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Oscillator strengths and excitation cross sections of samarium atoms
Volume 90A, number 4
5 July 1982
PHYSICS LETTERS
OSCILLATOR STRENGTHS AND EXCITATION CROSS SECTIONS OF SAMARIUM ATOMS R. PETERKOP Institute of Physics, Latvian SSR Academy of Sciences, 229021, Riga, Salaspils, USSR Received 2 March 1982
It is shown that the available theoretical data on the composition of odd parity levels of the samarium atom lead to a distribution of oscillator strengths and electron impact excitation cross sections which differs significantly from the experimental data.
We consider transitions from the ground multiplet 4f66s2(7F~0)(J0=O,1, 6). The composition66s6p of lower odd parityThe states includes configurations 4f caland 4f5 5d6s2. mixing coefficients have been culated by Carlier et al. [11and in a revised form (re-
I(n010,nl)=
...,
f
j~~.~PLAL [I(6s, 6p)]2 L
~
PJ~AJ~A-[I(4f,5d)]2) (1) LK where ~.Eis the transition energy (in atomic units), L is the total orbital angular momentum, K is the orbital angular momentum of 4f-electrons, PL is the percentage of state 4f6(7F)6s6p(1P)(7Lj), (L = 2,3,4),AL is angular coefficient for transition to this state, and +
where P~ 1(r)is the radial wave function. Interference effects in (1) are neglected since the percentages given in refs. [1,2] determine only the absolute values of the mixing coefficients. We obtained the following expressions for angular coefficients AL = ;(2L + l)(2J + 1)11 ~ 3 L (3)
j
1 ALK
=
9(2K
+
state 4f 1), (L = 2,3,4;K = 3,5). The summation takes place if of a level contains states with differentcomposition L and K.
182
~
2 3
312
U
AL,
(4)
where ~ is the 6/-symbol. The {~ electron impact excitation cross section in the Born approximation has the form U
18ira~ 100E J(~PLAL [R(6s, 6p, q)]2
=
+
~ PLKALK [R(4f, Sd, q)]2) q3 dq,
(5)
LK
R(n 010, ni, q)
PLK and5(6K)5d6s2 ALK are corresponding (7L quantities for the
(2)
0
duced to another scheme of coupling) have been given in the review article [2]. The consequences of these works can be compared with the experimental values of oscillator strengths [3,4] and electron impact excitation cross sections [5,6]. The theoretical level composition [2] includes states 6(7F)6s6p(1’3P) and 4f5(6H, 6F)5d6s2. The Sm atom can be excited by means of one-electron transi4f tions 6s—6p and 4f—5d. The oscifiator strength may be written in the form
f rPnoio(r)Pni(r)dr,
=
f j1(qr)P~010(r)P~,(r)dr,
(6)
0
where E is the energy the momentum incident electron, 2, q of is the changeia~ and = 88 X 10—18 cm ii (qr) is the first-order spherical Bessel function. The atomic radial wave functions in recent work 0 031-9163/82/0000—0000/$02.75 © 1982 North-Holland
Volume 90A, number 4
PHYSICS LETTERS
were determined by a semiempirical method used earlier for Eu, Yb and Tm [7,8]. The results of cross section calculations show that forE> 1 au(27.2 eV) the Born cross section within 1% error can be described by the Bethe formula
5 July 1982
a = (a ln E + i3)E~ira 0, where
(7)
od is used, integrals I(6s, 6p) and I(4f, Sd) depend on the level energy, but this dependence is weak. In the interval 14000—18225 cm—1, the integrall(6s, 6p) varies from 4.29 to 433, and in the interval 18225— 26962 cm—’ the integral I(4f, Sd) varies from 0.91 to 0.80. The mean value of [I(6s, 6p)]2 is 25 times lar2. Analogously, integral ger(6s, than [I(4f, Sd)] larger than R (4f, Sd, q). R 6p,that q) isofsignificantly
a —f/
‘
~8’
Thus,parameters tion large values a and of oscifiator ~3should strength correspond f andtoexcitalevels
2
—
.
