The radiative transition rates o f Nd*'*' in LaFs
H. Jagannath and D. Ramaohandba Rao Indian Institute of Technology, Kanpur
AND
P. Vbnkatbswablu
TIerzherg InsUtufe of Astrophysics, National Research Council of Canada, Ottawa-KIA O'RiS, Canada
(Received 5 May 1977, revised 22 August 1977)
Tho radiative transition rates o f excited electronic states o f Nd®*^
(upto 30000 cm~^) in LaFg have bei>n calculated for the first time using tho Judd-Ofolt’s theory. The energy level positions estab- Ushod, recently, in our Laboratory together with the earlier reported values of intensity parameters have been used in these calculations.
The c?alculatod radiative transition rates are compared with the reported decay rates o f some of the states. A Table of reduced matrix elements is also included.
Indian J. Phys,
52ttf 34-^6 (1973)
1. Introduction
Tho study o f the energy transfer processes and tho relaxation rates from the excited states of the rare earth ions in single crystals has aroused considerable interest in view of the observation o f a number o f laser transitions. The advent o f powerful lasers has brought out elegant experimental techniques for the study o f both radiative and non-radiative relaxation processes. Recently, studies in our laboratory l\avo established the energy level scheme o f Nd*"*^ in LaFg upto 30(X)0 cm~^ from absorption and laser excited fluorescence spectra. In this paper, Wo report the calculations of radiative transition rates from the excited electronic levels of Nd®*^' using these level positions.
Optical spectra o f rare earth ions arise predominantly from electric and magnetic dipole transitions. The magnetic dipole transitions are parity allowed in the lowest configuration 4 /^ while tho electric dipole transitions are parity f<irbidd(ui. The transitions become allowed duo to tho mixing o f the opposite parity states from the higher configurations into the states of tho configuration 4 /^ . Judd (1962) and Ofolt (1962) have shown that the probability o f electric dipole transitions betwtH^u electronic states of the rare earth ions can be expressed in terms of a small number of intensity parameters. These parameters include tho effects of tho configurational mixing o f the electronic states, and tho strength o f tho crystal field interaction. Good agreement between the experimentally observed spectral intensities and intensities calculated from tho above theory,
34
has been obtained in a number of spectral intensity studies o f the rare earth ions, both in solutions (Carnal et al 1965) and in the crystals (Knipke 1966, eber 1967, 1968, Weber et al 1973). In addition, the intensity parameters have been used to calculate the radiative transition rates from the electronic states.
In this paper the radiative transitio^ rates for a number o f excited electronic states o f Nd*+ in LaF3 are calculated the first time using Judd-Ofelt’s theory.
The transition probabilities for the ra|Uative transitions have been calculated previously, only for the level in (Weber 1968), YaAljOu (Krupke 1971)
YAIO3 (Weber & Varitimos 1975)| Most o f the interest in the electronic state has been due to the obser'^ation o f stimulated emission orginating
in this state. !
The absorption and fluorescence ap|ctra o f Nd®+ in LaFg have been reported previously. The energy level assignm^ts and positions have been well estab
lished upto 24000 cm -i from the studies o f Caspers et al (1965). This has been recently extended to 30000 orn'i in our laboratory by Kumar et al (1976). The intensity parameters required for the calculation o f the transition probabilities have been reported previously by Krupke (1966) from the measurement o f the integrated absorption spectrum. The results from the above studies—^the level positions and the intensity parameters, have been used for the calculation of the radiative transition rates in the present work. These radiative transition rates are of utmost importance in understanding various nonradiativo processes such as multiphonon and ion-ion interaction relaxation from the observed decay rates o f excited states.
The radiative transition rates o f Nd^+ in LaF^
35
2. Thboby
The optical spectra o f rare earth ions in crystals arise due to the 4 /^ electrons which are shielded b y the shells resulting in a weak interaction with the environment. The unperturbed (free ion) eigen functions o f the ion are obtained from the diagonalisation o f the combined spin-orbit and electrostatic energy matrices including the configuration interaction. The resulting states can be written as a linear combination o f the Russel-Saunders states \f^ocSLJ>
\fN{aSLJ)> = S C{a8L)\fN(a8LJ>
•SL (1)
where C(aSL) are the intermediate coupling coefi^ients. The J state mixing caused by the crystal field interaction is neglected in this approprimation. The different electronic states arising from the 4 /^ configuration are o f the same parity resulting in the magnetic dipole and electric quadrupole transitions which are parity allowed whereas the electric dipole transitions are parity forbidden.
