Chapter 1. In all the measurements/investigations involving basic. phenomenological study as well as application of X-ray emission, the

Transcription

1 Chapter 1 L & M SUBHELL EXCITATION & DE-EXCITATION PROCESSES 1.1 Introduction In all the measurements/investigations involving basic phenomenological study as well as application of X-ray emission, the primary interaction processes and cross-sections thereof are interpreted in terms of energies, intensities and other characteristics of the X-ray lines or group of lines emitted as a result of the initiating process. The process of X-ray emission follows the various vacancy rearrangement processes within the atomic subshells initiated after the creation of primary vacancies in the inner shells. The process of vacancy creation by different methods and subsequent filling through various vacancy rearrangement processes has been discussed in the subsequent sections. 1.2 Creation of Vacancies in Atomic Inner Shells The primary vacancies in the inner shells/subshells of the atoms are created either as a result of some nuclear processes such as internal conversion and orbital electron capture or by interaction of photons (X- 1

2 rays or γ-rays), protons, deuterons, He ions and heavy ions etc. with the inner shell electrons. A brief discussion of the processes is as under: Nuclear Processes Radioactive decay of the nuclei, in particular, Orbital Electron Capture and Internal Conversion, provide readily accessible means for producing atomic inner subshell vacancies Internal Conversion Although, the γ-ray emission is usually the most common mode for nuclear de-excitation, the transitions also occur through internal conversion process. The nuclear excitation energy is directly transferred to an atomic electron rather than emitting a γ-ray photon. This electron is ejected with kinetic energy equal to the excitation energy minus its atomic binding energy. While the K-shell electrons are most likely to be ejected, the electrons in higher shells may also receive the excitation energy. The ejection of electron from the inner shells leaves a vacant electronic site to be filled by electron transitions from higher shells/subshells Orbital Electron Capture As an alternative to the positron emission, the proton-rich nuclei may also transform themselves via the capture of an electron from one of the atomic orbitals resulting in a neutron and a neutrino. e + p n+ν 2

3 If the energy difference between the parent and the daughter nuclei is less than MeV, the positron emission is forbidden and electron capture is the sole decay mode. The capture of the electron leaves a hole in the inner shell which subsequently initiates a series of vacancy rearrangement processes leading to the characteristic X-ray emission or Auger emission Interaction of Projectiles with Inner Shell Electrons When a beam of projectiles like photons and charged particles (viz. electrons, protons, deuterons, He ions, and other heavy ions) strikes the atom, the electrons in the inner atomic shells may be excited to higher shells/subshells on absorption of energy. While the incident photons may be completely absorbed thus initiating subsequent processes, the charged particles transfer their kinetic energy to the inner subshell electrons mainly via inelastic collisions Interaction of Photons with Inner Shell electrons When a photon of energy greater than the binding energy of an electron in a particular shell/subshell interacts with it, it is probable that the incident photon may be completely absorbed and the electron is ejected out leaving behind a vacancy in the shell/subshell. This process is called photo-ionization. The probability of photo-ionization, in a shell/subshell of an element, depends upon the energy of the incident photon, quantum state of the shell/subshell electron and the atomic number of the element. The probability is measured as the photo- 3

4 ionization cross-section of the shell/subshell. Besides photo-ionization, other processes like Compton scattering from bound electrons and the interaction of the photo-electrons and the Compton recoil electrons with the shell/subshell electrons can also create vacancies in the atoms. But, due to their small contribution as compared to the photo-ionization process, these processes can be safely neglected in the study of photon induced X-rays. For creation of inner shell vacancies by photons, three types of sources are commonly used: Radio-isotopes A number of radio-isotopes can provide sufficient intensity of photons (through γ-ray emission and internal conversion, electron capture X-rays) in a wide energy range. These radio-isotopes offer a cheap, stable and compact source of radiation that is well suited for excitation of inner shell electrons. The radio-isotope Mn 54, Fe 55, Zn 65, Sr 85, Cd 109, Sn 113, Hg 203 and Am 241 are commonly used. Some radioisotopes which decay by the modes of electron capture or internal conversion have also been used to investigate the characteristic X-rays of the daughter and the parent element. Unfortunately, there are only few radioactive sources which emit mono-energetic photons of low energy in the X-ray energy region are available. However, the difficulty of nonavailability of low energy photon sources has been overcome by some workers Allawadhi et al. [20] and Sood et al. [21] by using external conversion X-rays for the investigation of atomic inner shell excitation 4

5 and de-excitation process. The external conversion X-rays obtained by irradiating targets of different elements in the range 13 Z 92 with mono-energetic γ-rays from suitable radioactive sources provide a convenient source of nearly mono-energetic photons of variable energy in the range 6 to 100 kev X-ray Tubes The X-ray tubes of different sizes, shapes and geometry with facilities of energy and intensity variation are available which provide good photon sources for the inner shell vacancy production by photoionization. The X-ray tube excitation of inner shell electrons is particularly good where the monochromatic nature of photons is not required Synchrotron photon sources Synchrotron photon sources are characterized by high brightness, high intensity (many orders of magnitude more than that of X-rays produced in conventional X-ray tubes), small angular divergence of the beam and wide tunability in energy/wavelength by monochromatization (sub ev up to the MeV range). Synchrotron excitation [22-23] is very useful in the study of the rates of individual transitions and X-ray lines Interaction of Charged Particles with Inner Shell Electrons When a target is bombarded by charged particles, atoms and molecules in the target are excited or ionized, and incident ions lose their 5

