Calculation of the Stevens factors α, β and γ in the intermediate coupling scheme for U and Np ions with f 2, f3 and f4 configurations

(1)

HAL Id: jpa-00209837

https://hal.archives-ouvertes.fr/jpa-00209837

Submitted on 1 Jan 1984

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Calculation of the Stevens factors α, β and γ in the intermediate coupling scheme for U and Np ions with f

2, f3 and f4 configurations

G. Amoretti

To cite this version:

G. Amoretti. Calculation of the Stevens factors α, β and γ in the intermediate coupling scheme for U and Np ions with f 2, f3 and f4 configurations. Journal de Physique, 1984, 45 (6), pp.1067-1069.

�10.1051/jphys:019840045060106700�. �jpa-00209837�

(2)

1067

Calculation of the Stevens factors 03B1, 03B2 ^and ^03B3

in the intermediate coupling ^scheme for ^{U and} _Np ^ions

with f2, ^f3 ^and ^f4 configurations

G. Amoretti (*)

Centre d’Etudes Nucléaires de Grenoble, Département ^de ^Recherche Fondamentale, Section de Physique ^du Solide, ⁸⁵ X, ³⁸⁰⁴¹ ^Grenoble Cedex, ^France

(Reçu le 6 octobre 1983, révisé le 24 janvier ^1984, accepte ^{le 3} février ¹⁹⁸⁴⁾

Résumé. 2014 Les facteurs de Stevens 03B1, 03B2 êt 03B3 ônt été calculés en couplage intermédiaire pour l’état fondamental des ions actinides U4+, U3+, Np4+ êt Np3+. Les résultats sont discutés par rapport ^à ûn ^calcul approché, ainsi que par rapport âux ^valeurs Russell-Saunders.

Abstract.

²⁰¹⁴

The Stevens factors 03B1, 03B2 ^and ^03B3 ^have been calculated in the intermediate coupling scheme for the ground

state of the actinide ions U4+, U3+, Np4+ ^and Np3+. The results are discussed in comparison ^with ^an approximate

calculation and the Russell-Saunders values.

J. Physique ⁴⁵ (1984) ^1067-1069 ^JUIN 1984,

Classification Physics ^Abstracts

71.70C

The factors a, fl ^and y, which multiply the Stevens

equivalent operators On ⁽ⁿ ^{= 2, 4,} ⁶ respectively) ^have

been calculated in the intermediate coupling (IC)

scheme for the ground ^state ^{of the} âctinide îons U4 +, U3 +, Np4+ ând Np3+ by ^standard ^tensor operator

techniques [1].

The starting wavefunctions are taken from the literature. The results of the complete calculation (IC)

are shown in table I, together ^{with the} approximate

results (IC*) ôbtained by taking înto âccount only ^the

main contributions (greater ^than ¹ %) ^to ^the ^wave-

functions. In the case of U3 + only these contributions

are available. For comparison, the Russell-Saunders values (RS) ^are given ^too. Moreover, the values of the

spectroscopic splitting factor gj, corresponding ^to ^the

wavefunctions chosen, ^are given ^for completeness.

For eacfi considered ion, ^the following ^remarks ^must

be made :

U4+-f2 configuration

The assumed IC ground state, corresponding ^to J = 4, is

This was calculated by Rahman and Runciman [2]

for U02.

(*) Scientific and Technical Fellowship of C.C.E. Bruxel- les, Belgium. ^On leave from University ^of Parma, Italy.

U3 +-f3 configuration

The ground ^state wavefunction is that given by

Camall and Wyboume [3] ^and ^more recently ^confirmed by Crosswhite et ^{al. for} U’+ : LaCl3 [4]. Unfortunately only the coefficients of the components ^{of the} ^J

⁼

9/2 ground state, which ^are greater ^than ^0.1 in absolute

value, ^are specified. ^{That is}

where the states are classified following the notation of Nielson and Koster [5]. ^This corresponds ^to ^98.5 % ^of

the whole wavefunction.

Np 4 1 _f3 configuration

The J

⁼

9/2 wavefunction of Gruber and Menzel [6]

has been choosen :

Starting from this function Gruber and Menzel already

calculated the factors ft = - ^2.090 ^x ^10-4 ^and

y = - 2.563 ^x 10- ’,which agree with ours within the calculation errors (no ^further digits ^are significant

other than those considered in the coefficients of the

wavefunction).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019840045060106700

(3)

1068

Table I.

^-

The calculated IC and IC* values and the RS values for ^the ^Stevens factors ^{and the} spectroscopic splitting factor.

The wavefunction calculated by Sharma and Art-

man [7]

gives ^values of the Stevens factors not significantly

different from the preceding ônes, âs ^shown ^{in table} ÎI.

