n t l y b y i n t u i t i o n .

organic Com-

p a r i s o n w i t h t h e o r y is essential for spectra a r i s i n g f r o m a n u m b e r v a l e n c e electrons.

of

T h i s is p a r t i c u l a r l y necessary for the l a n t h a n i d e s a n d

actinides because of the presence of /-electrons, w h i c h results i n m a n y levels.

Instead of s o l v i n g h i g h order secular equations for these, i t is

m o r e a p p r o p r i a t e to use the f o r m a l i s m of m a t r i x m e c h a n i c s . v a l u e of / the levels are d e s c r i b e d b y the eigenvalues a n d

F o r each

eigenvectors

of the H a m i l t o n i a n operator, the m a t r i x elements b e i n g expressed b y the same Slater parameters a c c o r d i n g to the tensor a l g e b r a of R a c a h (25, 16, Racah's m e t h o d s , a l t h o u g h a p p e a r i n g abstract, p e r m i t a great

17, 18).

s i m p l i f i c a t i o n i n c a l c u l a t i n g the coefficients

appearing i n each matrix

element a n d m a k e i t feasible to calculate t h e m b y c o m p u t e r .

Computer

c a l c u l a t i o n is u s u a l l y necessary because there are s t i l l m a n y c a l c u l a t i o n s to p e r f o r m . S o m e t y p i c a l configurations w h i c h are f o u n d i n a c t i n i d e spectra are s h o w n i n T a b l e I, w h i c h lists the n u m b e r of levels to b e e x p e c t e d for e a c h /-value.

I n most cases the n u m b e r of levels is l a r g e a n d i n some cases

enormous.

F o r the f

configurations the s i t u a t i o n is not f o r m i d a b l e , a n d


14.

Electronic

F R E D

183

Structure

J f o r Some A c t i n i d e C o n f i g u r a t i o n s


8%

91/2

I0y

2

111/2 I21/2

131/2

141/2

151/2

16%

Total 2 41 198 327 107 3675 893 1229 18131

1 9 18 2 216 29 32 1170

5 11

3 5

1 3

1

139 12 11 803

79 4 2 505

40

18

5

1

288

147

66

25

7

1

8

9

10

11

12

14

15

16

7 21 7 19 129 20 2746

2 8 2 11 87 11 1973

4 2 5 52 8 1308

1 27 2 793

13 2 435

13

5

1

213

91

i t w i l l b e i n s t r u c t i v e to c o n s i d e r these

first.

32

8

17

Total

1

13 214 457 107 384 1868 295 36230

T h e s e configurations

are

o b s e r v e d i n s o l i d c o m p o u n d s a n d i n solutions of the 3 ions, a n d the same +

levels also o c c u r i n the n e u t r a l atoms i n the configurations / V since the ^-electrons f o r m a c l o s e d s h e l l a n d d o not c o n t r i b u t e to the structure. T h e 4f

N

configurations h a v e b e e n s t u d i e d for a l o n g t i m e i n the l a n t h a n i d e

elements a n d are n o w w e l l e s t a b l i s h e d . T h e same t e r m s t r u c t u r e is f o u n d i n the 5/* configurations of the a c t i n i d e s , a l t h o u g h the spacings are d i f ferent because the electrostatic parameters are s m a l l e r a n d the s p i n - o r b i t p a r a m e t e r larger. T h e l o w terms are s h o w n s c h e m a t i c a l l y i n F i g u r e 1. T h e n u m b e r of terms increases w i t h the n u m b e r of /-electrons u p to a h a l f - c l o s e d s h e l l a n d t h e n decreases s y m m e t r i c a l l y . T h e m a x i m u m m u l t i p l i c i t y also increases a n d t h e n decreases, so that b o t h factors c o n t r i b u t e i n the same d i r e c t i o n to the d i s t r i b u t i o n of levels s h o w n i n T a b l e I. F o r e a c h c o n f i g u r a t i o n the lowest t e r m , w h i c h is the most i m p o r t a n t , is g i v e n b y H u n d ' s r u l e that the lowest t e r m is the t e r m of h i g h e s t m u l t i p l i c i t y ( S-value) h a v i n g the largest L - v a l u e ( o r b i t a l a n g u l a r m o m e n t u m ) . x

The

LS d e s i g n a t i o n for the lowest t e r m , i n fact for a l l the terms, is a n a p p r o x i m a t i o n because the c o u p l i n g is i n t e r m e d i a t e . E a c h t e r m consists i n g e n e r a l of a n u m b e r of levels, a n d a g i v e n l e v e l interacts w i t h the levels of other terms h a v i n g the same / - v a l u e . T h e terms m i x a n d e a c h is i m p u r e .


184

LANTHANIDE/ACTINIDE

CHEMISTRY

0

0|

—-5H

_ 5

- F, S — 4

4

-10

— F, S

1

5

-20-

— I 9

-50 -60

— 3 p

6

—V s

~"

-10

3h

—

5

G

-30

HSSp

01 ο ι Lu H Z

-40

4

20

~~

>

D3 by Nielson and Koster

(14),

there are six different P terms, a n d f o u r S terms. I f w e h a d a f a i r l y p u r e 3

1

c o u p l i n g scheme, e a c h l e v e l c o u l d b e c o n s i d e r e d i n d e p e n d e n t l y , a n d its e n e r g y i n z e r o ' t h a p p r o x i m a t i o n w o u l d b e g i v e n b y the v a l u e of the c o r r e s p o n d i n g d i a g o n a l m a t r i x element. c o m b i n a t i o n of

parameters.

