INTENSITIES OF 4f 4f TRANSITIONS IN GLASS MATERIALS

Transcription

1 ITESITIES OF 4f 4f TRASITIOS I GLASS MATERIALS ópco IV O.L. MALTA Deparameno de Químca Fundamenal CCE UFPE. Cdade Unversára, Recfe-PE, , Brazl. COTETS 1. Inroducon 1. Some characerscs of he rare earh ons.1. The Hamlonan for he free on... The egenfuncons n he nermae couplng The lgand feld The usual form of he lgand feld Hamlonan The lgand feld and symmery f 4f nenses Mechansms of 4f 4f ransons The Judd Ofel heory The dynamc couplng Inensy parameers n vreous maerals Concludng remarks Inroducon Glass maerals conanng rvalen rare earh ons have been wdely sud due o her poenal applcaons as opcal devces ( lasers and fbers for opcal amplfers, among ohers)[1 ]. Moreover, hese maerals have a grea advanage over crysallne sysems snce hey can be n general easly prepar wh hgh opcal qualy and n a large varey of chemcal composons. The opcal properes of hese maerals are drecly rela o he 4f 4f ransons n a 4f elecronc confguraon. In our days, he heorecal background for he raonalzaon of hese nraconfguraonal ransons, boh radave and non-radave, s well esablsh [ -1 ]. The sandard Judd-Ofel heory [,3 ] has been us o evaluae absorpon and emsson cross-secons

2 n a grea majory of works on hese rare earh dop glasses, and he so-call nensy parameers ( =, 4 and 6 ) have been us o afford nformaon on covalence, qualy and mechancal properes of he mum [ 1 ]. everheless, a ceran number of problems sll exs rela o he applcaon of he heory and o he nerpreaon of resuls oban from, parcularly n he case of glasses, as one may noe from he leraure. Among hese problems we may emphasze he sysemac neglec of he dynamc couplng mechansm conrbung o he 4f 4f nenses [ 5-9, 11 ]. We wsh here o oulne he man aspecs of he above-menon heorecal background and o dscuss brefly some raher problemac pons concernng he use of he heory and he nerpreaon of resuls.. Some characerscs of he rare earh ons.1. The Hamlonan for he free on The Hamlonan, H FI, for he rare earh free on s compos by one par due o he cenral feld, H 0, and several oher neracons whch are n general rea as perurbaons. Among hese neracons he nerelecronc repulson, H c, and he spn-orb neracon, H so, are he mos relevan. H FI = H 0 + H c + H so ( 1 ) The magnudes of hese neracons follow he order H 0 H c H so. In he dagonalzaon procure of he Hamlonan H FI he spn-spn, spn-oher-orb and orb-orb neracons are n general of much less mporance. Thus, n a frs sep, he egenfuncons of H FI may be consruc from he egenfuncons of he angular momenum operaors L, S, J and J Z where L = oal orbal angular momenum S = oal spn angular momenum J = oal angular momenum, J = L + S J Z = z componen of J

3 3 wh L = and S = s, and s beng monoelecronc orbal and spn angular momena, respecvely. The quanum number J mus sasfy he condon L S J L + S. For rare earh ons an adequae scheme o represen a bass of egenfuncons s he well-known L - S couplng scheme (4f )SLJM J. Ths noaon mples ha hese egensaes are pure 4f saes, or, n oher words, no confguraon neracon ( CI ) va H FI s aken no accoun. CI effecs, for each gven case, have been consder whou ncreasng he dmenson of he marx [H FI ] hrough he use of effecve operaors acng whn he 4f confguraon. In he consrucon of he egensaes (4f )SLJM J one frequenly fnds ha hey are no unambguously defn by he quanum numbers S, L, J and M J. Ths problem can be solv by he use of group heory. Racah [ 13 ] has demonsra ha he rrucble represenaons of ceran sub-groups of he GL(4 +) connuous group may be us as quanum numbers o classfy hese egensaes. Ths s due o he fac ha hey form bases for hese rrucble represenaons. Thus, n he above scheme represens he se of addonal quanum numbers necessary o specfy he egensae. A common procure n he leraure has been o dagonalze he Hamlonan H FI on a bass form by he above egensaes. The usual form of H FI s [ 14 ] H FI E b (4f ) E k0,1,,3 k e k 4f s CIconrbuons ( ) where E b s he energy of he barcener of he 4f confguraon(egenvalue of he cenral feld Hamlonan). The second and hrd erms n he rgh-hand-sde of hs expresson correspond o he nerelecronc repulson and spn-orb neracon, respecvely. The las erm conans confguraon neracon effecs. Marx elemens of he componens n eq.( ) are evalua by rrucble ensor operaor echnques [ ]. The radal quanes n eq.( ), E k and 4f,, he Racah and spn-orb parameers, respecvely, may n prncple be calcula from ab no mehods(he E 0 parameer can be absorb by E b ). However, hey are n general rea as adjusable parameers for whch he npu daa are he expermenally observ energes of he barceners of he J manfolds. The grea advanage of hs laer procure s ha, afer dagonalzaon, one ges usually much more relable free on wavefuncons, whch s essenal o he evaluaon of properes of rare earh on dop maerals.

