Measurement of radiative vacancy distributions for the L2,L3 subshell and M shell of some elements with atomic range 41⩽Z⩽68

Journal of Quantitative Spectroscopy & Radiative Transfer 74 (2002) 139–146 www.elsevier.com/locate/jqsrt

Measurement of radiative vacancy distributions for the L2; L3 subshell and M shell of some elements with atomic range 41 6 Z 6 68 4 a , H. Erdo3gana B. C / ali/skana , M. Ertu3grulb; ∗ , E. Oz a

Department of Physics, Faculty of Arts and Science, Pamukkale University, Denizli, Turkey b Department of Physics, Faculty of Education, Ataturk University, 25240 Erzurum, Turkey Received 26 February 2001; received in revised form 18 June 2001; accepted 18 June 2001

Abstract Radiative transitions K to L2 ; L3 subshell and M shell were measured using the K X-ray spectrum for 21 elements in the atomic range 41 6 Z 6 68. The targets were irradiated with  photons at 59:5 keV from Am-241 radioisotope source. The theoretical values were calculated using the radiative and nonradiative transition rates of these elements. It was observed that present values agree with previous theoretical results. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: X-ray Auorescence (XRF); Radiative transitions; Vacancy probabilities

1. Introduction A vacancy in an inner electron shell of an atom is rapidly Blled up by an electron from a higher (sub)shell, whereby in a radiative decay a photon and in a nonradiative decay an electron is emitted. In numerous Belds ranging from fundamental research on atomic collision processes to quantitative surface analysis by spectroscopic techniques, reliable accurate values of the decay probabilities are required in order to derive the vacancy creation from the observed photons or electrons [1– 4]. Beside these important applications, the decay rates provide a stringent test of atomic physics theory, since they reAect the intrinsic evolution of an atom in a nonstationary state. The sum of all decay rates determines the energy width of atomic levels according to Heisenberg’s uncertainty principle. ∗

Corresponding author. E-mail address: [email protected] (M. Ertu3grul). 0022-4073/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 1 ) 0 0 1 9 2 - 3

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The primary vacancies in the Li ; (i = 1; 2; 3) subshell can arise from either direct ionization by photons, electrons, heavy changed particles or from a shift of a K shell vacancy to the L shell. These vacancy decay through radiative, Auger and Coster–Kronig transitions [1]. There have been numerous calculations of radiative transition rates. Nonrelativistic calculations have been carried out by Metchnik and Tomlin [2], Tomlin [3]. Relativistic calculations have been performed by Massey and Burhop [4] and Babushkin [5]. In most of the early calculations, hydrogenic wave functions were used. Recently, several systematic studies with Hartree–Fock or Hartree–Slater wave functions have been performed. Manson and Kennedy [6] calculated the X-ray emission rates for all shells using nonrelativistic Hartree–Slater wave functions. Relativistic Hartree–Slater frozen-core calculations have been carried out by ScoBeld [7,8]. Anholt and Rasmussen [9] used relativistic Hartree–Fock wave functions. ScoBeld [10,11] performed the only relativistic Hartree–Fock calculations in the Coulomb gauge including relaxation eNects. The subject of relativistic transition rates has been reviewed by ScoBeld [12]. Rao et al. [13] has reviewed of the situation. The radiative transitions between K to L shells are K–L2 and K–L3 . A radiative K–L1 transition is forbidden by the electric-dipole selection rules. Ot = ± 1, where (Ol)h is the orbital angular momentum change. However, the K–L1 radiative transition probability does not completely vanish owing to higher multipoles, and contributes to the L-shell vacancies. For example, ≈ 0:005% of all L vacancies produced during K–L radiative transitions at Z = 80 are in the L1 subshell. Recently, ErtuQgrul et al. [14] measured radiative vacancy transfer probabilities for K to L2 ; L3 and M shell of some elements with the atomic range 69 6 Z 6 92 using K characteristic X-rays 4 intensity ratios. Durak and Ozdemir [15] deduced same quantities for the elements with the atomic number 60 6 Z 6 82. ErtuQgrul et al. [16] measured and presented total (radiative and nonradiative) vacancy transfer probabilities for the elements in the atomic region 79 6 Z 6 92 using to Am-241 and Co-57 radioisotopes. In the present work, radiative vacancy transfer probabilities from K to L2 ; L3 and M shell of Nb, Mo, Pd, Ag, Cd, In, Sn, Sb, Te, I, Cs, Ba, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho and Er were measured using to K =K intensity ratio. The targets were excited with photons at 59:5 keV from Am-241 radioisotope. The theoretical values were calculated using the radiative and nonradiative transition rates. 2. Experimental The experimental setup is shown Fig. 1. The targets are excited at 59:5 keV by Am-241 radioisotope source. The emitted X-rays from target were counted by a Si(Li) detector (resolution 160 eV at 5:96 keV) coupled to ND 66B multichannel analyzer. Spectroscopically pure targets of 1:72 cm2 area and thickness ranging from 10 to 50 mg cm−2 were used. To eliminate the counting errors to the minimum, X-ray spectra were accumulated in the time intervals ranging from 1800 to 7200 s. A typical spectrum of Cs K X-ray is given in Fig. 2. The average number of KLi of primary Li vacancies created in the Blling of a K-shell vacancy by an electron from an Li subshell can be written as the sum of two parts, KLi (R)