E a c h s u c h e l e m e n t is g i v e n b y a

T h e r e are f o r m u l a s for the

off-diagonal


elements w h i c h represent the i n t e r a c t i o n b e t w e e n the t w o different terms w h i c h e a c h one connects.

If the o f f - d i a g o n a l elements are s m a l l ( m o r e

a c c u r a t e l y i f t h e y are s m a l l c o m p a r e d w i t h the difference b e t w e e n the d i a g o n a l e l e m e n t s ) t h e n a c c o r d i n g to first-order p e r t u r b a t i o n t h e o r y the levels are r e p e l l e d , a n d e a c h is c h a n g e d i n e n e r g y b y a n a m o u n t g i v e n b y the s q u a r e of the o f f - d i a g o n a l element d i v i d e d b y the s e p a r a t i o n b e t w e e n the d i a g o n a l elements. T h i s amounts to t r e a t i n g e a c h p a i r of terms as a 2 X 2 m a t r i x . B y a p p r o p r i a t e m a t r i x m u l t i p l i c a t i o n the eigenvectors of a m a t r i x are a b l e to p r o d u c e a d i a g o n a l m a t r i x w h o s e elements are the eigenvalues.

I f t h e o r i g i n a l 2 X 2 m a t r i x is n e a r l y d i a g o n a l , e a c h

e i g e n v e c t o r consists of a l a r g e c o m p o n e n t a n d a s m a l l c o m p o n e n t , a n d the f r a c t i o n a l c o m p o s i t i o n of e a c h l e v e l is g i v e n b y t h e squares of these components.

T h e eigenvector c o m p o n e n t s are a measure of the m i x i n g

p r o d u c e d b y the p e r t u r b a t i o n . F o r T a b l e I I there are m a n y o f f - d i a g o n a l elements. S o m e are p u s h i n g u p o n a state, a n d others are p u s h i n g d o w n . for J =

0 Levels of f°s for P u I 2

46233 s

P4

42712 P5

3

9178 ?6

s

-435 814

456 1341 -1146

4936 -1319 -4133

-3723 -6578 -2430 50500 1058 -1861

1775 -9858 5886 1058 45127 -1548

19200 2612 -18548 -1861 -1548 40370

-1581 -3692 -4209

754

8151

-3502

131005

67757

*S1

'S2

-9906

-5195 -707 1066 -1581 754 8151

121739 -23334

-23334 56183 -3175 17260

62196

35881

>S3

'S4

-1651 -5953 -3692 -4209 -3502 -3175 61439 -2942


17260 -2942 47022

186

L A N T H A N I D E / A C T I N I D E

Table III. Eigen value

0 7

Term

51430 D1

36.5

D1 >D2 D3

18.0

43.5

22.3

22.3

D3

5

P1 P2 P3 sp4


s

?1

3

P3

3

P2

75.5

3

57.5 12.1

3

3

58542

77288

3

3

(Columns)

10.4 38.2

58.6

r

86414

5

5

7J? 5

20922

31405 D2

5

F

Percentage Composition

C H E M I S T R Y

15.2 16.9

13.1

P5 P6

10.9

11.1

*S1 !S2 *S3 *S4

19.3 17.0 16.8

10.8

T h e t o t a l effect is c o m p l i c a t e d a n d m u s t b e d e s c r i b e d b y the eigenvalues of the w h o l e m a t r i x . S o m e of the o f f - d i a g o n a l elements are l a r g e . C o n sider, for e x a m p l e , the states c a l l e d P 3 a n d P 6 . T h e d i a g o n a l elements 3

are a b o u t 8000 c m .

3

apart, b u t t h e y are c o n n e c t e d b y a n element of over

- 1

18,000 w h i c h w o u l d p r o d u c e a

first-order

p e r t u r b a t i o n of over

40,000.

T h i s w o u l d p u s h the P 6 state b e l o w the D states at a r o u n d 30,000. B u t 3

the

5

5

D states also i n t e r a c t w i t h P 6 , a n d the result of p u s h i n g the P 6 3

state t h r o u g h the

r ,

3

D states c a n b e t h o u g h t of as a n exchange, the P 6 3

b e c o m i n g a D . H o w e v e r , the D ' s also i n t e r a c t w i t h the g r o u n d state F , r ,

5

7

a n d the final result is a l a r g e m i x i n g of P 6 a n d F e v e n t h o u g h there is 3

7

?

no off-diagonal element directly connecting them. T h e c o m p o s i t i o n s of the levels are g i v e n i n T a b l e I I I . N o n e of the levels except the h i g h e s t is p u r e i n terms of L S basis states. T h e l e v e l c a l l e d P 6 a c t u a l l y contains m o r e of the 3

state.

7

F state t h a n does the g r o u n d

S i n c e the LS designations h a v e l i t t l e m e a n i n g , i t seems best to

r e t a i n the l a b e l F for the g r o u n d state because it t h e n corresponds better 7

w i t h the other

G

7

F levels of different / .

