Lanthanide and Actinide Chemistry and Spectroscopy - American

17 Optical Properties of Actinide and Lanthanide Ions J A N P. H E S S L E R and W . T. C A R N A L L

Downloaded by MONASH UNIV on October 20, 2012 | http://pubs.acs.org Publication Date: September 23, 1980 | doi: 10.1021/bk-1980-0131.ch017

Chemistry Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, I L 60439

The sharpness of many of the o p t i c a l absorption and emiss i o n l i n e s of the lanthanide ions in i o n i c c r y s t a l s has intrigued s c i e n t i s t s since 1908. We review some of the recent developments i n t h i s area of spectroscopy, emphasizing the o p t i c a l p r o p e r t i e s of the tripositive lanthanide and a c t i n i d e ions. In p a r t i c u l a r , we s h a l l d i s c u s s the s i n g l e i o n p r o p e r t i e s of l i n e p o s i t i o n , i n t e n s i t y , width, and fluorescence l i f e t i m e . Such e f f e c t s as the a p p l i c a t i o n of e x t e r n a l electric and magn e t i c fields, hyperfine i n t e r a c t i o n s , and cooperative e f f e c t s such as long range o r d e r i n g and energy t r a n s f e r , although d i r e c t extensions of the above p r o p e r t i e s , must be excluded i n such a short review. The o p t i c a l p r o p e r t i e s of the lanthanide and a c t i n i d e ions are due to the unpaired e l e c t r o n s of the i o n . The observed sharp t r a n s i t i o n s have been shown to be i n t r a c o n f i g u r a t i o n t r a n s i t i o n s . The most widely s t u d i e d systems have ground conf i g u r a t i o n s (Xe, 4f ) and (Rn, 5f ) for the lanthanide and a c t i n i d e ions r e s p e c t i v e l y . The number of f - e l e c t r o n s , n, ranges from 1 to 13. The i n e r t rare gas core allows us to d i s c u s s the systems i n terms of the f - e l e c t r o n s only. Even such a conceptually simple system i s complex enough to r e q u i r e a parameterization scheme. The p h y s i c a l s i g n i f i c a n c e of such a scheme and i t s r o l e i n developing an understanding of complex systems has been discussed by Newman (1). Our goal i s not to u n c r i t i c a l l y accumulate parameters i n some standard scheme which has l i m i t e d u t i l i t y , but i n s t e a d to develop as comprehens i v e and u n i v e r s a l a scheme as p o s s i b l e , one which can be a p p l i e d to the energy l e v e l s t r u c t u r e , r a d i a t i v e t r a n s i t i o n p r o b a b i l i t i e s , temperature-dependent l i n e widths, f l u o r e s c e n t l i f e t i m e s , e l e c t r i c and magnetic s u s c e p t i b i l i t i e s , hyperfine s t r u c t u r e , and cooperative phenomena. In p a r t i c u l a r , the parame t e r s we deduce should allow us to p r e d i c t observables i n an unmeasured r e g i o n , be c o n s i s t e n t w i t h appropriate ab initio c a l c u l a t i o n s , and be u s e f u l as input data i n t o other parameteri z a t i o n schemes. An example of the l a s t p o i n t i s the a n a l y s i s n

n

0-8412-0568-X/80/47-131-349$05.00/0 © 1980 American C h e m i c a l Society In Lanthanide and Actinide Chemistry and Spectroscopy; Edelstein, N.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

350

LANTHANIDE

AND

ACTINIDE CHEMISTRY

AND

SPECTROSCOPY

of c r y s t a l - f i e l d parameters by an e f f e c t i v e p o i n t charge or other model. We b r i e f l y summarize the p a r a m e t e r i z a t i o n schemes f o r f e l e c t r o n energy l e v e l s , i n t r a c o n f i g u r a t i o n t r a n s i t i o n probab i l i t i e s , and the electron-phonon i n t e r a c t i o n , and review the c u r r e n t experimental s i t u a t i o n f o r each area. We s h a l l a l s o speculate on p o t e n t i a l l y f e r t i l e areas of future i n v e s t i g a t i o n .