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Fig. 1. Experimental set-up.

Fig. 2. K X-ray spectrum of Cs with Am-241.

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Table 1 Experimental and theoretical KL2 ; KL3 and KM vacancy transfer probabilities Z

KL2 (R) Exp.

KL3 (R) Exp.

KM (R) Exp.

KL2 (R) Theo.

KL3 (R) Theo.

KM (R) Theo.

41

0:216 ± 0:012 0:218 ± 0:008 0:216 0:219 0:223 0:239 ± 0:011 0:237 ± 0:009 0:239 ± 0:014 0:240 ± 0:012 0:248 ± 0:014 0:244 ± 0:007 0:253 ± 0:012 0:251 ± 0:010 0:239 0:254 ± 0:015 0:255 ± 0:007 0:256 ± 0:010 0:259 ± 0:015 0:261 ± 0:013 0:259 ± 0:007 0:243 0:267 ± 0:013 0:244 0:267 ± 0:010 0:258 ± 0:015 0:265 ± 0:010 0:266 ± 0:013 0:269 ± 0:008

0:413 ± 0:024 0:416 ± 0:016 0:431 0:437 0:443 0:452 ± 0:022 0:446 ± 0:017 0:451 ± 0:027 0:452 ± 0:022 0:464 ± 0:027 0:456 ± 0:013 0:471 ± 0:023 0:466 ± 0:018 0:474 0:469 ± 0:028 0:470 ± 0:014 0:470 ± 0:018 0:475 ± 0:028 0:477 ± 0:023 0:471 ± 0:014 0:480 0:483 ± 0:024 0:481 0:481 ± 0:019 0:461 ± 0:027 0:474 ± 0:018 0:474 ± 0:023 0:478 ± 0:014

0:098 ± 0:005 0:100 ± 0:004 0:100 0:103 0:105 0:115 ± 0:005 0:115 ± 0:004 0:117 ± 0:007 0:119 ± 0:005 0:124 ± 0:007 0:123 ± 0:003 0:128 ± 0:006 0:128 ± 0:005 0:124 0:131 ± 0:007 0:133 ± 0:003 0:134 ± 0:004 0:137 ± 0:008 0:138 ± 0:006 0:138 ± 0:004 0:132 0:143 ± 0:007 0:133 0:145 ± 0:005 0:140 ± 0:008 0:145 ± 0:005 0:146 ± 0:007 0:148 ± 0:004

0:216 0:221 0:225 0:229 0:233 0:235 0:239 0:241 0:244 0:247 0:248 0:251 0:252 0:254 0:255 0:257 0:258 0:260 0:262 0:262 0:263 0:265 0:267 0:268 0:269 0:270 0:271 0:273

