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A comparative test of the models of atomic capture of negative particles using 321 experimental Coulomb-capture… Horváth, Dezsö; Entezami, Farrokh May 31, 1983

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TRIUMFA COMPARATIVE TEST OF THE MODELS OF ATOMIC CAPTURE OF NEGATIVE PARTICLES USING 321 EXPERIMENTAL COULOMB-CAPTURE RATIOSDezso  H o r v a t h *TRIUMFF a r r o k h  En te zam i  Depa r tm en t  o f  P h y s i c s ,  U n i v e r s i t y  o f  B r i t i s h  Co lumb ia*on  l e a v e  o f  absence  f r om  C e n t r a l  R esea r ch  I n s t i t u t e  f o r  P h y s i c s ,  H- 1 5 2 5  B u d a p e s t ,  P .O .  Box A 9 , HungaryMESON FAC IL ITY  OF:UNIVERSITY OF ALBERTA SIMON FRASER UNIVERSITY  UNIVERSITY  OF V ICTORIAUN I V ER S I T Y  OF B R I T I S H  COLUMBIA T R I - 8 3 - 1TRIUMFTRI-83-1A COMPARATIVE TEST OF THE MODELS OF ATOMIC CAPTURE OF NEGATIVE PARTICLES USING 321 EXPERIMENTAL COULOMB-CAPTURE RATIOSDezsd- Horvath*TRIUMFFarrokh Entezami Department of Physics, University of British Columbia*on leave of absence from Central Research Institute for Physics, H-1525 Budapest, P.O.Box 49, HungaryPostal address:TRIUMF4004 Wesbrook Mall Vancouver, B.C.Canada V6T 2A3 May 1983- 2 -E) In the energy region 10 eV < Ejj < 10 keV, where most of the mesons are captured, the meson wave function has many oscillations over the dimensions of the atom.This justifies a quasi— classical treatment of the capture process . 39-42, ^ -45, <+7, 49, 55F) In a mixture of elements of c jZ j + c 2Z 2 type (where Z ^ ,Z2 are t i^e atom:lc numbers and Cj,c2 the atomic concentrations) the atomic capture rates are proportional to the concentrations. This virtually evident statement has been thoroughly tested both theoretically47»52>56 and experimentally. 1 / 3-4 >11 > I9-28; 26-27, 29; 31, 35 ^ concentration dependence is predicted for the atomic capture in the lighter ele­ments56 but was not found in the mixtures of 3He with other gases.35G) A chemical compound is usually treated, in first approximation, as a mixture of elements. However, molecular effects have been observed in mesic X-rays and atomic capture rates (see for example reviews41-42;53). Therefore, at least for compounds of light elements, the influence of the chemical bond has to be considered.H) In the case of exotic hydrogen atoms a transfer of the meson from the hydrogen nucleus (proton, deuteron, or triton) to the heavy atom was observed (see reviews41-42>53) . The transfer is assumed to proceed via collisions of the small, neutral, and fast exotic hydrogen atom with the heavy nucleus.61 According to the experimental observations35 and the present theoretical picture of the transfer process, there is no particle transfer from atom ZM- if Z > 1.3. EXPERIMENTAL INFORMATIONThe Coulomb capture ratio seems to be the best observable quantity for testing the models of the atomic capture process. In the present paper we made an attempt to collect all available atomic capture ratios measured in binary mixtures of elements and simple binary compounds.1-38 We rejected, however:•the compounds with complicated chemical bond structure, e.g. CgCJlg or the peroxides;•the data which are related but not atomic capture ratios in the strict sense, e.g. line intensity ratios. 13/ 13/ 16-18^ •As a result, we have 321 experimental data points taken from Refs. 1-10, 12-18, 20-38. Unfortunately, there are systematic differences among the data measured at different places and times, using different methods, for the same compounds.48 Due to these and other inherent systematic errors, it is very difficult to perform a proper statistical test of the various theories. Following the generally accepted method, we shall compare the goodness of agreement between theory and experiment using the quantities:•the hydrogen-containing compounds and mixtures where the transfer effect obscures the atomic capture information;18/41-42;53(2a)(2b)- 3 -where Agxp ± aexp is the measured value, Atheor is a theoretical prediction and p is the number of fitted parameters. Quantities (2a) and (2b) are called - somewhat inaccurately - total chi-square and reduced chi-square.22>95»98>59The "best" parameters of the various models were estimated by minimizing (2). The computations have been performed using the MINUIT program62 on the VAX-11/780 computer at TRIUMF.In Table 1 we enlist our efforts to improve the models in order to obtain a better goodness of fit (x^)* In Tables 2 through 7 the experimental data are presen­ted in comparison with the predictions of five different models for various groups of chemical systems: mixtures, oxides, sulphides, halides, alloys and nitrides (BN). Table 8 summarizes the x^ -values for the various groups and