International Journal of Scientific & Engineering Research Volume 2, Issue 4, April-2011 1

ISSN 2229-5518

Investigation of X-ray Plasmon Satellites in

Rare Earth Compounds

Ajay Vikram Singh, Dr. Sameer Sinha

Abstract- We have Investigate and study to X-ray Plasmon Satellites in Rare earth compounds ( La2CuO4 , Nd2CuO4 , Gd2CuO4 ,

PrNiSb2 , NdNiSb2 , Pr(OH)3 , Nd(OH)3 , Sm(OH)3 )

Keywords- Surface Plasmon Satellites, Relative Intensity & Energy Separation

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INTRODUCTION

N the characteristic X-ray Spectra, Diagram as well as non Diagram lines are present. Those lines which fit in the conventional energy level diagram are
called Diagram lines. & those lines which do not fit in the conventional energy level diagram are called non diagram lines. It is also known as “Satellites or Second order lines”. Satellites are generally of weak intensity lines & are found close to more intense parent line. The satellites which are observed on higher energy side are called high energy satellites (HES) whereas
those are observed on lower energy side are called lower energy satellites (LES). First Siegbahn & Stenstroem observed these satellites in the K-Spectra of element from Cr (24) to Ge (32) while coster theraeus & Richtmyer in the L-Spectra of element from Cu (29) to Sb (51) & Hajlmar, Hindberg & Hirsch in the M-Spectra of elements from Yb (70) to U (92). Several theories were proposed from time to time to explain the origin of these satellites. Out of these theories the plasmon theory is found to be the most suitable theory especially for those satellites.
Plasmon theory was first proposed by Bohm
& pines which are extended by Housten, Ferrel, Noziers & Pines. According to this theory the low energy plasmon satellites are emitted when valence electron excites a plasmon during the annihilation of
core hole conversely if Plasmon pre exists, its energy add up to the energy of diagram line.
The radiation less reorganization of electronic shell of an atom is known as Auger effect. Auger satellites have also been observed by Korbar and Mehlhorn [1] Haynes et at. [2] Edward and Rudd [3]. Theoretical explanation for K series Auger spectrum was given by Burhop and Asaad [4] using intermediate coupling. Later on more refined theory, using relativistic and configuration interaction has been used by Listengarter [5] and Asaad [6]
In Auger primary spectra, one can also observe secondary electron peaks close to the primary peaks are produced by incident electrons which have undergone well energy losses. The most common
source of such energy loss in the excitation of collective plasma oscillations of the electrons in the solid. This gives rise to a series of plasma peaks of decreasing magnitude spaced by energy hmp where mp is the frequency of plasma oscillation.
Auger peaks are also broadened by small energy losses suffered by the escaping electrons. This gives rise to a satellite on the low energy of the Auger peak. Energy loss peaks have well defined energy with to primary energy.
The involvement of Plasmon oscillation in the X-ray emission or absorption spectra of solids has been widely studied during the last few decades and has
been recognized that the electron –electron interaction has played an important role.
This Paper is devoted to Investigate and study to X-ray Plasmon Satellites in Rare earth compounds

( La2CuO4 , Nd2CuO4 , Gd2CuO4 , PrNiSb2 , NdNiSb2 ,

Pr(OH)3 , Nd(OH)3 , Sm(OH)3 )

According to Plasmon theory , if the valence
electron , before filling the core vacancy , also excites a Plasmon ,then the energy hcop needed for the excitation of Plasmon oscillation is taken from the transiting valence electron so that the emitted radiation will be derived off an energy hcop and a low energy satellites will emitted whose sepration from the main X-ray line will correspond to hcop . On the other hand if the Plasmon pre exists , during the X-ray emission process , then , on its decay it can give its energy to the transiting valence electron before it annihilates the core vacancy . Thus the energy of emitted X-ray photon will be higher than the main emission line and by an amount hcop giving rise to high energy satellite .

