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This chapter deals with briefly explanation of experimental setup, the scheme of the technique which is used and the Accelerator.
3.1. Pelletron Accelerator:
Pelletron Accelerator Model 6SDH-2 is a 2 Million Volt tandem electrostatic accelerator  with a horizontal accelerating column. It is capable of accelerating different varieties of ion species where broad ranges of energies are used for PIXE analysis, ion implantation and nuclear physics experiments. The accelerator consists of two ion sources one is (RF) Radio Frequency plasma source and other is (SNICS-2) i.e Source of Negative Ions by using Cesium Sputtering. Currently two beam lines are available and five more beam lines can be installed. Schematic of the Accelerator is shown is the Fig. 3.1.
FIGURE 3.1. Schematic of an electrostatic Pelletron S tandem accelerator (mfd. By National Electrostatics Corp.)
3.2. RF (radio frequency) Plasma Source:
RF plasma source ions are generated from gases. Hydrogen gas is used for singly charge energy and helium gas is used for alpha particles. The source is called an inductively coupled RF ion source. For the extraction of the ions, the approach is used by Thonemann et al.  and consists of a positive W electrode-called the probe at close end of the discharge tube as shown the Fig3.2. Operating the source positive ion beam is extracted from plasma produced in RF source and accelerated into the charge exchange cell where some part of beam is converted to negative ions which are extracted by the accelerator to the desired energy.
Figure3.2: RF Charge Exchange Ion Source
3.3. SNICS (source of negative ions by cesium sputtering)-2 Source:
SNICS-2 was developed at the University of Wisconsin . SNICS-2 is a versatile source that produces negative ions of over 70 different elemental ions can be chosen from the periodic table. It sputter cathode source through extractor and produces ion beam which form stable negative ion. Cs vapor comes out from cesium oven towards the enclosed area between the cooled cathode and the heated ionizing surface as shown in the Fig3.3. Some of cesium condenses and some cesium ionizes by the hot surface. The ionized cesium accelerates towards the cathode by sputtering particles from the cathode through the condensed cesium layer. Hence as a result some material will sputter negative ions. Other materials will preferentially sputter neutral or positive particles which pick up electrons as they pass through the condensed cesium layer producing negative ions.
Fig:3.3 Source of Negative Ion by Cesium Sputtering
The negative ions from the ion sources are first preaccelerated and then guided to the accelerator entrance by the injector magnet. The einzel lens assembly preaccelerates the negative ions from the ion source and focuses them towards the Pelletron tank.
3.4. Pelletron Charging Chain:
This Pelletron tank consists of two pellet chains of metal links with nylon spacers providing a means of establishing the accelerating potential (see Fig.3.4). A 50kV power supply is used to charge an inductor, which pushes electrons off the links to the grounded drive pulley. The links are now positively charged and they move to the terminal shell, a hollow aluminum cylinder which is approximately 1ft in radius and 2 ft in length. Electrons move from the terminal shell to the links by obeying Gauss's law and leaving a net positive charge on the terminal shell . The terminal shell is located near the midpoint of the accelerator body shown in Fig. 3.1.
FIGURE 3.4. Accelerator Charging System (Source: Pelletronï£¨ Accelerator Charging System; http://www.pelletron.com/charging.htm)
3.5. Main Accelerator Unit:
The Pelletron tank of the accelerator consists of a number of accelerating columns on each side of the terminal. Each column consists of a pair of hollow circular aluminum casting supported by ceramic insulators. The central part of the tube is the high-voltage terminal. It is spherical in shape and it is charged by motor driven chains. The induction electrodes induce the charge onto the chain at the base of the tank. This charge is then deposited on the terminal, thereby raising its potential. The high potential terminal is supported by insulating columns consisting of two insulating plates. The ions passing through the terminal are made to pass through the gas stripper which changes the negative ions into positive ions. The positive ions are further accelerated in the accelerator column raising the energy of the beam to (1+q) V.
To stabilization the beam energy, the terminal voltage is stabilized by a feedback system. The feed back signal taken from the capacitive pickoff plate, on the control slit after the analyzing switching magnet, is combined with the absolute voltage signal . The complete accelerator column that contains the charging system and accelerator tube is enclosed within a pressure vessel filled with SF6 gas at a pressure of 80 psi. The SF6 is chosen because of its excellent dielectric strength .
As the ions leave the accelerator tube, they pass through a magnetic quadrupole lens, which focuses the beam to a small diameter (1cm or less). Then the ions enter the beam energy switching magnet.
