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Perturbed angular correlation measurements at 181Ta in Hf2Pd and Zr2Pd tetragonal MoSi2-type phases
Journal of
ALLOYS AND COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 219 (1995) 132-194
Perturbed angular correlation measurements at 181Ta in HfzPd and Zr2Pd tetragonal MoSi2-type phases B. W o d n i e c k a a M. Marszalek a, p. Wodniecki a, H. Saitovitch b P.R.J. da Silva b
A.Z. Hrynkiewicz
a
" tl. Niewodniczanski Institute of Nuclear Physics, Radzikowskiego 152, 31-342 Cracow, Poland b Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
Abstract The electric quadrupole interaction at ~S~Tain Hf2Pd and Zr2Pd compounds was studied by the perturbed angular correlation method in a broad temperature range. The powder X-ray analysis verified a single-phase Cllb structure of the samples. The least-squares fits of the perturbation factor to the experimental spectra measured for Hf2Pd and ZrzPd compounds yielded an electric interaction with a well-defined single quadrupole frequency (uo = 305(2) MHz for HfzPd and 291(4) MHz for Zr2Pd) and asymmetry parameter ~=0, reflecting the existence of one axially symmetric probe site. A decrease in the quadrupole interaction frequency with an increase of temperature is very rapid for both Hf2Pd and ZrzPd compounds. Keywords: Intermetallic compounds; Perturbed angular correlations; Electric lield gradient
I. Introduction
A study of the electric quadrupole hyperfine interaction gives information about electric field gradients (EFGs) at the site of a nucleus in the investigated specimen if one knows the nuclear quadrupole moment or vice versa. Systematic studies in different materials allow us to predict the approximate value of E F G and to learn about different mechanisms which are responsible for its observed value. Such studies give some new knowledge in solid state physics and provide a powerful tool for the determination of nuclear electric quadrupole moments. The E F G at a nucleus in non-cubic metallic environment arises from several sources. The lattice contribution of positively charged ion cores can be calculated when the symmetry and lattice constants are known. This lattice contribution is enhanced at the nuclear site by the Sternheimer antishielding factor 1-y~, which is associated with a distortion of closed electronic shells of the probe ion. Another contribution comes from conduction and valence electrons outside closed shells and can be subdivided into two terms corresponding to electrons inside and outside of the Wigner-Seitz cell of the probe ion. The effect of the local electronic structure appears to dominate all other contributions
0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)05067-8
to EFG. A distortion of the Fermi surface due to the quadrupole component of the lattice potential induces a redistribution of electrons among states of different spatial symmetry. For metals with large densities of states at the Fermi level such as the transition metals, electrons at the Fermi surface (where thermally induced repopulation can occur) may play a dominant role. Therefore the measurements of the E F G dependence on temperature or pressure can provide more information about the mechanisms mentioned above. In view of recent progress in the theoretical description of E F G s in metals it is important to enlarge the available base of experimental data. The temperature dependence of the E F G s for most metal systems follows the T 3/2 law [1] but that is not the case if the transition metals are involved [2]. The temperature dependence of the E F G s in transition metal compounds was not studied extensively. The present perturbed angular correlation (PAC) studies of Hf2Pd and Zr2Pd compounds began a systematic investigation of the lSlTa quadrupole interaction in the MoSi2-type intermetallic phases. The Cll~ family (space group, D ~ 17, 14/mmm) occurs at A2B stoichiometry. Most of the MoSi2 phases contain an element of the titanium group or a lanthanide as the A component and palladium or a m e m b e r of the copper group as
B. Wodniecka et al. /Journal of Alloys and Compounds 219 (1995) 132-134
~Pd OHf
• .....
I i
.
: ..... .....
.o
~ .....
...:.....
133
range 25 K-1123 K using a set-up with two BaF2 and two NaI detectors with an experimental time resolution of 1.8 ns full width at half-maximum (FWHM). For PAC measurements below room temperature a closed-cycle helium refrigerator was used and the experiments above 300 K were carried out using a small resistive vacuum oven.