4 4.. The egenfuncons n he nermae couplng Takng no accoun he fac ha he nerelecronc repulson s no dagonal n he quanum number and ha he spn-orb neracon s no dagonal n he quanum numbers, S and L, hese laer are no longer good quanum numbers. As a consequence, afer dagonalzaon of H FI he egensaes wll be gven by lnear combnaons of he saes (4f )SLJM J, ha s ( 4f ) JM C( SL) (4f ) SLJM ( 3 ) J SL J wh he condon SL C( SL) 1 ( 4 ) Eq.( 3 ) expresses he so-call nermae couplng scheme. The egensaes gven n hs scheme, as menon before, are essenal o descrbe he behavor of rare earh ons. A good example s he case of ransons beween mulples of dfferen mulplces, whch oherwse can no be descrb. A ypcal case s llusra by he ransons beween he 5 D J and 7 F J mulples of he Eu 3+ on. Labelng a mulple by he usual noaon S+1 L J s a mere ndcaon of he domnan componen n he summaon n eq.( 3 ). An neresng and useful aspec s ha, snce a chemcal envronmen raher weakly affecs he 4f orbals, for each rare earh on he egensaes n he nermae couplng scheme are essenally he same for dfferen envronmens. 3. The lgand feld 3.1. The usual form of he lgand feld Hamlonan Even hough weak, he neracon beween 4f elecrons and he chemcal envronmen s responsble for he mos neresng specroscopc feaures of rare earh ons. The non - sphercal even pary par of hs neracon, responsble for he Sark splng of 4f levels, s commonly wren as

5 5 k ( k HLF Bq C ) q ( ) ( 5 ) k, q, where he B k q s (k =, 4 and 6) are he so-call lgand feld parameers of even rank and C (k) s a Racah ensor operaor of rank k [ ]. The values of k are resrc by pary and rangulary rules for f orbals [ 14 ]. The allow values of q depend on he symmery of he lgand feld around he rare earh on, and n hs expresson he ndex run over he 4f elecrons. The Hamlonan H LF as gven by eq.( 5 ) s a one parcle operaor. A relevan pon here s ha he form of eq.( 5 ) has a more general characer han mgh be suppos, n he sense ha all one parcle lgand feld models lead o hs form of H LF. Despe he fac ha he B k q s, for a gven pon symmery, can be calcula from heorecal models, has been a common pracce o rea hem also as adjusable parameers call phenomenologcal or expermenal B k q s. As for he case of he free on radal parameers n eq.( ), he npu daa are he observ energes of he 4f levels under he acon of he lgand feld. The oal Hamlonan o be dagonalz s now H = H FI + H LF ( 6 ) The lgand feld neracon s also of fundamenal mporance o he case of 4f - 4f ranson nenses. These ransons are n prncple elecrc dpole forbdden by Lapore s rule. However, provd he se occup by he rare earh on does no presen a cener of nverson Lapore s rule s relax due o odd pary erms n he lgand feld Hamlonan. The more general form of H LF s acually H LF = H LF (even) + H LF (odd) ( 7 ) I s mporan o noe ha f he dagonalzaon of he oal Hamlonan H n eq.( 6) s resrc o a bass form by he saes (4f )SLJM J, due o pary selecon rules he componen H LF (odd) wll have no effec on he fnal resuls. Ths odd componen s n general express as ( ) H ( odd) r C ( ) ( 8 ) LF, p, p p