The beam energy-analyzing magnet works on the principle of bending the trajectory of a charged particle moving through a magnetic field. As we know, a moving charged particle has kinetic energy (Ep) equal to Â½(mv2), where m is the particle's mass and v is the particle's velocity. A charged particle moving through a magnetic field experiences a magnetic force (Fb), which changes the direction of its travel. This change of direction creates a centripetal force (Fc). By equating the two forces, the expression (mv2)/r = qvB is obtained. Solving this equation and also one for kinetic energy for v, we derive the equation, Ep = (qrB)2/(2m), where Ep is the energy of the particle, q is the charge on the particle, m is the particle's mass, B is the strength of the magnetic field, and r is the radius through which the particle's trajectory is bent. 
As the protons exit the switching magnet, they move into the beam line, an evacuated tube connected to the target chamber. The particles moves with the proper trajectory can be determined by their kinetic energy, q/m ratio, and the magnetic fields proceed down the center of the beam line. Before passing through the target chamber, the particle enters from vertical slit which is two horizontal insulated strips. Particles with more or less energy move to the inner or outer edges, respectively, of the beam line, encountering the slit strips in the process. The slit strips, thus, control the beam energy divergence according to the width of the slit opening and also controls the neutron splitting. The particles then proceed to the reaction chamber where they bombard the samples to be analyzed.
3.6. Target Chamber:
The chamber is enclosed by the evacuated (~10-5 Torr) area where the ion beam strikes the target. It is made up of steel provided with windows and ports to yield information about the charged particles. The Si(Li) detector is connected to the beam line through port of the chamber.Fig.3.5 shows the target chamber of PIXE.
Fig.3.5. Target chamber of PIXE analysis.
The targets are usually placed at 45â° to the beam direction. Thick targets are mounted on the target holder placed at the centre of the chamber. The target holder can be move about its axis externally. Since the X-rays are detected by the Si(Li) detector, the chamber is so designed that by using a flange, the end area of the detector can be inserted through the flange so that the distance from the target can be changed. Since the target chamber is highly evacuated (~10âˆ’5 Torr), it is preferable to prepare a rotating target holder on which many different samples can be loaded at any time and one must be in a position to place a particular target facing the beam by moving the target holder from outside manually.
It is not necessary require to vent the vacuum chamber after each sample Run. The target holder assembly is a pyramid type made of stainless steel. The position of the target can be determined from the outer window. The target holder could also be manually rotated from outside in order to orient the targets at the desired angle with respect to the beam direction.
3.7. Detection of X-rays
Hence X-rays are detected by Si(Li) energy dispersive system. Detector type is Nano trace equipped with NORVAR window. The active area of the detector is 30 mm2 and silicon crystal thickness is 3 mm. Aluminum coated window of thickness 0.04 Âµm is equipped with the detector. X-ray pulse processor is a complete detector supply which is connected to the detector with a single cable and it also controls temperature.
The ORTEC Amplifier is used for its excellent performance connected to the pulse processing unit. Data acquisition diagram in Fig.3.6 shows that it acquires the processing unit, pre amplifier and multi channel analyzer (MCA).
Fig 3.6: Block diagram of data acquisition.
3.8. Gupix Software
The software package GUPIX  was used specifically to analyse the PIXE spectra from thick specimens. It provides nonlinear least-squares fitting of the spectrum together with subsequent conversion of the fitted X-ray peak intensities to elemental concentrations with a defined standardization technique involving fundamental parameters and a user determined instrumental constant. Full account was taken of matrix effects and secondary fluorescence contributions in both the spectrum fitting portion and the calculation of concentrations. The GUPIXWIN 2000 version is used in over laboratory.
 R.Hellborg(Ed.) Electrostatic Accelerators Fundamentals and Applications.
 B.Wolf: Handbook of Ion Sources(CRC Press, Boca Raton, 1995).
 P.C Thonemann et al.: Proc. Phys. Soc. 61, 483 (1948).
 G.T. Caskey, R.A.Douglas, H.T. Richards, H.V. Smithe Jr.: Nucl. Instr. Meth. 157, 1 (1978).
 Pelletronï£¨ Accelerator Charging System, http://www.pelletron.com/charging.htm.
 H.R.Verma, Atomic and Nuclear Analytical Methods.
 A.H. Cookson: Proc. IEE A 128, 303 (1981).
 Waldemar H. Scharf, Particle Accelerators- Applications in Technology and Research (Research Studies Press Ltd., Somerset, England, 1988).
 J.A. Maxwell, J.L. Campbell and W.J. Teesdale. Nucl. Instr. and Meth. B 43 (1989) 218.
RESULTS AND DISCUSSIONS
As we know that experimental L-shell X-rays cross section data are scattered through individual publications and some of those are reported only in graphical form. This makes a systematic comparison with theories or among publications rather difficult. Therefore, a complete and systematic study of all available L shell cross sections similar to that performed by Paul and co-workers[1-5] for the k shell, is badly needed.
