Linear Stark effect of the F3+ center in LiF and NaF

Volume26A, number 12

LINEAR

STARK

PHYSICS LETTERS

EFFECT

OF

THE

F~

6 May 1968

CENTER

IN LiF

AND NaF

G.JOHANNSON, F. LANZL, W.VON DER OSTEN, R. PIEHL a n d W.WAIDELICH I. Physikalisches Institut der Technischen Hochschule, Darmstadt, Germany Received 10 April 1968

A linear Stark effect is observed widththe ionized R center in y-irradiated alkali halides by studying the zero-phonon absorption lines 4874 A in LiF and 5456 A in NaF in high electric fields.

F r o m u n i a x i a l s t r e s s m e a s u r e m e n t s the z e r o phonon a b s o r p t i o n l i n e s 4874 ~, in L i F and 5456 i n NaF a r e known to c o r r e s p o n d to a A ~ E t r a n sition of the i o n i z e d R c e n t e r (F~) [1-4]. T h e F~ c e n t e r exhibits C3v point s y m m e t r y and like in the c a s e of the R c e n t e r the lack of i n v e r s i o n s y m m e t r y r e s u l t s in a l i n e a r Stark effect, i.e. a splitting of the a b s o r p t i o n l i n e s a s s o c i a t e d with the r e m o v a l of both o r i e n t a t i o n a l and o r b i t a l d e g e n e r a c i e s by an e l e c t r i c field [5]. Due to the s i n g l e ground state of the F~ c e n t e r , however, no t e m p e r a t u r e dependence of the i n t e n s i t i e s of the splitting c o m p o n e n t s i s expected. Thus the splitting p a t t e r n s a r e found to be s y m m e t r i c with r e s p e c t to the energy shifts and i n t e n s i t i e s of the components. In this l e t t e r we r e p o r t on the S t a r k effect of the F~ z e r o - p h o n o n l i n e s in L i F and N a F at 4.2OK. Using a n e x p e r i m e n t a l technique d e s c r i b e d e a r l i e r [5] we applied e l e c t r i c fields up to 2.7 x x 10 ~ V / c m to the c r y s t a l s along (100). The opt i c a l d e n s i t y of the split 5466 ~ l i n e in NaF a s

o b s e r v e d e x p e r i m e n t a l l y i s shown in fig. 1 for light p o l a r i z e d p a r a l l e l (~) and p e r p e n d i c u l a r (a) to the field d i r e c t i o n . In this c a s e special c a r e in s a m p l e p r e p a r a t i o n had to be taken to p r e v e n t m e c h a n i c a l s t r e s s e s which lead to splittings of the line p r i o r t o application of the e l e c t r i c field. F o r the 4874 A l i n e in L i F i n s t e a d of a splitting into s i n g l e c o m p o n e n t s as r e p o r t e d in [6] only changes in line shape a r e observed. T h e a n a l y s i s of our r e s u l t s in both L i F and N a F was p e r f o r m e d by the method of m o m e n t s . As expected t h e o r e t i c a l l y within the l i m i t s of e r r o r no changes of the zeroth and f i r s t m o m e n t s of the l i n e s a r e found in the e l e c t r i c field. Using the t h e o r e t i c a l i n t e n s i t i e s and energy shifts of the y - and a - p o l a r i z e d components expected for a A ~ E t r a n s i t i o n of a C3v c e n t e r [7] the differ e n c e of the second m o m e n t s of the l i n e s with and without field is c a l c u l a t e d to be

A (M2)~ = (Uo2 + 4 U12 - 4 Uo U 1 ) ~ " and

d

1(c~I12" 4CM~)

t5 I 0,5

i

], o, I Fig. 1. F~ zero-phonon absorption line 5456 ~ in NaF: Experimental and theoretical splitting patterns for a (100) electric field; E = 1.4 × 105 V/cm.

(

) 1o5 v / ~ 2

Ez 4-

o

Fig. 2. F~ zero-phonon absorption line 4874 A in LiF: E 2 depend'ence of the difference of the second moment of the line with and without electric field. 629

Volume 26A. number 12

P H Y SI C S L E T T E R S

A(M2)a=(U2o+4U21+2UoU1)E2

for

E//'(IO0).