6 6 where r s he radal coordnae of he -h elecron and he p s ( = 1, 3, 5 and 7) are he so-call odd rank lgand feld parameers. The values of are resrc by pary and rangulary rules nvolvng f, d and g orbals [,3 ]. ow he ndex, n prncple, run over all elecrons of he rare earh on. As for he values of q n eq.( 5 ), he allow values of p depend on he symmery around he rare earh on. In he case of nenses he role of H LF (odd) s o connec (mx) saes belongng o elecronc confguraons of oppose pary. I follows ha ransons beween 4f levels become parally elecrc dpole allow. 3.. The lgand feld and symmery As menon above, he values of q and p n eqs.( 5 ) and ( 8 ), respecvely, are resrc by he symmery of he se occup by he rare earh on.thus, for example, n a C 4V symmery he allow values are : k =, q = 0 ; k = 4, q = 0, 4 ; k = 6, q = 0, 4 ; = 1, p = 0 ; = 3, p = 0 ; = 5, p = 0, 4 ; = 7, p = 0, 4. Ths s a consequence of he fac ha he lgand feld parameers are acually a summaon over he ndvdual conrbuons from he surroundng aoms. Each ndvdual conrbuon behaves as he sphercal harmoncs and he summaon vanshes n a gven symmery for ceran values of q and p. A deal work on hs subjec may be found n refs. [ 17 ] and [ 18 ]. One of he consequences of he acon of H LF (even) s ha J s no longer a good quanum number. Ths produces he so-call J - mxng effec (a raher small effec due o he weak neracon beween he 4f orbals and he chemcal envronmen), and as a resul of he dagonalzaon of he oal Hamlonan H n eq.( 6 ) he fnal egensaes have he general form ( 4f ) A(, S, L, J, M ; ) ( 4f ) SLJM, S, L, J, M J J J ( 9 ) wh he condon,s,l,j,m A(,S,L,J,M ; ) J J 1 ( 10 )

7 S+1 L J 7 Each egensae gven by eq.( 9 ) s now label by an rrucble represenaon,, of he symmery pon group. In he case of glasses, snce here s a varey of dfferen ses ha can be occup by he rare earh on, we canno alk abou a well-defn se of lgand feld parameers.the Sark splng s n general no well deermn n hs case, whch makes dffcul o defne even an average se of lgand feld parameers. In fgure 1 a schemac represenaon of he nraaomc and lgand feld neracons dscuss above s presen. 4f -1 5d S+1 L 10 5 cm -1 4f 10 4 cm cm -1 S+1 L J(Mj) 10 cm -1 H O H C H SO H LF Fgure 1. Schemac represenaon and order of magnude of he effecs of he nra-aomc and lgand feld neracons a- cng on a 4f confguraon. 4. 4f - 4f nenses 4.1. Mechansms of 4f - 4f nenses

8 8 The characersc absorpon and emsson specra of rare earh compounds n he vsble, near ulra-vole and near nfra-r s arbu o ransons beween 4f levels due o he fac ha hey presen sharp lnes, manly a low emperaure, wh oscllaor srenghs ypcally of he order of These ransons are o frs order elecrc dpole forbdden, bu are allow by he elecrc quadrupole, vbronc, magnec dpole and forc elecrc dpole mechansms. I has been noc, snce more han ffy years ago, ha among hese mechansms only he magnec dpole and forc elecrc dpole ones could accoun for he observ nenses [ 19 ]. The magnec dpole characer of he 5 D 0 7 F 1 ranson of he Eu 3+ on was demonsra n 1939 by Deuschben [ 0 ]. The coeffcen of sponaneous emsson beween wo manfolds J and J, due o he magnec dpole mechansm, s gven by A 4 e 3 c 3 3 J,J n S 3 md ( 11 ) where he magnec dpole lne srengh S md (n uns of e, where e s he elecronc charge = e.s.u. ), s S md 4m c e (4f ) J L S (4f ) J 1 J 1 ( 1 ) In he above equaons s he angular frequency of he ranson J J(= c, beng he ranson energy n cm -1 ), n s he ndex of refracon of he mum and he angular momenum operaors L and S are n uns of. The egensaes n eq.( 1 ) are gven n he nermae couplng scheme. Mos of he 4f - 4f ransons n he rare earh seres canno be accoun for by he magnec dpole mechansm, no only because he prc oscllaor srenghs are n general smaller han 10-6 bu also due o he resrcve selecon rules on he J quanum number (J = 0, 1), as far as J s consder a good quanum number. The forc elecrc dpole mechansm was rea n deal for he frs me n 196 by Judd [ ] and Ofel [ 3 ] hrough he powerful echnque of rrucble ensor operaors [ ]. Two years laer was propos by Jorgensen and Judd [ 1 ] ha an addonal mechansm of 4f - 4f ransons, orgnally referr o as he pseudoquadrupolar mechansm due o nhomogenees of

