CONTRIBUTIONS OF A2-, p'A-, AND RESONANT TERMS IN INELASTIC SCATTERING OF γ-RAYS BY DEEPLY BOUND ELECTRONS

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CONTRIBUTIONS OF A2-, p’A-, AND RESONANT TERMS IN INELASTIC SCATTERING OF γ -RAYS

BY DEEPLY BOUND ELECTRONS

Y. Ohmura, S. Sato

To cite this version:

Y. Ohmura, S. Sato. CONTRIBUTIONS OF A2-, p’A-, AND RESONANT TERMS IN INELASTIC

SCATTERING OF γ -RAYS BY DEEPLY BOUND ELECTRONS. Journal de Physique Colloques,

1987, 48 (C9), pp.C9-815-C9-818. �10.1051/jphyscol:19879143�. �jpa-00227254�

CONTRIBUTIONS OF A'-, p'A-, AND RESONANT TERMS IN INELASTIC SCATTERING OF Y-RAYS BY DEEPLY BOUND ELECTRONS

Y . OHMURA and S .

SATO

Department of Physics, Tokyo Institute of ~echnology, 2-12-1, Oh-okayama, Meguro-ku, Tokyo 152, Japan

Abstract

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Inelastic scattering of Y-rays by deeply bound electrons has been investigated theoretically for the case of qa+l where q is the momentum transfer of Y-rays and a is the orbital radius of the bound electron. The result of calculation was compared with the experimental resulgqlof Namikawa and Hosoya, where 59.57keV Y-rays from Am sources are used as primary photons and K-shell electrons of Cu and Fe are chosen as targets.

I

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INTRODUCTION In their experiment of inelastic scattering of Y-rays by K-shell electrons of Cu and Fe, Namikawa and Hosoya(NH)/l/ used a coincidence technique where the spectra of scattered Y-rays that are coincident with the K-fluorescent X- rays are obtained. After subtracting false coincidences, they found 3 peaks; DT peak, R peak and C peak from threshold. They interpreted these as Double Thomson ( resonant 2 photon emission process with 1 photon absorption), Raman and Compton peaks, respectively.

If qa+l, a local behavior around the K-shell electrons carries an important role in the spectrum even if the electron in the scattering state has such a high energy as the order of a few kev. Spectra obtained for this case, however, are neither the Compton band that gives the momentum d i s t r i b u t i o n nor the Raman band that gives a b s o r p t i o n spectra/l/. The present paper is a report of our recent study, a preliminary report being given in ref./3/, on spectra that could obtain for the scattering under the condition of q a ~ l , by taking into account of the local behavior of the wave function in the core parts of a single orthogonalized plane wave (OPW) function.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879143

C9-816 JOURNAL DE PHYSIQUE

I1

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THEORY The transition probability of the scattering process considered here is given by the standard formula as

Here, /O,p> means the initial state where the electron system is in the state 0, and the incident photon is in the state J J ,

similar notations being used also for the final state represented by /f,A>. E and are the initial and final state energies of the0tgtal sysf&~ respectively. _H is the electron- photon in erection t e r ~ ~ ~ t h a t

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is bilinear 'in the vector potential(A -term).

H 1 comes from the linear term of the

vector potential(p.A-term) through the second order perturbation.

H is the resonant term that comes from the higher order terms ofesthe vector potential A. All of these terms are given graphically in Fig.1. The electron wave functions used for core parts are based on the atomic orbitals proposed by Clementi and Raimondi/4/ with slight modifications.

c o n d u c t i o n

K-hole Z p - h o l e e l e c t r o n p h o t o n a 2 - v e r t e x

Fig.1 All the terms calcula$ed in the text for the scattering by K-shell electrons. (a):A -term, (b) and (c):resonant terms and (d)%(g):p.A-terms through the second order perturbation.