The transitions beooine allowed due to ^n admixture o f the states o f opposite
parity from higher configiirationH. This is brought about b y the interaction of lattice phonons or through the odd order terms in the expansion of the crystal field p )tontiaJ. Explicit calculations of the transition probabilities involves a summation ov(^r a large number o f states o f excited configuration. Following Judd (1962), Ofelt (1962) and W(^ber (1967), the radiative transition probability for (jlootrie <Ui)oJ(* transition between the states \f^(cXASL)J> and l/-^ (a % 9 'i')J '>
tian 1)(^ writt(‘n as
Aea\Fioc.^jL)JJ^(oc\S'L')J']
^ 047TW{Uy^2J + })~^Xed^ 1 <F{ocSL)J\\U^WfN{oc'8'L')J'>\^ ... (2) whe,r<^ V (in cm-^) is the mean frequency of transition, £2^ 8*re the intensity para- met(U*s whi(?h inoliuby the int(^grals involving the wavofimetioons of the excited cordigurations and Xed is the correction factor for tlie refractive index n o f the TUfidium given by (Weber 1966)
Xed ^ + 2 ) ^ 1 9 . ... (3)
Thfi matrix (d(^ments of C/x are given by
<f^ccSLJ \\U^\\f^x'S'L'J'> --={—)S+L'ij+A «(^ f^ f')f(2 ./+ l)(2 J '+ l)]l.
,J J ' A ,
\r, . 1 < / ^ a « W l l F a ' - S ' £ ' > ... (4) L L S
wUiclx aro ovahiatwl iishif; standard tables.
Tlw degemoraey factor (2 J + 1 ) appears in tho oq. (2) following tho assump
tions that all tho stark compouonts o f tJio initial J multiplet are oqually p.ipulatod m tho ca,s« of absorption and that they have equal probability for transition to components of the lower J multiplot in the case of emission. This assumption is not strictly valid in the case o f Nd*+ in L a i’, as can be seen from ho o n jg y separations o f tho stark components o f the J multiplets and the intensities of the transitions from the stark components o f tlio initial J multiplet to the d.ftorent terminating levels in the fluorescence spectra. However, in
. ’ ^ “ particular electronic state,
t v> oontubutions from the transitions to the stark components o f all the lower probabilities of tho different stark components.
Tho transition probability for magnetic dipole transition is given by Amal(acSL)J,{x'S'L')J'] = 64wM(3A)->(2J-f
36 Jagannath, Ramachandra Rao and Venkateswarlu
The radiative transition rates o f in LaF%
whore M is tho magnetic dipole operator given by
M 2mc
(L+2S).
37
(6) The matrix elements for tho magnetic dipole operator and the correction factor Xms are given by Weber (1967).
The elcwtric quadmpolo transitions l\|ive very .small transition probabilities (Weber 1967) and hence are not considei^.
3. Results
The total radiative transition rate f4>m an electronic state \f^{oc8L)J> is the sum o f the transition probabi]itio>s tp all the lower states • The contributions from the calculated i^ing eqs. (1), (2) and (4). The inter
mediate coupling wavefunctiona obtaine4 for PbMo04 : Nd**^ b y Minhaa (1972) have been used in tho calculations. This is justified as tho wavefjunctions of the ion do not vary much from host to host in the case o f weak crystal field interaction (Wong 1961). Tlu^, rofractive index o f LaFg has boon measured by Wrick (1966) as a function o f wavol(Uigth. Tho reported intensity parameters Qx’s for Nd8»- in LaFg are (Krupke 1966) Qg = (0‘35±Oa4)xlO~2o,
= (2*57±0-36) X 10“ 2o and ^ (2-5±0*33) x 10“ 2«.
The results o f the calculations arc shown in tables 1-3. Tho elements of the matrix for different electronic states are given in table 1. The same matrix elements can bo uBvd for the calculation o f oscillator strengths and transi
tion rates for Nd^+ in any host with weak crystal field interactions. Table 2 gives the calculated electric dipole transition rates. The contribution due to the magnetic dipole transitions is found to be negligible. Table 3 gives the total transition rates o f the different electronic states.