9 9 he delecrc consan, could be as operave as, or, for some ransons, even more relevan han he forc elecrc dpole one. These wo mechansms wll be brefly descrb n he nex wo subsecons. 4.. The Judd - Ofel heory s gven by The elecrc dpole srengh, S (n uns of e ), of a ranson beween wo saes and S r ( 13 ) If he saes and are pure 4f saes, as hose gven by eqs.( 3 ) and ( 9 ), han by pary selecon rule (Lapore s rule) he dpole srengh S s dencally null. However, provd here s no cener of nverson n he se occup by he rare earh on, hs selecon rule s relax by he odd componen of he lgand feld Hamlonan, H LF (odd), whch mxes saes of oppose pary elecronc confguraons. Thus, snce H LF (odd) s a one parcle operaor, he confguraons ha can be mx wh he ground 4f confguraon are hose of he ype 4f -1 nd, 4f -1 ng (n 5 ) and nd 4d+1 4f +1 (d =, n = 3 and 4, correspondng o core excaons ). In he sandard Judd-Ofel heory he nal sep s o consder hs mxng hrough perurbaon heory up o frs order n he wavefuncons. If we ake he perurbaon on he egensaes gven by eq.( 9 ), hen we may wrgh (4f ) B B H LF (odd) (4f E( ) E(B) ) B ( 14 ) where B desgnaes an oppose pary exc confguraon and s saes. The sae has a smlar expresson. The marx elemen n eq.( 13 ), abbreva as, s consequenly gven by

10 10 B (4f ) r B B H LF E( ) E(B) (odd) (4f ) (4f ) H LF (odd) B B E( ) E(B) r (4f ) ( 15 ) An neresng order of magnude esmae can be made from eq.( 15 ). For an elecrc dpole allow ranson he oscllaor srengh can be as hgh as 1. For rare earh ons he lgand feld neracon s ypcally of he order of 100 cm -1 and he nerconfguraonal energy dfferences for he lowes oppose pary exc confguraon (4f -1 5d ) s ypcally of he order of 10 5 cm -1. Ths gves a facor of 10-3 n eq.( 15 ), whch squar leads o he ypcal order of magnude of 4f - 4f oscllaor srenghs (10-6 ). The summaon over B and n eq.( 15 ) remnds he possbly of usng a closure procure, and nde hs s he nex sep n he Judd - Ofel reamen. Ths summaon becomes much more reaable f one assumes ha he nraconfguraonal energy dfferences are much smaller han he energy dfferences beween he barceners of he ground and exc confguraons, or, n oher words, f one assumes ha E( ) - E(B) E( ) - E(B) E b (4f ) - E b (B) = E(B). The man pon now s o use he followng relaon nvolvng wo rrucble ( k) ( k) ( k ) ( k ) ensor operaors Xq xq ( ) and Z q z q ( ) [,3 ] ( k) ( k) Q ( k) ( k) ( 4f ) X B B Z ( 4f ) ( 1) ( 1) 4f x n n z 4f q q, Q k k q q Q f k k f ( ) ( 4f ) U ( 4f ) ( 16 ) Q In hs equaon he quanes n and { } are 3-j and 6-j symbols, respecvely [ ]. The monoelecronc ruc marx elemens nvolvng x (k) and z (k) conan he radal par correspondng o hese operaors, and U () s an rrucble un ensor operaor [ ]. In he case of core excaons ( d, n 3 and 4 ) a mnus sgn appears n he rgh-hand-sde of eq.( 16

