**Angular Dependence of Fluorescence X-Rays and Alignment of Vacancy State Induced by Radioisotopes**

İbrahim Han *Ağr İbrahim Çeçen University Turkey* 

#### **1. Introduction**

114 Radioisotopes – Applications in Physical Sciences

Urch, D.S. (1979). Theory, Techniques, and Application; Brundle, C. R., Baker, A. D., Eds.;

Yamoto, I.; Kaji, H. & Yoshihara, K. (1986). Studies on Chemical Effects on X-Ray Intensity

Ratios of *Kβ*/*Kα* in Nuclear Decay of Technetium Nuclides 99mTc, 97mTc and 95mTc. *J*.

Academic Press: New York, *Electron Spectrosc.*, Vol.3, pp. 1-39.

*Chem*. *Phys*., Vol.84, pp- 522-527.

This chapter concerns angular distribution measurements for fluorescence X-ray and the alignments of atoms with inner-shells vacancy resulting from ionization by radioisotope sources. The discussion on this topic is done by evaluating measurements of X-ray fluorescence parameters (such as cross-section, alignment parameter, polarization degree) from sample in various emission angles.

When an atom is ionized in one of its inner shells, the electrons rearrange themselves to fill the vacancy, with the transition energy released as a photon or transferred to another electron. The following X-ray or Auger electron may have an isotropic or non-isotropic angular distribution. The study of alignment of the inner-shell vacancy in ions can provide information about ionization process and the wave functions of inner-shell electrons, and calculations showed that the alignment was a sensitive testing parameter for theoretical models. For the last five decades there have been both theoretically and experimentally renewed efforts towards better understanding of the physics concerned with alignment of atoms with inner-shells vacancy and/or angular dependence of fluorescent X-rays emitted atoms induced photons or charged particle (electrons, protons, heavy ions). Generally, the alignments of atoms with inner-shells vacancy resulting from ionization by photons are investigated by measuring the anisotropic emission of X-ray lines using a detector (such as Si(Li) or Ge(Li) ) and radioisotope photon source in various emission angles.

#### **2. Historical background and current status of topic**

The aim of paper interested in this topic is to determine the relationship between the angular distributions of X-rays with respect to total angular momentum values (*J*) of vacancy states. It is well-known that when radioisotope source, X-ray tube or charged particles produce vacancies in atoms at energy levels with *J*>1/2 , the resulting ions will be aligned. The signature of this alignment is the anisotropic angular distribution of the emitted characteristic X-ray radiation, or the degree of polarization of the X-ray radiation. Total angular momentum (J) of vacancy states after photoionization is greater than 1/2, the population of its magnetic sub-states is non-statistical by the ionized atoms and this is reason of this anisotropic behavior. A lot of theoretical studies have been reported so far

Angular Dependence of Fluorescence

was obtained by Küst, et al., (2003).

X-Rays and Alignment of Vacancy State Induced by Radioisotopes 117

L X-ray photons of Pb and Au. Although they found an isotropic distribution of the Pb L3 lines within the experimental errors, non-isotropic angular distribution of the Au L3 lines have been obtained. Papp and Campbell, (1992) reported the magnitude of the anisotropy and the alignment parameter for the *L* lines of Er. The alignment parameter of the ions of Xe

Kahlon et al., (1990a) reported experimental investigation of the alignment of the L3 subshell vacancy state produced after photoionization in lead by 59.57 keV photons. The values of differential cross sections for the emission of the ��, ��, �� and �� X-ray lines were determined at different emission angles varying from 40o to 120o. It was seen from the results that the ��, and �� peaks show anisotropic emission, while the �� and �� peaks are emitted isotropically. The angular dependence of emission intensity of L shell X rays induced by 59.57 keV photons in Pb and U was investigated by Kahlon et al., (1990b) measuring the normalized intensities of the resolved L X-ray peaks at different angles varying from 40o to 140o. It was observed that while the �� and �� peaks (originating from J=3/2 state) show some anisotropic angular distribution, the emission of the �� and �� peaks are emitted isotropically. Kahlon et al., (1991a) measured the angular distribution and polarization of the L shell fluorescent X-rays excited by 59.54 keV photons in Th and U. It was found that the �� group of L X-rays is isotropic in spatial distribution and unpolarized but, the �� and �� groups are anisotropically distributed and polarized. Although no anisotropy of the �� group is detected, it was slightly polarized. Kahlon et al., (1991b) investigated the differential cross sections for emission of ��, ���, ��, �� and �� groups of L X-ray lines induced in Au by 59.54 keV photons at different angles varying from 40o to 120o. The L X-rays represented by��, ��� and �� peaks were found to be anisotropic in the spatial distribution while those in �� and �� peaks were isotropic. Papp and Campbell, (1992) measured angular distributions of the ��� ����� and ������ transitions of erbium in the angular range of 70°–150° following photoionization by 8.904 keV photons. A Johanssontype monochromatic was used to select the Cu ��� line for ionization. Anisotropy parameters for ��� ����� and ������ were found as 0.052±0.016, 0.16±0.022 and 0.012±0.015, respectively. Ertugrul et al., (1995, 1996a, 1996b) measured differential cross-sections for the emission of ��, ��, �� and �� X-rays of Au, Hg, Tl, Pb, Bi, Tb and U at different emission angles varying from 45o to 135o. They found that �� and �� peaks are emitted isotropically, while �� and �� peaks show anisotropic emission. Sharma and Allawadhi, (1999) measured values of ��, �� and �� differential X-ray production cross sections in Th and U at 16.896 and 17.781 keV at emission angles 60o, 70o, 80o and 90o. From the results of the measurements it was evident that, in the present case, all the three ��, �� and �� differential X-ray production cross sections depend on the emission angle and thus, the emission is anisotropic. Demir et al., (2000) indicated differential cross-sections for the emission of M shell fluorescence X-rays from Pt, Au and Hg by 5.96 keV photons at seven angles ranging from 50o to 110o at. The differential cross-sections were found to decrease with increase in the emission angle, showing an anisotropic spatial distribution of M shell fluorescence Xrays. Seven and Koçak (2001, 2002) measured the ��, ��, �� and �� X-ray production crosssections in U, Th, Bi, Pb, Tl, Hg, Au, Pt, Re,W, Ta, Hf, Lu, and Yb using 59.5 keV incident photon energies in the angular range 40o-130o. Although differential cross sections for L*β* and L*γ* X-rays were found to be angle independent within experimental error, those for the L*l* and L*α* X-rays were found to be angle dependent. Ertugrul et al., (2002) measured the alignment parameter the ��� � ⁄ �� intensity ratio. The �� and �� X-rays of the elements were measured with a Si (Li) detector at a direction of 90° to the projectile. The L3 edges of Nd,