Table 1. Roduetd Matrix Elements of (/^ between i.hc electronic States o f Lal^3 : Nd«^-
\(aSL)J > » |(a'^'JD')J' > « \\<\m\>\^
3/2 (i?) 9/2 (Z) 0 0*236010 0*068370
11/2 (F ) 0 0*145165 0*408664
13/2 (X) 0 0 0*016456
16/2 (TT) 0 0 0*027666
5/2 (S) 9/2 (Z) 0000822 0*236129 0*397256
11/2 (F ) 0 0*169306 0*004782
13/2 (X ) 0 0 149698 0*398647
16/2 (W) 0 LO 0*232400
9/2 {S) 9/2 (Z) 0009287 0*007409 0*116417
11/2 (F ) 0003930 0*010929 0*166466
13/2 (X ) 0029124 0*006662 0*115300
16/2 (IF) 0 0*053088 0*105894
T a b le 1 (o o n td .)
38 Jagannath, Bamachandra Rao and Venkateswarlu
l(aSE)J > « t <lir/^ll> P ( <IIU*II> |» 1 <||17«((>
3/2 (A) 9/2 (X )
11/2 (K ) 13/2 (X ) 16/2 (IT)
0 0 0 0
0-002497 0-000002 00
0-233763 0-212483 0-298983 0-331718 7/2 (A) 9/2 (X )
11/2 (X ) 13/2 (X ) 15/2 (TT)
000059C 0001173 0 0
0-028662 0-103642
0- 326662
1- 604698
0- 432879 0-086261 0-000106
1- 866581
9/2 (B) 9/2 (X ) 11/2 (X ) 13/2 (X ) 15/2 (IT)
3/2 (JS)
0*000894 0 001636 0 002023 0 0
0-008849 0-036431 0-216276 0-691838 0-008219
0-041361 0-222624 0-512944 0-461016 0-111722 1 1 / 2 ( 0 9/2 (X )
11/2 (X ) 13/2 (X ) 16/2 (IT)
3/2 (B) 9/2 ( O 6/2 (B)
0*063747 0*000176 0*003266 0*088340 0 0*071413 0
0-042386 0 0-015061 0 0 6 2 2 2 0 0-000152 0-004761 0-002216
0-033021 0-009227 0-004314 0-000002 0-006210 0-109491 0-014162 6/2 (D ) 9/2 (X )
11/2 (X ) 13/2 (X ) 16/2 (IX) 3/2 (B ) 9/2 (B) 5/2 (B) 3/2 (^ ) 7/2 (^ )
0*667889 0 0 0 0*486722 0*001718 0*023796 0*000302 0*016662
0-378567 0-295641 0-034341 0 0-016156 0-001026 0-000333 0-182672 0 079016
0-029309 0-096637 0-047786 0-004424 0 0-048669 0 0 0-179863 7/2 (JO) 9/2 (X )
11/2 (X ) 13/2 (X ) 16/2 (IF) 3/2 (B) 9/2 (B) 5/2 (B) 3/2 (X ) 7/2 (X) 9/2 (fl) 1 1 / 2 ( 0
0*014416 0*364989 0 0 0*033708 0*036127 0*231789 0*000434 0*111392 0*000019 0*012192
0-146782 0-046046 0-071324 0-086664 0-019616 0-000933 0-008105 0-002472 0-051190 0-002402 0-001012
0-022397 0-012174 0-029624 0-053318 0 0-441739 0-036670 0 0-010739 0-000380 0-366649
7/2
(E) 9/2 (Z ) 11/2 ( D 13/2 (X ) 15/2 (IF) 3/2 (R) 6/2 iS) 2(53/2 (A ) TISi{A) 9/2 (B ) 11/2(0)0 006306 0-707933 0 0 0-066608 0-296911 0-014160 0-001461 0-191776 0-031106 0-018114
0-196238 0-198814 0-133706 0-000027 0-038318 0*000444 0-002661 0-209318 0-080624 0-174266 0-002124
0-066286 0-012716 0-068060 0-104446 0 0-126826 0-076966 0 0-002266 0-312663 0-219279
0191 00*
0 oo f^ so oe
= |^
6 12 9 t*
0 0 I0 0S 8I 0
mo xo
-o 00 99 L0
0 0 no or st
0 %L9ZW0
0 68 00 00
*0 98 L8 00 0
91 80 00 -0 O O- !^S 0 8=
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^f8 90 0*
0 99 91 00
*0 tl€
96 0- 0 X -o Z9- mo 0L oe SZ
69 90 01