I n the same w a y the P 3 state 3

w h i c h is p u s h e d u p b e c o m e s m i x e d u p w i t h the S states a n d is q u i t e X

i m p u r e . F o r the r e m a i n i n g levels the largest c o m p o n e n t agrees w i t h the L S designations, b u t the i m p u r i t i e s are s t i l l a p p r e c i a b l e . T h e l e v e l p r o p erties are not s t r i c t l y those i m p l i e d b y the d e s i g n a t i o n . the L S selection r u l e AL =

F o r example,

0, ± : 1 f o r b i d s transitions f r o m Ρ states to F

states, b u t since the F l e v e l of P u I contains a l a r g e a m o u n t of D state 7

G

i t c a n c o m b i n e w i t h a Ρ state w i t h c o n s i d e r a b l e i n t e n s i t y .


14.

Electronic

F R E D

for J =

0 L e v e l s of f V

46233

187

Structure

427J2

for P u I 9178

P5

131005

P6

3

3

67757

62196

'S2

*S3

35881 >S4

52.0


13.7

11.3

15.9 11.1

20.5

19.4

11.6

48.8 52.1

18.2 87.4 13.3

20.3 18.3 19.8

10.5 A n o t h e r p r o p e r t y w h i c h is affected

54.9 19.0

b y i m p u r i t i e s is the

w h i c h is g i v e n b y the s u m of the squares of the eigenvector e a c h m u l t i p l i e d b y the L S g-factor for that c o m p o n e n t .

g-value,

components

I n g e n e r a l , the

g-value is not that of a p u r e L S state b u t a n i n t e r m e d i a t e state. T h i s is v a l u a b l e i n i d e n t i f y i n g e x p e r i m e n t a l levels w i t h c a l c u l a t e d levels, espe c i a l l y w h e r e there are a n u m b e r of close levels w h i c h c a n change w i t h s m a l l changes i n the parameters.

order

T h e converse is not necessarily

t r u e : i f a m e a s u r e d g-value is near a p u r e L S g-value, i t does not neces s a r i l y i m p l y that the l e v e l is n e a r l y p u r e . A n e x a m p l e of this is the lowest n o n z e r o l e v e l of P u I, F 7

U

w h i c h has an L S g-factor of 1.5012 a n d w a s

m e a s u r e d to h a v e a g-value of 1.4975 ( 9 ) . the l e v e l c a l l e d F 7

5

t

D e s p i t e this close agreement

is o n l y 6 5 % p u r e . M o s t of the r e m a i n d e r is D r>

P i , b o t h of w h i c h h a v e L S g-factors of 1.5012. A n y m i x t u r e of

7

and

t

F , Di, t

r >

a n d Ρχ has a g-value of 1.5012, a n d so the g-value i n this case gives no 3

i n f o r m a t i o n about the c o m p o s i t i o n of the l e v e l . T h e m e a s u r e d g-value of a l e v e l gives e v i d e n c e for the i n t e r p r e t a t i o n w h i c h is often necessary b u t sometimes insufficient a n d does not r e p l a c e c a l c u l a t i o n . T h e r e w i l l be a separate energy m a t r i x for e a c h / - v a l u e , s i m i l a r to T a b l e I I , i n v o l v i n g the same set of electrostatic a n d s p i n - o r b i t parameters b u t w i t h different coefficients for e a c h m a t r i x element.

F o r the m i d d l e

range of / there are m a n y levels. F o r e x a m p l e , there are 46 levels for f , 6

7 =

4, w h i c h means that the energies for / =

4 are g i v e n b y the e i g e n

values of a 46 X 46 m a t r i x , a n d the eigenvectors ponents.

A n average l e v e l i n the configuration f

6

h a v e u p to 46 c o m has m a n y

components


188


w i t h no e s p e c i a l l y d o m i n a n t c o m p o n e n t , c a l l the l e v e l b y a n L S t e r m s y m b o l .

C H E M I S T R Y

a n d i t is meaningless to t r y to I t c a n o n l y b e d e s c r i b e d b y its

e n e r g y a n d a s t r i n g of n u m b e r s s p e c i f y i n g the m a g n i t u d e s of the c o m ponents.

T h e r e is n o t h i n g a m b i g u o u s a b o u t this d e s c r i p t i o n , a n d

one

c a n c a l c u l a t e p r o p e r t i e s of the c o n f i g u r a t i o n s u c h as g-values a n d i n t e n s i ties of transitions. It w o u l d b e u s e f u l a n d c o n v e n i e n t to h a v e a p h y s i c a l l y m o r e m e a n i n g f u l d e s c r i p t i o n for e a c h l e v e l , a n d i t is of interest to see i f another c o u p l i n g scheme m i g h t b e better—i.e., h a v i n g a n energy m a t r i x w h i c h is m o r e d i a g o n a l . Downloaded by UNIV OF ARIZONA on November 12, 2012 | http://pubs.acs.org Publication Date: June 1, 1967 | doi: 10.1021/ba-1967-0071.ch014

T h e energy

matrix shown i n T a b l e II can be

d i v i d e d into

sub-

matrices as i n d i c a t e d i n F i g u r e 2. T h e r e are square sub-matrices a l o n g the d i a g o n a l c o n t a i n i n g states of the same S a n d L h a v i n g d i a g o n a l a n d o f f - d i a g o n a l elements d e t e r m i n e d b y b o t h the electrostatic

parameters

a n d the s p i n - o r b i t p a r a m e t e r . T h e r e are r e c t a n g u l a r sub-matrices h a v i n g o n l y o f f - d i a g o n a l elements c o n n e c t i n g terms of adjacent S a n d L, deter m i n e d o n l y b y the s p i n - o r b i t p a r a m e t e r , a n d there are r e c t a n g u l a r s u b matrices w h i c h are f u r t h e r o f f - d i a g o n a l a n d c o n t a i n o n l y zeros. S i n c e the electrostatic parameters are i n g e n e r a l l a r g e r t h a n the s p i n - o r b i t p a r a m e ter, the l a r g e o f f - d i a g o n a l elements l i e w i t h i n the square s u b - m a t r i c e s , as i n the case of the P 3 - P 6 i n t e r a c t i o n m e n t i o n e d above. 3

