International Journal of Scientific & Engineering Research Volume 2, Issue 6, June-2011 1

ISSN 2229-5518

X-ray Satellites Spectra in the La1 Region of 4d

Transition Elements

Dr. Sameer Sinha, Vinay Kumar Pandey, Ajay Vikram Singh

Abstract- We have used Plasmon theory to explain Energy Satellites and relative intensity of high energy X-ray sat ellit es a3 , a4 & a5 with respect to La1 parent line in 4d Transition Metal ( Zr , Nb , Mo , Ru , Rh ) and estimat ed values are in agreement with the calculated values of Surendra Poornia and S.N.Soni.

Keywords - L a1 X-ray satellites, M vacancy Laotransitions, X-Ray emission spectra.

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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.

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

** Lecturer , Ganpat Sahai 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
** vinay_gspg@rediffmail.com
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 hcop where cop 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 Plasmon theory to explain the Energy Satellites and relative intensity of high energy X-ray satellites with respect to La1 parent line in 4d Transition Metal ( Zr , Nb , Mo , Ru , Rh , Rd ) and estimated values are in agreement with the calculated values of Surendra Poornia and S.N.Soni.

According to Plasmon theory , if the valence electron , before filling the core vacancy , also excites a Plasmon ,then the energy hmp 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 hmp and a low energy satellites will emitted whose sepration from the main X-ray line will correspond to hmp . On the other hand if the Plasmon pre exists , during the X-ray

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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 hmp giving rise to high energy satellite .
Surendra Poornia and S.N.Soni have observed low and
high energy satellite peaks in 4d Transition Metal ( Zr , Nb
, Mo , Ru , Rh , Rd ) A close approximation of their tables shows that some satellites are at a distance of hmp (Plasmon energy ) from the main emission line . This observation forced us to think that these might be due to Plasmons emission and absorption .

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 LE of the low and high energy Plasmon satellite from the corresponding main line should
be equal to the quantum of Plasmon energy hmp which is given by [10]

ev 1

Where Z = No.of unpaired electrons taking part in plasma oscillation
a = Specific gravity
co = 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 = hrop = h

In this equation we can write

n = , 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 LE 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 [11] and Lengreth [12] 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 also suggested by various Authors [12 , 15 , 16 , 17 18 ] as:

i = = an 4

The value of p is taken as p = 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.(13) . 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, p and rs in equation (4)
Using the equation (4), the author has for the first

time, calculated the relative intensity of high energy X-ray satellites with respect to La1 parent line in 4d Transition Metal ( Zr , Nb , Mo , Ru , Rh , Rd ) metals. Our calculated and estimated values are in agreement with the calculated values of Surendra Poonia and S.N.Soni [14].

Reference

1. Korbar H. & Mehlhorn W.A. ; Phys. 191, (1966) 217.
2. Haynes S.K. & Velinsky, M & Velinsky L.J. ; Nucl. Phys. A99 (1967), 537.
3. Rudd M.E. & Edward & Volz, D.J. ; Phys
Rev. 151, (1966), 28.
4. Asaad, W.N. & Burhop E.H.S. ; Proc. Phys.
Soc., London 71, (1958), 369.
5. Listengarten, M.A. ; Bull Acad. Sci. U.S.S.R., Phys. Ser. 26 (1962), 182.
6. Asaad, W.N. ; Nucl. Phy. 66, (1965b), 494.

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7. M.Scrocco in photoemission spectra of Pb.(II) halide; Phys. Rev. B25 (1982) 1535-1540 .
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32 (1985) 1301-1306
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12. D. C. Lengreth, Phys. Rev. Letter, 26,
1229, 1971
13. 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. B, 11, 3614, 1975.
14. Surendra poonia and S.N.Soni , Indian journal of pure and applied physics , vol.45,
feb.2007 pp-119-126
15. S. K. Srivastava, Amar Bahadur, Fizika A,
17, 117, 2008

16. S. K. Srivastava Leonardo Journal of

Sciences , 13 , 39 , 2008.
17. Sameer Sinha & Ajay Vikram Singh , International Journal of Scientific & Engineering Research, Volume 2, Issue 2, April -2011
18. Sameer Sinha & Ajay Vikram Singh , International Journal of Scientific & Engineering Research, Volume 2, Issue 2, February-2011

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Energy sepration AE at La1 satellite of 4-d Transistion element

Relative Intensity of La1 satellite of 4-d Transition element

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