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mi
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le tT OO
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1 -0 10 09 91 -0
00 89 60 -0 9tZ.000 0 fl- 90 90 0
08 10 00 -0
OiOOtl- 0
60 16 80
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0 -0 01 69 89 11 69 00-0
9W 80 00
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99 80 00
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60 -0
ISW IO O -0 10 18 19
90 00 00 -0
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*0 O -0 O 0 O O lfO ltOO O 00 01 00
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0 0 0^ 80 09 0 0 -0 00 10 t8 16 00 00 -0
96 00 00 -0
61 00 00 -0
000 1 lO -O 00 00 91 -0
91 98 00
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10 91
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80 19 91 -0
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909^10*0 61 99 10 -0
61 91 00
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01
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lt 69 01 -0
f0 09 90 0
10 9t 08 -0 o-o O-O 90 90 ^ll 19 lOno 08 -0
091000*0 lOflOO-0 60 60 10 -0
911000*0 0 OO lO OtO
89 00 00
-0 10 10 10
-0 88 19 10 -0
18 81 00-0
88 19 10 -0
89 61 00 -0
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0 0 0 0 -0 00 00 00
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90 00 00 -0 0
€0 10 10 -0-0 100 190
09 t 100 -0
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60 08 90 -0 0 O -0 10 06 98
i8 90 90
-0 oo oo po
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^9 88 01 -0
J9 10 00 0-0
fB ig eio
-o 1-0 80 00 58
^8 08 19 -0
1880600-0
;0 09 08
t-0 ?
0 '
0 06 0^ 89 0
91 01 01
-0 O O O fO l^O
0 K d)
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/l ziL ) (a
(a ) 0/9
io ) zl ii zif (a)
i /iiz ) z (F) o (F
(S) zif i
(S ') zl9
i s)
0/9 ) 0/0 (ff (M ) z l9 1 o/o ) (X
i u zl i) (J
(Z ) 0 /6
id ) 0/6
id )
I z
l
ia )
I z
l
i a)
0/9 o
i o)
/ii zif ) ia
i
(F) o/l
(F ) O /O
(S ') 0/6
is ) 0/9
ia ) zi z
iM ) 0/9
1 o/o (X)
i O/l ) iA
l (Z ) 0 /6
i a)
o
/l /ix/6 0/9 o ) 0
i o)
(ari a)
(F )
I z
l
iv ) zi z
is ) 0/6 ) is
0/9
i a)
z Iz
) iM0/9 1 /0 ) 0 (X 1
iA ) O/t l
(Z ) 0 /6
i a)
0/1 (c r) 0/9
( -
) 0 9
/1 [
ia ) zlQ
iv )
I z
l
iv ) z iz
is ) Zl6
is ) 0/9
ia ) zi z
iM ) 0 /9 1
(x ) 0 /0 1 ll )Z iA l
(Z ) 0 /6
(J) 0/9
i o)
0/9 1
(£>
) 0 /6
id 0/6 )
sl<
llo /lll
>^
cK IU /ll l>
l I< b
II /3 c
II>
I
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v <r
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m
( p^
juo o) I a jq -BX
+
P z
S[ j
9a
%fo
%'p njt
Table 1 (contd.)
40 Jagannath, K am achandra R ao and V enkatesw arlu
\{olSL)J:.