3

another c o u p l i n g scheme for the c o n f i g u r a t i o n f

I n l o o k i n g for

one is h a n d i c a p p e d b y

the difficulty that the c o n f i g u r a t i o n contains o n l y i d e n t i c a l particles w h i c h m u s t b e t r e a t e d e q u i v a l e n t l y . H e n c e , the o n l y other c o u p l i n g p o s s i b i l i t y is /'/—i.e., the zero-order c o m b i n a t i o n s of / / Γ )

states are c o n s i d e r e d as m a d e u p of v a r i o u s

and f / 7

2

electrons.

2

T h e m a t r i x elements of

these

states l i e a l o n g the d i a g o n a l w i t h m a g n i t u d e s g i v e n b y v a r i o u s m u l t i p l e s of the s p i n - o r b i t s p l i t t i n g of one / - e l e c t r o n . actions b e t w e e n

the electrons

must b e

T h e n the electrostatic i n t e r

added, w h i c h will

contribute

o f f - d i a g o n a l elements not r e s t r i c t e d to s m a l l sub-matrices near the d i a g o n a l . T h e result for 5 f is a n e n e r g y m a t r i x i n w h i c h the d i a g o n a l elements v

are s m a l l e r a n d the o f f - d i a g o n a l elements l a r g e r t h a n for L S c o u p l i n g . T h i s m a t r i x is a t r a n s f o r m a t i o n of the L S m a t r i x a n d has the same e i g e n values, b u t because of the l a r g e r a n d m o r e n u m e r o u s o f f - d i a g o n a l

ele

ments the eigenvectors w i l l b e s p r e a d over m o r e components, w h i c h is not w h a t w e are l o o k i n g for.

It m u s t be c o n c l u d e d that the L S scheme

is the best that c a n be d o n e w i t h the 5f

configurations of the actinides.

F o r configurations w h i c h i n v o l v e several different types of electrons a d d e d to the f

core, s u c h as 5f 7s7p, 6

the g e n e r a l a p p r o a c h is s i m i l a r b u t

m o r e c o m p l i c a t e d . T h e r e are m o r e interactions a n d m o r e levels a n d also m o r e c o u p l i n g p o s s i b i l i t i e s . T h e outer electrons c a n be a d d e d to the core one at a t i m e , or first, t h e y c a n b e c o m b i n e d

f

together, a n d the

resultant a d d e d to the core. I n a n y case there are l a r g e e n e r g y m a t r i c e s w h o s e elements are g i v e n b y v a r i o u s c o m b i n a t i o n s of the electrostatic


14.

F R E D

Electronic

189

Structure

a n d s p i n - o r b i t parameters. T h e p r o b l e m of i n t e r p r e t a t i o n is to find a set of p a r a m e t e r s g i v i n g eigenvalues w h i c h agree as closely as possible w i t h the e x p e r i m e n t a l energy levels a n d agree i n other p r o p e r t i e s s u c h as g-values, h y p e r f i n e s t r u c t u r e , a n d so o n . I f there is g o o d agreement, t h e levels c a n b e i d e n t i f i e d w i t h the c o n f i g u r a t i o n , a n d t h e values of t h e parameters t h e n d e s c r i b e the c o n f i g u r a t i o n . T h e first p r o b l e m is to

find


the e x p e r i m e n t a l levels.

ELECTROSTATIC SPIN-ORBIT

Figure 2.

PARAMETERS

PARAMETER

Schematic algebraic energy matrix of î ,J = 6

0

Actinide Spectroscopy T h e spectroscopy of t h e actinides is difficult because these elements are u s u a l l y h a z a r d o u s , r e a c t i v e , scarce, a n d h a v e c o m p l e x spectra.

A

s u i t a b l e l i g h t source w h i c h has b e e n d e v e l o p e d is s h o w n i n F i g u r e 3. I t consists of a short l e n g t h of q u a r t z t u b i n g i n t o w h i c h is s u b l i m e d a b o u t 200 m i c r o g r a m s of t h e e l e m e n t as i o d i d e , after w h i c h the t u b e is sealed off u n d e r v a c u u m . M i c r o w a v e e x c i t a t i o n p r o d u c e s a b r i g h t source w h i c h lasts f o r m a n y h o u r s , gives s h a r p s p e c t r u m lines, a n d c a n also b e o p e r a t e d i n a m a g n e t f o r Z e e m a n exposures. quiring high resolving power

B e c a u s e there are m a n y l i n e s , r e -

a n d also h i g h a c c u r a c y i n w a v e l e n g t h

measurements, a l a r g e g r a t i n g s p e c t r o g r a p h is most s u i t a b l e . T h e A r -


190


C H E M I S T R Y

g o n n e s p e c t r o g r a p h is c o n v e n i e n t , because it covers a l a r g e range i n one exposure.

M o s t w a v e l e n g t h measurements h a v e b e e n m a d e m a n u a l l y

w i t h t h e a i d of a d i g i t a l c o m p u t e r .