I.

Line

Positions

A. Energy L e v e l Parameterization Scheme. The parame t e r i z a t i o n scheme to d e r i v e the f r e e - i o n p r o p e r t i e s of the f - e l e c t r o n system i s based upon d i r e c t p h y s i c a l assumptions. The approximate Hamiltonian d e s c r i b i n g N-electrons moving about a nucleus of charge Ze, as discussed by Condon and Shortley (2^), can be w r i t t e n

i=l

i>j=l

where the symbols have t h e i r usual meaning. To t r e a t a system of s e v e r a l e q u i v a l e n t f - e l e c t r o n s , Racah developed the concepts of tensor operators and the c o e f f i c i e n t s of f r a c t i o n a l parentage. These concepts have been reviewed by Judd (3_) . The f i r s t approximation to paramterize equation (1) i s to assume that a l l e l e c t r o n s move i n a c e n t r a l p o t e n t i a l . I f we then l i m i t the a n a l y s i s to a s i n g l e c o n f i g u r a t i o n , we need d i s cuss only the Coulomb and s p i n - o r b i t i n t e r a c t i o n between the equivalent f-electrons. With the a i d of tensor operators the Coulomb i n t e r a c t i o n can be expressed as ^coui

=

° a

E

e

+

E

\

+

\

E

+

S-

E

( 2 )

1

The E ' s are parameters which may be expressed as a l i n e a r combination of the S l a t e r i n t e g r a l s , F ^ ) . k = 0, 2, 4, and 6. The e^'s are tensor o p e r a t o r s . The s p i n - o r b i t i n t e r a c t i o n w i t h i n a s i n g l e c o n f i g u r a t i o n may be parameterized by a s i n g l e spin-orbit r a d i a l i n t e g r a l , £ , therefore f

n e o s.o.

=5

7

(3) r / > I I i=l The sum i s over the n e q u i v a l e n t f - e l e c t r o n s . Bethe (_4) pointed out that when the f r e e - i o n i s put i n t o a c r y s t a l the e l e c t r i c f i e l d s d i s t o r t the i s o t r o p y of f r e e space. T h i s causes a s p l i t t i n g i n the f r e e - i o n energy l e v e l s , with any r e s i d u a l degeneracy determined by the symmetry of the c r y s t a l . f

In Lanthanide and Actinide Chemistry and Spectroscopy; Edelstein, N.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

17.