0:413 0:421 0:428 0:434 0:441 0:445 0:451 0:453 0:457 0:462 0:464 0:467 0:468 0:471 0:473 0:474 0:474 0:476 0:477 0:478 0:479 0:480 0:481 0:481 0:483 0:483 0:484 0:484

0:098 0:102 0:105 0:115 0:111 0:113 0:116 0:118 0:121 0:123 0:125 0:127 0:129 0:131 0:133 0:134 0:135 0:137 0:138 0:140 0:142 0:143 0:144 0:145 0:147 0:148 0:149 0:150

Nb Mo 43 Tca 44 Rua 45 Rha 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xea 55 Cs 56 Ba 57 La 58 Ce 59 Pr 60 Nd 61 Pma 62 Sm 63 Eua 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 42

a

Fitted values.

due to radiative transitions KLi (A) due to Auger transitions: KLi = KLi (R) + KLi (A):

(1)

The number of KLi (R) is proportional to the probability that K–Li radiative transitions takes place. KLi (R) = !K [I (KLi )=IK (R)];

(2)

where I (KLi ) is the K–Li X-ray intensity and IK (R) is the total intensity of K X-rays. For L2 and L3 subshells, we can express this quantity in terms of K X-ray intensity ratios in the following way (Rao et al. [13]; ErtuQgrul et al. [14]):
 

 I (K ) −1 I (K 2 ) I (K 2 ) KL2 (R) = !K 1+ x 1+ ; (3) I (K 1 ) I (K 1 ) I (K )

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Table 2 Comparison of present experimental and theoretical K-shell intensity ratios Z

I (K )=I (K ) (Exp.)

I (K )=I (K ) (ScoBeld)

I (K 2 )=I (K 1 ) (ScoBeld)

 I (K1 )=I (K 1 ) (ScoBeld)

R (KL2 ) (ScoBeld)

R (KL3 ) (ScoBeld)

R (KM )a (ScoBeld)

(K)

41

0:186 ± 0:011 0:203 ± 0:008 0:186 ± 0:009 0:216 ± 0:008 0:220 ± 0:013 0:231 ± 0:011 0:209 ± 0:012 0:241 ± 0:007 0:211 ± 0:010 0:231 ± 0:009 0:239 ± 0:014 0:243 ± 0:007 0:247 ± 0:010 0:240 ± 0:014 0:240 ± 0:012 0:260 ± 0:008 0:236 ± 0:011 0:248 ± 0:010 0:303 ± 0:018 0:272 ± 0:010 0:273 ± 0:014 0:266 ± 0:008

0:177 0:181 0:193 0:196 0:199 0:203 0:206 0:210 0:213 0:217 0:224 0:227 0:230 0:232 0:234 0:235 0:239 0:243 0:244 0:245 0:246 0:248

0:524 0:525 0:529 0:531 0:532 0:533 0:535 0:536 0:537 0:539 0:542 0:543 0:545 0:546 0:548 0:549 0:553 0:556 0:559 0:560 0:562 0:564

0:237 0:241 0:255 0:258 0:261 0:264 0:267 0:270 0:273 0:275 0:281 0:283 0:286 0:288 0:291 0:293 0:298 0:302 0:304 0:306 0:308 0:310

0:874 0:970 1:433 1:571 1:719 1:878 2:047 2:228 2:420 2:625 3:070 3:320 3:580 3:850 4:150 4:450 5:120 5:860 6:260 6:680 7:130 7:590

1:669 1:848 2:707 2:961 3:230 3:520 3:830 4:160 4:500 4:870 5:680 6:110 6:570 7:060 7:570 8:110 9:270 10:540 11:230 11:940 12:690 13:470

0:396 0:446 0:690 0:765 0:844 0:930 1:023 1:122 1:229 1:342 1:593 1:731 1:878 2:035 2:200 2:375 2:757 3:181 3:410 3:65169 3:90566 4:17204

4:041 4:387 6:089 6:566 7:130 7:700 8:294 8:970 9:645 10:410 12:000 12:902 13:859 14:828 15:858 16:955 19:296 21:895 23:274 24:733 26:296 27:851

Nb Mo 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 55 Cs 56 Ba 57 La 58 Ce 59 Pr 60 N 62 Sm 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 42

a

R (KM ) = R (KM2 ) + R (KM3 ) + R (KM4 ) + R (KM5 ).