along this topic (Mehlhorn 1968; Mc Farlene, 1972; Berezhko and Kabachnik 1977; Sizov and Kabachnik, 1980, 1983) and the predictions of these researchers have been experimentally supported by some researchers (Schöler and Bell, 1978; Pálinkás, 1979, 1982; Wigger et al., 1984; Jesus et al., 1989; Mitra et al., 1996). The experimental study of alignment generally involves measurements of the angular distribution or polarization of the induced X-rays (Hardy et al., 1970; Döbelin et al., 1974; Jamison and Richard, 1977; Jistchin et al., 1979, 1983; Pálinkás, et al., 1981; Stachura et al., 1984; Bhalla, 1990; Mehlhorn, 1994; Papp 1999). In 1969, Cooper and Zare, (1969) first suggested a theoretical model relevant to aligned photon induced atoms. According to calculation by Cooper and Zare, (1969), after photoionization the inner-shell vacancy states have statistical population of magnetic substates. The vacancies produced after photoionizationin sub-shells are not be aligned at all and so the angular distribution of the fluorescent X-rays subsequent to photoionization will be isotropic. In 1972, 3 years after Cooper and Zare, the predictions of Flügge et al., (1972) showed that when vacancies are created in states with *J*>1 2, the population of its magnetic sub-states are non-statistical and therefore the resulting ions will be aligned. Mc Farlane (1972) calculated the polarization of X-rays from the decay of a vacancy in the 2p2/3 sub-shell using hydrogenic wave- functions in the Bethe approximation and the first Born approximation. After Caldwell and Zare (1977) first made an experimental investigation of the photon-induced alignment of Cd and they measured the degree of polarization of the emitted radiation from Cd. Since then, many experiments and calculations have been done to study the alignment of atoms and angular dependence characteristic X-rays by measuring either the angular distribution or the degree of polarization of the emitted X-rays. All these studies confirmed either alignment or not-alignment of the atoms after photoionization. The angular correlation between ionizing and fluorescent X-rays has been calculated relativistically, including all the radiation multipoles using single particle wavefunctions calculated in the Hartree–Slater model, by (Scofield, 1976). More recently, Scofield, (1989) used a relativistic model to study the angular distribution of the photoelectrons produced from photo- ionization by linear polarize photons and its inverse process (radiative recombination) in the energy region of 1–100keV. Scofield, (1989) found that the crosssection has a maximum at 90o compared to the direction of the incoming photons in the x–z plane (polarization plane) while the cross-section is independent of the angle between the incoming photon and the ejected electron in the y–z plane (normal to the polarization plane). Kamiya et al., (1979) measured L X-rays of Ho and Sm produced by protons and 3He impacts with Si(Li) detector over the incident energy ranges Ep = 0.75–4.75MeV and ܧଷಹ = 1,5–9,4 MeV in the direction of 90° to the projectile. Kamiya, et al., (1979) reported that the ratios of X-ray production cross-sections for the L*α* and L*l* lines depend clearly on projectile energy, but are independent of the projectile charge. Theoretical values of the alignment parameter for different states of various atoms calculated using the Herman-Skillman wave functions, have been reported by Berezhko and Kabachnik, (1977). The very strong anisotropy was reported for the emission of L lines for various elements by several scientists (Kahlon, et al., 1990a,b, 1991a,b; Ertuğrul, et al., 1995, 1996; Ertuğrul, 1996, 2002; Kumar, et al., 1999 Sharma and Allawadhi, 1999; Seven and Koçak, 2001,2002; Seven, 2004; Demir, et al., 2003). However, in all these investigations, the observed anisotropy is much higher than the predicted theoretical values of Scofield, (1976) and Berezhko and Kabachnik, (1977). On the other hand, anisotropic emission for L X-rays of Pb, Th and U was reported by some scientists (Mehta, et al., 1999; Kumar, et al 1999, 2001). Recently, Yamaoka et al., (2002, 2003) performed experiments using synchrotron radiation to determine the angular distribution of