6 energy in the target material by various processes. If inner shells of the atom are ionized, vacancies are produced and consequently, characteristic X-rays or Auger electrons are emitted. The phenomenon of producing X-rays by bombardment of targets with charged particles was first demonstrated by Chadwick [24] in He observed characteristic X-rays of atoms bombarded by α-particles from natural radioactive substances. The probability, that a particular shell/subshell will be ionized by the incident charged particle is defined in terms of the Ionization Cross-section and depends on many factors, namely, the atomic numbers of the target and the projectile, mass of incident projectile and charge state of the incident projectile etc.. Inelastic collisions of charged particles with atoms create innershell vacancies, whose subsequent filling may lead to X-ray emission. X- rays have traditionally been generated by slamming accelerating electrons into the solid targets. One of the main advantages of electron excitation is the easy production of electron beam from electron gun, with controllable energy and intensity. Secondly, greater excitation crosssections for low atomic number targets can be achieved with the electrons. The main disadvantage of electron induced ionization is the presence of continuous radiation (bremsstrahlung) which results from the interaction of incident electrons with the target nuclear field. Besides this, the specimen heating and deterioration after long exposure as well as the low penetrating power limit the electrons' use as exciting 6

7 projectiles. If the projectiles are charged sub-atomic particles which are heavier than the electron, or if they are ions whose atomic number Z1 is small as compared to the target atomic number Z2 (i.e. light ions like protons, deuterons & He ions etc.), then coulomb excitation dominates the inner shell vacancy production through (direct) ionization to the continuum of the target atom, or by electron capture into an unoccupied state of the projectile [25]. Excitation by heavy ions differ in phenomenology from excitation by electrons & light ions due to interaction between electron shells of two colliding atomic centers, showing large cross-sections. In case of heavy ion bombardment, one may observe transitions from both, the projectile and the target atom. Further, the target atoms may acquire significant recoil velocities. Another phenomenon of molecular excitation is observed when incident ion and the target atom are of comparable atomic number. The light and heavy ion excitation offers an advantage over the photon or electron excitation. Due to greater mass of these projectiles as compared to electrons, they are not much deflected or decelerated by the target atom and as a result, the bremsstrahlung continuum in the X-ray spectrum is greatly reduced. 1.3 Processes Initiated After Creation of Primary Vacancies in Inner Shells When vacancies are created in inner shells either by some radioactive process (e.g. internal conversion or orbital electron capture) 7

8 or by bombardment of target elements by photons or charged particles as explained above, many processes are initiated. The excited atom tends to attain minimum potential energy state with the initiation of vacancy transfer processes through various modes of decay in a very short interval of time of the order of to seconds. This process of returning of the atom to its ground state electronic configuration is called De-excitation. The filling up of a vacancy in an atomic inner shell involves a series of rearrangement processes leading to additional/redistributed secondary vacancies, particularly in higher shells. In K shell, these vacancies are filled up by transitions from higher shells leading to either X-ray emission (radiative process) or Auger electron emission [26-27] (non-radiative process). In the shells above K shell (L, M and higher shells), in addition to the creation of primary vacancies as above, some additional processes are involved which modify these primary vacancies by transfer of electrons either among the different subshells of the same shell (Intra-shell Vacancy Transfer Processes) or by the transfer of vacancies from other shells (Inter-shell Vacancy Transfer Processes). It is clear that these modifications in the primary vacancies are made in the shells above the K shell Inter-shell Vacancy Transfer Processes The discussion has been divided in two parts: (1) For K Shell and (2) For L, M and higher Shells: 8

9 Vacancy transfer processes for K shell In the case of K shell, following the loss of K-shell electron as a result of processes discussed in section 1.2, one of the higher shell electrons will fall in to the vacated orbital followed by the emission of either a K X-ray photon (radiative transfer) or an Auger electron (nonradiative transfer) from one of the higher shells. In the radiative transfer process, a vacancy in the inner shell is filled by the jump of an electron from the higher shell and the difference in energy of two shells/subshells is emitted in the form of characteristic X-rays. These radiative transitions, which obey a definite set of selection rules are called diagram/allowed lines. These normal radiative transitions are found to obey the following set of selection rules. n 1 l = ± 1 (1.1) j = ± 1 or 0 Where n, l and j are the changes in principle, orbital and the total angular momentum quantum numbers, respectively, of the electron undergoing transition. Figure 1.1 shows some of the X-ray transitions under K, L and M series. The table 1.1 shows the Siegbahn and the latest IUPAC [28] nomenclature for X-ray transitions of the K, L and M series and the correspondence between the two systems. The transitions which don t obey these selection rules are called Forbidden or Non-Diagram transitions. 9

10 Figure 1. 1 Some of the K, L and M series X-ray transitions and related subshell parameters. 10

11 Table 1. 1 Nomenclature [28] for X-ray transitions of the K, L and M series The other type of radiative transitions which may result from the de-excitation process, are satellite lines. The satellite lines are due to additional electron vacancy in a doubly ionized atom. Due to the absence of second electron, the energy levels shift to higher energy side (relative to those of singly ionized atom) due to reduced Coulomb screening. As a result, single electron transitions in such atoms (doubly ionized) are on slightly higher energy side compared to those in singly ionized atoms. As the probability of simultaneous creation of two electron vacancies in an atom is much smaller than that of single vacancy, the 11