As shown i n fig,. 2 for the 4874 A line in L i F this E 2 d e p e n d e n c e f s indeed found e x p e r i m e n t a l l y . F r o m the slope of the s t r a i g h t l i n e s the coefficients Uo and U 1 can be d e t e r m i n e d which d e s c r i b e the s p l i t t i n g due to the r e m o v a l of the o r i e n t a t i o n a l and o r b i t a l d e g e n e r a c y , r e s p e c tively. We obtained for IAF: Uo = ±2.7

and

U 1 = +2.0

NaF: Uo = ±1.4

and

U 1 = ±2.3

and for

in units of 10 "6 c m - 1 / V / c m . T h e s e p a i r s of coefficients a r e not unique. The s a m e splitting p a t t e r n s a r e obtained with U0 = 2 U1 and Ui = i Uo. Using the t h e o r e t i c a l i n t e n s i t i e s and: the coefficients for the 5456 A l i n e the s c h e m a t i c a l s p l i t t i n g p a t t e r n on the

ON T H E

HIGH

FREQUENCY

DIELECTRIC

a b s z i s s a of of the Stark tions of the m i n a t i o n of

6 May 1968 fig. 1 was calculated. M e a s u r e m e n t s effect along other s y m m e t r y d i r e c c r y s t a l s which allow an unique d e t e r Uo and U1 a r e in p r o g r e s s .

The work was supported by the Deutsche F o r schungsgemeinschaft.

1. A.E.Hughes and W.A.Runciman, Proc. Phys. Soc. 86 (1965) 615. 2. G. Baumarm, W. Von der Osten and W. Waidelich, Z. angw. Physik 22 (1967) 246. 3. G. Baumaan, F . Lanzl, W. Von der Osten and W. Waidelich, Z. Physik 197 (1966) 367. 4. L.F.Stiles and D.B.Fitchen, Phys. Rev. Letters 17 (1966) 689. 5. G.Johannson, F.Lanzl, W. Von der Osten and W. Waidelich, Phys. Letters 25A (1967) 598. 6. A.A. Kaplyanskii and V. N. Medvedev, JETP Letters 6 (1967) 323. 7. F. Lanzl, Phys. Letters 25A (1967) 596.

CONSTANT

OF

THE

ELECTRON

GAS

J. DA PROVIDENCIA

LaboratOrio de Fisica , Universidade , Coimbra, Portugal Received 11 April 1968

It is shown that the zero point motion of the plasmon mode yields a finite contribution to the imaginary part of the electron gas dielectric constant for frequencies above the plasmon frequency.

In the p r e s e n t note we d e s c r i b e a calculation of the i m a g i n a r y p a r t of the longitudinal d i e l e c t r i c constant of the e l e c t r o n gas at f r e q u e n c i e s above the p l a s m o n f r e q u e n c y , for which the r e a l p a r t b e c o m e s zero. We have c o n s i d e r e d the d i r e c t excitation of a p l a s m o n coupled to a n o n - c o l l e c t i v e p a r t i c l e - h o l e mode. Such a p r o c e s s i s made p o s s i b l e by the ground state c o r r e l a t i o n s due to the p l a s m o n z e r o - p o i n t motion. In ref. 1 it has been shown that p r o c e s s e s of this type may lead to the a p p e a r e n c e of c o n s i d e r able a m o u n t s of t r a n s i t i o n s t r e n g t h at h i g h - e n e r g i e s . We denote by ~ q ( p ) the RPA a m p l i t u d e (in the notation of ref. 2) c o r r e s p o n d i n g to a p l a s m o n of m o m e n t u m q and by ~0p the p l a s m o n frequency. We obtain for the d i e l e c t r i c c o n s t a n t a modified g e o m e t r i c s e r i e s which m~y be s u m m e d up, leading to the following r e s u l t for the i m a g i n a r y p a r t E2(q'w) = 74~e2 t ~

O(p)(1 -O(p+q))5(w - E ( p + q ) + ~ ( p ) ) + p~k [ ~ * - k ( P + k ) J / ' k ( P + k )

+

+ tp*k(p+ k +q)tp_k(p+ k +q) _ t~*k(p+ k +q)V,,_k(P+k ) - ~ * ( p + k ) t p _ k ( p + k + q)] x x 0(p)(1 - O(p+ k+ q))5(w - Wp - ¢ ( p + q + k ) + ¢(p)) l " The f i r s t t e r m i n s i d e the b r a c e s i s the R P A r e s u t l [3]. The second t e r m i s the c o r r e c t i o n due to l o n g 630