along this topic (Mehlhorn 1968; Mc Farlene, 1972; Berezhko and Kabachnik 1977; Sizov and Kabachnik, 1980, 1983) and the predictions of these researchers have been experimentally supported by some researchers (Schöler and Bell, 1978; Pálinkás, 1979, 1982; Wigger et al., 1984; Jesus et al., 1989; Mitra et al., 1996). The experimental study of alignment generally involves measurements of the angular distribution or polarization of the induced X-rays (Hardy et al., 1970; Döbelin et al., 1974; Jamison and Richard, 1977; Jistchin et al., 1979, 1983; Pálinkás, et al., 1981; Stachura et al., 1984; Bhalla, 1990; Mehlhorn, 1994; Papp 1999). In 1969, Cooper and Zare, (1969) first suggested a theoretical model relevant to aligned photon induced atoms. According to calculation by Cooper and Zare, (1969), after photoionization the inner-shell vacancy states have statistical population of magnetic substates. The vacancies produced after photoionizationin sub-shells are not be aligned at all and so the angular distribution of the fluorescent X-rays subsequent to photoionization will be isotropic. In 1972, 3 years after Cooper and Zare, the predictions of Flügge et al., (1972) showed that when vacancies are created in states with *J*>1 2, the population of its magnetic sub-states are non-statistical and therefore the resulting ions will be aligned. Mc Farlane (1972) calculated the polarization of X-rays from the decay of a vacancy in the 2p2/3 sub-shell using hydrogenic wave- functions in the Bethe approximation and the first Born approximation. After Caldwell and Zare (1977) first made an experimental investigation of the photon-induced alignment of Cd and they measured the degree of polarization of the emitted radiation from Cd. Since then, many experiments and calculations have been done to study the alignment of atoms and angular dependence characteristic X-rays by measuring either the angular distribution or the degree of polarization of the emitted X-rays. All these studies confirmed either alignment or not-alignment of the atoms after photoionization. The angular correlation between ionizing and fluorescent X-rays has been calculated relativistically, including all the radiation multipoles using single particle wavefunctions calculated in the Hartree–Slater model, by (Scofield, 1976). More recently, Scofield, (1989) used a relativistic model to study the angular distribution of the photoelectrons produced from photo- ionization by linear polarize photons and its inverse process (radiative recombination) in the energy region of 1–100keV. Scofield, (1989) found that the crosssection has a maximum at 90o compared to the direction of the incoming photons in the x–z plane (polarization plane) while the cross-section is independent of the angle between the incoming photon and the ejected electron in the y–z plane (normal to the polarization plane). Kamiya et al., (1979) measured L X-rays of Ho and Sm produced by protons and 3He impacts with Si(Li) detector over the incident energy ranges Ep = 0.75–4.75MeV and ܧଷಹ = 1,5–9,4 MeV in the direction of 90° to the projectile. Kamiya, et al., (1979) reported that the ratios of X-ray production cross-sections for the L*α* and L*l* lines depend clearly on projectile energy, but are independent of the projectile charge. Theoretical values of the alignment parameter for different states of various atoms calculated using the Herman-Skillman wave functions, have been reported by Berezhko and Kabachnik, (1977). The very strong anisotropy was reported for the emission of L lines for various elements by several scientists (Kahlon, et al., 1990a,b, 1991a,b; Ertuğrul, et al., 1995, 1996; Ertuğrul, 1996, 2002; Kumar, et al., 1999 Sharma and Allawadhi, 1999; Seven and Koçak, 2001,2002; Seven, 2004; Demir, et al., 2003). However, in all these investigations, the observed anisotropy is much higher than the predicted theoretical values of Scofield, (1976) and Berezhko and Kabachnik, (1977). On the other hand, anisotropic emission for L X-rays of Pb, Th and U was reported by some scientists (Mehta, et al., 1999; Kumar, et al 1999, 2001). Recently, Yamaoka et al., (2002, 2003) performed experiments using synchrotron radiation to determine the angular distribution of

L X-ray photons of Pb and Au. Although they found an isotropic distribution of the Pb L3 lines within the experimental errors, non-isotropic angular distribution of the Au L3 lines have been obtained. Papp and Campbell, (1992) reported the magnitude of the anisotropy and the alignment parameter for the *L* lines of Er. The alignment parameter of the ions of Xe was obtained by Küst, et al., (2003).