12 intensity of satellite lines is much less than that of normal lines. Because, the most dominant mode of de-excitation of vacancy states through radiative transitions is allowed transitions, so, the diagram lines constitute the major part of the X-ray spectrum. Satellite lines & Forbidden lines constitute only the small part of X-ray spectra and are not of any significance. The radiative filling of the vacancies is interpreted in terms of the Fluorescence yields for the shell/subshell in which the vacancy resides. Barkla [29], in 1918, introduced the concept of Fluorescence Yield defining it as the ratio of energy carried by the fluorescent radiation to the energy carried by the radiation absorbed in the sample. More recently, it has been defined in terms of probability that a vacancy in the given shell results in a radiative transition. The fluorescence yield of the ith subshell of the X shell of an atom, ωxi, is the probability that a vacancy in that subshell is filled by a radiative transition. If ΓXi is the total width of an excited state related to its mean life τ as Γ = ħ τ and is also equal to the sum of radiative width R Γ Xi and non-radiative width subshell of the X th shell is defined as NR Γ Xi, the fluorescence yield ω Xi for the i th Xi R Xi Γ ω = (1.2) Γ Xi where R NR Xi Xi Xi Γ = Γ +Γ For K shell (having only one subshell), the fluorescence yield is 12

13 simply given as: ω = I n (1.3) K K K Where, IK is the total number of characteristic X-rays photons emitted from the K shell and nk is the total number of primary vacancies in the K shell. The existence of more than one subshell with different sets of primary vacancies (depending upon the method of ionization) and the presence of additional decay channels complicate the definition of fluorescence yield in case of L & M shells, which is detailed in next section. Another parameter associated with the radiative filling of the vacancies is the Radiative Decay Rate. The Radiative fraction of the total rate of decay of an excited state is known as radiative decay rate of the transition. As already discussed, the mean life time τ of an atomic state is related to energy width Γ of an atomic state through Heisenberg s uncertainty principle ( Γ τ =ħ). The decay probability (per unit time) of a state is therefore, 1 τ =Γħ. If we denote ΓR(i), ΓA(i) & ΓCK(i) as radiative decay probability, Auger decay probability and the Coster Kronig decay probability, then we have the total width Γ i = Γ R (i) + Γ A (i) + Γ CK (i) (1.4) The fluorescence yield of the i th state is ΓR (i) ω i = (1.5) Γ (i) + Γ (i) + Γ (i) R A CK 13

14 The X-rays emitted as a result of radiative filling of vacancies are estimated in terms of X-ray production cross-sections. The X-ray production cross-section is the probability of emission of X-rays as a result of the primary ionization process. These can be defined for K shell as the product of ionization cross-section σk i and the fluorescence yield ωk as X i K K K σ = σ ω (1.6) Further, the cross-sections for the emission of experimentally observable X-ray lines/groups, e.g. Kα, can be estimated by taking the fractional intensities (FKα) of the concerned X-ray in to account. X i Kα K K F Kα σ = σ ω (1.7) In the higher shells with more than one subshell, the effect of vacancy shifting due to other rearrangement process has to be taken in to account while defining the total or partial X-ray production crosssections. In the non radiative transfer (Auger) process, an inner shell vacancy is filled by an electron from an outer shell and the excess energy instead of being emitted as a photon, is consumed in ejecting out a second electron (called Auger electron) from the atom. This is a radiation less process leading to double ionization Vacancy transfer for L, M and higher Shells In case of K-shell, as mentioned above, the X-rays production will be purely due to the primary vacancies only. In case of L, M and higher 14

15 shells, the case becomes a lot different from that of the K-shell. In case of these shells, some additional processes are involved which modify the initial vacancy distribution among various subshells. In case of L & M shell (for example), besides the primary vacancies produced in Li (Mi) subshells due to primary ionization processes, the secondary vacancies may be produced through transitions from lower shells. The vacancy rearrangement processes, in their bid to fill the K-shell vacancies, tend to create additional secondary vacant electronic states in the higher atomic subshells viz. L, M & higher subshells before their original vacant states are filled by electron transitions from higher shells. Both, the radiative (X-ray emission) transfer as well as the non-radiative Auger process contribute to this class of Li & Mi subshell vacancies that appear at the second stage of the cascade of events initiated with creation of a vacancy in the shells with lesser value of n, the principal quantum number. Nonradiative filling of K vacancies with L-shell electrons falls in two categories; K-LL transitions, in which one electron from an Li subshell fills the K-shell vacancy while the excess energy is carried away by another L-subshell electron and K-LX transition, in which the ejected electron is from an outer shell (M, N,....). In both the cases, atom is left in doubly ionized state. The inter-shell vacancy transfer probability is defined as the probability that a vacancy in the K(L) shell is filled by the L(M) shell electron with the binding energy difference either being emitted as an X- 15

