HAL Id: jpa-00227259
https://hal.archives-ouvertes.fr/jpa-00227259
Submitted on 1 Jan 1987
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.
INELASTIC AND ANOMALOUS ELASTIC SCATTERING OF 88.03 keV GAMMA RAYS
P. Kane, G. Basavaraju, S. Lad, K. Varier, L. Kissell, R. Pratt
To cite this version:
P. Kane, G. Basavaraju, S. Lad, K. Varier, L. Kissell, et al.. INELASTIC AND ANOMALOUS
ELASTIC SCATTERING OF 88.03 keV GAMMA RAYS. Journal de Physique Colloques, 1987, 48
(C9), pp.C9-835-C9-837. �10.1051/jphyscol:19879148�. �jpa-00227259�
JOURNAL DE PHYSIQUE
Colloque C9, supplement au n 0 1 2 , Tome 48, decembre 1987
INELASTIC AND ANOMALOUS ELASTIC SCATTERING OF 88.03 keV GAMMA RAYS
P.P. K A N E ' ~ ) , G. BASAVARAJU, S.M. LAD, K.M. VARIER(^), L. KISS ELL*,(^) and R.H. PRATT*
Department of Physics, Indian Institute of Technology, Powai, Bombay 400076, India
* ~ e p a r t m e n t of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.
Cross sections for the elastic scattering of 88.03 keV gamma rays through 125 degrees by aluminium, g o l d , lead and bismuth have been measured with a semiconductor detector. Simultaneously information has been obtained regarding resonance Raman scattering and Compton scattering in the case of bismuth, and K shell photoeffect cross sections in the case of gold and lead. Values accurate to about 8% were determined with the help of a normalization technique relying on a comparison with the Compton scattering counts from the low atomic number aluminium target. The elastic scattering cross section of aluminium at the chosen photon energy, which is far above the aluminium K shell threshold, is in reasonable accord with form factor and S matrix calculations based on the independent particle approximation. For gold, 7.3 keV above its threshold, the experiment agrees with the S matrix prediction. However, for lead some 25 eV above threshold, the experimental value is about 40% larger than predicted; while for bismuth (2.5 keV below threshold), experiment lies 70% above theory. The measured K shell photo effect cross section of lead is within 10% of the prediction based on the independent particle approximation.
1. ~ntroduct ion
The 88.03 keV gamma energy from a cadmium-109 source is only about 25 eV higher than the K shell binding energy of lead (88.006 keV) and about 2.5 keV lower than the K shell binding energy (90.527 keV) of bismuth. To our knowledge, anomalous scattering amplitudes have not so far been studied in the close vicinity G£ K shell thresholds of such high Z elements. Earlier studies of anomalous scattering have been summarised in a recent review 111. The available theoretical calculations [21 for 88 keV gamma rays indicated that near x = 6.3 the real parts of the scattering amplitudes make a very small contribution to the lead elastic scattering cross section. Here x = sin(@/Z)/X(A). O is the angle of scattering and
A(A)
is the wavelength of the gamma radiation in Angstroms. Accordingly, measurements were made with several elements at a mean scattering angle of 125 degrees in an effort to understand the salient features of the anomalous scattering amplitudes. The imaginary amplitudes due to the bismuth K shell are of course zero. Since the photon energy is as much as 7.3 keV higher than the gold K shell binding energy, the anomalous scattering contributions are less important in the case of gold than in the case of lead and bismuth. Since all electrons in a low Z element such as aluminium are weakly bound, the scattering cross sections for this case are predicted fairly reliably by the form factor approximation with minor corrections. In support of the experiment, new relativisitic second order S-matrix calculations were also performed for the four elements mentioned above.-
(l)~ddress until 30th April 1988 : Department of Physics. University of Warwick. GB-Coventry CV4 7AL.
Great-Britain
("permanent address : Department of Physics, University of Calicut, Kerala State 673635. India (3)~ermanent address : Test Planning and Diagnostics Division, Sandia National Laboratories.
AlbuqUerCiUe. NM 87185, u.S.A.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879148
C9-836 JOURNAL DE PHYSIQUE
Since the chosen photon energy is a little lower than the bismuth K shell binding energy, there was clearly a possibility of a simultaneous study of the recently discovered process of X-ray resonance Raman scattering (RRS) corresponding to virtual K-L and K-M transitions. K-L2 and K-M2,3 RRS have indeed been observed.