Kahlon et al., (1990a) reported experimental investigation of the alignment of the L3 subshell vacancy state produced after photoionization in lead by 59.57 keV photons. The values of differential cross sections for the emission of the ��, ��, �� and �� X-ray lines were determined at different emission angles varying from 40o to 120o. It was seen from the results that the ��, and �� peaks show anisotropic emission, while the �� and �� peaks are emitted isotropically. The angular dependence of emission intensity of L shell X rays induced by 59.57 keV photons in Pb and U was investigated by Kahlon et al., (1990b) measuring the normalized intensities of the resolved L X-ray peaks at different angles varying from 40o to 140o. It was observed that while the �� and �� peaks (originating from J=3/2 state) show some anisotropic angular distribution, the emission of the �� and �� peaks are emitted isotropically. Kahlon et al., (1991a) measured the angular distribution and polarization of the L shell fluorescent X-rays excited by 59.54 keV photons in Th and U. It was found that the �� group of L X-rays is isotropic in spatial distribution and unpolarized but, the �� and �� groups are anisotropically distributed and polarized. Although no anisotropy of the �� group is detected, it was slightly polarized. Kahlon et al., (1991b) investigated the differential cross sections for emission of ��, ���, ��, �� and �� groups of L X-ray lines induced in Au by 59.54 keV photons at different angles varying from 40o to 120o. The L X-rays represented by��, ��� and �� peaks were found to be anisotropic in the spatial distribution while those in �� and �� peaks were isotropic. Papp and Campbell, (1992) measured angular distributions of the ��� ����� and ������ transitions of erbium in the angular range of 70°–150° following photoionization by 8.904 keV photons. A Johanssontype monochromatic was used to select the Cu ��� line for ionization. Anisotropy parameters for ��� ����� and ������ were found as 0.052±0.016, 0.16±0.022 and 0.012±0.015, respectively. Ertugrul et al., (1995, 1996a, 1996b) measured differential cross-sections for the emission of ��, ��, �� and �� X-rays of Au, Hg, Tl, Pb, Bi, Tb and U at different emission angles varying from 45o to 135o. They found that �� and �� peaks are emitted isotropically, while �� and �� peaks show anisotropic emission. Sharma and Allawadhi, (1999) measured values of ��, �� and �� differential X-ray production cross sections in Th and U at 16.896 and 17.781 keV at emission angles 60o, 70o, 80o and 90o. From the results of the measurements it was evident that, in the present case, all the three ��, �� and �� differential X-ray production cross sections depend on the emission angle and thus, the emission is anisotropic. Demir et al., (2000) indicated differential cross-sections for the emission of M shell fluorescence X-rays from Pt, Au and Hg by 5.96 keV photons at seven angles ranging from 50o to 110o at. The differential cross-sections were found to decrease with increase in the emission angle, showing an anisotropic spatial distribution of M shell fluorescence Xrays. Seven and Koçak (2001, 2002) measured the ��, ��, �� and �� X-ray production crosssections in U, Th, Bi, Pb, Tl, Hg, Au, Pt, Re,W, Ta, Hf, Lu, and Yb using 59.5 keV incident photon energies in the angular range 40o-130o. Although differential cross sections for L*β* and L*γ* X-rays were found to be angle independent within experimental error, those for the L*l* and L*α* X-rays were found to be angle dependent. Ertugrul et al., (2002) measured the alignment parameter the ��� � ⁄ �� intensity ratio. The �� and �� X-rays of the elements were measured with a Si (Li) detector at a direction of 90° to the projectile. The L3 edges of Nd,

Angular Dependence of Fluorescence

X-Rays and Alignment of Vacancy State Induced by Radioisotopes 119

differential cross-sections in Pb at the 13.6 keV incident photon energy (*E*L3 < *E*inc < *E*L2, *E*Li being the Li sub-shell binding energy) and in the angular range 90-160◦. At this incident photon energy, the L3 sub-shell vacancies (*J* = 3/2) are produced only due to the direct ionization and the reduction in the observed anisotropy in the emission of the ��, �� and ����������� X-rays due to the transfer of unaligned L1 and L2 subshell vacancies (*J* = 1/2) to the L3 sub-shell through Coster–Kronig transitions was eliminated. The differential crosssections for various x-rays were found to be angle-independent within experimental error. The L X-ray production (XRP) differential cross sections in Th and U have been measured by Kumar et al., (2001b) at the 17.8 keV incident photon energy (*E*L3 *< E*inc *< E*L2 , *E*Li is the Li subshell ionization threshold) in an angular range 90o-160oand at the 25.8 and 46.9 keV incident photon energies (*E*L1 *< E*inc *< E*K) at an angle of 130o. The present measurements rule out the possibility of a strong angular dependence of differential cross sections for various L3 subshell X-rays following selective photoionization of the L3 subshell. Tartari et al., (2003) investigated the anisotropy of L X-ray fluorescence induced by 59.54 keV unpolarized photons by means of an experimental procedure which allows the relative L X-ray production cross section to be evaluated without taking account of the angular set-up and the instrumental efficiency. Thick targets of Yb, Hf, Ta, W and Pb are considered, and the angular trend of the relative experimental ratios, ��� � ⁄ ��, is calculated by simple evaluations of the peak area alone. Within the experimental uncertainties, which were found to be of the order of 1.6% in the worst cases, the results do not show any significant angular dependence of the L*α* emission lines. Santra et al., (2007) measured the angular distribution of the *L* X-ray fluorescent lines from Au and U induced by 22.6-keV X-rays in the angular range of 70°–150°. No strong anisotropy was observed as mentioned by some groups. In the case of Au, a maximum anisotropy of 5% was observed while for U it was within experimental errors 2%. From the angular distribution of the �� line of Au, the alignment parameter was obtained and its value was found to be 0.10±0.14. Kumar et al., (2008) investigated alignment of the *M*3(*J*= 3/2), *M*4(*J*= 3/2) and *M*5(*J*= 5/2) subshell vacancy states produced following photoionization in the *Mi* (*i*=1-5) subshells of Au, Bi, Th and U through angular distribution of the subsequently emitted *M* X-rays. The unpolarized Mn *K* X rays (*EKX*=5.97 keV) from the 55Fe radioisotope were used to ionize the *Mi* subshells in an angular range 90°-160°and the emitted *M* X-rays were measured under vacuum using a low energy Ge detector. The *M* X-ray spectra taken at different emission angles were normalized using the isotropically emitted *K* shell (*J*= 1/2) X-rays measured simultaneously from a 23V thin target placed adjoining the *M* X-ray target. The present precision measurements infer that anisotropy in the *Mαβγ* X-ray emission shows trends and order of magnitude predicted

by theoretical calculations, i.e., anisotropy parameter (β2)~0.01.

