Within the vast field of atomic physics, collisions of heavy ions with atoms define

Transcription

1 Chapter 1 Introduction Within the vast field of atomic physics, collisions of heavy ions with atoms define one of the most active areas of research. In the last decades, the design and construction of accelerators needed for these experiments, as well as the theoretical description of ion-atom collisions has advanced considerably. In an ion-atom collision, an ion or atom with velocity v or energy E impinges on a target, which is usually at rest in the laboratory system. Figure 1.1 shows a classical picture of the collision between the two nuclei, one or both of them carrying bound-state electrons. An important parameter for describing a classical collision is the impact parameter b, which describes the lateral displacement of the asymptotic trajectory at time t from the symmetry axis taken as the z-axis. The plane spanned by the z-axis and the vector b is denoted as the scattering plane. For structureless particles, e.g., point charges, the geometry is axially symmetric around the z-axis, so that, for example, differential cross sections are independent of the azimuthal angle. Of the various fundamental processes occurring during ion-atom collision, the production of core vacancy states, in which one or more of the relatively tightly 1

2 1.1. De-excitation of atoms with vacant inner shell Figure 1.1: Classical trajectory of the projectile in the laboratory system bound target electrons is either excited or ionised. Decay of such highly excited systems is usually studied via measurements of electrons, photons, or both emitted in subsequent relaxation of the state. Study of these processes provides a better insight in to the ion-atom interactions and gives us important information about the (fundamentally many-body) collision interactions themselves, the nature of transient excited states formed, and the relaxation processes by which the ions and atoms return to neutral or charged ground states. 1.1 De-excitation of atoms with vacant inner shell The excited atom with an vacant inner shell relaxes through various processes which can be categorised into two groups viz. (i) non-radiative transition and (ii) radiative transition. A schematic diagram of both the radiative and non radiative transitions are shown in Figure Non-radiative transition In this process the inner-shell vacancy is filled by an electron from the outer shell of the atom and the available energy of transition is used to eject an electron from another loosely bound higher shell. The ejected electron is called the Auger 2

3 1.1. De-excitation of atoms with vacant inner shell Figure 1.2: Schematic diagram for radiative and non-radiative transitions electron and the process is known as Auger process. The term Auger transition is used for transitions in which a vacancy in an atomic shell leads to two vacancies in principal shells other than the shell containing the initial vacancy. The transitions, where one of the two vacancies produced in such decay process is in a different sub-shell of the same principal shell containing the initial vacancy, are called as Coster-Kronig (CK) transitions. Various authors have published the theoretical Auger and Coster-Kronig transition rates for different shells [1-3] The non-radiative width (Γ NR ) can be expressed as the sum of Auger (Γ A ) and Coster Kronig (Γ CK ) widths. Γ NR = Γ A + Γ CK (1.1) 3

4 1.1.2 Radiative transitions 1.1. De-excitation of atoms with vacant inner shell In radiative transitions, the inner-shell vacancy is filled by an electron from outer shell thereby shifting the vacancy of the inner shell to the outer shell and the difference in energy is released in form of x-rays. The emission of x-rays is governed by the following selection rules for allowed electric dipole (E1) transitions; n 1, (1.2) l = ±1, j = 0, ±1. X-ray transitions that violate the electric dipole selection rules are said to be forbidden and have much lower transition rates. The dipole-allowed x-ray transitions to the K and L shells of single-vacancy atoms are shown in Figure 1.3. The probability that an inner vacancy will be filled in an x-ray transition is known as the fluorescence yield (ω). For each excited state of an isolated atom, the fluorescence yield is defined as; ω = Γ R Γ tot, (1.3) where the Γ R and Γ tot represent the radiative and total transition probabilities respectively. Thus the fluorescence yield is the ratio of the number of x-rays emitted to the number of total vacancies created in that shell. The de-excitation of K-shell vacancies is straightforward in that there is only one possible initial state. However, the de-excitation process is complicated for L-shell or higher shell vacancies by two factors: i) shells higher than the K-shell consist of more than one sub-shell and the de-excitation process depends on how the sub-shells are ionised, since different methods of ionization will yield differ- 4

5 1.2. Target inner-shell ionisation studies Figure 1.3: Energy level diagram showing the allowed K and L x-ray transitions for a single-vacancy atom. ent primary vacancy distributions, and ii) The original vacancies in a shell may rearrange through Coster- Kronig transitions. Various data based upon different theoretical models are available in literature for the radiative emission rate of different shells [4-6]. 1.2 Target inner-shell ionisation studies Many details of the atomic excitation accompanying the vacancy production by ion impact can be studied by examining the spectral distributions of the x-ray and Auger electron lines. By summing over all modes of de-excitation, one can obtain a 5