3. Results and discussion
The usual ratio
R(t) = 2[N(180 °, t ) - N ( 9 0 °, t)l/[N(180 °, t)+ 2N(90 °, t)] (1)
Fig. 1. T h e u n i t cell o f t h e H f 2 P d c o m p o u n d .
the B component [3]. The A atoms occupy the unique 4(e) (4ram) sites and the B atoms the 2(a) (4/rnmm) sites in the lattice. The compounds can be classified in two groups on the basis of their axial ratios. A unit cell of a tetragonal Cllb compound containing two molecules of Hf2Pd is shown in Fig. 1. This compound is a member of a group characterized by c/a values between 3.188 and 4.684. The coordination shell around the Hf atom has ten next neighbours, five atoms of like kind and five unlike. Eight of them (four Pd and four Hf atoms) are equidistant and the distance to the two atoms (one Hf and one Pd atom) in the c direction is 25% greater.
2. Experimental details
The Hf2Pd sample was obtained by argon arc melting followed by 100 h of annealing at 1100 K in an evacuated and sealed quartz tube. Powder X-ray analysis verified a single-phase product of the Cllb structure. The ISlTa probes were produced by neutron irradiation of the Hf2Pd compound. In order to remove the irradiation defects the sample was annealed for 2 days at 1000 K. The PAC spectra were measured with a standard slow-fast coincidence set-up with four BaF2 detectors positioned at relative angles of 180° and 90°. The time resolution of the system was 800 ps for the 133 keV-482 keV y--y cascade in 181Ta. The measurements were performed in the temperature range 45 K-1100 K. The (Zro.99Hfo.ol)2Pd sample was prepared and measured in Centro Brasileiro de Pesquisas Fisicas in Rio de Janeiro. The stoichiometric amounts of the constituent elements, including neutron-irradiated Hf, were melted together in an argon arc furnace. The sample was then annealed for 48 h at 923 K in vacuum. The PAC measurements were performed in the temperature
was formed from the measured coincidence time spectra N(O, t) (where 0 is the interdetector angle) corrected for the accidental coincidence background. The R(t) ratio was then fitted with the perturbation factor G2(t) for the static quadrupole interaction [4,5]:
R(t) =AfffGz(t) 3
=A2 elf ~, {sz~(~7) cos[g,(r/)uot] exp[-g,(~)&]} (2) ,=0
where A2err is the effective anisotropy coefficient. The information about the EFG is contained in the quadrupole coupling constant uo=eQV=/h, the asymmetry parameter ~7= (V=-V~)/V=, and the width 6 of a lorentzian distribution around vo. Here Vu are the components of the diagonalized EFG tensor and Q is the electric quadrupole moment of the intermediate state of probe atom• s, and g, in Eq. (2) are known functions of ~7 [6,7]• The functions g,(~7) give the relation between the transition frequencies in the quadrupole-split intermediate state, which can be displayed via the Fourier transform of the R(t) function. The s2~ coefficients depend on the orientation of the EFG principle axis relative to the detectors. The least squares fits of Eq. (2) to the experimental spectra measured for Hf/Pd and Zr~Pd compounds yielded in each case an electric quadrupole interaction with a single frequency vo and an asymmetry parameter, r/= 0. This reflected the existence of one axially symmetric probe site in the Cllb structure of the investigated samples. Both samples exhibited a non-random orientation of crystallites and the PAC data had to be fitted with free s2, parameters. Two examples of PAC spectra taken at 45 K for different geometries of Hf2Pd sample with regard to the detector plane are shown in Fig. 2. They reveal a texture of the sample. For spin 5/2 and an axially symmetric interaction only the fundamental frequency and its first and second harmonic can be present in the perturbation factor• The fundamental frequency makes a dominant contribution for the ge-
B. Wodniecka et aLI Journal of Alloys and Compounds 219 (1995) 132-134
134
-R(t)[
P(vo)
02E 0.0 \
~ m
__
r
....
/
~' i
0.2I; o.1 I
t,I i
0
!I
r,
~,
40
t[ns]
80
0
5oo vQ [MHz] 1000
1
Fig. 2. PAC spectra (with the corresponding Fourier transforms taken at 45 K for different geometries of the Hf2Pd samples with regard to the detector plane.
-R(t) o.
Hf2Pd +~' ¢ "
00 , r , ; ~
[ ¢,, .7 +
" -/
vQ[MHz]
300
, "
HfiPd .
•
[ i
"
Zr2PO
Zr2Pd
°
0.1
300"" " . .