In the recent experimental study (Han et al., 2008), the angular distribution of characteristic K and L X-rays, emitted from Sm, Eu, Gd Tb, Dy, Ho, and Er as a result of K and L shell vacancies produced by 59.54 keV photon impact was investigated. Thus, K and L X-rays emitted from these elements were simultaneously measured in the same experimental geometry. In this study, Sm, Eu, Gd, Tb, Dy, Ho, and Er lanthanides were chosen since both K shell and L shell electrons of these elements can be excited simultaneously by an Am-241 point source. Also, K and L peaks of the chosen elements are well resolved. Earlier experimental investigations have been only performed on the K X-ray cross sections or on the angular distribution of L X-rays. This is the first report of the angular distributions of L*i*  X-ray and K*i* X-ray (*i* = *α*, *β*) cross sections for Sm, Eu, Gd, Tb, Dy, Ho, and Er at different angles. It is well known that K X-ray cross sections have no angular dependency (*J* = 1*/*2). The experimental investigation on K X-ray cross sections at different angles was made to

Gd, Tb, Dy, Ho, Er, Yb, Hf, Ta, W, Au, Hg, Tl, Pb, Bi, Th and U the elements were excited with the K X-ray energy of 17.781(MoKα,β), 16.896(NbKα,β), 14.980(RbKβ), 13.300(BrKβ), 12.503(SeKβ), 12.158(BrKα,β), 10.983(GeKβ), 10.073(GeKα1,β), 9,572(ZnKβ), 8.976(CuKβ2), 8.907(CuKβ), 8.265(NiKβ), 7.649(CoKβ1), 6.490(MnKβ1) keV from the selected elements, respectively. They noticed that the L3 X-rays show large anisotropy, the measured alignment parameter varying from -0.115 to +0.355. Demir et al., (2003) reported ��, ��, �� and �� Xray differential cross-sections, fluorescence cross-sections and σL1, σL2 and σL3 subshell fluorescence cross-sections for Er, Ta, W, Au, Hg and Tl at an excitation energy of 59.6 keV. The differential cross-sections for these elements have been measured at different angles varying from 54o to 153o. The �� and �� groups in the L X-ray lines were found to be spatially anisotropic, while those in the �� and �� peaks are isotropic. The ��, ��, ���,�, ���,� and �� X-ray production cross-sections and L-subshell fluorescence yields ω1 and ω2 in Th and U have been determined by Seven (2004) at an incident photon energy of 59.54 keV by measuring differential cross-sections with angles changing from 40° to 130°. The ��, �� and ���,� X-rays have an anisotropic spatial distribution while ���,� and �� X-rays have isotropic spatial distributions. Özdemir et al., (2005) measured the angular dependence of L3 subshell to M-shell vacancy transfer probabilities for the elements Lu, Hf, Ta, W, Os and Pt at the excitation energies of 5.96 keV and K X-rays of Zn, Ga, Ge, and As, respectively, at seven angles varying from 120° to 150°. It was observed that angular dependence from L3 subshell to M-shell vacancy transfer probabilities increase with increasing cosθ. The angular dependence of M X-ray production differential cross-sections for selected heavy elements between Lu and Pt have been measured by Durak (2006) at 5.59 keV of incident photon energy and at seven emission angles in the range of 120o-150o. Angular dependence of M Xray production differential cross sections has been derived, using the M-shell fluorescence yields, experimental total M X-ray production cross sections and theoretical M-shell photoionization cross sections. M X-ray production differential cross-sections were found to decrease with increase in the emission angle, showing an anisotropic spatial distribution of M X-rays. Angular dependence from L3 subshell to M-shell vacancy transfer probabilities for selected heavy elements from Au to U were measured by Özdemir and Durak (2008) at different angles varying from 120o to 150o. It was observed that angular dependence from L3-subshell to M-shell vacancy transfer probabilities increase with increasing cosθ. Apaydn et al., (2008) measured M*i* (*i* = *α* + *β*) X-ray production differential cross sections for Re, Bi and U elements at the 5.96 keV incident photon energy in an angular range 135o-155o. They found that the angular dependence M X-rays production cross sections decrease with increase in the emission angle, showing anisotropic spatial distribution

Kumar et al., (1999) investigated the angular dependence of emission of L x-rays following photoionization at 22.6 and 59.5 keV in 82Pb by measuring the intensity ratios ��� � ⁄ ��, ��� � ⁄ �� and ��� � ⁄ �� at different angles varying from 50o to 140o. The measured intensity ratios for various L x-rays were found to be angle independent within experimental error. Mehta et al., (1999) measured the ��, ��, ��, ���, ���,�, ���,�, ���,�� and �� x-ray production differential cross sections in 92U using the 22.6- and 59.5-keV incident photon energies in an angular range 43°–140°. Differential cross sections for various *L* x rays were found to be angle independent within experimental error. Puri et al., (1999) measured The ��, ��, ���,�, ���,� and ���,� X-ray production differential cross sections in 90Th have at 22.6 keV incident photon energy in an angular range 50o -130o The measured differential cross sections for various L X-rays were found to be angle-independent within experimental error. Kumar et al., (2001a) measured the the ��, �� and ���,�,�,��� X-ray fluorescence (XRF)