 I (K ) −1 I (K 2 ) x 1+ : (4) I (K 1 ) I (K ) For the M shell, we can express this quantity in terms of K X-ray intensity ratios in the following way:
 

 I (K ) −1 I (K1 ) I (K 2 ) KM (R) = !K 1+ x 1+ ; (5) I (K 1 ) I (K 1 ) I (K )

KL3 (R) = !K

1+

where, !K is the Auorescence yields of K shell that it is taken in table of Hubbell et al. [17] I (K 2 )=I (K 1 ); I (K1 )=I (K 1 ) and (K )=(K ) are the intensity ratio of K X-rays. I (K 2 )=I (K 1 ) and I (K1 )=I (K 1 ) intensity ratios were taken ScoBeld [11]. The (K )=(K ) intensity ratio is observed by using the following relation: I (K ) N (K ) (K ) (Kj ) = ; (6) I (K ) N (K ) (K ) (K ) where N (K ) and N (K ) are the net counts observed under the photopeaks corresponding to I (K ) and I (K ) X-ray, respectively.  is the self absorption correction factor that it is calculated

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the following relation: =

1 − exp−(p sec 1 + e sec 2 )t ; (p sec 1 + e sec 2 )t

(7)

where p and e are the total mass absorption coeUcients of target at primer and emitted energy that it is evaluated table of Storm and Israel [18], 1 and 2 are the angle of primer and emitted ◦ ◦ X-ray with the normal of target surface that it is equal to 45 and 90 , respectively.  is the detector eUciency that it depends on energy. KL2 (R); KL3 (R) and KM (R) and the relative intensity ratios are given in Tables 1 and 2, respectively. The theoretical KL2 (R) and KL3 (R) radiative vacancy transfer probabilities were calculated using the relations [13,14] KL2 (R) =

R (KL2 ) ; (K)

(8)

KL3 (R) =

R (KL3 ) (K)

(9)

and the probability for the radiative transfer of a vacancy from K to M -shell KM (R) is deBned as the average number of M -shell vacancies created per K-shell vacancy decay through a radiative K–M transition. KM (R) was calculated by the relation [13,14] KM (R) =

R (KM2 ) + R (KM3 ) + R (KM4 ) + R (KM5 ) ; (K)

(10)

where R (KXi ) is the radiative K shell partial widths and (K) is the total K shell width that it is evaluated table of ScoBeld [8].

Fig. 3. KL2 (R) versus atomic number.

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145

Fig. 4. KL3 (R) versus atomic number.

Fig. 5. KM (R) versus atomic number.

3. Results and discussion The calculated values of KL2 (R); KL3 (R) and KM (R) are listed in Table 1 and shown in Figs. 3–5. The measured intensity ratios were compared by values of ScoBeld [11] (Table 2 and Fig. 6). The intensity ratios and the KL2 and KM (R) values are increased with increasing atomic number, but KL3 (R) values are decreased with increasing atomic number. In general, the present

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Fig. 6. I (K )=I (K ) versus atomic number.

results are in agreement with theoretical results. The present results diNer by approximately 4%, 4.3% and 1.3% from theoretical results (evaluated from [10,11] for KL2 (R); KL3 (R) and KM (R), respectively. The overall error in the present measurement is estimated to be 6 –8%. This error quadrate is the sum of the uncertainties in the diNerent parameters used to calculate the experimental values, namely, the evaluation of peak areas (3%), in the absorption correction factor (2%) and counting statistics (3%). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

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