1/2(1)
3/2 (K )
6/2 (/>)
3/2
(Z)(1/2 (^ ) 11/2 (Y ) 13/2 (X ) 15/2 ( IV) 3/2 (Ji) 6/2 (^S') 9/2 (.S) 3/2 (^ ) 7/2 M ) 9/2 (B) 11/2(0) 5/2 (D) 7/2 (D) 7/2 9/2 (F ) 16/2 (Z) 13/2 ( y ) H / 2 (X) 9/2 ( W) 3/2 (i?) 6/2 (.V)
»/2 (.V) 2/2 (A ) T/2(A) 9/2 (B) n / 2 (O) 6/2 (/>) 7/2 (i)) 7/2 (B) 9/2 (i?*) 16/2 «7) 9/2 ((7) 16/2 (^ ) 13/2 (F ) 11/2 (X) 9/2 ( JF) 3/2 (B) 6/2 (.V) 9/2 (B) 3/2 (^ ) 7/2 (^ ) 9/2 (B) 11/2 (C)
6/2 ( B ) 7/2 (B ) 7/2 9/2 (i?’) 16/2 (O)
9/2 (O) 16/2 (Z ) 13/2 (F ) 11/2 ( X)
9/2 (W) 3/2 (B) 5/2 iS) 0/2 (B) 3/2 U )
*7/2 ( 4 ) 9/2 (B)
O 0o 0 0-000206 0006411 0 0016897 O 0 0 0033383 0 0 0
0 0
0 0 0 0007862 0 0-014270 0-004620 0O 0064302 0-009867 0-007808 0 O0 0-000107 0 O 0 0-015683 0-210868 0-238226 0-364042 0-163727 0-083073 O 0-024648 0*169229 0-108398 0-488063 0 0-104801 0 0 0o 0*046376 0-060691 0 0*213622 0*079793 0
0-049422 (»O o 0 0 0-077942 0 0-020034 0*004730 O 0 0-009808 0-001997 0-013812 0-006063 0-030597 O 0 0 0-008667 0*030154 O 0-003202 0-032412 0*000280 0*000088 0-002969 0-010509 0*056218 0 0*139030 0*077617 0-330964 0-658878 0 0-172281 0-036514 0*193321 0-002098 0-069766 0*213106 0-001783 0*000046 0*065364 0*006186 0*004680 0 0-000002 0*267462 0*408688 0 0 0 0*204079 0-028688 0 0-016928 0*181263
O 0-000288 0-000034 0 0 0 0 0O 0 0*163663 0 0 0 0 0*001208 0-001066 0*001829 0*003611 O 0 0-064769
0O 0-052782 0*102877 0 O 0 0-064885 0-336212 0*137860 0*026431 0-019464 0*000063 0*038843 0 0 0-022107 0 0*000064 0*001612 0*026936 0 0*039626 0-106823 0-163776 0-004980 0*066833 0-016666 0-002636 0-026826 0*008624 0 0 0*004820 O0 0*001724
The radiative traneitum rates o f in L a t*a 41
Table 1 (contd.)
3/2 ( i )
11/2 ( L )
1/2{ L )
15/2 {L)
11/2 (C) 7/2 (/>) 6/2 (Z>) 7/2 (J5) 9/2 (J") 15/2 (O) 9/2 (O) 15/2 (Z ) 13/2 (V ) 11/2 (X) 912 (W) 3/2 (/?) 5/2 (S ) 9/2 (-S) 3/2 ( 4 ) 7/2 ( 4 ) 9/2 (B ) 11/2 (C) 5/2 (X>) 7/2 (D) 7/2 (B) 9/2 (B) 15/2 ((?)
9/2 ( « ) 15/2 (B) 1 3 /2 (1 ') 11/2 (X) 9/2 (IT) 3/2 (B) 5/2 (-S) 9/2 (B) 3/2 ( ^ ) 7/2 ( 4 ) 9/2 (B) 11/2 (C) 5/2 (B ) 7/2 (B ) 7/2 (B ) 9/2 (B) 16/2 ((?) 9/2 (G) 15/2 (B) 13/2 (B ) 11/2 (X )
9/2 ( 3/2 (B ) 5/2 (B) 9/2 (B) 3/2 (A ) 7/2 (X ) 9/2 (B ) 11/3 (O) 6/2 (B ) 7/2 (B ) 7/2 (B) 9/2 (B) 15/2 (G) 9/2 (G)
0 0-047342 0-011362
0-810622 0-000815 0
0-540389 0-049212 0
0 174924 0-021274 0
0 0-000181 0-091548
0 ' 0 0-001432
0 0-001109 0-034816
0-000000 0-023428 0-012961
0-0004(18 0*000480 0*000597
0-000125 0*008380 0-000862
0-002019 0-002473 0-002906
0 1 0-000032 0-004094
0 1 0-001043 0-004965
0 -1 8 3 3 ^ 0-218633 0-401612
0 ? 0-004804 0*000439
0-004387 0-014901 0-006100
O-O412I2 0-040065 0-009703
0-001 i l l 0-000017 0-072092
0 0-000142 0*00247
0-032672 0-089895 0-067410
()-015226 0-047380 0-050825
0-000181 0-012152 0-016909
0-269737 0-004652 0-168627
0-058168 0-002408 0*149186
0 0-361777 0
0-018897 0 0
0-013987 0 0
0 0 0
0-000041 0 0
0-055448 0 0
0 0-015479 0
0-088360 0 0
0 0-182188 0
0 0*036728 0
0-001371 0 0
0-326119 0 0
0 0-018700 0
0 0-007785 0
0 0-000120 0
(» 0 0
0 0-001130 0
0 0-025690 0-015981
0-000343 0-005155 0-004105
0000100 0-007668 0-002950
0 00
0-003388 0
0-006269 0-010576
0 0-000175
00
0-399605 0
0-181588 0-001916
0 0-002290 0-044763
0 0-234367 0-170173
0-003053 0
0-151678 0
0-324103 0-005683
0 0-019678 0-348456
0 0*004159 0-166987
0 0 ‘ 166273 0-115140
0-062162 0-276361 0*109309
0 0-164363 0-281113
rrK« « r 7 KtetoB o f Nd»+ arc denoted on ly b y their J quantum num bers, H - - v . r . a » o o „ p l . « . S L J notation for these states is given m table 3.