E x i s t i n g e q u i p m e n t c a n b e s a i d to

b e a d e q u a t e i n the p h o t o g r a p h i c r e g i o n , b u t there is a n e e d for better


facilities i n the i n f r a r e d , w h i c h is a n i m p o r t a n t r e g i o n for the actinide

CM

-CAVITY

-MICROWAVES IN DISCHARGE TUBE LIGHT

ELECTRODELESS DISCHARGE in M I C R O W A V E C A V I T Y

OUT

TUBE

Figure 3. Light source commonly used to excite actinide spectra I n the e m p i r i c a l t e r m analysis of a s p e c t r u m , the lines are o r g a n i z e d i n t o a n a r r a y i n w h i c h the r o w s are c h a r a c t e r i z e d b y the t e r m values of o d d p a r i t y a n d the c o l u m n s b y the t e r m values of e v e n p a r i t y (or v i c e versa).

E a c h element of the a r r a y is defined b y the difference

between

a n o d d a n d a n e v e n t e r m a n d thus represents the w a v e n u m b e r of a transition.

T h e p r o b l e m i s : g i v e n the o b s e r v e d w a v e n u m b e r s ,

find

the

t e r m values. F o r spectra of o n l y m o d e r a t e c o m p l e x i t y this was d o n e b y l o o k i n g for constant differences—i.e.,

p a i r s of lines for w h i c h the differ-

ence i n w a v e n u m b e r is constant w i t h i n e x p e r i m e n t a l error. If a g i v e n d i f ference is r e p e a t e d a n u m b e r of times, i t c a n n o t be a t t r i b u t e d to c h a n c e b u t m u s t represent a t e r m difference—i.e., the pairs of transitions a l l e n d o n the same p a i r of terms. I n v e r y c o m p l e x spectra c o n t a i n i n g thousands of lines there are m i l l i o n s of possible differences f o r m i n g a p r a c t i c a l l y


14,

F R E D

continuous

Electronic

191

Structure is r e p e a t e d m a n y times

by

c h a n c e w i t h i n e x p e r i m e n t a l error. H e n c e , the r e a l differences cannot

d i s t r i b u t i o n , a n d a n y difference

be

d i s t i n g u i s h e d a b o v e the noise.

M o r e i n f o r m a t i o n t h a n just

wavenumbers

is n e e d e d , a n d i n a d d i t i o n to the l a b o r of extensive w a v e l e n g t h

measure

ments the analysis of a c t i n i d e spectra requires d a t a o n the Z e e m a n effect, h y p e r f i n e structure, isotope shift, t e m p e r a t u r e

classification, intensities,

a b s o r p t i o n or self-reversal b e h a v i o r , a n d t h e o r e t i c a l p r e d i c t i o n s . Zeeman E f f e c t . of i n f o r m a t i o n .

T h e Z e e m a n effect is the most u s e f u l single source

T y p i c a l patterns are s h o w n i n F i g u r e 4.

I n most cases


these p r o v i d e the / - v a l u e a n d g - v a l u e for e a c h l e v e l i n v o l v e d i n a t r a n s i t i o n . F o r e x a m p l e , one sees i m m e d i a t e l y that the U l i n e Λ6392 is a / ===== 6 ~* / =

6 t r a n s i t i o n , w h i l e the l i n e Λ6395 i s a / =

w i t h g's as d e t e r m i n e d b y m e a s u r i n g the patterns. g-value for the / =

6 -

>

/

=

7 transition,

It turns out that the

6 l e v e l of A6395 is i d e n t i c a l w i t h one of the g-values

for A6392 ( g == 0.751 ) w h i c h s t r o n g l y suggests that b o t h lines e n d o n the same / =

6 l e v e l . It is the l o w e s t l e v e l L 5

6

of U I. N o n e of this c o u l d be

guessed f r o m just l o o k i n g at the t w o no-field lines s h o w n i n the of the patterns.

center

I n a d d i t i o n to i n d i c a t i n g possible r e l a t i o n s h i p s b e t w e e n

v a r i o u s lines, the Z e e m a n

effect shows w h e t h e r

a l i n e belongs to

the

n e u t r a l a t o m or the first i o n . T h i s is because the / - v a l u e s m a y b e i n t e g r a l , i m p l y i n g a n even n u m b e r

of electrons,

i m p l y i n g a n o d d n u m b e r of electrons.

or t h e y m a y be h a l f - i n t e g r a l ,

T h e m i c r o w a v e source gives b o t h

types, b u t the e x c i t a t i o n is not h i g h e n o u g h for t h i r d spectra.

Figure 4. Zeeman patterns for two lines of U I The no-field lines are shown in the middle Hyperfine

Structure.

A n o t h e r source of i n f o r m a t i o n is

hyperfine

structure. F i g u r e 5 shows t w o lines f r o m the s p e c t r u m of s i n g l y i o n i z e d A m o r i g i n a t i n g f r o m a c o m m o n u p p e r l e v e l a n d e n d i n g o n the t w o lowest levels. It w i l l be seen that f r o m w e l l - r e s o l v e d patterns the l e v e l splittings c a n be d e r i v e d , a n d the / - v a l u e s c a n t h e n be d e d u c e d . O t h e r transitions


192


C H E M I S T R Y

to the same levels m u s t g i v e the same l e v e l s p l i t t i n g s a n d / - v a l u e s , a n d so the h y p e r f i n e s t r u c t u r e c a n be u s e d i n the same w a y as Z e e m a n d a t a to find r e l a t e d lines. T h i s a p p r o a c h was u s e d to m a k e a p a r t i a l t e r m analysis of A m I a n d A m I I (7).