Gd, Tb, Dy, Ho, Er, Yb, Hf, Ta, W, Au, Hg, Tl, Pb, Bi, Th and U the elements were excited with the K X-ray energy of 17.781(MoKα,β), 16.896(NbKα,β), 14.980(RbKβ), 13.300(BrKβ), 12.503(SeKβ), 12.158(BrKα,β), 10.983(GeKβ), 10.073(GeKα1,β), 9,572(ZnKβ), 8.976(CuKβ2), 8.907(CuKβ), 8.265(NiKβ), 7.649(CoKβ1), 6.490(MnKβ1) keV from the selected elements, respectively. They noticed that the L3 X-rays show large anisotropy, the measured alignment parameter varying from -0.115 to +0.355. Demir et al., (2003) reported ��, ��, �� and �� Xray differential cross-sections, fluorescence cross-sections and σL1, σL2 and σL3 subshell fluorescence cross-sections for Er, Ta, W, Au, Hg and Tl at an excitation energy of 59.6 keV. The differential cross-sections for these elements have been measured at different angles varying from 54o to 153o. The �� and �� groups in the L X-ray lines were found to be spatially anisotropic, while those in the �� and �� peaks are isotropic. The ��, ��, ���,�, ���,� and �� X-ray production cross-sections and L-subshell fluorescence yields ω1 and ω2 in Th and U have been determined by Seven (2004) at an incident photon energy of 59.54 keV by measuring differential cross-sections with angles changing from 40° to 130°. The ��, �� and ���,� X-rays have an anisotropic spatial distribution while ���,� and �� X-rays have isotropic spatial distributions. Özdemir et al., (2005) measured the angular dependence of L3 subshell to M-shell vacancy transfer probabilities for the elements Lu, Hf, Ta, W, Os and Pt at the excitation energies of 5.96 keV and K X-rays of Zn, Ga, Ge, and As, respectively, at seven angles varying from 120° to 150°. It was observed that angular dependence from L3 subshell to M-shell vacancy transfer probabilities increase with increasing cosθ. The angular dependence of M X-ray production differential cross-sections for selected heavy elements between Lu and Pt have been measured by Durak (2006) at 5.59 keV of incident photon energy and at seven emission angles in the range of 120o-150o. Angular dependence of M Xray production differential cross sections has been derived, using the M-shell fluorescence yields, experimental total M X-ray production cross sections and theoretical M-shell photoionization cross sections. M X-ray production differential cross-sections were found to decrease with increase in the emission angle, showing an anisotropic spatial distribution of M X-rays. Angular dependence from L3 subshell to M-shell vacancy transfer probabilities for selected heavy elements from Au to U were measured by Özdemir and Durak (2008) at different angles varying from 120o to 150o. It was observed that angular dependence from L3-subshell to M-shell vacancy transfer probabilities increase with increasing cosθ. Apaydn et al., (2008) measured M*i* (*i* = *α* + *β*) X-ray production differential cross sections for Re, Bi and U elements at the 5.96 keV incident photon energy in an angular range 135o-155o. They found that the angular dependence M X-rays production cross sections decrease with

increase in the emission angle, showing anisotropic spatial distribution

Kumar et al., (1999) investigated the angular dependence of emission of L x-rays following photoionization at 22.6 and 59.5 keV in 82Pb by measuring the intensity ratios ��� � ⁄ ��, ��� � ⁄ �� and ��� � ⁄ �� at different angles varying from 50o to 140o. The measured intensity ratios for various L x-rays were found to be angle independent within experimental error. Mehta et al., (1999) measured the ��, ��, ��, ���, ���,�, ���,�, ���,�� and �� x-ray production differential cross sections in 92U using the 22.6- and 59.5-keV incident photon energies in an angular range 43°–140°. Differential cross sections for various *L* x rays were found to be angle independent within experimental error. Puri et al., (1999) measured The ��, ��, ���,�, ���,� and ���,� X-ray production differential cross sections in 90Th have at 22.6 keV incident photon energy in an angular range 50o -130o The measured differential cross sections for various L X-rays were found to be angle-independent within experimental error. Kumar et al., (2001a) measured the the ��, �� and ���,�,�,��� X-ray fluorescence (XRF) differential cross-sections in Pb at the 13.6 keV incident photon energy (*E*L3 < *E*inc < *E*L2, *E*Li being the Li sub-shell binding energy) and in the angular range 90-160◦. At this incident photon energy, the L3 sub-shell vacancies (*J* = 3/2) are produced only due to the direct ionization and the reduction in the observed anisotropy in the emission of the ��, �� and ����������� X-rays due to the transfer of unaligned L1 and L2 subshell vacancies (*J* = 1/2) to the L3 sub-shell through Coster–Kronig transitions was eliminated. The differential crosssections for various x-rays were found to be angle-independent within experimental error. The L X-ray production (XRP) differential cross sections in Th and U have been measured by Kumar et al., (2001b) at the 17.8 keV incident photon energy (*E*L3 *< E*inc *< E*L2 , *E*Li is the Li subshell ionization threshold) in an angular range 90o-160oand at the 25.8 and 46.9 keV incident photon energies (*E*L1 *< E*inc *< E*K) at an angle of 130o. The present measurements rule out the possibility of a strong angular dependence of differential cross sections for various L3 subshell X-rays following selective photoionization of the L3 subshell. Tartari et al., (2003) investigated the anisotropy of L X-ray fluorescence induced by 59.54 keV unpolarized photons by means of an experimental procedure which allows the relative L X-ray production cross section to be evaluated without taking account of the angular set-up and the instrumental efficiency. Thick targets of Yb, Hf, Ta, W and Pb are considered, and the angular trend of the relative experimental ratios, ��� � ⁄ ��, is calculated by simple evaluations of the peak area alone. Within the experimental uncertainties, which were found to be of the order of 1.6% in the worst cases, the results do not show any significant angular dependence of the L*α* emission lines. Santra et al., (2007) measured the angular distribution of the *L* X-ray fluorescent lines from Au and U induced by 22.6-keV X-rays in the angular range of 70°–150°. No strong anisotropy was observed as mentioned by some groups. In the case of Au, a maximum anisotropy of 5% was observed while for U it was within experimental errors 2%. From the angular distribution of the �� line of Au, the alignment parameter was obtained and its value was found to be 0.10±0.14. Kumar et al., (2008) investigated alignment of the *M*3(*J*= 3/2), *M*4(*J*= 3/2) and *M*5(*J*= 5/2) subshell vacancy states produced following photoionization in the *Mi* (*i*=1-5) subshells of Au, Bi, Th and U through angular distribution of the subsequently emitted *M* X-rays. The unpolarized Mn *K* X rays (*EKX*=5.97 keV) from the 55Fe radioisotope were used to ionize the *Mi* subshells in an angular range 90°-160°and the emitted *M* X-rays were measured under vacuum using a low energy Ge detector. The *M* X-ray spectra taken at different emission angles were normalized using the isotropically emitted *K* shell (*J*= 1/2) X-rays measured simultaneously from a 23V thin target placed adjoining the *M* X-ray target. The present precision measurements infer that anisotropy in the *Mαβγ* X-ray emission shows trends and order of magnitude predicted by theoretical calculations, i.e., anisotropy parameter (β2)~0.01.