The experimental data are directly fitted to deduce the empirical L X-ray production cross sections. A comparison is made between the empirical cross sections reported in this work to the empirical ones reported by "Reis and Jesus" [M.A. Reis, A.P. Jesus, Atom. Data Nucl. Data Tables 63 (1996) 6] and also with the corrected ECPSSR theory .
In this field the first contribution is by Orlic et al.  who reported empirical formulas for the calculation of empirical ionization cross sections for protons. Other important contribution as mentioned earlier is reported by Reis and Jesus  who tried to perform the same procedure for the L X-ray production cross sections as done by Paul  for the K lines. Strivay and Weber  reported empirical formula, which is used in this dissertation based on the direct fitting of experimental L X-ray production cross sections.
In this work, I report on the determination of the L X-ray production cross sections by 0.5-3.5MeV proton impact on elements "Tungsten and Gold". L shell X-ray spectrum of the Au is shown in the Fig4.1.
Fig.4.1. X-ray spectrum showing L lines of Au at 1.5 MeV.
To determine reliable, empirical L X-ray production cross sections, the ideal situation is to perform the fitting of the experimental data for each element separately at different proton energies. The database in the present work relies on the compiled experimental data for proton impact is the same as that of Strivay and Weber.
To compare our results, those of Reis and Jesus and of ECPSSR treatment for the first part we calculate them by the sets of coefficients reported by the authors and the second part D.D Cohen corrected ECPSSR values are taken. The deviations or changes between the empirical one graphically shown in Fig 4.2 and 4.3, which explains us the L X-ray production cross sections normalized to their corresponding ECPSSR results as a function of proton beam energy. In this dissertation, I have pointed out the different spread of the data in each case.
FIG 4.2.L X-ray production cross sections from this work compared to those of Reis and Jesus  as a function of the proton energy for W. (Black box symbol shows this work and triangle shows the Reis and Jesus. All these cross sections normalized to their corresponding ECPSSR theory.
FIG 4.3.L X-ray production cross sections from this work compared to those of Reis and Jesus  as a function of the proton energy for Au.
The data numbers which are used for the empirical cross section which contains most of the LÎ± and LÎ² lines because of the fact that LÎ± and LÎ² are the prominent L X-ray lines and corresponding cross sections are measured correctly rather comparing with the LÎ³ lines.
By comparing the empirical approach in this work, I notice that the results reported by the formula agree generally for the LÎ±, LÎ² and LÎ³ lines for the elements W (Z = 74) and Au (Z = 79). The results are compared with theory and with the empirical one are shown in Fig4.4 (a), (b), (c) and (d). The advantage of the empirical method is that it not requires an ECPSSR program.
(i) LÎ± subshell the agreement between our empirical cross sections with Ries and Jesus and also with the theoretical ionization cross sections is excellent for the whole range of the proton energy for both elements W and Au.
(ii) LÎ² subshell the situation is similar to that of the LÎ± subshell for the empirical cross sections. The agreement between the Ries and Jesus of empirical cross sections is quite satisfactory. In contrast, the deviation from the ECPSSR cross sections increases with decreasing proton energy. The empirical cross sections exceed the theoretical ones at 0.5 MeV proton energy.
(iii) LÎ³ subshell the results are less satisfactory as large discrepancies are observed for both elements W and Au. The values of Ries and Jesus are systematically the highest and deviate significantly for Au but are close to the W. On the other hand, our empirical values are closest to those of Ries and Jesus, which are expected to be the most reliable results. In this case it is difficult to draw any conclusion but I believe that the poor agreement observed depends more strongly on the spread of the experimental data than on the number used in the fitting.
FIG.4.4.Plots of LÎ±, LÎ² and LÎ³ subshell ionization cross sections of elements W and Au. The empty boxes are ECPSSR data and the curves are the fitted by the Eq. (2). Fig (a), (b), (c) and Fig (d).
This argument is confirmed by the fact that in spite of the nearly same numbers of experimental data we used for the three L subshells, the results are less and less good when going from LÎ± to LÎ³ subshell. It must be noticed again that although the ECPSSR calculations and the experimental data, they still remain somewhat far to get any agreement with either our empirical cross sections or those reported by the other authors [8 and 12]. This ascertainment points out the need for more studies for better agreements.
In this dissertation, i report on LÎ±, LÎ² and LÎ³ subshells of empirical cross sections for elements with atomic numbers 74 and 79 for protons of energy 0.5-3.5 MeV. However, because of the scattering of the experimental data for the LÎ³ subshell, the theoretical ionization cross sections cannot be deduced as reliable as in the cases of the LÎ± and LÎ² subshells. But on the other hand, Reis and Jesus values for the LÎ± and LÎ² lines are in good agreement with the empirical cross section values for the whole energy range. But situation for the LÎ³ sub shell is still quite uncertain and more work should be done on its improvement.