HESSLER AND CARNALL

In tensor operator written


k,q

Optical

Properties

of Ions

351

n o t a t i o n the c r y s t a l - f i e l d i n t e r a c t i o n i s

1=1

k (k) The B s are parameters and the C ^ s are tensor operators which are r e l a t e d to the s p h e r i c a l harmonics. T h i s b a s i c parameterization scheme, used at the time of the l a s t A.C.S. symposium on lanthanide and a c t i n i d e chemistry (5) , has been discussed i n d e t a i l by Wybourne (6) . In a p p l y i n g the scheme, the f r e e - i o n Hamiltonian was f i r s t d i a g o n a l i z e d and then the c r y s t a l - f i e l d i n t e r a c t i o n was t r e a t e d as a p e r t u r b a t i o n . T h i s procedure y i e l d e d f r e e - i o n energy l e v e l s t h a t f r e q u e n t l y deviated by s e v e r a l hundred cm~"-^ from the observed energy levels. In a d d i t i o n , the d e r i v e d parameters such as the S l a t e r r a d i a l i n t e g r a l , F ( 2 ) , and the s p i n - o r b i t r a d i a l i n t e g r a l did not f o l l o w an expected systematic p a t t e r n across the l a n thanide or a c t i n i d e s e r i e s (7). These d e v i a t i o n s are due t o n e g l e c t i n g the Coulomb i n t e r a c t i o n between d i f f e r e n t c o n f i g u r a t i o n s . To b o l d l y proceed t o enlarge the b a s i s set of wave f u n c t i o n s t o i n c l u d e a d d i t i o n a l c o n f i g u r a t i o n s would have r e s u l t e d i n an unmanageably l a r g e matrix. Instead, Rajnak and Wybourne (8) assumed t h a t the Coulomb i n t e r a c t i o n between c o n f i g u r a t i o n s was weak enough to be t r e a t e d w i t h p e r t u r b a t i o n techniques. They modified the Hamiltonian that operated w i t h i n the ground c o n f i g u r a t i o n to i n c l u d e the greater p a r t of the e f f e c t s of a l l weakly p e r t u r b i n g c o n f i g u r a t i o n s . T h i s approach modifies the p h y s i c a l i n t e r p r e t a t i o n of the S l a t e r r a d i a l i n t e g r a l s by i n t r o d u c i n g conf i g u r a t i o n i n t e r a c t i o n c o r r e c t i o n s and introduces a d d i t i o n a l parameters i n t o the scheme. The a d d i t i o n a l parameters a, B, and y are r e q u i r e d to complete the d e s c r i p t i o n of two-body e l e c t r o s t a t i c c o n f i g u r a t i o n - i n t e r a c t i o n e f f e c t s . The dominant c o n t r i b u t i o n s due to three-body i n t e r a c t i o n s r e q u i r e an a d d i t i o n a l s i x parameters, k=2, 3, 4, 6, 7, and 8, d e f i n e d by Judd (9). a

Judd, Crosswhite, and Crosswhite (10) added r e l a t i v i s t i c e f f e c t s to the scheme by c o n s i d e r i n g the B r e i t operator and thereby produced e f f e c t i v e s p i n - s p i n and s p i n - o t h e r - o r b i t i n t e r a c t i o n Hamiltonians. The reduced matrix elements may be expressed as a l i n e a r combination of the Marvin i n t e g r a l s , M^: k = 0, 2, and 4. They a l s o considered the e f f e c t of a d d i t i o n a l c o n f i g u r a t i o n s on the s p i n - o r b i t i n t e r a c t i o n t o produce the e l e c t r o s t a t i c a l l y c o r r e l a t e d s p i n - o r b i t i n t e r a c t i o n . t r a d i t i o n a l l y the s p e c t r o s c o p i s t has measured energy i n cm \ In t h i s system of u n i t s Plank's constant and the v e l o c i t y of l i g h t are equal to 1. To convert to SI u n i t s , m u l t i p l y values i n c i r r i by he = 19.86484 x 1 0 " J-cm . 24