T h e m e t h o d is r e s t r i c t e d to lines s h o w i n g

h y p e r f i n e s t r u c t u r e i n the o d d Ζ elements. "/2


22509 J - 3

:

I3

/o-

,

/

2

I

2

~\ 9/ 2

-9/

2

7/ 2

\-

3/ 2

X444I λ 5020

0

1000

Figure 5.

Hyperfine

-1000

-2000

structure of two lines of Am II

The bar diagram at the bottom (scale in 10~ cm.' ) has been calcu lated from the level splittings averaged from a number of lines 3

1

Isotope S h i f t . F u r t h e r i n f o r m a t i o n comes f r o m isotope shift, i l l u s t r a t e d i n F i g u r e 6 for a l i n e of U I. I n a n e m p i r i c a l t e r m analysis the isotope shift of a l e v e l c a n b e c o n s i d e r e d a c h a r a c t e r i s t i c p r o p e r t y i n the same w a y as the g-value or h y p e r f i n e s p l i t t i n g . O n e cannot d e t e r m i n e the isotope shifts of the t w o levels i n v o l v e d i n a t r a n s i t i o n f r o m the one


14.

Electronic

F R E D

Structure

193

l i n e alone, i n contrast to g-values a n d h y p e r f i n e s p l i t t i n g s , b u t o n l y t h e difference

i n shifts b e t w e e n

the levels.

T h e s i t u a t i o n is the same

as

d e t e r m i n i n g energy levels f r o m a t r a n s i t i o n , w h i c h gives o n l y the e n e r g y difference b e t w e e n the levels. Isotope shifts present another i n d e p e n d e n t p r o p e r t y w i t h w h i c h to test for constant differences—i.e., the

difference

i n isotope shifts for p a i r s of lines e n d i n g o n the same p a i r of levels m u s t be constant, just l i k e the p a i r s of w a v e n u m b e r s of the lines.

Moreover,

the isotope shift of a l e v e l is i m p o r t a n t i n i n t e r p r e t i n g the l e v e l , as d i s cussed b e l o w . Downloaded by UNIV OF ARIZONA on November 12, 2012 | http://pubs.acs.org Publication Date: June 1, 1967 | doi: 10.1021/ba-1967-0071.ch014

Intensities.

F i n a l l y , there are intensities a n d the w a y t h e y v a r y u n d e r

different c o n d i t i o n s .

T h e s t r o n g lines t e n d to i n v o l v e l o w levels, b u t

the c o r r e l a t i o n is not close. I n a d d i t i o n the s t r o n g lines t e n d to l i e a l o n g the d i a g o n a l of a m u l t i p l e t so that t h e y d o not s h o w m a n y differences.

constant

F o r these reasons i t is not f r u i t f u l to attempt a n analysis

w i t h just the strong lines. A better a p p r o a c h is to b e g i n w i t h lines w h i c h m u s t i n v o l v e l o w levels because t h e y a p p e a r i n a b s o r p t i o n i n a f u r n a c e or are self-reversed i n a hot electrodeless d i s c h a r g e tube.

The number

of s u c h lines is u s u a l l y large, a n d one s t i l l r e q u i r e s the other i n f o r m a t i o n .

Figure 6.

Isotope shift in χ 4244 of U I

Assigning Configuration W i t h the a i d of a l l these d a t a a n d m u c h tedious w o r k one

makes

a n analysis, e n d i n g u p w i t h most of the strong lines classified a n d p e r h a p s h a l f of the w e a k lines. T h i s e m p i r i c a l analysis gives the positions of some h u n d r e d s of levels w i t h / - v a l u e s a n d other p r o p e r t i e s , the latter u s u a l l y far f r o m complete.

T h e p r o b l e m t h e n b e c o m e s one of i n t e r p r e t a t i o n . O f

course, o n the basis of p r e v i o u s experience a n d t h e o r e t i c a l p r e d i c t i o n s one


194


C H E M I S T R Y

k n o w s w h a t configurations to expect a n d has a r o u g h i d e a of the o r d e r i n w h i c h t h e y w i l l l i e . H o w e v e r , the c o m p l e x i t y of the levels is so great that these expectations are l i t t l e h e l p i n assignments. T h e Z e e m a n d a t a , w h i c h are i n d i s p e n s a b l e i n the analysis, g i v e the / - v a l u e s a n d g-values, b u t t h e y say n o t h i n g about configurations.

It is i m p o s s i b l e to assign

configurations f r o m the Z e e m a n d a t a alone since e a c h c o n f i g u r a t i o n has m a n y levels, the configurations o v e r l a p , a n d t h e y often interact. T h e most u s e f u l i n f o r m a t i o n for a s s i g n i n g configurations comes f r o m


isotope shifts. I n the h e a v y elements isotope shift is p u r e l y a n u c l e a r v o l u m e effect. W h i l e the size of the nucleus is s m a l l c o m p a r e d w i t h the size of a n a t o m , the C o u l o m b a t t r a c t i o n b e t w e e n e l e c t r o n becomes enormous

the nucleus a n d a n

at s m a l l distances, a n d deviations f r o m a

C o u l o m b p o t e n t i a l near the center of the a t o m h a v e a m e a s u r a b l e effect o n the average e n e r g y of the electron.