16 ray photon or transferred to an electron in the higher shell, which is ejected. For K to L transfer, the number of Li vacancies, η KLi created in the filling of a K-shell vacancy by an electron from an Li subshell can be written [30, 2] as the sum of two parts, η KLi (R) due to radiative transitions and η KLi (A) due to Auger transitions: η = η (R) + η (A) (1.8) KLi KLi KLi The fraction of vacancies shifting from K-to-M shell and L-to-M shell can be similarly estimated in terms of η KMj & η LiMj (where 1 i 3 and 1 j 5) Intra-shell Vacancy Transfer Processes Other processes, responsible for rearrangement of inner shell vacancies owing to redistribution among the subshells of the same shell (intra-shell), are the Coster-Kronig transfer and the Super Coster-Kronig transfer. These processes apply on L, M and higher shells only. Whenever energetically allowed, the CK (Coster-Kronig) & the SCK (Super Coster- Kronig) transitions shift the vacancies to the higher subshells within the L & M shells in a short interval of the order of seconds. Coster & Kronig [31] discovered these radiationless transitions among L subshells through the study of satellite lines in the X-ray emission spectra. These transitions do not compete with the Auger or radiative transitions due to very large difference in their decay times. In the CK process, the vacancy transition is between two levels with same 16

17 principle quantum number (i.e. within the same shell; n = 0) and an electron from some outer shell (different n) is ejected out. Another nonradiative process that presents itself as a decay channel for the inner shell vacancies, if energetically allowed, is the Super Coster-Kronig (SCK) process. It involves the transition, wherein, not only the vacancy transition is within the same shell ( n = 0 as in a CK transition), but the electron is also ejected out from the same shell. The probability that a vacancy in the i th subshell of a shell is filled by an electron transition from higher subshell j th of the same shell with the removal of a higher shell electron is estimated as the Coster-Kronig yield fij. The Super Coster-Kronig yields, represented by SMij, give the probability that an electron from the Mj subshell shifts to a lower Mi subshell and the binding energy difference is consumed in removing an Mk electron such that k > i, j. The presence of these radiationless transitions alter the initial distribution of primary vacancies in Li & Mi subshells and they must be taken in to account while computing individual subshell fluorescence yields from the measured average yields for the whole shell. The mean fluorescence yield of the shell X, ω X, which is an experimentally measurable quantity, can be written as the linear combination of the subshell fluorescence yields ω Xi for all the k subshells as follows: k X X Vi Xi i= 1 ω = ω (1.9) 17

18 Here, the coefficients Vi X denote the relative number of vacancies in the subshells Xi including the vacancies shifted to each subshell by CK transitions. The quantities Vi X obey the relation k i= 1 X i V > 1, because some of the vacancies created in subshells below Xi would be counted more than once as the CK transitions shift them to higher subshells. X V i can be written generally in terms of relative number X N i of primary vacancies as: V X X 1 = N1 X X X X 2 = V N f N X X X X X X X X 3 = V N f N (f f f ) N (1.10) X X X X X X X X k = k + k 1, k k k 2, k + k 2, k 1 k 1, k 1 V N f N... (f f f ) N X X X X X X X 1k 12 2k k (f + f f + f f f +...) N In the absence of the CK transitions, the vacancy distribution in the subshells of a shell is proportional to their ionization cross-sections only. Thus, the average fluorescence yield ω L(M) for the L and M shells is given by 3(5) ω L(M) = N ω (i = 1 3 for Lshellandi = 1 5for Mshell) (1.11) i= 1 L(M) i L(M)i Where L(M) N i is the fractional number of primary vacancies in the i th subshell such that 3/5 L(M) N = 1 and ω L(M)i is the subshell fluorescence yield of the i th subshell. i i 18

19 It is worth mentioning here that in some regions of the periodic table, some CK transition probabilities vanish (due to energetically forbidden transitions). The table 1.2 signifies the appearance (onset) of CK transitions in different Z-regions [32]. Table 1. 2 Regions of atomic numbers where strong Coster-Kronig transitions are energetically possible Transition Z-region Transition Z-region L1 L2O(P,.) All Z, where O-, Levels are occupied L1-L2M4 21 Z 40 L1-L2N1 19 Z 70 L1-L2M5 26 Z 41 L1-L2N2 31 Z 76 L1-L3N (O,P,...) All Z, where N-, Levels are occupied L1-L2N3 33 Z 81 L1-L3M1 11 Z 31 L1-L2N4 39 Z 91 L1-L3M2 13 Z 35 L1-L2N5 Z 42 L1-L3M3 15 Z 36 L1-L2N6 Z 58 L1-L3M4 21 Z 49, Z 77 L1-L2N7 Z 63 L1-L3M5 26 Z 50, Z 74 L1-L2M1 11 Z 29 L2-L3N (O,.) All Z, where N-, Levels are occupied L1-L2M2 13 Z 32 L2-L3M4 26 Z 30 L1-L2M3 15 Z 33 L2-L3M5 26 Z 30, Z 91 19

20 1.4 Review and present status of parameters relating to the creation of primary vacancies in inner shells and the processes initiated in L and M shells thereafter The parameters related to the creation of primary vacancies following interaction of inner shell electrons with those of photons, protons, deuterons and He ions etc. can be classified in to two categories; viz. Inner Shell Excitation parameters and the Inner Shell De-excitation parameters. The first category of parameters include the Ionization Cross-sections for photons and charged particles while the second category includes the parameters associated with various vacancy rearrangement processes leading to L and M shell X-ray/Auger electron emission i.e. the Inter Shell Vacancy Transfer Probabilities, the L and M Subshell Fluorescence Yields, L and M Shell CK Transition Probabilities,, the L and M subshell Radiative Decay Rates, L and M Subshell X-ray Production Cross-sections, and the X-ray Intensity Ratios etc. The subsequent subsections elaborate on the status of theoretical as well as experimental work related to these excitation and de-excitation parameters Photoionization Cross-Sections A number of calculations of photoionization cross-sections using different assumptions and approximations have been made by different workers [33-42]. The shell wise calculations in energy region from 1 to 100 kev have been made by Rakavy & Ron [37], Schmickley & Pratt [38], 20