,"
.
2001 20
t[ns]
40
60
L 0
" • 500
.
i
1000
Pd ions when combined with the Sternheimer antishielding factor l-y® = 62 [9] give a lattice contribution of ca. - 2 × 1018 V cm -2 for Hf2Pd and Zr2Pd. This value is 4 times larger than that found experimentally, so the sizeable role of the electronic contribution to the EFG is evident. As can be seen in Fig. 3 the decrease in the quadrupole interaction frequency with increasing temperature is very rapid for both Hf2Pd and Zr2Pd compounds. The data cannot be well reproduced with the T 3/2 function of the temperature [1,2]. The measured vo(T) dependence is linear in a wide temperature range (broken line in Fig. 3): vo(T) : vo(0)(1 - a T )
(3)
The fitted slopes a of both re(T) curves are very similar and amount to about 5X10 -4 K -1 (a=4.9(2)×10 -4 K i for Hf2Pd and a =5.2(2)× 10 .4 K -1 for Zr2Pd). A linear temperature dependence was also reported for some other metal systems involving transition metals as impurities and hosts [2]. Unfortunately, a lack of experimental data on the thermal expansion parameters for the compounds studied did not allow us to compare the measured EFG temperature dependence with the variation in its lattice contribution.
T [K]
Fig. 3. Room temperature PAC spectra and the temperature dependence of quadrupole interaction frequencies for tS~Ta in Hf2Pd and Zr2Pd samples. - - - , least-squares fits of Eq. (3) to the vo(T ) data in the temperature range 170 K-900 K.
ometry in which the crystalline c axis is perpendicular to the detector plane. A broadening of the EFG described by a lorentzian distribution width ~ was ca. 3% of vo for the Hf2Pd sample. In the case of the Zr2Pd sample this broadening was about two times larger. The room temperature spectra for Hf2Pd and Zr2Pd samples and the measured temperature dependence of the quadrupole frequencies are shown in Fig. 3. The fitting procedure yielded the room temperature quadrupole interaction frequency values vo = 305(2) MHz for Hf2Pd and vo=291(4 ) MHz for Zr2Pd. The corresponding EFGs are about 0.5 × 1018 V cm- 2 when the quadrupole moment value Q=2.51 b [8] of the 482 keV lSlTa excited state is used in the calculations. These almost identical values of vo reflect a chemical similarity of Hf and Zr and very close lattice constants of both compounds [3]. Thus, the substitution of Zr 4(e) sites by the Hf probe atoms in the ZrzPd sample is confirmed. The point charge model calculations of the ionic contribution to the EFG with the assumption of + 4 charge on Hf and Zr sites and 0 charge on the
Acknowledgments The authors would like to express their thanks to Dr. A. Bajorek for X-ray analysis of the sample. Some of the hafnium activities were performed by courtesy at the reactor IPEN-CNEN/SP (Brazil). This work was supported by the State Committee for Scientific Research (Grant 2 0457 91 01) and the program RHAE/ CNPq (Brazil).
References [1] J. Christiansen, P. Heubes, R. Keitel, W. Klinger, W. Loeftler, W. Sandner and W. Witthuhn, Z. Phys. B, 24 (1976) 177. [2] H.C. Verma and G.N. Rao, Hyperfine Interact., 15-16 (1983) 207. [3] M.V. Nevitt, in J.H. Westbrook (ed.), Intermetallic Compounds, Wiley, New York, 1967. [4] A.R. Arends, C. Hohenemser, F. Pleiter, H. de Waard, L. Chow and R.M. Suter, Hyperfine Interact., 8 (1980) 191. [5] H. Frauenfelder and R.M. Steffen, in K. Karlsson, E. Mathias and K. Siegbahn (eds.), Alpha-, Beta- and Gamma-Ray Spectroscopy, Vol. 2, North-Holland, Amsterdam, 1963, p. 1118. [6] J. Kajfosz, Institute of Nuclear Physics (Cracow), Rep. 858/PM, 1973 (unpublished). [7] T. Butz, Hyperfine Interact., 52 (1989) 189. [8] G. Netz and E. Bodenstedt, Nucl. Phys. A, 208 (1973) 503. [9] F.D. Feiock and W.R. Johnson, Phys. Rev., 187 (1969) 39.