11 11 ). In our case he ranks k and k are equal o 1(from he dpole operaor) and (from H LF (odd)), respecvely. Thus, may be shown ha he only dfference beween he wo erms n he rghhand-sde of eq.( 15 ) s n he 3 - j symbols whch are rela by 1 ( 1) q p Q 1 1 p q Q Snce s odd only even values of wll lead o nonvanshng values of. From he rangulary rules for he 6 - j symbol n eq.( 16 ) one has f,.e., 6. The un ensor operaor U (0) s a scalar and canno conrbue o ranson probables. Therefore, he operave values of are, 4 and 6. The marx elemen may hen be pu n he form Q ( 1 ) ( 1 ) 1 p Q q q p Q B ( 4f ) U ( ) ( 4f ) e ( 17 ),, Q, p, q where he sphercal un vecors sasfy he condon e e gven by where B p q q q q, and he quanes B p are (, ) ( 18 ) p (, ) n, f 1 f ( 1) ( ) f C C f 4f r n n r 4f 1 E( n) ( 19 ) If one s no neres on ranson nenses beween Sark levels (, ) bu raher on negra nenses beween J and J manfolds, o a frs approxmaon J mxng effecs may be neglec and he 4f egensaes n eq.( 17 ) may be replac he egensaes n he nermae couplng scheme defn n eq.( 3 ). Thus, he oal elecrc dpole srengh s a sum over M J and M J dvd by J+1, whch assumes ha he componens of he nal J manfold are equally

12 1 hermally popula.usng he Wgner-Eckar heorem and he orhogonaly relaon beween 3 j symbols, may be easly shown ha he oal elecrc dpole srengh n eq.( 13 ) s hen gven by S 1 J 1,4,6 (4f ) J U ( ) (4f ) J ( 0 ) where ( 1),p B p 1 ( 1 ) An alernave way of performng he summaon n eq.( 15 ) has been us hrough he average energy denomnaor mehod nroduc by Bebb and Gold [ ]. The advanage s ha one has o deal wh a sngle average energy dfference n eq.( 15 ). I has been shown ha he prc values of he so-call nensy parameers B and p are very smlar o hose gven by he sandard Judd-Ofel reamen [ 9 ]. The coeffcen of sponaneous emsson akng no accoun boh he forc elecrc dpole and magnec dpole mechansms s hen gven by A J J 4e 3 3c 3 n(n ) 9 S n 3 S md ( ) I should be no, however, ha he above equaon s vald as far as J mxng s neglec, oherwse a cross erm beween he elecrc dpole and magnec dpole ranson momens may appear. The correspondng expresson for he oscllaor srengh may be oban from he relaon P J J 3 J 1 mec A J J ( 3 ) J 1 e n 4.3. The dynamc couplng

13 13 Ths mechansm was orgnally propos by Jorgensen and Judd [ 1 ] n an aemp o explan he uncommon nensy varaon of ceran 4f - 4f ransons denomna hypersensve ransons. A smplf vsualzaon of hs mechansm s shown n fgure. TOTAL FIELD= E E ( j) j DC DYAMIC COUPLIG FIELD E DC j E j j LIGAD RARE EARTH IO ICIDET FIELD E Fgure. A pcoral represenaon of he dynamc couplng. The ncden radaon feld nduces oscllang dpoles n he surroundng aoms and, as a consequence, an addonal oscllang elecrc feld s produc. Ths elecrc feld, beng produc close o he rare earh on, has large local gradens and may nduce 4f - 4f ransons wh oscllaor srenghs of he order of, or even greaer han To a frs approxmaon he nduc oscllang dpoles depend on he soropc dpolar polarzables of he surroundng aoms, as ndca n fg.. The neracon energy wh he 4f elecrons, H DC, s gven by