21 Brysk & Zerby [39] and Storm & Israel [40]. The quantum mechanics of this process has been worked out in considerable details by Pratt et al. [41] following the non-relativistic calculations of photoionization crosssections using Hartree-Slater model by McGuire [42]. Subshell wise calculations of photoionization cross-sections have been made by Scofield [43] using relativistic Hartree-Slater potential for atoms with Z from 1 to 101 for photons of energy ranging from 1 to 1500 kev. The photoionization cross-sections have been measured by direct or indirect methods at various photon energies ranging from 10 to 1500 kev for different elements. Variety of experimental data is available for atomic K and L subshells, while, the measurements on M and higher shells are scanty. Most of the initial measurements have been compiled by Pratt [44]. The M shell/subshell X-ray measurements published more recently include M shell X-ray production measurements for heavy elements by 5.96 kev-12 kev photons [45-48] and M subshell X-ray measurements by 5.96 kev photons [49]. In general, an agreement exists between experiment and theory within the uncertainties of measurements Ionization and X-ray Production Cross-sections for Charged Particle Impact Inner shell vacancy production by direct coulomb interaction between a projectile ion and the target electron has been studied by using different models; The binary encounter approximation (BEA) by Garcia & co-workers [50-52], Semi-Classical Approximation (SCA) by 21

22 Bang & Hansteen [53] and the Plane Wave Born Approximation (PWBA) by Merzbacher & Lewis [54]. These models describe the situation where the ion atomic number is much smaller than the target atomic number and for ion velocities of a few MeV/a.m.u.. For inner shell ionization induced by a slow & heavy projectile ion moving with velocity less than the target electron Bohr velocity, the direct ionization theories need to be modified. Brandt and coworkers [55-57] recognizing this problem, resolved the order of magnitude discrepancies between predictions of PWBA or the SCA with straight line trajectories, and the experimental ionization cross-sections. This was done by inclusion of two effects that were absent on the PWBA; (i) the coulomb repulsion (C) of the projectile by the target nucleus that leads to retardation and deflection from the straight line paths during collision, and (ii) the increase in binding energy of the inner shell electron to be ionized due to proximity of the ionizing particle. Increased binding was incorporated in the framework of the Perturbed Stationary State (PSS) theory and jointly, the approach was referred to as CPSS theory [56]. The incorporation of relativistic correction, which becomes increasingly important with decreasing projectile velocity, resulted in the CPSSR theory [25]. Later on, Brandt & Lapicky [58] introduced another factor to account for the finite kinetic energy loss suffered by the projectile in the inner shell excitation process. A result of all these modifications in the PWBA led to the ECPSSR theory. Another modification of the PWBA theory is the RPWBA-BC, i.e. 22

23 relativistic PWBA model with corrections for modified electron binding energy and coulomb deflection effects [59-60]. Out of the two, the ECPSSR approximation has become the most successful theory for predicting inner shell ionization cross-section for ion impact on most targets. This theory has been found to give more accurate results where ratio of ion atomic number to the target atomic number is less than 0.3. Initial tabulations for the ionization cross-sections are generally given in terms of reduced electron binding and ion energy parameters (e.g. Benka and Kropf [61] for protons and Rice et al. [62] for heavy ions). In order to obtain the ECPSSR cross-sections from quoted parameters, additional calculations are required. Cohen and Harrigan [63] produced tabulations for the K and L shell ECPSSR cross-sections for protons and He ions. These tables for protons cover the energy range from 100 kev to 10 MeV for targets between C and Am for K shell and Li subshell ionization cross-sections. Their values of cross-sections differ in two areas from the ECPSSR theory given by Brandt and Lapicky [25, 58]. Firstly, Cohen and Harrigan replaced the ion velocity by its relativistic form to account for small relativistic ion velocity corrections. Secondly, they used the exact limits of the integral in PWBA ionization crosssection and therefore, did not factor out Brandt and Lapicky energy loss correction for the K and L shells equal to unity. The tabulation of K & L subshell ionization cross-sections for the light ions and most of the 23

24 targets using ECPSSR theory was augmented by Cohen [64] with his calculations for deuteron bombardment. Regarding M subshell ionization cross-sections, to the best of our knowledge, no ECPSSR tabulation is available in the literature. However, the ISICS (Inner-Shell Ionization Cross-Sections) program written by Liu & Cipolla [65] and further developed by Sam J. Cipolla [66-67] proves to be a versatile and fast tool to exactly calculate subshell ionization crosssections by various projectiles using the ECPSSR theory. The latest version offers the user options for including the United Atom modification to ECPSSR and a scaling function correction for the K shell calculations to correct for the relativistic DHS nature of the K shell. There is also an option, whether to include the modification of the ECPSSR theory proposed by Cohen and Harrigan [63], as discussed above, which has been opposed by Lapicky [68]. On the experimental side, the first successful experiment was performed by Gerthsen & Reusse [69] with protons as projectiles. They used Geiger counters to observe K radiation from Al & Mg and L radiation from Se using 40 to 150 kev protons. Cork, in 1941 [70], used deuterons with energies up to 10 MeV and examined the blackening of photographic plates by X-rays from 38 elements. He observed that crosssections increased with increase in energy of deuterons and decrease in target atomic number. Garcia et al. [71] have reviewed the status of theoretical as well as experimental work related to atomic inner shell 24