ALLOYS AND COMPOUNDS ELSEVIER
Journal of Alloys and Compounds 219 (1995) 132-194
Perturbed angular correlation measurements at 181Ta in HfzPd and Zr2Pd tetragonal MoSi2-type phases B. W o d n i e c k a a M. Marszalek a, p. Wodniecki a, H. Saitovitch b P.R.J. da Silva b
A.Z. Hrynkiewicz
a
" tl. Niewodniczanski Institute of Nuclear Physics, Radzikowskiego 152, 31-342 Cracow, Poland b Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
Abstract The electric quadrupole interaction at ~S~Tain Hf2Pd and Zr2Pd compounds was studied by the perturbed angular correlation method in a broad temperature range. The powder X-ray analysis verified a single-phase Cllb structure of the samples. The least-squares fits of the perturbation factor to the experimental spectra measured for Hf2Pd and ZrzPd compounds yielded an electric interaction with a well-defined single quadrupole frequency (uo = 305(2) MHz for HfzPd and 291(4) MHz for Zr2Pd) and asymmetry parameter ~=0, reflecting the existence of one axially symmetric probe site. A decrease in the quadrupole interaction frequency with an increase of temperature is very rapid for both Hf2Pd and ZrzPd compounds. Keywords: Intermetallic compounds; Perturbed angular correlations; Electric lield gradient
I. Introduction
A study of the electric quadrupole hyperfine interaction gives information about electric field gradients (EFGs) at the site of a nucleus in the investigated specimen if one knows the nuclear quadrupole moment or vice versa. Systematic studies in different materials allow us to predict the approximate value of E F G and to learn about different mechanisms which are responsible for its observed value. Such studies give some new knowledge in solid state physics and provide a powerful tool for the determination of nuclear electric quadrupole moments. The E F G at a nucleus in non-cubic metallic environment arises from several sources. The lattice contribution of positively charged ion cores can be calculated when the symmetry and lattice constants are known. This lattice contribution is enhanced at the nuclear site by the Sternheimer antishielding factor 1-y~, which is associated with a distortion of closed electronic shells of the probe ion. Another contribution comes from conduction and valence electrons outside closed shells and can be subdivided into two terms corresponding to electrons inside and outside of the Wigner-Seitz cell of the probe ion. The effect of the local electronic structure appears to dominate all other contributions
0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)05067-8
to EFG. A distortion of the Fermi surface due to the quadrupole component of the lattice potential induces a redistribution of electrons among states of different spatial symmetry. For metals with large densities of states at the Fermi level such as the transition metals, electrons at the Fermi surface (where thermally induced repopulation can occur) may play a dominant role. Therefore the measurements of the E F G dependence on temperature or pressure can provide more information about the mechanisms mentioned above. In view of recent progress in the theoretical description of E F G s in metals it is important to enlarge the available base of experimental data. The temperature dependence of the E F G s for most metal systems follows the T 3/2 law [1] but that is not the case if the transition metals are involved [2]. The temperature dependence of the E F G s in transition metal compounds was not studied extensively. The present perturbed angular correlation (PAC) studies of Hf2Pd and Zr2Pd compounds began a systematic investigation of the lSlTa quadrupole interaction in the MoSi2-type intermetallic phases. The Cll~ family (space group, D ~ 17, 14/mmm) occurs at A2B stoichiometry. Most of the MoSi2 phases contain an element of the titanium group or a lanthanide as the A component and palladium or a m e m b e r of the copper group as
B. Wodniecka et al. /Journal of Alloys and Compounds 219 (1995) 132-134
~Pd OHf
• .....
I i
.
: ..... .....
.o
~ .....
...:.....
133
range 25 K-1123 K using a set-up with two BaF2 and two NaI detectors with an experimental time resolution of 1.8 ns full width at half-maximum (FWHM). For PAC measurements below room temperature a closed-cycle helium refrigerator was used and the experiments above 300 K were carried out using a small resistive vacuum oven.