Talilo 2. Calculated Electric dipole Transition for Different electronie states of LaFg : Nd®+
42
tTaganiiath, Ramachandra Rao and Venkateswarlu
l(aSL)J:: l(u'S'L')J'>
Transition rate in
sec”^ \{ol8 L )J > \{ol'S'L')J'>
Transition rate in
seo”^
3/2 {li)
5(2 (S)
9/2 iS)
3J2{A)
7/2 M)
9/2 {B)
11/2 (C)
«/2 (i>)
9/2(2))
9/2 (Z) 731 7/2 (X)
11/2 (F) 787
13/2 (X) 11
16/2 (IF) 8
9/2 (Z) 1349
11/2 (F) 228
13/2 (X) 378
16/2 (IF) 68
9/2 (Z) 166
11/2 (F) 136
13/2 (X) 64 9/2 (F)
16/2 (TF) 30
9/2 (Z) 964
11/2 (F) 640
13/2 (X) 429
16/2 (TF) 228
9/2 (Z) 933
11/2 (F) 244
13/2 (X) 241
16/2 (TF) 1206
9/2 (Z) 107
11/2 (F)
13/2 (X) 359
622 9/2 {G)
15/2 (TF) 463
3/2 (JR) 3
9/2 (Z) 186
11/2 (F) 14
13/2 (X) 19
16/2 (TF) 41
3/2 (i2) 1
6/2(5) 1
9/2 (5) 2
9/2 (Z) 2946
11/2 (F)
13/2 (X) 1612
219 16/2 ((?)
15/2 (TF) 7
3/2 (2?) 18
5/2 (5) 1
9/2 (5) 6
3/2 (4) 11
7 /2(4) 16
9/2 (Z) 752
11/2 (F) 330
13/3 (X) 204
15/2 (IF) 169
3/2 (JB) 4
5/2(5)
9/2 (5) 7
37 6/2(J)
3/2 (4 ) 1
7 /2 (4 ) 4
9/2 (Z) 1566
11/2 (F ) 1336
13/2 (X) 596
1612 {W) 193
3/2 (JR) 17
6/2 (5) 40
9/2 (5) 18
3/2 (4 ) 31
7/2 (4 ) 16
9/2 (5) 33
11/2 (C) 6
9/2 (Z) 476
11/2 (F ) 1436
13/2 (X) 1331
15/2 (TF) 1627
3/2 (JB) 67
5/2 (5) 32
9/2 (5) 42
3/2 (4 ) 32
7 /2 (4 ) 24
9/2 (5) 18
1 1 /2 (0 7
6/2 (/)) 2
7/2 (1>) 2
9/2 (Z) 245
11/2 (T) 13/2 {X) 16/2 (TF) 3/2 (2J) 6/2 (^) 9/2 (iS) 3/2 (^) 7/2 (^) 9/2 (JB) 11/2 (O) 5/2 (2>) 7/2 (2)) 9/2 (Z) 11/2 ( D 13/2 (X) 16/2 (TF) 3/2 (jR)*
5/2 (5 ) 9 /2(5) 3/2(4) 7 /2 (4 ) 9/2 (5) 11/2 (O) 5/2 (2)) 7/2 (D) , 9/2 (Z) 11/2 (T ) 13/2 (X) 15/2 (TF)
763 682 947 37 26 76 19 36 67 66 7 31 11 40 38 3 1 177 51 11 87 1 3 38 11 174 3
The radiative transition rates o f Nd^'*' in LaFt Table 2 (oontd.)