-1



352

LANTHANIDE

A N D ACTINIDE

CHEMISTRY

A N D SPECTROSCOPY

Although t h i s i n t e r a c t i o n has p r o p e r t i e s very s i m i l a r t o the s p i n - o t h e r - o r b i t i n t e r a c t i o n , i t i s d i s t i n c t enough t o r e q u i r e the a d d i t i o n a l paramters : k = 2, 4, and 6 . This completes the current f r e e - i o n p a r a m e t e r i z a t i o n scheme. I t i n v o l v e s twenty parameters which can be determined by comp a r i s o n t o experimental observations. The most important parameters are the four S l a t e r r a d i a l i n t e g r a l s , the s p i n o r b i t r a d i a l i n t e g r a l , and the three two-body c o n f i g u r a t i o n i n t e r a c t i o n parameters. With these eight parameters the f r e e ion l e v e l s can g e n e r a l l y be f i t t o w i t h i n a hundred cm"^. The p r e c i s e e v a l u a t i o n o f the three-body c o n f i g u r a t i o n i n t e r a c t i o n parameters i s c r i t i c a l l y dependent upon the o b s e r v a t i o n o f c e r t a i n l e v e l s . Because i t i s o f t e n d i f f i c u l t t o o b t a i n a complete set o f experimental l e v e l s , the three-body parameters are sometimes p o o r l y d e f i n e d . The Marvin i n t e g r a l s and the s p i n o t h e r - o r b i t parameters produce changes i n the f r e e - i o n l e v e l s which are on the order o f the c r y s t a l - f i e l d s p l i t t i n g . Their evaluation, therefore, r e q u i r e s both extensive experimental data and an adequate model f o r the c r y s t a l - f i e l d i n t e r a c t i o n . Unfortunately, there has been no systematic e v a l u a t i o n o f the e f f e c t o f adding parameters t o the scheme. More importantly, only the root-mean-squared d e v i a t i o n between observed and c a l c u l a t e d energy l e v e l s has been used t o t e s t the q u a l i t y o f the t h e o r e t i c a l p r e d i c t i o n s . No study o f the c o r r e l a t i o n between f i t t e d parameters has been undertaken. Such a study would be u s e f u l i n e s t a b l i s h i n g the importance o f i n d i v i d u a l parameters and the o v e r a l l adequacy o f the scheme. Ab initio c a l c u l a t i o n s o f the e f f e c t i v e parameters are d i f f i c u l t because o f the need t o p r o p e r l y sum t o i n f i n i t e order the v a r i o u s c o n f i g u r a t i o n i n t e r a c t i o n c o n t r i b u t i o n s t o the parameters. Morrison and Rajnak (11) used p e r t u r b a t i o n theory and g r a p h i c a l methods t o c o r r e c t Hartree-Fock theory and thereby c a l c u l a t e d the parameters, a, 3, Yf and c o r r e c t i o n s to the S l a t e r r a d i a l i n t e g r a l s . T h e i r work pointed out the need t o p r o p e r l y i n c l u d e h i g h angular momentum continuum s t a t e s i n any c a l c u l a t i o n o f e f f e c t i v e parameters. To i n c l u d e the continuum states, Morrison (12) used a p e r t u r b e d - f u n c t i o n approach t o c a l c u l a t e the e f f e c t o f core p o l a r i z a t i o n on the two-body and S l a t e r i n t e g r a l s . Newman and T a y l o r (13) modified the Hartree-Fock p o t e n t i a l t o change the form o f the e x c i t e d state spectrum and c a l c u l a t e d S l a t e r i n t e g r a l s and P parame t e r s . L a t e r , Balasubramanian, Islam, and Newman (14) i n t r o duced an i n f i n i t e l y deep p o t e n t i a l w e l l t o c a l c u l a t e the threep a r t i c l e c o r r e l a t i o n paramters/T^. No systematic c a l c u l a t i o n has been p u b l i s h e d f o r e i t h e r a f i n i t e number o f parameters across an e n t i r e s e r i e s o r f o r a l l twenty parameters f o r a single ion. With t h e s i g n i f i c a n t improvements i n high speed d i g i t a l computers which have occurred w i t h i n the l a s t ten years, i t i s now p o s s i b l e t o d i a g o n a l i z e a complete f r e e - i o n p l u s c r y s t a l k


17.