Np3 +-f configuration

The J

⁼

4 ground ^state ^is taken from Carnall and

Wybourne [3] and Carnall et al. [8]. ^The coefficients of the 1 % ^terms ^are adjusted ^{from the} Z2 ^and Z5 ^states

in table III of Carnall et al., taking ^into ^account ^the

normalization condition of the whole function. In any ^case, small variations of these coefficients are

ineffective. The wavefunction used in the calculation is then :

Table I shows that in general ^the contributions of the

small coefficient terms are significant, both for the Stevens factors and for gj.

This is evident also in figure 1, where the trends of

Fig. ^1.

^-

^The ^ratios ^{of the} intermediate coupling ^{and the}

Russell-Saunders values of the Stevens factors for the con-

sidered U and Np ^ions. (a) : ^the ^ratios IC/RS. (b) : ^{the ratios} IC*/RS.

Table II.

^-

Comparison between the IC values for N p4 + calculated from ^the wavefunction of Gruber and Menzel [6]

and of ^Sharma ^and ^Artman [7].

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1069

the ratios between the IC or the IC* values and the RS values are shown.

For this reason the values given ^for ^{U3 +} ^are ^to ^be

considered only ^as approximative, ⁱⁿ particular ^with regard ^to y.

The general trend of the calculated Stevens factors for the quoted ^{ions is} ^a ^reduction ^with respect ^to ^the RS values. This reduction becomes more and more

important ^{as we} proceed ^from ^U4+ ^to Np4+, ^while Np3 + presents ^a different behaviour.

The ratios IC/RS (or IC*/RS ^{in the} ^case ofU3+) ^do

not vary much from ^a _{to y} for f and f3 ions. Conse-

quently, ^we expect ^{in these} ^cases ^a reduction of the

crystal ^field splitting, ^but ^not â drastic modification of the _energy level scheme for the split ground ^multi- plet, âs ân ^{effect of} intermediate coupling.

References

[1] DIEKE, ^G. H., Spectra ^and Energy ^Levels of ^Rare ^Earth

Ions in Crystals, ^edited by H. M. Crosswhite and H. Crosswhite (Interscience Publishers, ^New York)

1968.

[2] RAHMAN, ^{H. U. and} RUNCIMAN, ^W. A., ^J. Phys. ^Chem.

Solids 27 (1966) ^1833.

[3] CARNALL, W. T. and WYBOURNE, ^B. G., ^J. ^Chem.

Phys. ⁴⁰ (1964) ^3428.

[4] CROSSWHITE, ^H. M., CROSSWHITE, H., CARNALL, ^{W. T.}

and PASZEK, ^A. P., ^{J. Chem.} Phys. ⁷² (1980) ^5103.

[5] NIELSON, C. W. and KOSTER, ^G. F., Spectroscopic Coefficients for pn, ^dn and fn Configurations (MIT Press, Cambridge, Mass.) ^1964.

[6] GRUBER, J. B. and MENZEL, ^E. R., ^{J. Chem.} Phys. ⁵⁰ (1969) ^3772.

[7] ^SHARMA, ^{K. K. and} ^ARTMAN, ^J. O., ^J. ^Chem. Phys. ⁵⁰ (1969) ^1241.

[8] CARNALL, ^W. T., CROSSWHITE, H., CROSSWHITE, ^H. M., HESSLER, ^J. P., EDELSTEIN, N., CONWAY, ^J. G., SHALIMOFF, ^{G. V. and} SARUP, R., ^J. ^Chem. Phys.

72 (1980) ^5089.

Calculation of the Stevens factors α, β and γ in the intermediate coupling scheme for U and Np ions with f 2, f3 and f4 configurations

HAL Id: jpa-00209837

https://hal.archives-ouvertes.fr/jpa-00209837

Submitted on 1 Jan 1984

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Calculation of the Stevens factors α, β and γ in the intermediate coupling scheme for U and Np ions with f

2, f3 and f4 configurations

G. Amoretti

To cite this version:

G. Amoretti. Calculation of the Stevens factors α, β and γ in the intermediate coupling scheme for U and Np ions with f 2, f3 and f4 configurations. Journal de Physique, 1984, 45 (6), pp.1067-1069.