T h i s w i l l b e effective

o n l y for

those electrons h a v i n g a p r o b a b i l i t y d i s t r i b u t i o n w h i c h r e m a i n s finite as r —» 0, that is, ^-electrons.

T h e effect is a d d i t i v e a n d is a b o u t t w i c e as

m u c h for the c o n f i g u r a t i o n 7sr as for 7 s.

( T h e effect for the i n n e r s-elee-

trons is m u c h l a r g e r b u t u n o b s e r v a b l e since these r e m a i n u n d i s t u r b e d d u r i n g a n o p t i c a l t r a n s i t i o n . ) T h e m a g n i t u d e of the effect also

depends

o n w h a t other outer electrons are present because of s h i e l d i n g . If t w o 7s electrons are present, e a c h shields the other, i n c r e a s i n g the p r o b a b i l i t y d i s t r i b u t i o n p e r e l e c t r o n for l a r g e r a n d d e c r e a s i n g i t at s m a l l r. the isotope shift for 7s

2

Hence,

is o n l y a b o u t 1.6 that of a single 7s electron.

The

5f electrons are also effective i n s h i e l d i n g the 7s e l e c t r o n since the 5 f s stay i n s i d e the r a d o n core a n d t e n d to squeeze the 7s f u r t h e r outside, t h e r e b y r e d u c i n g the 7s charge d e n s i t y at the n u c l e u s .

T h e a m o u n t of

this s h i e l d i n g is p r o p o r t i o n a l to the n u m b e r of 5/ electrons present.

The

other outer electrons w h i c h m a y be present also c o n t r i b u t e to the s h i e l d i n g of the 7s e l e c t r o n b u t to a lesser extent t h a n the 5 f s because t h e y e x t e n d f u r t h e r out.

H e n c e , i f a 5f e l e c t r o n is c h a n g e d to a 6d electron,

the net s h i e l d i n g is decreased, a n d i f the 6d is c h a n g e d to a 7s or 7 p , it is s t i l l f u r t h e r r e d u c e d . H e n c e , the isotope shift is i n c r e a s e d i n this process: 5f7s

2

«! 14 2 12 ec Lu LU

h-

10 8 6 4 2 0

Figure

9.

Comparison of observed and levels of i s for Pu I G

take F

2

as the i n d e p e n d e n t p a r a m e t e r a n d to fix F

r a t i o to F . F o r the 5f e l e c t r o n i n h y d r o g e n F / F 2

0.0161.

4

4

and F

6

i n a constant

== 0.142 a n d F / F

2

6

2

==

If one uses the F's i n this r a t i o , one c a n fit the o b s e r v e d s p e c t r a

fairly well well).

calculated

2

(of

course, i t is necessary to a d d the s p i n - o r b i t e n e r g y as

T h e values of F

2

are s h o w n i n F i g u r e 8.

derived by Fields, Wybourne, and Carnall T h e linear dependence

(4)

o n a t o m i c n u m b e r is

s t r i k i n g a n d is the k i n d of r e l a t i o n s h i p one g e n e r a l l y hopes to o b t a i n for the a c t i n i d e s . H o w e v e r , these values of F t i o n of h y d r o g e n i c ratios for F

4

2

are b a s e d o n the a s s u m p

a n d F . T h e g o o d fit does not p r o v e the 6

h y d r o g e n i c r a t i o b u t just the i n s e n s i t i v i t y of the o b s e r v e d terms to the r a t i o . T h e h i g h e r terms o b s e r v e d i n the n e u t r a l atoms for f V d o not fit those c a l c u l a t e d for these ratios.

F i g u r e 9 shows the c o m p a r i s o n

P u I. It is s t i l l too e a r l y to g i v e better values for F

4

and F

6

for

i n most cases.

T h e h y d r o g e n i c a p p r o x i m a t i o n shows that H u n d ' s r u l e is o b e y e d for f Y , w h i c h is sufficient to i d e n t i f y the l o w e s t t e r m of the c o n f i g u r a t i o n .


14.

F R E D

Electronic

Structure

199

B e c a u s e o f t h e d i f f i c u l t y i n i d e n t i f y i n g o b s e r v e d levels w i t h c a l c u l a t e d levels i n t h e configurations f V , i t is i n s t r u c t i v e to c o n s i d e r t h e c o n figurations

I n these configurations there are m o r e levels to b e fitted

fds . 2

a n d m o r e p a r a m e t e r s to b e d e t e r m i n e d , b u t o n e has t h e a d v a n t a g e of a m o d e l w h i c h is a f a i r l y g o o d a p p r o x i m a t i o n . T h i s m o d e l is J i / c o u p l i n g , t r e a t e d b y J u d d ( 1 0 ) . I t is a s s u m e d t h a t t h e s p i n - o r b i t i n t e r a c t i o n of the d - e l e c t r o n is l a r g e r t h a n t h e electrostatic f-d i n t e r a c t i o n . T h e n o n e has t w o levels, d / 3

2

each level of the f

a n d d >/ s e p a r a t e d b y t h e D i n t e r v a l , c o u p l e d t o r

angular momentum J


2

2

core. T h e core or p a r e n t levels are c h a r a c t e r i z e d b y

N

L 9

w h i c h c o m b i n e s w i t h t h e / o f t h e ^ - e l e c t r o n to

p r o d u c e a t o t a l a n g u l a r m o m e n t u m / h a v i n g values f r o m | / i — /| to / i + /. F i g u r e 10 shows t h e l o w o d d levels of P u I a r r a n g e d a c c o r d i n g to this c o u p l i n g scheme.