HESSLER AND CARNALL

Optical

Properties

353

of Ions

f i e l d Hamiltonian. T h i s procedure reproduces the observed energy l e v e l s w i t h a root-mean-squared d e v i a t i o n on the order of twenty-five cm"!. Because the c r y s t a l f i e l d i s not i n t r o duced as a p e r t u r b a t i o n , J-mixing o f the wave f u n c t i o n s i s p r o p e r l y accounted f o r . T h i s i s e s p e c i a l l y important i n s t u d i e s of the a c t i n i d e s because J-mixing d r a s t i c a l l y a l t e r s the p r o p e r t i e s o f the wave f u n c t i o n s . The v i r t u e s o f the c u r r e n t scheme are r e l a t i v e l y r e l i a b l e p r e d i c t i o n s o f the energy l e v e l p o s i t i o n s , e f f e c t i v e parameters t h a t vary s y s t e m a t i c a l l y across a s e r i e s , and wave f u n c t i o n s that may be u t i l i z e d f o r a d d i t i o n a l c a l c u l a t i o n s . The pred i c t i o n o f energy l e v e l s has aided the experimental study o f new systems such as G d i n CaF2 (15). The systematic v a r i a t i o n o f parameters across a s e r i e s has been used t o estimate parameters f o r the i n i t i a l a n a l y s i s o f an i o n . The p r o p e r l y admixed wave f u n c t i o n s w i l l improve the t r a n s i t i o n p r o b a b i l i t y a n a l y s i s o f the a c t i n i d e s .


3 +

3+ 3+ B. Current Status on Ln and An Ion Energy L e v e l s . The f r e e - i o n energy l e v e l s up t o approximately 30000 cm"l f o r a l l o f the t r i p o s i t i v e lanthanide ions i n LaCl3 s i n g l e c r y s t a l s are shown i n F i g u r e 1. Crosswhite (16) has r e c e n t l y t a b u l a t e d and d i s c u s s e d the f r e e - i o n and c r y s t a l - f i e l d parameters needed to d e s c r i b e the lanthanide data. The t r i p o s i t i v e a c t i n i d e l e v e l s are shown i n F i g u r e 2. Table I summarizes the f r e e - i o n parameters f o r the a c t i n i d e s which have been s t u d i e d i n d e t a i l . The d e t a i l e d analyses o f the and N p ions have r e c e n t l y been completed , 18) . The analyses presented i n Table I f o r P u , Am , and Cm are based on p u b l i s h e d s p e c t r a (^19, 20, 21, 22) obtained by Conway and coworkers. Crosswhite (23) has used the c o r r e l a t e d m u l t i c o n f i g u r a t i o n Hartree-Fock scheme o f F r o e s e - F i s h e r and Saxena (24) w i t h the approximate r e l a t i v i s t i c c o r r e c t i o n s o f Cowan and G r i f f i n (25) to c a l c u l a t e the S l a t e r , s p i n - o r b i t , and Marvin r a d i a l i n t e g r a l s f o r a l l o f the a c t i n i d e i o n s . A comparison o f the c a l c u l a t e d and e f f e c t i v e parameters i s shown i n Table I I . The r e l a t i v e l y l a r g e d i f f e r e n c e s between c a l c u l a t i o n and experiment are due to the f a c t t h a t c o n f i g u r a t i o n i n t e r a c t i o n e f f e c t s have not been p r o p e r l y i n c l u d e d i n the c a l c u l a t i o n . In s p i t e o f t h i s f a c t , the d i f f e r e n c e s vary smoothly and o f t e n monotonically across the s e r i e s . Because the Marvin r a d i a l i n t e g r a l M ° agrees w i t h the experimental v a l u e , the c a l c u l a t e d r a t i o s M (HRF)/M° (HRF) =0.56 and M (HRF)/M°(HRF) =0.38 f o r a l l t r i p o s i t i v e a c t i n i d e i o n s , are used t o f i x M^ and M4 i n the experimental scheme. The a n a l y s i s o f c r y s t a l - f i e I d components has remained a t the s i n g l e - p a r t i c l e l e v e l introduced by Bethe (4). C r y s t a l f i e l d parameters f o r the a c t i n i d e ions i n lanthanum t r i c h l o r i d e are shown i n Table I I I . They are approximately twice as l a r g e as the values found f o r the l a n t h a n i d e s . Although the values 3 +

3 +

3+

3+

2

4


354

CHEMISTRY

AND

SPECTROSCOPY


L A N T H A N I D E A N D ACTINIDE

Ce Pr Figure 1.

Nd Pm Sm Eu

Gd Tb

Dy

Ho

Er

Tm

Yb

Energy-level structure of the tripositive lanthanide ions in LaCl


3

17.

