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THE SCATTERING RESONANCE CROSS-SECTION FOR NON-AXIAL SYMMETRIC HYPERFINE INTERACTION INCLUDING AN ANISOTROPIC
DEBYE-WALLER-FACTOR
H. Bokemeyer, D. Eckardt, K. Wohlfahrt
To cite this version:
H. Bokemeyer, D. Eckardt, K. Wohlfahrt. THE SCATTERING RESONANCE CROSS-SECTION FOR NON-AXIAL SYMMETRIC HYPERFINE INTERACTION INCLUDING AN ANISOTROPIC DEBYE-WALLER-FACTOR. Journal de Physique Colloques, 1974, 35 (C6), pp.C6-389-C6-392.
�10.1051/jphyscol:1974673�. �jpa-00215830�
JOURNAL DE PHYSIQUE
Colloque C6, supplément au no 12, Tome 35, Décembre 1974, page C6-389
THE SCATTERING RESONANCE CROSS-SECTION FOR NON-AXIAL SYMMETRIC HYPERFINE INTERACTION INCLUDING
AN ANISOTROPIC DEBYE-WALLER-FACTOR
H. BOKEMEYER
Gesellschaft für Schwerionenforschung, Darmstadt, Germany D. ECKARDT and K. WOHLFAHRT
Institut für Kernphysik der TH Darmstadt, Germany
Résumé. -
La section efficace de diffusion résonnante est calculée pour un facteur de Debye- Waller anisotrope et pour une interaction hyperfine de symétrie non axiale. Les formules incluent bien sûr les cas particuliers de l'effet Karyagin-Goldanskii en géométrie de transmission et de l'interaction hyperfine
àsymétrie axiale.
Abstract.
- The scattering resonance-cross-section has been calculated for a
non-isotropieDebye-Waller-factor and non-axial symmetric hyperfine-interaction. The formulae include of course the special cases of
Goldanskii-Karyagin-effectin transmission geometry and axial-symmetric hyperfine-interaction.
In the technique of measuring Mossbauer-spectra by observing the resonantly scattered y's or conversion- electrons the line intensities and shapes are influenced by the angular correlation between the incoming y-ray and the outgoing electron or
y.This holds even for unpolarized incoming y's and/or isotropic absorber as first mentioned by Gabathuler and Leisy [l].
By using Mossbauer-conversion-spectroscopy [2, 31
the problem arose of fitting the quadrupole-splitted tungsten-fluorides under the assumption of a strong Goldanskii-Karyagin-effect [4], which influence should be altered compared to transmission-geometry. Follow- ing the procedure as outlined in [5] the scattering cross- section including Goldanskii-Karyagin-effect for unpo- larized incoming y-radiation, no observation of the polarization of the scattered particle, and polycrystalline absorbers can be computed to
:- J J
' ~ z ~ml> ~D?-,,.(el ( e ql>f(el ~ a l ) wZ(e1ol) d o ,
- 4 2
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974673
C6-390
with
:H. BOKEMEYER, D. ECKARDT A N D K. WOHLFAHRT
S =
(vl
q , v2q2 LI L', L2 E2
ni ni n,M l ml m!'
mz) ;vl, v, even
ol, :
conversion coefficient of shell
x<
x:> 1
f (6' <pi)
=exp ( - -;ii- ) exp ( [6,, -
- 6,cos 2
<pl2
(Lorentz line as defined in [8])
di,, =
((w
n i -@ii)lr2)
The bv(nL, n' L i ,
e;)and Fv(L2 L i ,
IiIf) are the well known particle-parameters and angular distribution- coefficients respectively, as tabilized in [6]. The c:,,, are linear-combination-coefficients as defined by
$ ~ , = ~ c i i m , I I i m i > , sothat ~ t , h ~ , = E , , t h ~
mi
FIG. 1. - Explanation of symbols : a) used angles (Z = crystal axis) ; b) nuclear symbols : left : resonance absorption, right :
deexcitation.
For non-axial quadrupole-interaction the ci,, for
Ii =2 are given in table 1. In the case of axial-symmetric interaction the c ~ , , , are equal to d,,,,.
wz(B1 cpl) describes the polarization of the absorber. If one uses isotropic samples wz(B1
cpl)has to be replaced
by #(O1 <pl)
= 114 n.THE SCATTERING RESONANCE CROSS-SECTION C6-39 1
TABLE 1 4 relative intensities
Eigenfunctions for I
= 2and non-axial quadrupole-interaction
for
y # O= 2-'12(1 2 - 2
> +
12+
2>)
for
=0
FIG. 2. - Relative line intensities as function of
(aL
= 0) for : a) line 5 ; b) line 3 ; c) line 2 and 4 and for different detec- tion angles : transmission (solid line), 30°-70° (dashed line) and6g0-71° (dot-dash line).
If the Lorentz-distribution L(ni n! n,,
v) is independent of n, (for axial-symmetric interaction of mg)the summa-
tion over
mg, ngcan be done. For
1, =O or 3 in the case of quadrupole interaction and polycristalline absorber the
formula may be condensed to
:C6-392 H. BOKEMEYER, D. ECKARDT AND K. WOHLFAHRT
For a 2 + O transition figure 2 shows for example
the intensities of the five lines as a function of for
6, = Oand y
=0.85 for three different sets of detec- tion-angles
:1) 8,
=300, 8,
=700, cp,
=00, cp,
=2 n, which corresponds to the P-spectrometer of the orange- type [7] used for the experiments of [3, 51
;2) 8,
=690, 8,
=710,
cp, =00, cp,
=2 n, which may correspond to e--detection with a solid-state- detector
;3) the transmission-geometry
: 19, =4 2 , 8,
=n/2,
cpl =00,
cp, =2
71,which may be compared with an approximation given in
[4].Acknowledgment. -
The authors thank Prof.
Dr. E. Gerdau and Dr. A. Gedikli for their hint to the strong Goldanskii-Karyagin-effect in the tungsten- fluorides long before publication, which partly ini- tiated this work.
References
[l] GABATHULER, K. and LEISI, H. J., Hyperfine Interactions in Excited Nuclei, Rehovot, Israel(1972).
[2] KANKELEIT, E., Z. Phys. 164 (1961) 442.
[3] BOKEMEYER, H., WOHLFAHRT, K. and KANKELEIT, E., International Conference on Application of the MB- Efect (Ayeleth Hashahar, Israel) 1973.
[4] GEDIKLI, A., WINKLER, H. and GERDAU, E., 2. Phys. 267 (1974).
[5] BOKEMEYER, H., Thesis, Institut für Kernphysik, Technische Hochschule Darmstadt, to be published.
WOHLFAHRT, K., Thesis, Institut für Kernphysik, Technische Hochschule Darmstadt, to be published.
[6] HAGER, R. S. and SELTZER, E. C., NUCI. Data A 4 (1968) Nos 5-6.
[7] MOLL, E. and KANKELEIT, E., Nukleonik 7 (1965) 180.
[8] EICHER, H., Z. Phys. 212 (1968) 176.