The f

3

p a r e n t terms

6

H a n d °F are k n o w n f r o m

c r y s t a l s p e c t r a ( 2 ) , a n d t h e positions of these terms s h o u l d b e s i m i l a r i n the free a t o m . T h e o b s e r v e d levels o f P u I a p p e a r i n t w o groups

about

e a c h p a r e n t l e v e l . T h e lowest set consists of a d%/ e l e c t r o n c o u p l e d to a 2

β

Η / 2 p a r e n t , g i v i n g / - v a l u e s of 1 to 4. T h e levels w i t h i n e a c h set a r e Γ)

s p l i t b y t h e electrostatic f-d i n t e r a c t i o n , w h i c h is seen to b e s m a l l e r t h a n the m e a n d%/ -d / 2

5

2

separation.

T h e a d v a n t a g e of this m o d e l f o r t h e

a c t i n i d e s is that t h e e n e r g y m a t r i x is m o r e d i a g o n a l , t h e eigenvectors p u r e r , a n d t h e g-values closer to t h e J j l i m i t t h a n for t h e same levels x

d e s c r i b e d i n LS c o u p l i n g . T h i s is a r e a l a d v a n t a g e i n a t t e m p t i n g t o c o r r e late o b s e r v e d a n d c a l c u l a t e d levels. I t is t r u e t h a t i n p r a c t i c e t h e c o u p l i n g is i n t e r m e d i a t e , b u t i n t h e process of c h a n g i n g t h e p a r a m e t e r s to p r o v i d e

1/2

3/2

Figure 10.

5/2

7/2

The configuration

9/2

î ds

M/2

5

2

13/2

of Pu I in ] j t

coupling


15/2


200


Figure

11.

of f V and F M s and actinides

Approximate relative positions figurations of neutral lanthanides

a better fit b e t w e e n

C H E M I S T R Y

calculated and observed

con-

2

levels one has a better

i n s i g h t i n t o h o w the levels s h o u l d be o r g a n i z e d . I n the case of the c o n figuration

/ V , w h e r e o n l y LS c o u p l i n g a p p l i e s , the c o r r e l a t i o n is m o r e

difficult. T h e hj c o u p l i n g scheme is most a p p l i c a b l e for configurations h a v i n g one e l e c t r o n outside the f core ( other t h a n s ). I n P u I, for instance, one 2

c a n r e c o g n i z e the levels of f V p i n the same w a y as i n F i g u r e 10, f r o m the existence of groups because of the a d d i t i o n of a p\/

2

c o u p l e d to the f

core.

or p / 3

2

electron

F o r most elements the levels are s t i l l too i n c o m -

p l e t e at present to assign m a n y of t h e m w i t h confidence a c c o r d i n g to Jij q u a n t u m n u m b e r s for the a p p r o p r i a t e c o n f i g u r a t i o n , a n d the parameters r e m a i n u n d e t e r m i n e d . I n these cases w i t h o u t either a J j or a n L S a s s i g n t

m e n t of the e x i s t i n g levels one cannot b e c e r t a i n that they b e l o n g to a


14.

Electronic

F R E D

given configuration.

201

Structure

T h e r e is one fortunate c i r c u m s t a n c e w h i c h makes

the i d e n t i f i c a t i o n of the lowest t e r m of a c o n f i g u r a t i o n q u i t e p r o b a b l e , n a m e l y the fact that for most configurations H u n d ' s r u l e is v a l i d . I n the case of fds

2

of P u I s h o w n i n F i g u r e 10 i n J i / c o u p l i n g , the lowest l e v e l

r e s u l t i n g f r o m c o u p l i n g a 4 / 2 e l e c t r o n to e a c h l e v e l of the lowest p a r e n t t e r m , H / - i 5 / 2 , is also a m e m b e r of the lowest fds 6

5

t e r m expressed i n

2

2

L S coupling, K . i . 7

4

T h u s , i n spite of the fact that for most levels J i /

0

c o u p l i n g is closer t h a n L S , for the lowest t e r m the t w o d e s c r i p t i o n s are e q u i v a l e n t . T h e p u r i t y is h i g h for each l e v e l of the H u n d s r u l e t e r m , Downloaded by UNIV OF ARIZONA on November 12, 2012 | http://pubs.acs.org Publication Date: June 1, 1967 | doi: 10.1021/ba-1967-0071.ch014

a n d the o b s e r v e d g-value is close to the p u r e L S g-factor.

The

lowest

t e r m of a configuration c a n u s u a l l y be r e c o g n i z e d , a n d the r e l a t i v e p o s i tions of different configurations established. F o r the p h y s i c a l a n d c h e m i c a l properties of atoms the e l e c t r o n c o n figurations

of most interest are the lowest.

there is a c o m p e t i t i o n b e t w e e n 5f 7s N

2

I n the n e u t r a l a c t i n i d e atoms

a n d 5 ~ 6d7s . N

1

2

Some actinides h a v e

one of these as the l o w e r a n d some h a v e the other. A n analogous s i t u a t i o n exists for the configurations 4 f 6 s v

a n d 4*~ 5

Electronic Structure of the Actinide Elements - Advances in Chemistry

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