14 14 H DC (r R j) e j ( 4 ) 3, j r R j whch mus be add o he neracon, wh he ncden feld, ha leads o he forc elecrc dpole mechansm. When expand n erms of rrucble ensor operaors [ 14 ], he even rank componens of H DC lead o a ranson momen(n uns of e) ha has exacly he same form as he ranson momen gven n eq.( 17 ), ha s DC Q DC p Q q q p Q B f U ( ) ( 1) ( 1) 1 ( 4 ) ( 4 f ) e ( 5 ),, Q, p, q where 1/ DC ( 1)( 3) ( ) B p f r f f C f p 4 4 ( 1 ), 1 ( 6 ) ( 1) and p 4 1 1/ j Y ( j) ( 7 ) 1 R p j j Y p beng a sphercal harmonc and (1 - ) n eq.( 6 ) s a sheldng facor due o he 5s and 5p DC fll sub-shells of he rare earh on [ 9 ].The oal nensy parameer s now B B B, p p p whch s he quany o be us n eq.( 1 ) o oban he oal parameers. Several neresng aspecs may be dscuss on he forc elecrc dpole and dynamc couplng mechansms. An analyss from ypcal values of he quanes ha appear n eqs.( 18 ) and ( 6 ) ndcaes ha hese wo mechansms conrbue o he oal ranson momen wh oppose sgns [ 11 ]. Boh he odd rank lgand feld parameers, p, and he polarzably

15 15 dependen quanes p conan n general he same ype of sum over he surroundng aoms. Therefore, hey carry ou he same symmery nformaon. The only dfference s ha p does no depend on he sphercal harmonc of rank 1 ( Y p 1 ) as may be no from he Kronecker s dela n eq.( 6 ). As he se occup by he rare earh on becomes more symmerc, he lower rank p and p end o vansh more rapdly han he hgher rank ones, or n a more general way, he former quanes are more sensve o changes n symmery han he laer ones, hough he hgher rank p and p are more sensve o changes n dsances. Ths goes n he correc sense owards he raonalzaon of he so-call hypersensve ransons, whch are n general hose ransons domna by he effecve operaor U (). However, has been observ ha symmery alone canno accoun for he enormous varaon somemes observ n he nenses of hese ransons for dfferen chemcal envronmens. Theorecal esmaes have shown ha he dynamc couplng conrbuon s able o accoun for hs enormous nensy varaon hrough he polarzables of he surroundng aoms, or groups of aoms. Thus, for example, n gong from he gaseous compound df 3 o gaseous di 3 here s a change n polarzably, from he on F - o he on I -, of almos one order of magnude. Ths mgh produce a change of almos wo orders of magnude n he nenses domna by U (). Abnormal changes n he nenses domna by 4 U (4) and 6 U (6) may no occur snce for hese cases he consderable ncrease n he dsance d - X(X = F and I) may compensae for he ncrease n he polarzably values. A pon ha should be sress here s ha, n conras o a common procure found n he leraure n he case of rare earh dop glasses, he dynamc couplng mechansm canno n any crcumsance be neglec. When he nensy parameers are deermn phenomenologcally from expermenal nenses, he forc elecrc dpole and dynamc couplng mechansms are absorb smulaneously and canno be dsngush. Thus, when reang energy ransfer processes beween rare earh ons one should keep n mnd ha n he dpole-dpole or dpole- quadrupole expressons for he ransfer raes he s whch appear refer only o he forc elecrc dpole conrbuon, ha s,. Ths s one of he reasons ha movae heorecal calculaons of DC he ndvdual B p and B p conrbuons. These heorecal calculaons urn ou o be an enormous problem, n vreous maerals, due o he large varey of dfferen se symmeres occup by he rare earh on, unless a model sysem wh a sascally well defn dsrbuon

16 16 of se symmery ypes s avalable. In hs case he parameers represen average values over all ypes of ses. 5. Inensy parameers n vreous maerals One of he effecs of a dsrbuon of dfferen symmery ses occup by he rare earh on s o produce he nhomogeneous lne broadenng. The Sark levels overlap n such a way ha, n mos cases, even he fluorescence lne-narrowng echnque canno help o denfy a parcular se occup by he rare earh on. Fgure 3 shows he emsson specrum of he Eu 3+ on n fluoroborae glasses [ 3 ], where hs effec can be clearly no, parcularly n he 5 D 0 7 F hypersensve ranson a 61 nm. Fgure 3. Lumnescence specrum of he Eu 3+ on, n he presence (a) and n he absence (b) of slver parcles, n a fluoro- borae glass. As already menon above he nensy parameers n vreous maerals correspond o sascal average values over all ses, and hese values, deermn expermenally, ncorporae boh he forc elecrc dpole and dynamc couplng conrbuons. The dependence wh he polarzables of he neghborng ons confers o he laer mechansm a sronger dependence wh he naure of he chemcal envronmen (for he sake of comparson, n a 100% onc model of he