‘
The parameter ~3can be obtained by comparing (7) with the cross section calculated using (5). The energy E in (5) and (7) should be expressed in atomic units, Calculation results for transitions from the ground state are given in table 1. It is seen that there exists a significant difference in distribution of theoretical and experimental oscillator strengths. The maximum calculated values correspond to levels within 14000— 1 while the maximum experimental values 18000 cm— to those within 20000—26000 cm—’. The largest experimental f-values and excitation cross sections are for levels 21194 cm~and 22914 cm—’ which have small theoretical values. The main contribution to oscifiator strength comes from the transition 6s—6p. If the semiempirical meth-
which have considerable percentages of4f6(7 F)6s6p(1P). Theoretical data show such values for low levels while the experiment indicates higher levels. The small role of transition 4f—5d has been confirmed for Eu, Yb and Tm [7—9]. We investigated also transitions from initial sublevels J 0 > 0 to levelsJ> 0. The parameters for the transition 6s—6p within an error of aofI(6s, few percent can be estimated using the mean values 6p) and R (6s, 6p, q). When neglecting the transition 4f—5d, we have a=O.19pLAL,
(~3.5a.
(9)
The oscifiator strength can be found from (8). In general, the situation is similar to the case
Table 1 Oscillator strengths and election impact excitation parameters for transitions from the ground state 4f66s2(7F 0) to levels with
J=
1. Level (cm’)
L
Percentages
PL 14000 14864
F D
15651
G
16112 16691 17770 18225
F D F F G F G G D F G G
18475 18986 20091 21194 22314 22914 23244
G 26281 26962
F D
PLH
AL or ALK
ftheor.
fexp.
a
13
0.44 0.32 0.57 0.44 0.32 0.44 0.44 0.45 0.45 0.45 0.45 0.24 0.45 0.04 0.45 0.04 0.29 0.24
0.021 0.15 0.60 0.10 0.24 0.18
0.0038 0.0085 0.0011
0.33 2.2 8.4 1.3 3.2 2.2
1.3 8.2 30.6 4.7 11.0 7.2
0.22 0.020 0.005 0.004 0.002 0.011 0.001
0.061 0.014 0.18 0.31 0.22 0.37
2.7 0.24 0.06 0.04 0.02 0.11 0.01
8.8 1.1 0.27 0.19 0.07 0.45 0.03
0.15 0.062
0.09 0.11 0.13
0.38 0.41 0.47
PLF
4 37 79 16 53 26 31 21 65 16 12 8 31 21 22 67 58 82
0.010 0.013 0.016
0.0042 0.031
183
Volume 90A, number 4.
PHYSICS LETTERS
0, J = 1. Theoretical data [2] show that noticeable components of 4f6(7 F)6s6p(1P) correspond to levels <20000 cm—1 while the maximum experimental values are for levels >20000 cm—’. The experimental data [5,6] on excitation cross sections have been obtamed for levels ~17770 cm—1, however, they show that the maximum values are for levels >20000 cm1. In order to explain the discrepancy, new theoretical and experimental investigations are necessary. We can expect that the main part of the discrepancy is due to the approximate nature of the calculation [1] where the empirical method was used. Strong mixing of configurations exists also in the thulium atom. In that case, experiment [3] is in agreement with theoretical level composition [9], which gives the maximum f-values for levels in the interval 23000—27000 cm—1. =
184
5 July 1982
References [1] A.
Carlier, J. Blaise and M.-G. Schweighofer, J. de Phys. 29 (1968) 729. 121 W.C. Martin, R. Zalubas and L. Hagan, Nat. Stand. Ref. Data Ser. 60 (1978) 162. [3] N.P. Penkin and V.A. Komarovsky, J. Quant. Spectrosc. Radiat. Transfer 16 (1976) 217. [4] K.B. Blagoev, V.A. Komarovsky and N.P. Penkin, Opt. Spektr. 42 (1977) 424. [5] L.L. Shimon, N.y. Golovchak and 1.1. Garga, Opt. Spektr. 51(1981) 36. [6] A.A. Mityureva, Opt. Spektr. 49 (1980) 1016. [7] R. Peterkop, Opt. Spektr. 48 (1980) 10. [8] R. Peterkop, Opt. Spektr. SC) (1981) 990.