�10.1051/jphys:019840045060106700�. �jpa-00209837�

1067

Calculation of the Stevens factors 03B1, 03B2 and 03B3

in the intermediate coupling scheme for U and Np ions

with f2, f3 and f4 configurations

G. Amoretti (*)

Centre d’Etudes Nucléaires de Grenoble, Département de Recherche Fondamentale, Section de Physique du Solide, 85 X, 38041 Grenoble Cedex, France

(Reçu le 6 octobre 1983, révisé le 24 janvier 1984, accepte le 3 février 1984)

Résumé. 2014 Les facteurs de Stevens 03B1, 03B2 et 03B3 ont été calculés en couplage intermédiaire pour l’état fondamental des ions actinides U4+, U3+, Np4+ et Np3+. Les résultats sont discutés par rapport à un calcul approché, ainsi que par rapport aux valeurs Russell-Saunders.

Abstract.

The Stevens factors 03B1, 03B2 and 03B3 have been calculated in the intermediate coupling scheme for the ground

state of the actinide ions U4+, U3+, Np4+ and Np3+. The results are discussed in comparison with an approximate

calculation and the Russell-Saunders values.

J. Physique 45 (1984) 1067-1069 JUIN 1984,

Classification Physics Abstracts

71.70C

The factors a, fl and y, which multiply the Stevens

equivalent operators On (n = 2, 4, 6 respectively) have

been calculated in the intermediate coupling (IC)

scheme for the ground state of the actinide ions U4 +, U3 +, Np4+ and Np3+ by standard tensor operator

techniques [1].

The starting wavefunctions are taken from the literature. The results of the complete calculation (IC)

are shown in table I, together with the approximate

results (IC*) obtained by taking into account only the

main contributions (greater than 1 %) to the wave-

functions. In the case of U3 + only these contributions

are available. For comparison, the Russell-Saunders values (RS) are given too. Moreover, the values of the

spectroscopic splitting factor gj, corresponding to the

wavefunctions chosen, are given for completeness.

For eacfi considered ion, the following remarks must

be made :

U4+-f2 configuration

The assumed IC ground state, corresponding to J = 4, is

This was calculated by Rahman and Runciman [2]

for U02.

(*) Scientific and Technical Fellowship of C.C.E. Bruxel- les, Belgium. On leave from University of Parma, Italy.

U3 +-f3 configuration

The ground state wavefunction is that given by

Camall and Wyboume [3] and more recently confirmed by Crosswhite et al. for U’+ : LaCl3 [4]. Unfortunately only the coefficients of the components of the J

9/2 ground state, which are greater than 0.1 in absolute

value, are specified. That is

where the states are classified following the notation of Nielson and Koster [5]. This corresponds to 98.5 % of

the whole wavefunction.

Np 4 1 _f3 configuration

The J

9/2 wavefunction of Gruber and Menzel [6]

has been choosen :

Starting from this function Gruber and Menzel already

calculated the factors ft = - 2.090 x 10-4 and

y = - 2.563 x 10- ’,which agree with ours within the calculation errors (no further digits are significant

other than those considered in the coefficients of the

wavefunction).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019840045060106700

1068

Table I.

The calculated IC and IC* values and the RS values for the Stevens factors and the spectroscopic splitting factor.

The wavefunction calculated by Sharma and Art-

man [7]

gives values of the Stevens factors not significantly

different from the preceding ones, as shown in table II.

Np3 +-f configuration

The J

4 ground state is taken from Carnall and

Wybourne [3] and Carnall et al. [8]. The coefficients of the 1 % terms are adjusted from the Z2 and Z5 states

in table III of Carnall et al., taking into account the

normalization condition of the whole function. In any case, small variations of these coefficients are

ineffective. The wavefunction used in the calculation is then :

Table I shows that in general the contributions of the

small coefficient terms are significant, both for the Stevens factors and for gj.

Calculation of the Stevens factors 03B1, 03B2 ^and ^03B3

in the intermediate coupling ^scheme for ^{U and} _Np ^ions

with f2, ^f3 ^and ^f4 configurations

Centre d’Etudes Nucléaires de Grenoble, Département ^de ^Recherche Fondamentale, Section de Physique ^du Solide, ⁸⁵ X, ³⁸⁰⁴¹ ^Grenoble Cedex, ^France

(Reçu le 6 octobre 1983, révisé le 24 janvier ^1984, accepte ^{le 3} février ¹⁹⁸⁴⁾

The Stevens factors 03B1, 03B2 ^and ^03B3 ^have been calculated in the intermediate coupling scheme for the ground

state of the actinide ions U4+, U3+, Np4+ ^and Np3+. The results are discussed in comparison ^with ^an approximate

J. Physique ⁴⁵ (1984) ^1067-1069 ^JUIN 1984,

Classification Physics ^Abstracts

The factors a, fl ^and y, which multiply the Stevens

equivalent operators On ⁽ⁿ ^{= 2, 4,} ⁶ respectively) ^have

scheme for the ground ^state ^{of the} âctinide îons U4 +, U3 +, Np4+ ând Np3+ by ^standard ^tensor operator

are shown in table I, together ^{with the} approximate

results (IC*) ôbtained by taking înto âccount only ^the

main contributions (greater ^than ¹ %) ^to ^the ^wave-

are available. For comparison, the Russell-Saunders values (RS) ^are given ^too. Moreover, the values of the

spectroscopic splitting factor gj, corresponding ^to ^the

wavefunctions chosen, ^are given ^for completeness.