3. Results and discussion
The usual ratio
R(t) = 2[N(180 °, t ) - N ( 9 0 °, t)l/[N(180 °, t)+ 2N(90 °, t)] (1)
Fig. 1. T h e u n i t cell o f t h e H f 2 P d c o m p o u n d .
the B component [3]. The A atoms occupy the unique 4(e) (4ram) sites and the B atoms the 2(a) (4/rnmm) sites in the lattice. The compounds can be classified in two groups on the basis of their axial ratios. A unit cell of a tetragonal Cllb compound containing two molecules of Hf2Pd is shown in Fig. 1. This compound is a member of a group characterized by c/a values between 3.188 and 4.684. The coordination shell around the Hf atom has ten next neighbours, five atoms of like kind and five unlike. Eight of them (four Pd and four Hf atoms) are equidistant and the distance to the two atoms (one Hf and one Pd atom) in the c direction is 25% greater.
2. Experimental details
The Hf2Pd sample was obtained by argon arc melting followed by 100 h of annealing at 1100 K in an evacuated and sealed quartz tube. Powder X-ray analysis verified a single-phase product of the Cllb structure. The ISlTa probes were produced by neutron irradiation of the Hf2Pd compound. In order to remove the irradiation defects the sample was annealed for 2 days at 1000 K. The PAC spectra were measured with a standard slow-fast coincidence set-up with four BaF2 detectors positioned at relative angles of 180° and 90°. The time resolution of the system was 800 ps for the 133 keV-482 keV y--y cascade in 181Ta. The measurements were performed in the temperature range 45 K-1100 K. The (Zro.99Hfo.ol)2Pd sample was prepared and measured in Centro Brasileiro de Pesquisas Fisicas in Rio de Janeiro. The stoichiometric amounts of the constituent elements, including neutron-irradiated Hf, were melted together in an argon arc furnace. The sample was then annealed for 48 h at 923 K in vacuum. The PAC measurements were performed in the temperature
was formed from the measured coincidence time spectra N(O, t) (where 0 is the interdetector angle) corrected for the accidental coincidence background. The R(t) ratio was then fitted with the perturbation factor G2(t) for the static quadrupole interaction [4,5]:
R(t) =AfffGz(t) 3
=A2 elf ~, {sz~(~7) cos[g,(r/)uot] exp[-g,(~)&]} (2) ,=0
where A2err is the effective anisotropy coefficient. The information about the EFG is contained in the quadrupole coupling constant uo=eQV=/h, the asymmetry parameter ~7= (V=-V~)/V=, and the width 6 of a lorentzian distribution around vo. Here Vu are the components of the diagonalized EFG tensor and Q is the electric quadrupole moment of the intermediate state of probe atom• s, and g, in Eq. (2) are known functions of ~7 [6,7]• The functions g,(~7) give the relation between the transition frequencies in the quadrupole-split intermediate state, which can be displayed via the Fourier transform of the R(t) function. The s2~ coefficients depend on the orientation of the EFG principle axis relative to the detectors. The least squares fits of Eq. (2) to the experimental spectra measured for Hf/Pd and Zr~Pd compounds yielded in each case an electric quadrupole interaction with a single frequency vo and an asymmetry parameter, r/= 0. This reflected the existence of one axially symmetric probe site in the Cllb structure of the investigated samples. Both samples exhibited a non-random orientation of crystallites and the PAC data had to be fitted with free s2, parameters. Two examples of PAC spectra taken at 45 K for different geometries of Hf2Pd sample with regard to the detector plane are shown in Fig. 2. They reveal a texture of the sample. For spin 5/2 and an axially symmetric interaction only the fundamental frequency and its first and second harmonic can be present in the perturbation factor• The fundamental frequency makes a dominant contribution for the ge-
B. Wodniecka et aLI Journal of Alloys and Compounds 219 (1995) 132-134
134
-R(t)[
P(vo)
02E 0.0 \
~ m
__
r
....
/
~' i
0.2I; o.1 I
t,I i
0
!I
r,
~,
40
t[ns]
80
0
5oo vQ [MHz] 1000
1
Fig. 2. PAC spectra (with the corresponding Fourier transforms taken at 45 K for different geometries of the Hf2Pd samples with regard to the detector plane.
-R(t) o.
Hf2Pd +~' ¢ "
00 , r , ; ~
[ ¢,, .7 +
" -/
vQ[MHz]
300
, "
HfiPd .
•
[ i
"
Zr2PO
Zr2Pd
°
0.1
300"" " . .