[9] P. Camus, J. de Phys. 31(1970) 985.
5 July 1982
PHYSICS LETTERS
OSCILLATOR STRENGTHS AND EXCITATION CROSS SECTIONS OF SAMARIUM ATOMS R. PETERKOP Institute of Physics, Latvian SSR Academy of Sciences, 229021, Riga, Salaspils, USSR Received 2 March 1982
It is shown that the available theoretical data on the composition of odd parity levels of the samarium atom lead to a distribution of oscillator strengths and electron impact excitation cross sections which differs significantly from the experimental data.
We consider transitions from the ground multiplet 4f66s2(7F~0)(J0=O,1, 6). The composition66s6p of lower odd parityThe states includes configurations 4f caland 4f5 5d6s2. mixing coefficients have been culated by Carlier et al. [11and in a revised form (re-
I(n010,nl)=
...,
f
j~~.~PLAL [I(6s, 6p)]2 L
~
PJ~AJ~A-[I(4f,5d)]2) (1) LK where ~.Eis the transition energy (in atomic units), L is the total orbital angular momentum, K is the orbital angular momentum of 4f-electrons, PL is the percentage of state 4f6(7F)6s6p(1P)(7Lj), (L = 2,3,4),AL is angular coefficient for transition to this state, and +
where P~ 1(r)is the radial wave function. Interference effects in (1) are neglected since the percentages given in refs. [1,2] determine only the absolute values of the mixing coefficients. We obtained the following expressions for angular coefficients AL = ;(2L + l)(2J + 1)11 ~ 3 L (3)
j
1 ALK
=
9(2K
+
state 4f 1), (L = 2,3,4;K = 3,5). The summation takes place if of a level contains states with differentcomposition L and K.
182
~
2 3
312
U
AL,
(4)
where ~ is the 6/-symbol. The {~ electron impact excitation cross section in the Born approximation has the form U
18ira~ 100E J(~PLAL [R(6s, 6p, q)]2
=
+
~ PLKALK [R(4f, Sd, q)]2) q3 dq,
(5)
LK
R(n 010, ni, q)
PLK and5(6K)5d6s2 ALK are corresponding (7L quantities for the
(2)
0
duced to another scheme of coupling) have been given in the review article [2]. The consequences of these works can be compared with the experimental values of oscillator strengths [3,4] and electron impact excitation cross sections [5,6]. The theoretical level composition [2] includes states 6(7F)6s6p(1’3P) and 4f5(6H, 6F)5d6s2. The Sm atom can be excited by means of one-electron transi4f tions 6s—6p and 4f—5d. The oscifiator strength may be written in the form
f rPnoio(r)Pni(r)dr,
=
f j1(qr)P~010(r)P~,(r)dr,
(6)
0
where E is the energy the momentum incident electron, 2, q of is the changeia~ and = 88 X 10—18 cm ii (qr) is the first-order spherical Bessel function. The atomic radial wave functions in recent work 0 031-9163/82/0000—0000/$02.75 © 1982 North-Holland
Volume 90A, number 4
PHYSICS LETTERS
were determined by a semiempirical method used earlier for Eu, Yb and Tm [7,8]. The results of cross section calculations show that forE> 1 au(27.2 eV) the Born cross section within 1% error can be described by the Bethe formula
5 July 1982
a = (a ln E + i3)E~ira 0, where
(7)
od is used, integrals I(6s, 6p) and I(4f, Sd) depend on the level energy, but this dependence is weak. In the interval 14000—18225 cm—1, the integrall(6s, 6p) varies from 4.29 to 433, and in the interval 18225— 26962 cm—’ the integral I(4f, Sd) varies from 0.91 to 0.80. The mean value of [I(6s, 6p)]2 is 25 times lar2. Analogously, integral ger(6s, than [I(4f, Sd)] larger than R (4f, Sd, q). R 6p,that q) isofsignificantly
a —f/
‘
~8’
Thus,parameters tion large values a and of oscifiator ~3should strength correspond f andtoexcitalevels
2
—
.