HESSLER AND CARNALL

x 10 cm

Optical

Properties

355

of Ions


FREE ION ENERGY LEVELS OF THE +3 ACTINIDES

_ H

Np'

Figure 2.

Hi

5/2

Pu

% Am

S Cm

8

\

Bk

I

F

4 n

l5/2

Cf

A

Es

2

15/2

Fm

r

Md

Energy-level structure of the tripositive actinide ions in LaCl


7/2

No

3

356

L A N T H A N I D E A N D ACTINIDE

CHEMISTRY

A N D SPECTROSCOPY

Table I. Free-Ion Parameters f o r T r i v a l e n t A c t i n i d e Ions i n Lanthanum T r i c h l o r i d e . U n i t s are cm"-*-.


Param.

u

3

+

Np

3 +

PU

3 +

_ 3+ Am

Cm

64124

19544

29999

39631

53700

3+

F

( 2 )

39715

44907

48670

[51800]

F

( 4 )

33537

36918

39188

[41440]

43803

23670

25766

27493

[30050]

32610

1623

1938

2241

[2580]

2903

a

27.6

31.5

29.7

[29]

28.3

e

-772

-740

-671

[-660]

[-650]

Y

[1000]

899

1067

[1000]

825

ip2

217

278

186

[200]

[200]

ip3

63

44

48

[50]

[50]

a

55109

T

4

255

64

38

[40]

[40]

T

6

-107

-361

-364

[-360]

[-360]

617

434

364

[390]

[390]

[350]

353

332

[340]

[340]

[0.67]

0.68

0.95

[0.99]

[1.09]

1276

894

822

[850]

T

7

T

p

8

2 O

A [] i n d i c a t e s t h a t the parameter was estimated and h e l d constant f o r a l l f i t t i n g . For a l l cases: ?

For a l l cases:

2

4

M / M ° = 0.56 and M / M ° = 0.38. 4

P /P

2

6

=0.75 and P / P

2

= 0.50.


912

HESSLER AND CARNALL

17.

Optical

Properties

357

of Ions

Table I I . Comparison o f R e l a t i v i s t i c Hartree-Fock I n t e g r a l s f o r (Rn, 5 f ) and E f f e c t i v e Parameters f o r T r i p o s i t i v e A c t i n i d e Ions i n Lanthanum T r i c h l o r i d e . U n i t s are cnT^. n

XT + Np

_ 3+ Pu

_ 3+ Am

31727

30037

29553

29546

29222

(4

12833

11815

11754

11604

11246

( 6 )

10248

9918

9842

8855

7793

275

244

238

212

216

1.00

0.88

1.08

1.00

0.99

3

Param.

AF

( 2 ) a

AF >


AF A?

Cm

M°(exp) M°(HRF)

a (k) A F

=

p

k

< >(HRF) - F< > (exp). k

Table I I I . C r y s t a l - F i e l d Parameters f o r T r i v a l e n t A c t i n i d e Ions i n Lanthanum T r i c h l o r i d e . U n i t s are cm" • 1

Param.

»5

»S

u

3

+

Np

3 +

Pu

TV Am

3

+

Cm

3+

246

a

260

163

226

[230]

-533

-632

-543

[-610]

-671

-1438

-1625

-1695

[-1590]

-1410

1025

1028

1000

[980]

921

A [] i n d i c a t e s t h a t the parameter was estimated and h e l d constant f o r a l l f i t t i n g .