6 1.3. Particle induced x-ray emission (PIXE) number which is proportional to the probability of producing the original vacancy. The x-ray emission is almost completely dominated by one-photon electric dipole radiation. Therefore, the accessible final states are severely restricted by the usual dipole selection rule. Auger emission, on the other hand, proceeds via e 2 /r ij (scalar) interaction repulsion which is unrestricted process, since the ejected electron may in principle have any angular momentum, and thus the number of states accessible to the residual atomic system is unrestricted. These remarks lead to the correct conclusion that the x-ray spectrum should be relatively simple, with the Auger spectrum perhaps richer in information [7]. The majority of inner-shell ionisation cross section data is obtained out of total x-ray production cross sections, since x-ray detector systems are less complex than those of Auger. The x-ray spectrum associated with energetic ion-atom impact can be detected and analysed experimentally by means of conventional nuclear instruments, namely, appropriate detector, preamplifier, amplifier, voltage bias supply, and multi-channel analyser. A high resolution detector is often required. Usually lithium drifted Silicon (Si(Li)) and high purity germanium (HPGe) detectors offer proper detection capability that suits the complex nature of x-ray spectra. Therefore they widely utilised for such measurements. Data is always recorded and transferred from detector system to a computer using suitable interfacial procedure in order to carry out the analysis that involves the analytical fitting of the x-ray spectrum and peak area determinations. 1.3 Particle induced x-ray emission (PIXE) In this process the x-rays are induced by the impact of energetic ions due to the Coulomb interaction between the incident ion and inner-shell bound electron, 6

7 1.4. Trace elemental analysis of forensic samples giving rise to vacancy in the target atom. This vacancy is consequently filled by an outer shell electron, and the atom subsequently de-excites by emitting a characteristic x-ray or an Auger electron. Accordingly, in multi-elemental samples, each element can be traced and identified by referring to its characteristic x-ray lines. The study of x-rays produced by light ions bombardments has received a great impetus by the development of analytical techniques. Protons of energy 2-4 MeV are found to be the most suitable ionising agents to use the PIXE principle as one of the leading multi-elemental analysis technique [8]. Compared to the other excitation processes, PIXE has relatively high cross sections. Therefore, the characteristic x-rays are produced in abundance with relatively low background and only a small amount of sample s material is required for the analysis. Under favourable conditions it is possible to detect 1-2 parts per million over a wide range of elements. This process is classified as non-destructive and surface contaminants, such as oxide layers, do not affect the analysis since PIXE is usually insensitive to elements with Z < 13. For thick target samples one is able to detect through a few micro-meter depth, which is the typical range of light ions in solids, taking into account the energy loss of the ion and self absorption effects. 1.4 Trace elemental analysis of forensic samples Forensic science may be defined as the application of various scientific disciplines to aid the criminal justice system. The primary tools in the investigation of forensic cases have been the observation and the interpretation of physical evidence. Physical evidence may exist in any form or size depending upon the nature and environment of the criminal event. The examination and analysis of physical evidence by the forensic scientist involves the physical or chemical identification of 7

8 1.5. Overview of this work materials to the highest degree of scientific certainty possible with current technology. Often the minute sizes of materials, referred to as trace evidence, are collected from the scene of crime. Elemental analysis of the evidences is one of the most commonly used methods to differentiate and associate them with one another. The analytical technique used for such analysis must be highly sensitive, quite precise and accurate in addition to being fast and non destructive. Mass spectrometry and chromatographic techniques are the most commonly employed for elemental analysis in forensic science [9]. PIXE technique has an edge over these techniques by being non-destructive and mutielemental in nature. In some instances the trace evidence found from the crime scene is to be preserved or to be analysed using different techniques. This type of situation forbids the use of any destructive techniques for their analysis. PIXE technique can be successfully used in cases where some types of physical evidence comparisons are needed to reveal similarities with class characteristics. This means that the evidence can only be associated with a group of similar material and not a unique source. A detailed study and maintenance of a database on a specific type of samples is necessary for the examination and comparison of the physical evidence to reveal unique features, they are referred to as individual characteristics and there may be a high probability of a common source. 1.5 Overview of this work With reference to the above perspectives, studies on the K and L x-ray production and ionisation cross sections of different elements induced by heavy ions were carried out. Using PIXE technique, studies on the elemental profile of gunshot residue (GSR) deposited on target, natural and synthetic gemstones, and Indian 8

9 1.5. Overview of this work banknotes were carried out from a forensic point of view. The second chapter deals with the theoretical descriptions of the inner shell ionization process and a brief account of various models used for understanding of the phenomena. In chapter 3, different aspects of the experimental techniques and facilities used in the present work along with data analysis procedures were discussed. The fourth chapter gives the details on the development of the ion beam analysis setup at Variable Energy Cyclotron (VEC), Chandigarh. In chapter 5, details about the experiment carried out to study the inner-shell x-ray production process are discussed. Chapter 6 contains the detailed description of the PIXE analysis of GSR samples, gemstones and banknotes and their results. The summary and conclusion of this work along with future perspectives are given in chapter 7. 9

10 1.5. Overview of this work References 1. J.H. Scofield, Phys. Rev. A 9 (1974) J.H. Scofield, Phys. Rev. A 10 (1974) M.H. Chen, B. Crasemann and H. Mark, Phys. Rev. A 21 (1980) M.H. Chen, B. Crasemann and H. Mark, Phys. Rev. A 24 (1980) M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) J. L. Campbell, At. Data Nucl. Data Tables 85 (2003) Garcia, J. D., R. J. Fortner, and T. M. Kavangh, Rev. Mod. Phys., 45(1973), S.A.E. Johansson and J.L. Campbell, PIXE: A novel technique for elemental analysis, John Wiley and sons Ltd. (1988) U.K. 9. R. Saferstein, Forensic Science Handbook, Prentice-Hall, Englewood Cliffs, NJ,