I11

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RESULTS OF CALCULATION Figure 2 and Fig.3 show the spectra

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inelastic scattering of Y-rays obtained theoretically by the A -term with full width at half the maximum (FWHM) being equal to 560eV and that obtained experimentally by NH. Targets are K-shell electrons of Cu in Fig.2 and Fe in Fig.3. The C peak and the R peak are found theoretically at approximately the same positions in the spectra as obtained by experiment. These peaks are, however, neither the Compton nor the Raman peak/8i:

The C peak is shifted to the position of larger photon energy compared to the position of the Compton peak expected by the impulse approximation and the R peak is born by sum of contributions of many core parts having no simple relation with the absorption spectra.

energy o f the bound electron. In the present case, I / 3 v o is approximately 1/6 and p.A-terms that could account for the discrepancy between the theoretical and the experimental results are shown graphically in Fig.l(d)*(g). A solid line in Fig.4 shows the result which includes the correction by the p,$terms while a broken line is the result obtained only by the A -term.

The targets are K-shell electrons of Cu. Fig.4 shows clearly that the p,A-terms do not have ,such a strong influence on the spectral shape as to account for the discrepancy between the theory and the experiment shown in Fig.2. The spectra in Fig.4 are obtained with FWHM=O. A sharp peak near threshold in Fig.4 vanishes when we take account of the experimental broadening of FWHMz560eV as shown in Fig.2 by a solid line "Theory". See ref./3/ for details.

Since a sharp peak near threshold obtained by the lowest order contribution of the vector potential A is irrelevant to the DT peak, terms to reproduce the DT peak could be due to the resonant terms which are the higher order terms of the vector potential A. Such terms that could meet the requirement of experimental conditions of NH are given graphically in Fig.l(b) and (c). Of these, a term given by Fig.l(c) has the dominant contribution, being larger than the term given by Fig.l(b) calculated by Marchetti and Franck/6/. This, however, is still too small to explain the 2T peak: being of the order of 1/100 of the contribution of the A -term given in Fig.2 or Fig.3.

R CU : K-ELECTRON k

Colncldence

Fig.2 Spectra obtained theoretically for the scattering by K-shell electrons of Cu. Experimental result is obtained by Namikawa and Hosoya.

0 Fe :I<-ELECTRObl False

h v0=59.57keV Co~ncidence 8=135

FWHM = 560eV

PHOTON ENERGY (keW

Fig.3 The same as in Fig.2 but by K-shell electrons of Fe.

C9-818 JOURNAL DE PHYSIQUE

IV

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DISCUSSION AND CONCLUSION To summarize, our recent study supports the experimental result of NH as for the existence of the R peak, though the height of the R peak is approximately 1/3 of the experimental result. Neither the R peak nor the DT peak, however, was not found in the experiment of Manninen/7/ using the same geometry of experiment as NH but a stronger source and better resolution. Further experimental investigation without any false coincidence is most required to clarify the apparent discrepancy of these two experimental results/7,8/. We could not find the term that could reproduce the DT peak theoretically by eq.(l). The DT peak found experimentally by NH could be due to a false coincidence as claimed by Manninen/7/. Details of our results will be published elsewhere/9/.

C U: /<-ELECTRON

nu, = 59.571ce~

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Total 0=135' --- ~ ' - t e r m only FWI-IM = 0

4 0 4 5 50

PI-IOTON ENERGY (IteV)

Fig. 4 The graph showing the result with and without the contribution of the p.A-tyms. The solid line represents the spectra obtained by the A2-term plus the pad-terms, while the broken line, that by the A -term only.

References

/1/ Namikawa,K. and Hosoya,S., Phys.Rev.Lett.53(1984)1606.

/2/ Mizuno,Y. and Ohmura,Y., J.Phys.Soc.Jpn.22(1967)445.

/3/ Ohmura,Y. and Sato,S., J.Phys.Soc.Jpn.56(1987)1657.

/4/ Clementi,E. and Raimondi,D.L., J.Chem.Phys.38(1963)2686.

/5/ Ohmura,Y. and Suzuki,T., J.Phys.Soc.Jpn.53(1984)2807.

/6/ Marchetti,V. and Franck,C., Phys.Rev.A35(1987)3128.

/7/ Manninen,S., Phys.Rev.Lett.57(1986)1500.

/8/ Namikawa,K. and Hosoya,S., Phys.Rev.Lett.57(1986)1501.

/9/ Sato,S. and Ohmura,Y., submitted to J.Phys.Soc.Jpn.