358

LANTHANIDE

AND

ACTINIDE CHEMISTRY

AND

SPECTROSCOPY

are approximately constant across a s e r i e s , there are s i g n i f i c a n t v a r i a t i o n s t h a t d i s t o r t the monotonic behavior. T h i s may be i n d i c a t i v e of an incomplete p a r a m e t e r i z a t i o n scheme f o r the c r y s t a l - f i e l d i n t e r a c t i o n , j u s t as the non-systematic behavior of the S l a t e r and s p i n - o r b i t i n t e g r a l s i n d i c a t e d the need f o r the a d d i t i o n of 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 . 3+ C. Advances i n Experimental Techniques. The ions U through C m have been s t u d i e d by c l a s s i c a l photographic techniques, which may a l s o be a p p l i e d t o the study of Bk + and Cf . The i o n E s i s too r a d i o a c t i v e to u t i l i z e these t e c h niques. To overcome t h i s problem and t o extend the experimental c a p a b i l i t i e s i n t o the time domain, we have a p p l i e d pulsed dye l a s e r technology. Selective e x c i t a t i o n of a s p e c i f i c ion w i t h i n the background of daughter ions i s used t o d i s c r i m i n a t e against the r a d i o a c t i v e induced f l u o r e s c e n c e . Time r e s o l v e d d e t e c t i o n of f l u o r e s c e n c e i s used t o i d e n t i f y groups of f l u o r e s c i n g l e v e l s w i t h a s i n g l e upper l e v e l . By monitoring a known f l u o r e s c e n c e l i n e as a f u n c t i o n of the dye l a s e r wavelength, the e q u i v a l e n t of an absorption spectrum may be obtained. With these techniques (26) , both absorption and fluorescence data may be obtained f o r E s . The p r e c i s i o n of the data i s comparable t o t h a t obtained with c l a s s i c a l methods. S i m i l a r techniques may a l s o succeed i n l o c a t i n g some l e v e l s i n Fm . J+

3


3 +

3 +

3 +

3+

II.

Line I n t e n s i t i e s

A. T r a n s i t i o n P r o b a b i l i t y P a r a m e t e r i z a t i o n Scheme. As e a r l y as 1937 Van Vleck (27) r e f e r r e d to the "puzzle of the i n t e n s i t i e s of the a b s o r p t i o n l i n e s of the lanthanide i o n s " . L a t e r Broer, G o r t e r , and Hoogschagen (28) showed t h a t the observed i n t e n s i t i e s were too l a r g e to be accounted f o r by magnetic d i p o l e or e l e c t r i c quadrupole r a d i a t i o n , but t h a t induced e l e c t r i c d i p o l e t r a n s i t i o n s could account f o r the i n t e n s i t y . The c e n t r a l problem w i t h e l e c t r i c d i p o l e t r a n s i t i o n s w i t h i n a c o n f i g u r a t i o n i s t h a t they are LaPorte (or p a r i t y ) forbidden. To o b t a i n non-vanishing matrix elements f o r the e l e c t r i c d i p o l e operator r e q u i r e s that opposite p a r i t y conf i g u r a t i o n s be admixed i n t o the s t a t e s of the f c o n f i g u r a t i o n . Judd (29), i n h i s c l a s s i c paper of 1962, used the odd p a r i t y terms of the l i g a n d f i e l d t o accomplish t h i s admixture. A f t e r a p p l y i n g second order p e r t u r b a t i o n theory and s e v e r a l s i m p l i f y i n g assumptions, he showed t h a t the e l e c t r i c d i p o l e l i n e s t r e n g t h between J-manifolds may be expressed as the sum of three terms, each being the product of an i n t e n s i t y parameter and a reduced matrix element of the tensor operator \jM of rank X. The e l e c t r i c d i p o l e l i n e s t r e n g t h , S j , can be w r i t t e n i n the form n

e (


17.

S

HESSLER

AND CARNALL

(aJ,a'J') = e

2

Optical

X!

Properties

n

^ .

(5)

A=2,4,6

Thefi-^s are the i n t e n s i t y parameters. The l i n e s t r e n g t h f o r the magnetic d i p o l e t r a n s i t i o n s i s given by

S ^(aJ,a'J') = y < f y j | |L + 2 S I I f ^ ' J ^ md B 2


where u

B

n

2

(6)

= eh/4iT mc.