25 vacancy creation by collision of atoms & ions. In this work, the X-ray production measurements related to protons, deuterons and alpha particles till April, 1972 have been tabulated and analysed. Sokhi and Crumpton [72], in 1984, published a compilation of data for L-shell X-ray production and ionization by protons from 1975 to November This set of values has further been extended by Orlic et al. [73] in They have tabulated the results of experiments related to proton induced L shell X-ray production & ionization cross-sections published in the period between 1982 and For L subshell X-ray production by protons, some more experimental results have been published for energy regions MeV [74-80] and MeV [81]. More recently, Cipolla [82] has measured L subshell X-ray production cross-section for proton impact on thick targets of some 4d transition elements in the energy range kev using ultra-thin window Si(Li) detector. Regarding ionization by He ion bombardment, one of the initial works is that of Braziewicz et al. [83]. They have studied the individual X- ray line & total L X-ray production cross-sections for elements with 47 Z 83 at incident He ion energies of 1.5 to 3.8 MeV using thin targets. They have discussed the influence of collisionally-induced alignment on measured cross-sections. McNeir et al. [84] have reported L X-ray production cross-sections in low atomic number elements (Z=26-32) by 0.5 to 8 MeV He ions. They have used thin targets manufactured using a cleaning process that reduced the level of light element impurities with a 25

26 windowless Si(Li) detector. Yu et al. [85] have published L subshell X-ray production measurements for Lanthanides using 1-5 MeV helium ions. They have used very thin foils as targets and the X-ray yields were measured simultaneously with elastically scattered ions. More recent measurements have been reported by Awaya et al. [86] who have studied multiple K- and L-shell ionizations of low atomic number targets (Cr, Ti, Fe, Ni, Y, V, Cu) with high energy ions. To the best of our knowledge, experimental values for the deuteron induced X-ray measurements for the L shell have not been reported. Jaskola et al. [87], who have reported M X-ray production cross-sections for 0.2 to 2 MeV deuterons with selected elements between Ta & Th as targets, also support our observation. Owing to the complexities involved in the experimentation & analysis, comparatively lesser work has been undertaken in case of M shell for protons as projectiles. Jopson et al. [88] were the pioneers in the measurement of M X-rays induced by protons. They used thick targets of heavy elements with incident proton energy range of kev. They were followed by a systematic study of total M X-ray production crosssections by Needham et al. [89-90] using thick targets of Z = with different projectiles including protons. Ishii et al. [91] have reported M shell ionization measurements for Pb, Au & U using protons & He ions in the energy regions MeV & MeV respectively. In a more refined measurement, Sarkar et al. [92] have reported M shell X-ray 26

27 production cross-sections for various M X-ray groups in elements with Z=62-79 at incident proton energies ranging from 250 to 400 kev using thin targets. Braich et al. [93-94] have reported M subshell X-ray production cross-section measurements in Pb, Bi and Au by 1 to 5 MeV proton impact. They have attributed the discrepancies in experimental & theoretical results to multiple ionization process which changes the values of atomic parameters. Amirabadi et al. [95] have, for the first time, reported total M shell experimental X-ray production cross-sections of Hg for protons of energy MeV. Yeshpal & Tribedi [16] have studied M subshell X-ray production in Gold by MeV protons and other ions. More recently, Phinney et al. [96] have studied M subshell X-ray production by MeV protons and MeV helium ions for Thorium and Uranium with ultra-thin polymer window Si(Li) detector, They have reported deviation of the theoretical predictions from the measured experimental results L subshell X-ray Intensity Ratios The accurately determined L subshell X-ray intensity ratios are important for their wide use in the field of non-destructive testing, medical research and trace elemental analysis using PIXE and electronic structure studies of the materials [15]. These X-ray intensity ratios depend strongly on the L subshell vacancy distribution as well as on the radiative decay rates. In the X-ray experiments, the uncertainties involved in the parameters like geometrical efficiency, beam currents and 27

28 target self-absorption correction etc. can be reduced if relative intensities are measured instead of absolute X-ray production cross-sections due to (i) factors like geometrical efficiency & corrections for absorption of X- rays between target and detector get cancelled out, (ii) the need for beam current measurements is eliminated. These ratios are, thus, more precise and reliable than the cross-sections. The intensity ratios represent the intensity of various group of lines relative to the Lα group and are denoted by I(L α )/I(Ll), I(L α )/I(L β ) and I(L α )/I(L γ ). Experimental values of L subshell Intensity ratios using photo-ionization have been reported by Chang & Su [97], Shatendra et al. [98] Garg et al. [99-100], Kahlon et al. [101], Rao et al. [ ], Ertugrul et al. [ ], Allawadhi et al. [106], Baydas et al. [107], Gurol & Karabulut [108] and Oz et al. [109], while Close et al. [110], Datz et al. [111], Benka et al. [112], Cohen [113], Sokhi & Crumpton [114], Jesus et al. [115], Xu & Xu [116], Hallak [ ] have studied L subshell X-ray Intensity ratios for L X-rays induced by charged particles. These studies have been limited to the elements with atomic number 56 Z L & M Subshell Fluorescence Yields & Coster Kronig Transition Probabilities The first theoretical calculations of fluorescence yield and CK transition probabilities were made by Wentzel [119]. The references to various calculations made by different workers prior to 1970 are included in the review article by Bambynek et al. [13] on this subject. 28