MATHEMATICAL CALCULATION –

In order to confirm the involvement of Plasmon in the emission of X-ray satellites the relative intensity of single Plasmon satellites must be calculated . In this process first we deal with mathematical details of canonical transformation carried out over the model Hamiltonian of the system . Thus the energy separation �E of the low and high energy Plasmon satellite from the

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corresponding main line should be equal to the quantum of Plasmon energy hcop which is given by [10]

ev 1

Where Z = No.of unpaired electrons , cr = Specific gravity & m = Molecular Weight
This equation can be derived as given below .
From the classical consideration , we get the frequency of Plasmon oscillation as

2

Hence the amount of energy given to Plasmon becomes

Ep = brop = b

In this equation we can write n =

Where cr , Z and W are defined above and L is the Avogadro number .By putting the numerical value of constant , we get the Plasmon energy as

ev 3

Our calculated values of �E have been compared with the Scrocco’s experimental value. And We have also calculated the relative intensity of plasmon satellites, which is different in different processes. If the excitation of plasmon occurs during the transport of the electron through the solid, it is known as extrinsic process of plasmon excitation. The plasmon can also be excited by another method known as intrinsic process. In this process, excitation of plasmon takes place simultaneously with creation of a hole. Bradshaw et al have further divided core hole excitation into two classes,
1 - Where the number of slow electrons are conserved.
2 - Where the number of slow electrons are not conserved
The Author has calculated relative intensity in both the cases with new modification in the light of Bradshaw [12] and Lengreth [13] work, which explains that not only intrinsic process but extrinsic process and their relative contribution may also contribute in relative intensities. The combined effect of intrinsic and extrinsic plasmon excitation intensity variation was suggested by Lengreth as:

i = = an 4

The value of � is taken as � = 0.12rs which is purely
intrinsic, rs = (47.11/ hws) 2/3 is dimensionless
parameter and a = 0.47 rs1/2 in the place of a = (1+l/L)-
1 used by Pardee et. al.(14) . The equation (3) contains a series of terms. The first term of the equation is purely extrinsic, while second term is purely intrinsic. The other terms are containing the relative contributions of both extrinsic and intrinsic. The specialty of this formula is that each term alone or simultaneously with other terms is able to give the relative intensity. This formula also includes both the categories mentioned by Bradshaw and gives better results as compared than traditional methods for calculation of the relative intensity. Using the values of a, � and rs in equation (4)
Using the equation (4), the author has for the

first time, calculated the relative intensity of Rare earth compounds ( La2CuO4 , Nd2CuO4 , Gd2CuO4 , PrNiSb2 , NdNiSb2 , Pr(OH)3 , Nd(OH)3 , Sm(OH)3 ) and Our calculated and estimated values are in agreement with the calculated values of J. C. Parlebas et al. [ 15 ] and A. Szytula , B. Penc, A. Jezierski [ 16 ]

Reference

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U.S.S.R., Phys. Ser. 26 (1962), 182.
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Mendlowitz; Adv. Electronic and Electro Physics; edited by L.M arton Academic , New York 7 (1955) , 225 .
11. Surendra poonia and S.N.Soni , Indian
journal of pure and applied physics , vol.45, feb.2007 pp-119-126
12. A. M. Bradshaw, Cederbaurn S.L, Domeke
W. & Krause Jour. Phys C: Solid State
Phys. 7, 4503, 1974
13 D. C. Lengreth, Phys. Rev. Letter, 26,
1229, 1971
14. W. J. Pardee, G.D. Mahan, D. E. Eastman, R.A. Pollak, L. Ley, F.R. McFeely, S.P. Kowalczky and D.A. Shirely, Phys. Rev.
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15 J.C.Parlebas et al. , J.Phys. France 51 , (1990) ,

639-650

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16. A. Szytula, B. Penc, A. Jezierski, Materials

Science-Poland, Vol.26, No.3, 2008

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Table -1 Energy sepration AE of Rare Earth compounds

Table -2 Relative Intensity of Rare Earth compounds

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* Reader , Ganpat Salmi Post Graduate College , Sultanpur ,U.P. India

** Associate Professor, Rajarshi Rananjay Sinh Institute of Management & Technology, Amethi , CSJ Nagar, U .P. , India

**E-Mail ID- ajay_gspgcs@rediffmail.com

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