The wave f u n c t i o n s used i n the expressions f o r the l i n e strengths are p r e c i s e l y those deduced by an a n a l y s i s o f the f r e e - i o n energy l e v e l s t r u c t u r e . Therefore, only three new parameters, the 9,-^ s, have been introduced t o account f o r the l i n e s t r e n g t h s . T h i s scheme has been remarkably s u c c e s s f u l i n modeling experimental observations i n both c r y s t a l and s o l u t i o n environments. I t a l s o accommodates the e x i s t e n c e o f the "hypersensitive" transitions. Peacock (30) has r e c e n t l y reviewed the f i e l d with regard t o lanthanide f - f t r a n s i t i o n s . The s i m p l i c i t y o f t h i s scheme has been u t i l i z e d by Krupke (31) and C a i r d (32) t o p r e d i c t p o t e n t i a l l a s e r t r a n s i t i o n s i n the lanthanides. 3 +

B. Current Status o f A n Ion Line Strengths. As with the l a n t h a n i d e s , s o l u t i o n s p e c t r a were the f i r s t t o be i n v e s t i gated i n terms o f the Judd p a r a m e t e r i z a t i o n scheme. The l i g h t a c t i n i d e s U , Np3+, and Pu have a r a t h e r high d e n s i t y o f s t a t e s i n the o p t i c a l r e g i o n , t h e r e f o r e the f r e e - i o n J-manifolds o v e r l a p and a n a l y s i s i s d i f f i c u l t . Am i s a s p e c i a l case. Only t r a n s i t i o n s between the ground J = 0 and even J-manifolds are allowed i n the context o f the f r e e - i o n approximation. F o r Cm and the heavier a c t i n i d e s B k , C f , and E s a number of the f r e e - i o n J-manifolds are w e l l r e s o l v e d as can be seen i n the absorption s p e c t r a shown i n F i g u r e 3. The i n t e n s i t y parameters f o r these systems are given i n Table IV. For C m and Cf3+ the p a r a m e t e r i z a t i o n scheme y i e l d s a good f i t t o the experimental observations. For the case o f B k the l a r g e value o f &2 i s c o n s i s t e n t w i t h neighboring values o f the s e r i e s . The source o f t h i s discrepancy has not yet been i d e n t i f i e d . We note, i f l i g a n d - f i e l d i n t e r a c t i o n s are not i n c l u d e d i n the determination o f f r e e - i o n wave f u n c t i o n s , then J-mixing between the manifolds w i l l not occur. T h i s J-mixing w i l l be very important i n the c a l c u l a t i o n o f t r a n s i t i o n p r o b a b i l i t i e s i n the a c t i n i d e systems. 3 +

3+

3+

3 +

3 +

3 +

3+

3 +

n

o

t

C. L i n e I n t e n s i t i e s Between I n d i v i d u a l Stark Components. Simultaneously w i t h Judd's work, O f e l t (33) independently


360

LANTHANIDE

A N D ACTINIDE

CHEMISTRY

n


II

II

ii

M i l l

1— + 3

Es

M i l

Fm

II 28

26

24

22

20

18

16 cm

-1

14

SPECTROSCOPY

cf

II II II 1

11

Bk

AND

+

+

II 12

x I0

10

8

6

4

2

0

3

Figure 3. Intraconfiguration absorption spectra of the heavier tripositive actinide ions in aqueous solution. The vertical lines are the calculated positions of the free-ion energy levels. A broad background absorption has been subtracted from the data. No measurements have been obtained for fermium.


17.

HESSLER AND CARNALL

Optical

Properties

361

of Ions

Table IV. I n t e n s i t y Parameters f o r the Heavier A c t i n i d e s i n Dilute Acid Solution. U n i t s are pm , 1 pm = 10"" Q 2 2

2

2

c m

Ion

3


^ + Cm

°2

Lanthanide and Actinide Chemistry and Spectroscopy - American

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