17 17 lgand feld neracon he charge on he fluorne and chlorne ons, for example, s 1,n uns of he elecronc charge, whle her dpolar soropc polarzables are, respecvely, 1 A 3 and 3 A 3 ). Ths may accoun for he hypersensve behavor of ceran 4f 4f ransons, hose whch are n general domna by U (). A correlaon has been no n he sense ha compounds expec o have a hgher degree of covalence end o presen hgher values of [ 1 ], suggesng ha n hese cases he dynamc couplng mechansm domnaes. Ths correlaon can be clearly seen from he values collec n able 1 of ref.[ 1 ], where he oxdes and chalkogendes presen hgher values for hs nensy parameer han he fluordes. Anoher correlaon has also been no beween he 4 and 6 parameers and he ampludes of localz vbraonal modes nvolvng he rare earh on [ 1 ], gvng an ndcaon of he rgdy of he maeral. I s, however, raher dffcul o raonalze hs correlaon n erms of he quanes ha appear n eqs.( 18 ) and ( 6 ). An neresng and conroversal case of nensy parameers s he Pr 3+ on. In many compounds wh Pr 3+ s found ha he phenomenologcal parameer s negave, whch, from he defnon of he (eq.( 1 )), s no accepable. I has been argu [ 4 ] ha for hs on he lowes oppose pary exc confguraon, 4f5d, s oo close(50000 cm -1 ) o he ground confguraon(4f ), nvaldang he approxmaon made on he energy denomnaors n eq.( 15 ). There are dfferen ways n whch correcons could be nroduc. One s o ake he 4f wavefuncons up o hgher han frs order n perurbaon heory [ 7 ]. Anoher one s, for example, o make approprae expansons on he nverse of he energy dfferences n eq.( 15 ) as has been done n ref.[ 4 ]. In eher way one fnds ha he odd rank effecve operaors U () ( = 1,3 and 5 ) may be of sgnfcance when E(5d) s small, as n he case of he Pr 3+ on. However, one should keep n mnd ha even n hs case, dependng on he chemcal envronmen, he dynamc couplng mechansm may domnae, whch would make more dffcul o evaluae precsely he effec of he odd rank effecve operaors. There are evdences n he case of he soelecronc on U 4+ (5f ), found by F.Auzel [ 5 ], ndcang a raher ndependen behavor of he 5f 5f ranson nenses wh he poson of he 5f6d oppose pary exc levels, suggesng a domnance of he dynamc couplng mechansm. Anoher aspec on Pr 3+ compounds concerns he sascal procure whch s usually adop o exrac he nensy parameers from expermenal oscllaor srenghs (leas-squares mehod). I s possble ha n hs case he se of lnear equaons s parcularly sensve o very small varaons, whn expermenal errors, n he