‘
The parameter ~3can be obtained by comparing (7) with the cross section calculated using (5). The energy E in (5) and (7) should be expressed in atomic units, Calculation results for transitions from the ground state are given in table 1. It is seen that there exists a significant difference in distribution of theoretical and experimental oscillator strengths. The maximum calculated values correspond to levels within 14000— 1 while the maximum experimental values 18000 cm— to those within 20000—26000 cm—’. The largest experimental f-values and excitation cross sections are for levels 21194 cm~and 22914 cm—’ which have small theoretical values. The main contribution to oscifiator strength comes from the transition 6s—6p. If the semiempirical meth-
which have considerable percentages of4f6(7 F)6s6p(1P). Theoretical data show such values for low levels while the experiment indicates higher levels. The small role of transition 4f—5d has been confirmed for Eu, Yb and Tm [7—9]. We investigated also transitions from initial sublevels J 0 > 0 to levelsJ> 0. The parameters for the transition 6s—6p within an error of aofI(6s, few percent can be estimated using the mean values 6p) and R (6s, 6p, q). When neglecting the transition 4f—5d, we have a=O.19pLAL,
(~3.5a.
(9)
The oscifiator strength can be found from (8). In general, the situation is similar to the case
Table 1 Oscillator strengths and election impact excitation parameters for transitions from the ground state 4f66s2(7F 0) to levels with
J=
1. Level (cm’)
L
Percentages
PL 14000 14864
F D
15651
G
16112 16691 17770 18225
F D F F G F G G D F G G
18475 18986 20091 21194 22314 22914 23244
G 26281 26962
F D
PLH
AL or ALK
ftheor.
fexp.
a
13
0.44 0.32 0.57 0.44 0.32 0.44 0.44 0.45 0.45 0.45 0.45 0.24 0.45 0.04 0.45 0.04 0.29 0.24
0.021 0.15 0.60 0.10 0.24 0.18
0.0038 0.0085 0.0011
0.33 2.2 8.4 1.3 3.2 2.2
1.3 8.2 30.6 4.7 11.0 7.2
0.22 0.020 0.005 0.004 0.002 0.011 0.001
0.061 0.014 0.18 0.31 0.22 0.37
2.7 0.24 0.06 0.04 0.02 0.11 0.01
8.8 1.1 0.27 0.19 0.07 0.45 0.03
0.15 0.062
0.09 0.11 0.13
0.38 0.41 0.47
PLF
4 37 79 16 53 26 31 21 65 16 12 8 31 21 22 67 58 82
0.010 0.013 0.016
0.0042 0.031
183
Volume 90A, number 4.
PHYSICS LETTERS
0, J = 1. Theoretical data [2] show that noticeable components of 4f6(7 F)6s6p(1P) correspond to levels <20000 cm—1 while the maximum experimental values are for levels >20000 cm—’. The experimental data [5,6] on excitation cross sections have been obtamed for levels ~17770 cm—1, however, they show that the maximum values are for levels >20000 cm1. In order to explain the discrepancy, new theoretical and experimental investigations are necessary. We can expect that the main part of the discrepancy is due to the approximate nature of the calculation [1] where the empirical method was used. Strong mixing of configurations exists also in the thulium atom. In that case, experiment [3] is in agreement with theoretical level composition [9], which gives the maximum f-values for levels in the interval 23000—27000 cm—1. =
184
5 July 1982
References [1] A.
Carlier, J. Blaise and M.-G. Schweighofer, J. de Phys. 29 (1968) 729. 121 W.C. Martin, R. Zalubas and L. Hagan, Nat. Stand. Ref. Data Ser. 60 (1978) 162. [3] N.P. Penkin and V.A. Komarovsky, J. Quant. Spectrosc. Radiat. Transfer 16 (1976) 217. [4] K.B. Blagoev, V.A. Komarovsky and N.P. Penkin, Opt. Spektr. 42 (1977) 424. [5] L.L. Shimon, N.y. Golovchak and 1.1. Garga, Opt. Spektr. 51(1981) 36. [6] A.A. Mityureva, Opt. Spektr. 49 (1980) 1016. [7] R. Peterkop, Opt. Spektr. 48 (1980) 10. [8] R. Peterkop, Opt. Spektr. SC) (1981) 990.
[9] P. Camus, J. de Phys. 31(1970) 985.