43
\{»8L)J> \{a'8'L')J’ >
Transition rate in
800”^ \{dSL)J> \{a'S'L')J'>
Transition rate in
seo~^
6/2(J)
1/2 (J)
3/2 (K)
6/2{ L )
Z I 2 { R)
9/2(5) 6/2(5) 3/2 (A) 112 {A) 9/2 (B) 11/2 (0)
6/2 (B) 7/2 (B) 9/2 (Z) 11/2(7) 13/2 (X) 16/2 (Tf) 3/2 (B) 9/2(5) 6/2(5) 3/2 (^) 7/2 (^) 9/2 (B) 11/2 (C) 6/2 (B) 7/2 (B) 9/2 (Z) 11/2(7) 13/2 (X) 16/2 (F ) 3/2 (B) 6/2(5) 9/2(5) 3/2 (^) 7/2 (il) 9/2 (B) 11/2 (O) 5/2 (B) 7/2 (B) 7/2 (B) 9/2 (B) 16/2 (B) 9/2 (B) 9/2 (Z) 11/2(7) 13/2 (X) 16/2 (F ) 3/2 (B) 6/2 (5) 9/2 (5) 3/2 (X) 7/2 (X) 9/2 (B) 11/2 (0)
6/2 (B) 7/2 (B) 7/2 (B) 9/2 (B) 16/2 (B) 9/2 (B)
3
1
460
2
33 17 168 1 80 2336 10 1 0
1
4 366 9 74 12 261 4 9 232 810 36 60 0 43 403 7 14 214 187
11
6 7 60 74 62 2774 7711 11486 496 969 297 1109 196 360 668 60 6 192 113 169
2
n
3/2 (B)
11/2 (B)
1/2 (B)
9/2 (Z) 11/2(7) 13/2 (X) 16/2 (F ) 3/2 (B) 6/2(5) 9/2 (5) 3/2 (X) 7/2 (X) 9/2 (B) 11/2 (B) 6/2 (B) 7/2 (B) 7/2 (B) 9/2 (B) 16/2 (B) 9/2 (B) 9/2 (Z) 11/2(7) 13/2 (X) 16/2 (F )
3/2 (B)
16/2 (B)
7/2(5) 3/2 (X) 7/2 (X) 9/2 (B) 11/2 (B) 6/2 (B) 7/2 (B) 7/2 (B) 9/2 (B) 16/2 (B) 9/2 (B) 9/2 (Z) 11/2(7) 13/2 (X) 16/2 (F )
3/2 (B) 6/2(5) 9/2 (5) 3/2 (X) 7/2 (X) 9/2 (B) 11/2 (B) 6/2 (B) 7/2 (B) 7/2 (B) 9/2 (B) 16/2 (B) 9/2 (B) 9/2 (Z) 11/2(7) 13/2 (X) 16/2 (F )
11666 13696 632 168 63 1474 226 166 168 798 196 226 281 61 104
22
0 489 12 81 37 10 14 1423 10 41 80 782
122 46
11
46 34 29476 170 100 0 0 106 208 137 2067 321
1
204
86
21 0 0 2 76 69 42
Tablo 2 (contd.)