,"
.
2001 20
t[ns]
40
60
L 0
" • 500
.
i
1000
Pd ions when combined with the Sternheimer antishielding factor l-y® = 62 [9] give a lattice contribution of ca. - 2 × 1018 V cm -2 for Hf2Pd and Zr2Pd. This value is 4 times larger than that found experimentally, so the sizeable role of the electronic contribution to the EFG is evident. As can be seen in Fig. 3 the decrease in the quadrupole interaction frequency with increasing temperature is very rapid for both Hf2Pd and Zr2Pd compounds. The data cannot be well reproduced with the T 3/2 function of the temperature [1,2]. The measured vo(T) dependence is linear in a wide temperature range (broken line in Fig. 3): vo(T) : vo(0)(1 - a T )
(3)
The fitted slopes a of both re(T) curves are very similar and amount to about 5X10 -4 K -1 (a=4.9(2)×10 -4 K i for Hf2Pd and a =5.2(2)× 10 .4 K -1 for Zr2Pd). A linear temperature dependence was also reported for some other metal systems involving transition metals as impurities and hosts [2]. Unfortunately, a lack of experimental data on the thermal expansion parameters for the compounds studied did not allow us to compare the measured EFG temperature dependence with the variation in its lattice contribution.
T [K]
Fig. 3. Room temperature PAC spectra and the temperature dependence of quadrupole interaction frequencies for tS~Ta in Hf2Pd and Zr2Pd samples. - - - , least-squares fits of Eq. (3) to the vo(T ) data in the temperature range 170 K-900 K.
ometry in which the crystalline c axis is perpendicular to the detector plane. A broadening of the EFG described by a lorentzian distribution width ~ was ca. 3% of vo for the Hf2Pd sample. In the case of the Zr2Pd sample this broadening was about two times larger. The room temperature spectra for Hf2Pd and Zr2Pd samples and the measured temperature dependence of the quadrupole frequencies are shown in Fig. 3. The fitting procedure yielded the room temperature quadrupole interaction frequency values vo = 305(2) MHz for Hf2Pd and vo=291(4 ) MHz for Zr2Pd. The corresponding EFGs are about 0.5 × 1018 V cm- 2 when the quadrupole moment value Q=2.51 b [8] of the 482 keV lSlTa excited state is used in the calculations. These almost identical values of vo reflect a chemical similarity of Hf and Zr and very close lattice constants of both compounds [3]. Thus, the substitution of Zr 4(e) sites by the Hf probe atoms in the ZrzPd sample is confirmed. The point charge model calculations of the ionic contribution to the EFG with the assumption of + 4 charge on Hf and Zr sites and 0 charge on the
Acknowledgments The authors would like to express their thanks to Dr. A. Bajorek for X-ray analysis of the sample. Some of the hafnium activities were performed by courtesy at the reactor IPEN-CNEN/SP (Brazil). This work was supported by the State Committee for Scientific Research (Grant 2 0457 91 01) and the program RHAE/ CNPq (Brazil).
References [1] J. Christiansen, P. Heubes, R. Keitel, W. Klinger, W. Loeftler, W. Sandner and W. Witthuhn, Z. Phys. B, 24 (1976) 177. [2] H.C. Verma and G.N. Rao, Hyperfine Interact., 15-16 (1983) 207. [3] M.V. Nevitt, in J.H. Westbrook (ed.), Intermetallic Compounds, Wiley, New York, 1967. [4] A.R. Arends, C. Hohenemser, F. Pleiter, H. de Waard, L. Chow and R.M. Suter, Hyperfine Interact., 8 (1980) 191. [5] H. Frauenfelder and R.M. Steffen, in K. Karlsson, E. Mathias and K. Siegbahn (eds.), Alpha-, Beta- and Gamma-Ray Spectroscopy, Vol. 2, North-Holland, Amsterdam, 1963, p. 1118. [6] J. Kajfosz, Institute of Nuclear Physics (Cracow), Rep. 858/PM, 1973 (unpublished). [7] T. Butz, Hyperfine Interact., 52 (1989) 189. [8] G. Netz and E. Bodenstedt, Nucl. Phys. A, 208 (1973) 503. [9] F.D. Feiock and W.R. Johnson, Phys. Rev., 187 (1969) 39.