29 The computation of accurate theoretical values of these parameters using different atomic models and wave functions became possible in early 70 s, only after the high speed computers became available. The major part of the calculations of these parameters is due to McGuire [ ], Koustron et al. [122], Walters & Bhalla [123], Chen et. al. [ ] and Crasemann et al. [127]. A survey of literature reveals that these parameters related to K shell have been very well explored [2, ] for most of the elements with Z > 5, but the measurements of L & M shell/subshell fluorescence yields and CK transition probabilities [2, 13, 132] are still less dependable owing to absence of conformity to the theoretical models and less refined experimental techniques. The data for the M subshell yields are really scanty. Krause et al. [133] carried out a semi-empirical compilation of atomic Li subshell X-ray fluorescence yields ωi (i=1, 2, 3), Auger transition yields ai and CK yields f12, f13, f23 for the elements with atomic number Z=12-110, in which the assessment of the Li subshell yields was mainly based on some existing theoretical calculations pertaining to singly ionized atoms because only a few experimental data were available at that time. On the theoretical side, Chen et al. [126], in their widely referenced paper have presented IPM values (based on DHS calculations) of these six L sub shell quantities. They performed ab initio relativistic calculation of the yields for the selected atoms with 18 Z 100 by resorting to perturbation theory with the Dirac-Hartree-Slater (DHS) 29

30 wave function. Puri et al. [134] have presented the values of fluorescence yields & CK transition probabilities for all elements with 25 Z 96 from the DHS based radiative emission rates given by Scofield [135] and nonradiative emission rates obtained by interpolating the DHS based Chen et al. s [136] values of non-radiative emission rates. Many experiments were conducted by various workers in the two decades from 1980 to 2002 and values of L subshell CK yields & Fluorescence yields based on radionuclide based photo-ionization using γ-rays from a radioactive source [3, ] & secondary K X-rays from primary target [ ], L X-ray K X-ray coincidence experiments [ ] and Photo-ionization using monochromatic synchrotron radiation [22, , 23, 161] were reported. With the advancement in technology, significant improvement in experimental methods for measurement of these atomic parameters has been achieved. Improved analytical techniques have facilitated the incorporation of various corrections in the interpretations of these experiments [162]. Hubbel et al. [128] have tabulated K, L, M and higher shell atomic X-ray fluorescence yields, fitted to standard empirical parametric formulations. In his review paper, Campbell [162] has critically analyzed the recent data regarding CK transitions and fluorescence yields based on radio-nuclide, synchrotron radiation measurements and the theoretical values. He has recommended values for the atomic numbers for which there was significant density of data points recorded by more 30

31 than one experimental method. More recent contribution to the fluorescence yields and CK yields data has been made for some elements in the atomic number 56 Z 92 based on the radionuclide photoionization studies [ ]. The new results for the L1 subshell parameters using radionuclide ionization have been incorporated by Campbell [169] in his latest compilation of L1 subshell data. He has also incorporated one synchrotron based data source that was left in previous compilation owing to a missing electron correlation correction, which needs further work for clarification. The uncertainties quoted in the paper [169] have stopped us from incorporating the new recommended values. We agree with Campbell s [169] view that there is a need for more refined experimental measurements related to L1 subshell to bring down the uncertainties. M subshell fluorescence yields & CK yields values are really scarce [ ]. Purely theoretical values based on two models are available in literature. One is by McGuire [176], in which the Mi (i = 1 3) subshell yields have been tabulated for 30 elements with 20 Z 92 and Mi (i = 4,5) subshell yields have been tabulated for 20 elements with 32 Z 92 on the basis of NRHS wave functions with Herman Skillman potential. In the second set, Chen & Crasemann have tabulated the relativistic Dirac Hartree Slater (RDHS) model-based Mi (i = 1 3) subshell yields for 10 elements with 67 Z 95 [177] and Mi (i = 4,5) subshell yields for eight elements with 70 Z 100 [178]. In 2002, Sogut et al. [179] presented 31

32 the values for Mi subshell fluorescence yields and CK transition probabilities for 20 Z 90. They obtained the values by using least squares fitted to obtain polynomials, which were plotted by using the McGuire s [176] values, representing them as a function of atomic number. More recently, Yogeshwar Chauhan & Sanjeev Puri [180] have tabulated the CK yields & Fluorescence yields for all the elements with 67 Z 92 by interpolating the Direc-Hartree-Slater (DHS) model based values [ ]. They have also presented another set of Mi subshell fluorescence yields by incorporating the DF (Dirac-Fock) based radiative widths [ ] with DHS model [ ] based recalculated nonradiative widths for 67 Z Radiative Decay Rates for L and M subshells For the radiative decay rates, the first calculation, incorporating the relativistic calculations dates back to 1936 by Massey and Burhop [183]. Later on, the contributions to this effect were also made by Payne & Levinger [184], Laskar [185], Taylor & Payne [186], Babuskin [187], Krishnan & Nigam [188], McGuire [189, , 190] and Bhalla [ ]. An extensive theoretical tabulation of the K & Li subshells X-ray emission rates was derived by Scofield using Dirac-Hartree-Slater (DHS) model [135] while accounting the finite extent of nuclear charge distributions for the range of elements Z = 5 to 104 and based on relativistic Dirac Fock model [ ] for 21 elements in the range Z = 18 to 94. Campbell & Wang [198] completed the tabulation of two- 32