However in view of space limitations and a recent paper [3] by another group concerning the same topic, we will not here discuss our measurements of RRS and Compton scattering cross sections. In the present work, the Kill X-rays of gold and lead, and the different elastic scattering counts were compared with the Compton scattering counts obtained with an aluminium target, and the resulting ratios were used to determine respectively the K shell photoeffect cross sections and the elastic scattering cross sections.
2. Experimental Procedures
The experiment was performed with an annular cadmium -109 source of about 3 mCi strength, relatively thin targets in reflection geometry with effective transmission factors in the neighbourhood of 0.8, and a Si(Li) detector of 0.5 cm thickness and 1.6 cm diameter. The full width at half maximum of the pulse height distribution for 88 keV gamma rays was 630 eV. The large flux of lower energy radiations such as scattered silver K X-rays was attenuated with the help of a graded copper-aluminium absorber in front of the detector. The absorber was helpful in reducing the total count rate to less than 70 per second. Thus effects due to pile up were negligible. As usual, the net count rate due to a given target was determined from the difference between the target in and target out rates.
Let us suppose that the elastic scattering cross section duel/dQ of a target atom is to be determined. Then
where riel and nA1 are respectively the net count rates obtained with the given L
target corresponding to elastic scattering and with an aluminium target corresponding to Compton scattering, Nsc and N A ~ are the numbers of atoms of the given target and of the aluminium target, ( d ~ ~ / d ~ ) ~ ~ is the well known Compton
8 8 C
scattering cross section of aluminium, Tsc and T A ~ are respectively the average transmission factors of the target for Compton scattered photons of about 69.3 kev,
8 8 C
TA and TA are the transmission factors of the previously mentioned absorber for 88 keV and for Compton scattered photons, and and
nC
are the photopeak efficiencies of the detector at 88 keV and at the Compton energy.Values of the ratio l'188/llC are needed only over an energy range from about 65 keV to 88 keV. With targets of gold and lead, prominent Kil21 Kill, KB1' and ~ 6 2 ' X-ray components were observed at energies between about 67.0 and 87.4 keV. Values of the branching ratios for the different K X-ray components were obtained from the calculations of Scofield 1 4 1 . Thus from the counts under the different K X-ray peaks, ratios of detector efficiencies for the different K X-ray energies could be determined. In reporting the elastic scattering cross sections, an error of f 5 per cent has been adopted for the efficiency ratio in equation 1.
3. Results and Discussion
The experimental values of elastic scattering cross sections are summarised in Table 1. In the same table, we also show the new S-matrix predictions obtained in indeparticle particle approximation (IPA) in a Kohn-Sham potential with latter tail, shifting the energy scale to coincide with experimental threshold energies.
These represent the best currently available theoretical predictions.
The observed slight disagreement between experiment and theory in the case of aluminium is not considered very significant in view of the difficulty of measuring
Table 1: Elastic scattering cross sections duel/dn obtained at 125 degrees with 88.03 keV gamma rays. New s-matrix predictions are given in Column 3.
Element doel/dn cm2/sr)
Experiment Theory
...
Aluminium Gold Lead Bismuth
a very small cross section with a weak source. In the case of gold, there is excellent agreement between experiment and theory. The experimental value in the case of lead is about 40% larger than theory. Here so close to K shell threshold, one may worry about the validity of IPA, the determination of threshold position and the possible effects of the large width ( - 66 eV) of K shell hole states [51.
Some encouragement for the view that IPA is adequate for the imaginary amplitude follows from our value for the K shell photoeffect cross section which is within 10% of the value extrapolated to just above threshold from the IPA predictions of Scofield [61. In the case of bismuth, the experimental elastic scattering cross section is about 70% above theory. The near threshold departure of the real amplitude from the IPA prediction required for the explanation of the experimental values is of the order of 1.4 ro in the case of lead and about 0.4 ro in the case of bismuth, where ro is the classical electron radius.
These results suggest that further studies in this field are needed.
References
[I] KANE, P.P., KISSEL, LYNN, PRATT, R.H., and ROY, S.C., Phys Reports
140
(1986) 75.[ 2 1 PARKER, J.C. and PRATT, R.H., Phys Rev (1984) 152
[3l MACKENZIE, J.K. and STONE, R.J., Solid State Comm
5
(1985) 751.[4I SCOFIELD, J.H., Phys Rev (1974) 1041.
[5l BREMER, J., J Phys (Lond)
B12
(1979) 2797.LC1 SCOFIELD, J.H., Lawrence Radiation Laboratory Report, UCRL 51326 Livermore, Calif, USA (1973).