44
Jagannath, Bamachandra Rao and Venkateswarlu
15/2 (A)
Transition
rate in \{xSL)J> \{ct'S'L')J'>
{x,SL)J Energy®
(in cm~^) Transition rate in sec"^
^^3/2 (-^)
^1^512
^Hq!2 {S) {A) {A) (B)
^Biii2 {C)
11417 12416 12579 13451 14099 15853
1537 2019 384 2624 2151 1644 262 (f>)
17260 4836
®(3*7/2 (i>) 1607
*Ojf2 (jB ) 19044 3841
(r) 19465 4994
^ ^ 1 6/2 (^)
21067 461
^ 9 /2 (G') 2853
(f)
23730 3085
^A'S/2 (/) 980
=^ 3,2 (if) 26189 2214
(ii) 26619
* ^ 3 /2 (/■-) 29742
*^UI2 W 28342 2534
^A;2 (i) 32897
*^ 15,2 (i) 2970
of tho S t e r k T i S u
gravity of ground state Stark S i ^ e t
Transition rate in
sec*"^)
:t;)/2 (It) 21 15/2 (Z) 6/2 (D) 3
fi/2 (-V) 0 7/2 (Zi) 205
7/2 (,V) 970 7/2 (Z7) 53
2/2 (A) 3 9/2 (Z’) 81
7/2 M) 65 16/2 (0) 64
»/2 (B) 436 912(0) 71
11/2(0) 391
Tal.k 3. Total ladiativo rat(s of tho ((liffei '*j)t
<;loctronio states of LaF3 :
A comparison of the calculated and observed radiative transition rates is possible only for the state ^r3/2(i?). This state is separated from the next state
®®i6/2(^) SOOO and hence, nonradiative multiphonon relaxation rate from this level can be neglected. The experimentally observed decay rate which is the sum o f the radiative and nonradiative transition rates is, thus, mostly due to radiativ(5 transitions in the case of state The reported decay rate, from the state is 1430 sec~^ (Asawa & Robinson 1966). This compares well with the calculated rate of 1537±200 sec” ^.’ The estimated error in the calculated rate is due to tlie error in tlie reported Values of fll^s which is 13%. The decay rates have not been reported for any dther state except the group o f states around 29000 em h* This group is admixture of five J states. ^©3/2,
^®i/2 ^J^d ^Li5/2 in the ascending order o f energy. The observed decay rate from this group is 3-45x10^ soc*f^ at liquid nitrogen temperature which includes the contribution from the mulflphonon transitions. The rate o f multi
phonon transitions can be estimated fr<>m the energy gap rule (Riseberg & Moos 1968). This comes out to be M 5 x l 0 ^ sec““^ for this group. The contribution duo to the radiative transitions is, thus, 2*3x10^ sec“ ^ which is comparable to the calculated transition rates o f (2*97±0-39) X 10^ sec"^ and (2*66iO*35)'X 10^
fiec” ^ from the states J = ^I>3/2 and J = ^I>5/2- It is to be noted that the applica
tion o f the Judd-Ofelt’s theory is not strictly valid foi the group L as the assumx>- tion that tre J mixing o f states is mvgligible, is not tru^. The agreement between the calculated and observed rates is fortuitous. But, in the case o f states which are well separated from the other states, the theory can l>c expected to give comparable lesults as has been observed by many others in diffeient systems (Weber 1968, Weber et al 1973). Alteinatively, the calculated radiative transi
tion rates can be used to evaluate the nonradiative transition rates from the observed decay rates.
Re f b b e k c e s
Asawa C. K. & Robinson M. T. 1966 Phya. Rev. 141, 261.
Caspers H. H., Kast H. E. & Buchanan R. A. 1965 ./. Chem. Phya. 42, 3214.
Carnall W. T., Fields P. R. & Wybourne B. G. 1966 J. Chem. Phya. 42, 3797.
Judd B, R. 1962 Phya. Rev. 127, 150.
Krupke W. F. 1966 Phya. Rev. 146, 326.
Krupke W. F. 1971 IEEE J. Qvantum Electronica QE 7, 163.
Kumar U* V., Jagannath H,. Ramachandra Rao D. & Venkateswarlu P. 1976 Indian J. Phya.
50,90.
The radiative transition rates o f in LaF^
45
* The decay time of this group has been measured by us at six different temperatures using a pulsed nitrogen laser as the excitation source. This group has been observed to decay by both radiative and non-radiative processes whose rates are comparable. The experimental details as well as the discussion on the different non-radiative processes which contribute to the relaxation o f group L, will be published separately.
Minhas I. 8. 1972 Ph.D. Thesis. Indian Institute of Technology. Kanpur. India.
Nielsen C. W, & Koster 0. F. 1063 Spectroscopic Coefficidents for tiie jfl, d» andf’» eonfigwatioM (MIT Press Cambridge, Massachusetts).
Ofelt 0. S. 1962 .7. Ghem. Phys. 37, 611.
Rotonberg M., Bivens R., Metropolis N. & Wooten J. K. 1964 The 3-J and 6-j
Symboh
(MIT Proas. Cambridge. Massachusetts), Rweberg L. A. & Moos H. W. 1968 Phys. Bev.174,429.WongE. y. 1961 J. Chem. Phys. 35, 544.
Wirick M. P. 1966 App. Optics 5,1966.
Weber M. J. 1967 Phys. Bev. 157, 262.
Weber M. ,T. 1968 Phys. Bev. 171, 28.1.
Weber M. .1. Varitimos T. E. & Motsinger B. H. 1973 Phys. Bev. B8, 47.
Weber M. J. & Varitimos T. E. 1976 J. Appl. Phys. 4 6 ,1191,