33 potential L subshell X-ray emission rates for all elements in the range 18 Z 94 using interpolation procedures on the Scofield s DF values. For M subshell X-ray emission, Bhalla [191] has computed the radiative decay rates based on the relativistic Hartree-Fock-Slater model for six elements only in the range 48 Z 93, while, Chen & Crasemann [181] have presented relativistic Dirac-Fock model based values for 10 elements in the range 48 Z 92. The radiative decay rates of N shell/subshells have also been calculated by McGuire [190] for some elements in the range 35 Z 103. On the experimental side, some measurements of radiative decay rates derived from the relative X-ray intensity measurements [30, ] have been reported by some workers for K and L shell. In the case of K shell, it is easy to derive the values, but in case of L and M shells, the intra-shell vacancy transfer makes the derivation difficult. The values of these parameters derived from the relative L X-ray intensity measurements and branching ratio contain large errors Inter Shell Vacancy Transfer Probabilities Regarding the probabilities of L shell vacancy creation following the decay of K shell vacancy, the theoretical calculations were published in the form of graphs by Robinson & Fink [ ], Wapstra et al. [213], and Listengarten [ ] in the period between In 1971, McGuire [121] computed the average number of M shell vacancies ηlim, 33

34 arising from the decay of Li subshell vacancy and has tabulated these values for some elements with 50 Z 90. Later, in 1972, Rao et al. [30] calculated, semi-empirically, the probability of shifting of a K shell vacancy to Li subshells, ηkli, from a comprehensive set of available data on radiative and Auger transition rates for the elements 20 Z 94. They have also studied M shell vacancy production in the decay of K and Li vacancies for selected elements with 16 Z 93. Puri et al. [216] have reported measurements of K to L shell vacancy transfer probabilities (ηkl) for some elements in the atomic number range 37 Z 42. Ertugrul et al. [217] have measured K to L shell vacancy transfer probability (nkl) in some elements with atomic number 73 Z 92. Radiative vacancy transfer probabilities from K to L2, L3 and M shell have been deduced by Durak & Ozdemir [218] for the selected elements from Nd to Pb using K X-rays. Simsek [4] has reported L3 to M, N shell radiative vacancy transfer probabilities for Pb, Th & U by using selective ionization of L3 subshell. Another work related to probabilities of radiative vacancy transfer Li to M, N and higher shells was published by Sharma et al. [219] for elements with atomic number 77 Z 92 using radioisotope excitation. More recently, L3 to M and N shell radiative vacancy transfer probabilities have been deduced for W, Re & Pb targets excited using monochromatic synchrotron radiation by Bonzi [220]. Chauhan et al. [221] have published average vacancy transfer probabilities from the K 34

35 shell and Li (i=1-3) subshells to all Mj (j=1-5) subshells for selected elements in the range 67 Z Conclusion & Scope of the Work When vacancies in the inner shells are created by any of the processes discussed in section 1.2, the X-rays resulting from these primary vacancies contain information on the concerned process responsible for creation of vacancy [1]. However, it is seen that in all shells above K shell, some processes, faster in time, alter the initial primary vacancy distribution in different subshells of a shell before these vacancies are filled either through X-ray emission or Auger process. Due to these alterations, the emitted X-ray line/group may not directly reveal the information about the primary interaction process. The processes initiated after the primary vacancy creation, which result in alteration of the primary vacancy distribution in L and higher subshells, include the following. The primary vacancies in L, M and higher shells may be altered by the non-radiative Coster-Kronig and Super-Coster-Kronig transitions which are much faster in time (nearly seconds) in comparison to the time involved in normal shell to shell transitions. Similar is the case when the energy of incident radiation or the transition energy of the vacancy creating radioactive process is higher than the lower shell/subshell (say K shell) and the X-ray line/group being measured is of higher shell (say L shell). Then the lower to higher 35

36 subshell transitions (say K to Li) being faster in time will alter the primary subshell vacancy status of the higher shell (say L shell). Thus, it is clear that in measurements involving inner shells, the X-ray energies and intensities do not reveal true characteristics of the primary vacancies and the contribution of processes initiated after the primary interactions have to be properly taken care of. Further, When L3 subshell of an atom is ionized by protons with incident energy greater than the K shell binding energy of the element, the vacancies produced in the subshell of that atom include the direct vacancies produced by the proton impact and the indirect vacancies produced due to inter-shell K to L3 and the intra-shell L1 to L3 and L2 to L3 transfer (Coster-Kronig transfer) of vacancies. Thus, in experiments involving measurement/determination of alignment related parameters, the measured values of L3 X-ray intensities used to determine these parameters are to be corrected/modified for processes responsible for creation of unaligned vacancies in the L3 sub shell (indirect processes). In the work done in past, these contributions to the primary vacancies have either been eliminated/controlled experimentally [2-5] or accounted for otherwise by different workers under their typical experimental conditions only. Very little work has been done for a detailed insight into the contribution of the vacancies initiated after the primary interaction processes leading to X-ray emission. 36