For eacfi considered ion, ^the following ^remarks ^must

The assumed IC ground state, corresponding ^to J = 4, is

(*) Scientific and Technical Fellowship of C.C.E. Bruxel- les, Belgium. ^On leave from University ^of Parma, Italy.

The ground ^state wavefunction is that given by

Camall and Wyboume [3] ^and ^more recently ^confirmed by Crosswhite et ^{al. for} U’+ : LaCl3 [4]. Unfortunately only the coefficients of the components ^{of the} ^J

9/2 ground state, which ^are greater ^than ^0.1 in absolute

value, ^are specified. ^{That is}

where the states are classified following the notation of Nielson and Koster [5]. ^This corresponds ^to ^98.5 % ^of

calculated the factors ft = - ^2.090 ^x ^10-4 ^and

y = - 2.563 ^x 10- ’,which agree with ours within the calculation errors (no ^further digits ^are significant

The calculated IC and IC* values and the RS values for ^the ^Stevens factors ^{and the} spectroscopic splitting factor.

gives ^values of the Stevens factors not significantly

different from the preceding ônes, âs ^shown ^{in table} ÎI.

4 ground ^state ^is taken from Carnall and

Wybourne [3] and Carnall et al. [8]. ^The coefficients of the 1 % ^terms ^are adjusted ^{from the} Z2 ^and Z5 ^states

in table III of Carnall et al., taking ^into ^account ^the

normalization condition of the whole function. In any ^case, small variations of these coefficients are

Table I shows that in general ^the contributions of the

Fig. ^1.

^The ^ratios ^{of the} intermediate coupling ^{and the}

sidered U and Np ^ions. (a) : ^the ^ratios IC/RS. (b) : ^{the ratios} IC*/RS.

Comparison between the IC values for N p4 + calculated from ^the wavefunction of Gruber and Menzel [6]

and of ^Sharma ^and ^Artman [7].

For this reason the values given ^for ^{U3 +} ^are ^to ^be

considered only ^as approximative, ⁱⁿ particular ^with regard ^to y.

The general trend of the calculated Stevens factors for the quoted ^{ions is} ^a ^reduction ^with respect ^to ^the RS values. This reduction becomes more and more

important ^{as we} proceed ^from ^U4+ ^to Np4+, ^while Np3 + presents ^a different behaviour.

The ratios IC/RS (or IC*/RS ^{in the} ^case ofU3+) ^do

not vary much from ^a _{to y} for f and f3 ions. Conse-

quently, ^we expect ^{in these} ^cases ^a reduction of the

crystal ^field splitting, ^but ^not â drastic modification of the _energy level scheme for the split ground ^multi- plet, âs ân ^{effect of} intermediate coupling.

[1] DIEKE, ^G. H., Spectra ^and Energy ^Levels of ^Rare ^Earth

Ions in Crystals, ^edited by H. M. Crosswhite and H. Crosswhite (Interscience Publishers, ^New York)

[2] RAHMAN, ^{H. U. and} RUNCIMAN, ^W. A., ^J. Phys. ^Chem.

Solids 27 (1966) ^1833.

[3] CARNALL, W. T. and WYBOURNE, ^B. G., ^J. ^Chem.

Phys. ⁴⁰ (1964) ^3428.

[4] CROSSWHITE, ^H. M., CROSSWHITE, H., CARNALL, ^{W. T.}

and PASZEK, ^A. P., ^{J. Chem.} Phys. ⁷² (1980) ^5103.

[5] NIELSON, C. W. and KOSTER, ^G. F., Spectroscopic Coefficients for pn, ^dn and fn Configurations (MIT Press, Cambridge, Mass.) ^1964.

[6] GRUBER, J. B. and MENZEL, ^E. R., ^{J. Chem.} Phys. ⁵⁰ (1969) ^3772.

[7] ^SHARMA, ^{K. K. and} ^ARTMAN, ^J. O., ^J. ^Chem. Phys. ⁵⁰ (1969) ^1241.

[8] CARNALL, ^W. T., CROSSWHITE, H., CROSSWHITE, ^H. M., HESSLER, ^J. P., EDELSTEIN, N., CONWAY, ^J. G., SHALIMOFF, ^{G. V. and} SARUP, R., ^J. ^Chem. Phys.

72 (1980) ^5089.