18 18 oscllaor srenghs. A mehod n whch branchng raos are nclud n he leas-squares procure has been propos by Qumby and Mnscalco [ 6 ], and a mehod n whch he sandard devaon for each ndvdual oscllaor srengh s nroduc n he mnmzaon procure has been us by Goldner and Auzel [ 7 ], boh leadng o relable nensy parameers. 6. Concludng remarks Some very basc aspecs of he heory of 4f 4f ranson nenses appl o vreous maerals have been dscuss above. The characerscs of he nra-aomc rare earh free on and lgand feld neracons, as well as he formalsms of he forc elecrc dpole and dynamc couplng mechansms of 4f 4f nenses, have been ouln. One of he man pons was o call aenon o he conrbuon from he dynamc couplng mechansm o he nenses, a pon ha has been commonly overlook n he leraure of rare earh dop glass maerals. o akng no accoun hs mechansm s equvalen o assume ha he phenomenologcal nensy parameers concde wh, correspondng o he forc elecrc dpole conrbuon alone. Ths would be a clear msnerpreaon of he heory. From he heorecal expressons gven n eqs.( 18 ) and ( 6 ) s possble o raonalze he correlaon beween and covalence, as dscuss n ref.[ 1 ]. However, he same s no evden concernng he correlaon beween 4 and 6 and he rgdy of he mum. The case of he Pr 3+ on has been brefly dscuss under he lgh of he forc elecrc dpole and dynamc couplng mechansms, and aenon has been call o he fac ha, for hs on, sascal problems may arse when deermnng phenomenologcal nensy parameers from expermenal oscllaor srenghs. References [ 1 ]. R.Resfeld and C.K.Jorgensen, Handbook on he Physcs and Chemsry of Rare Earhs, Ch.58, 1987 ( by K.A.Gschnner Jr. and L.Eyrng, Elsever Scence Publshers ). [ ]. B.R.Judd, Phys. Rev. 17 ( 196 ) 750. [ 3 ]. G.S.Ofel, J. Chem. Phys. 37 ( 196 ) 511. [ 4 ]. R.D. Peacock, Srucure and Bondng ( 1975 ) 83. [ 5 ]. B.R.Judd, J. Chem. Phys. 70 ( 1979 ) 4830.

19 19 [ 6 ]. M.F.R, J.J.Dallara and F.S.Rchardson, J. Chem. Phys. 79 ( 1983 ) [ 7 ]. L. Smenek-Melczarek and B.A.Hess Jr., J. Chem. Phys. 87 ( 1987 ) [ 8 ]. M.F. R and.g.bey, Mol. Phys. 67 ( 1989 ) 407. [ 9 ]. O.L.Mala, S.J.L.Rbero, M.Faucher and P.Porcher, J. Phys. Chem. Solds 5 ( 1991 ) 587. [ 10 ]. Y.V.Orlovsk, K.K.Pukhov, T.T.Basev and T.Tsubo, Opcal Maerals 4 ( 1995 ) 583. [ 11 ]. O.L.Mala, M.A.Couo dos Sanos, L.C.Thompson and.k.io, J. Lumnescence 69 ( 1996) 77. [ 1]. T.T.Basev, Y.V.Orlovsk, K.K.Pukhov, V.B.Sgachev, M.E.Doroshenko and I..Vorob ev, J. Lumnescence 68 ( 1996 ) 41. [ 13 ]. G.Racah, Phys. Rev. 76 ( 1949 ) 135. [ 14 ]. B.R.Judd, Operaor Technques n Aomc Specroscopy ( McGraw-Hll Book Company,.York, 1963 ). [ 15 ]. B.L.Slver, Irrucble Tensor Mehods: An Inroducon for Chemss ( Academc Press, London, 1976 ). [ 16 ]. E.U.Condon and Hals Odabas, Aomc Srucure ( Cambrdge Unversy Press, 1980 ). [ 17 ]. J.L.Praher, Aomc Energy Levels n Crysals. aonal Bureau of Sandards Monograph 19 ( BS, Washngon, 1961 ). [ 18 ]. C.Görller-Walrand and K.Bnnemans, Handbook on he Physcs and Chemsry of Rare Earhs, Vol.3 ( 1996 ) p.11. [ 19 ]. L.J.F.Broer, C.J.Gorer and J.Hoogschagen, Physca 11 ( 1945 ) 31. [ 0 ]. O.Deuschben, Ann. Physk 36 ( 1939 ) 183. [ 1 ]. C.K.Jorgensen and B.R.Judd, Mol. Phys. 8 ( 1964 ) 81. [ ]. H.B.Bebb and A.Gold, Phys. Rev. 143 ( 1966 ) 1. [ 3 ]. O.L.Mala, P.A.Sana-Cruz, G.F.de Sá and F.Auzel, J. Lumnescence 33 ( 1985 ) 61. [ 4 ]. A.Flórez, O.L.Mala, Y.Messaddeq and M.Aegerer, J. on-crysallne Solds 1314 ( 1997 ) 315. [ 5 ]. F.Auzel, prvae communcaon. [ 6 ]. R.S.Qumby and W.J.Mnscalco, J. Appl. Phys. 75 ( 1994 ) 613. [ 7 ]. P.Goldner and F.Auzel, J. Appl. Phys. 79 ( 1996 ) 797.

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