In the recent experimental study (Han et al., 2008), the angular distribution of characteristic K and L X-rays, emitted from Sm, Eu, Gd Tb, Dy, Ho, and Er as a result of K and L shell vacancies produced by 59.54 keV photon impact was investigated. Thus, K and L X-rays emitted from these elements were simultaneously measured in the same experimental geometry. In this study, Sm, Eu, Gd, Tb, Dy, Ho, and Er lanthanides were chosen since both K shell and L shell electrons of these elements can be excited simultaneously by an Am-241 point source. Also, K and L peaks of the chosen elements are well resolved. Earlier experimental investigations have been only performed on the K X-ray cross sections or on the angular distribution of L X-rays. This is the first report of the angular distributions of L*i*  X-ray and K*i* X-ray (*i* = *α*, *β*) cross sections for Sm, Eu, Gd, Tb, Dy, Ho, and Er at different angles. It is well known that K X-ray cross sections have no angular dependency (*J* = 1*/*2). The experimental investigation on K X-ray cross sections at different angles was made to

Angular Dependence of Fluorescence

angles (Han and Demir, 2011b).

**3. Conclusion** 

present discrepancies

**4. Acknowledgment** 

16, 255–262.

**5. References** 

X-Rays and Alignment of Vacancy State Induced by Radioisotopes 121

values and results of others and fairly good correspondence was observed. The L*γ* X-rays, originating purely from the L1 and L2 subshells, having isotropic emission were used to normalize the intensities of the anisotropic L*l* and the L*a* X-rays originating from the L3 subshell. It was observed from measurements that L*l* and L*a* X-ray for the L3 sub-state depended on the emission angle, meaning that L*l* and L *a* X-rays had an anisotropic spatial distribution. On the other hand, the L*β* and L*γ* X-rays don't show any significant anisotropy. The fluorescence cross sections for L*l* and L*a* X-rays are decreased with increased emission

In the light of all these, above; data from different researchers show contradictory and the existing results on the angular dependence of fluorescence X-ray and the alignment of atoms with inner-shells vacancy following ionization are still controversial and quite confusing. Therefore, more experimental and theoretical investigations should be required to settle the

Apaydn*,* G., Trasoglu, E., Sogut, O., 2008. Measurement of angular dependence of M X-ray production cross-sections in Re, Bi and U at 5.96 keV Eur. Phys. J. D 46, 487–492 Berezhko, E.G., Kabachnik, N.M., 1977. Theoretical study of inner-shell alignment of atoms

Bhalla, C.P., 1990. Angular distribution of Auger electrons and photons in resonant transfer

Caldwell, C.D., Zare, R.N., 1977.Alignment of Cd atoms by photoionization. Phys. Rev. A

Cooper, J., Zare, N., 1969. Potoelectron angular distributions. In:Geltman, S., Mahanthappa,

Demir, L., Şahin, M., Kurucu, Y., Karabulut, A., Şahin, Y., 2000. Measurement of angular

Demir, L., Şahin, M., Kurucu, Y., Karabulut, A., Şahin, Y., 2003. Angular dependence of *Ll*,

Döbelin, E., Sandner, W., Mehlhorn, W., 1974. Experimental study of inner shell alignment

Durak, R., 2006. Measurement of angular dependence of M X-ray production differential cross-sections in heavy elements at 5.96 keV. Can. J Anal. Sci. Spectrosc. 51, No. 2.

in electron impact ionisation: angular distribution and polarization of X-rays and

and excitation in collisions of ions with light targets. Phys. Rev. Lett. 64, 1103–1106.

K.T., Brittin, W.E.(Eds.), Lecturesin Theoretical Physics: Atomic Collision Processes,

dependence of photon-induced differential cross-sections of M X-rays from Pt, Au

*Lα*, *Lβ* and *Lγ* X*-*ray differential and fluorescence cross-sections for Er, Ta, W, Au,

I thank to M.R. Kacal for his help and advice during the preparation of this chapter.

Auger electrons. J. Phys. B At. Mol. Opt. Phys. 10, 2467–2477.

vol. X1C. Gordon and Breach, NewYork, pp. 317–337.

and Hg at 5.96 keV. Radiat. Phys. Chem. 59 355-359

of atoms in electron impact ionization. Phys. Lett. A 49, 7–8.

Hg and Tl Radiat. Phys. Chem. 67, 605–612

check the validity of the angular dependency of experimental L X-ray cross sections. The experimental K X-ray cross sections were compared with theoretically calculated values and fairly good correspondence was observed. This means that the present measurements regarding angular dependency of L X-rays are reliable.

In following the work of us (Han et al., 2009) experimental results of the angular distribution of characteristic X-rays were introduced. We preferred to use of *ILa* /*ILl*(θ) intensity ratios to obtain the values of alignment parameters (A2). In that case, the background subtraction problem is considerably reduced and statistical errors are significantly less. It was observed from measured intensities that L*a* and L*l* X-ray intensities for the L3 sub-state depended on the emission angle, meaning that L*a* and L*l* X-rays had an anisotropic spatial distribution. Thus, the L*a* to L*l* intensity ratios for a set of elements was determined and alignment parameters for each element were obtained using these ratios. In this study, three L subshells electrons were excited. Therefore, alignment parameter values are influenced by Coster–Kronig transitions from vacancies induced in the L1 or L2 sub-shells. L1 and L2 subshells have the same J= 1/2 value therefore the transferred vacancies are not-aligned and the observed anisotropy of the X-rays is attenuated. For this reason, corrected value of the alignment parameter was calculated using attenuation factor F. If photon energies exciting only L3 sub-shell electrons are chosen, the alignment parameter will be independent from Coster–Kronig transitions

In more recently study (Han and Demir, 2011a), we investigated the angular distribution of characteristic L X-rays emitted from heavy elements (Pt, Au, Pb, Bi, Th and U) as a result of L shell vacancy production by 59.54 keV photon impact and angular distribution of Compton scattering photons from the same elements. Thus, emitted fluorescent L X-rays and Compton scattering photons from elements were simultaneously measured in the same experimental geometry. Earlier experimental investigations have been only performed on the angular distribution of L X-rays or Compton scattering photons. This is the first report of the angular distribution of L*i* (*i*= *l*, *a*, *β* and *γ*) X-rays fluorescent and Compton scattering differential cross sections for Pt, Au, Pb, Bi, Th and U at different angles in the same experimental geometry. It is well known that Compton scattering differential cross sections have angular distribution. The experimental investigation on Compton scattering differential cross sections at different angles was made to check the validity of angular distribution of experimental L X-rays fluorescent differential cross sections. The experimental Compton scattering differential cross sections were compared with theoretically calculated values and fairly good correspondence was observed. This means that the present measurements regarding angular distribution of L X-rays are reliable. In the meantime, L3-subshell alignment of Th and U ionized by 59.5 keV photons has been investigated by evaluating the angular dependence of L*i* (*i*=*l*, *a*, η, *β* and *γ*) X-ray lines. The angular dependence measurements were performed by measuring the fluorescence cross section, σ*Li* (*i*= *l*, *a*, η, *β* and *γ*) and σ*Ll*/σ*Lγ*, σ*<sup>L</sup>*η/σ*Lγ*, σ*La* /σ*Lγ* and σ*Lβ*/σ*Lγ* ratios at different angles. It was observed from the measurements that L*i* (i=*l* and *a*) X rays for the L3-subshell depended on the emission angle and had an anisotropic spatial distribution. On the other hand, there was no dependence of emission angle and any significant anisotropy for other L X rays. The both L*l* and L*a* X-rays originate from the filling of vacancies in states L3-subshell with *J* = 3/2. The results of measurements indicate that the L3-subshell vacancy states with *J* =3/2 are aligned, whereas L1, and L2 vacancy states with *J* =1/2 are non-aligned. Integral cross-sections for the L*i* (*i*= *l*, *a*, η, *β* and *γ* ) X-rays and L subshell fluorescence yields ω*<sup>i</sup>* (*i*= 1, 2 and 3) were also determined and results were compared with theoretically calculated values and results of others and fairly good correspondence was observed. The L*γ* X-rays, originating purely from the L1 and L2 subshells, having isotropic emission were used to normalize the intensities of the anisotropic L*l* and the L*a* X-rays originating from the L3 subshell. It was observed from measurements that L*l* and L*a* X-ray for the L3 sub-state depended on the emission angle, meaning that L*l* and L *a* X-rays had an anisotropic spatial distribution. On the other hand, the L*β* and L*γ* X-rays don't show any significant anisotropy. The fluorescence cross sections for L*l* and L*a* X-rays are decreased with increased emission angles (Han and Demir, 2011b).