models.4. DISCUSSION OF THE ATOMIC CAPTURE MODELSAs mentioned earlier, our aim is to aid the experimentalists in choosing among calculation methods when estimating atomic capture probabilities. To start with, we try to reproduce the gross atomic number dependence (Z-dependence) of the atomic cap­ture probabilities, possibly including the quasi-periodic oscillations first observed by Zinov e£ £l.8 on oxides (see Fig. 1); the consideration of molecular and solid- state effects 11_ 13/ 17- 18/ 28; 31/ 39/ 1*0-l+2/ 53-54 comes next.In their classic paper39 Fermi and Teller estimated the capture probabilities of mesons in atoms to be roughly proportional to their atomic numbers (Z-law):A(Z j,Z2) = Zj/Z2 • (3)Relation (3) has been deduced using the assumption that the capture rates are propor­tional to the stopping powers of the atoms. This is in contradiction with considera­tion B) when studied in detail, but has been commonly used for estimating the capture rates.The Z-law underwent numerous experimental tests1-38 and modifications. Baijal jit al^ .6 observed that the experimental capture ratios could be described as follows:A(Z1,Z2) = (|l)n , (4)and most of the results happened to be in the region 0.5 < n < 1.5 (n = 1 corresponds to the (3) Z-law).Zinov et^  al. proposed a modified, empirical Z-law for metallic halides and alloys8:A(Z1,Z2) = 0 .6 6  (Z j /Z 2) . (5 )Vogel £t al.,97 using a semi-classical approximation with the Thomas-Fermimodel of the atom, deduced a Z-dependence similar to Eqs. (3) and (4):A(Z1,Z 2) = (Z j /Z 2) 7 /6  . (6 )It has been shown in several works6;8/33/98 that the Z-law cannot give a satisfactory prediction of the atomic capture ratios in any of its forms (3-6). We98765432I0I2086420i987B54321- 4 -1 2 3 4 5 6 7 8 9 10 11Z 1 / Z 2Fig. 1. Atomic capture ratios A(Z1,Z2) measured in oxides, fluorides and chlorides1-38 against the ratio of the corresponding atomic numbers Zj/Z?. Note the characteristic oscillations in each case. The upper solid line corresponds to the Fermi-Teller Z-law and the lower one to the (7) modified Z-law. The dashed curve represents the predic­tions of the SPP model with the (26) parameter values (i.e. model 4 in Tables 2 through 8).Atomic capture ratio- 5 -tried to find an "optimal" Z-law by fitting parameters a and b of the general expressionA(Z1,Z2) = a(Zj/Z2)b . (7)As seen from Table 1, the best fit was obtained at a = 0.69 and b = 0.86 with a much X2 than for (3). This "empiric" Z-law is close to (5) but with a somewhat weaker Z-dependence.Having considered the energy loss of the meson in the atom along a trajectory which is close enough to the nucleus for the meson to be subsequently captured in an atomic orbit, H. Daniel45 deduced a Z-dependence of the following formZ1/32n(0.57Z )A(Z1»Z2> ° Zl/3to(0.57Z1) » (8)2 2which fitted the atomic capture ratios measured in metal halides rather well.16*45 Later, in order to describe the oscillations observed in oxides,8 Daniel55 revised Eq. (8) by including the atomic radii R(Z):Z1/32n(0.57Z )R(Z )A( z 1 > z 2) -  z l / 3 to (0V5^ W )  • ^2 2 1This expression predicts the oscillations in the oxides fairly well.33 However, its use is hindered by the somewhat undefined nature of the R(Z) radius. In his paper55 Daniel used the metallic radii of the metal atoms and the ionic radius R(0-2) of theoxygen. At the same time most of the oxides have a highly covalent chemical bond, andthere are considerable differences between the atomic, metallic, covalent and ionic radii. Even the best-defined crystal ionic radii have high systematic uncertainties: "Numerical values of the radii of the ions may vary depending on how they weremeasured. They may have been calculated from wave functions and determined from thelattice spacings or crystal structure of various salts. Different values are obtained depending on the kind of salt used or the method of calculating." (Quotation from Ref. 63.) Equation (9) is highly instructive for the theory of atomic capture but - in our opinion - cannot be used for predicting atomic capture ratios.Daniel's formula (8) gives a poor agreement with the experimental data; the surprisingly high x2 is mostly due to the systems with light elements such as He, Li, Be, B. We made attempts to improve Eq. (8) by using the form:Z1/3Jln(aZ +b)A(Z,,Z,) = — T75----- ---- . (10)1 2 Z1/32n(aZ +b) v J2 2As shown in Table 1, the best fit was obtained at a = 0.83 and b = 0.69 but with areduced x2 still considerably higher than that for Z-law ( 7 ) .A Z-dependence, somewhat similar to Eq. (8), has been empirically found by Petrukhin and Suvorov19 in an experimental study of pion capture in mixtures of hydro­gen with noble gases. After the removal of the contribution of pion transfer, the- 6 -observed atomic capture ratios A(Z,H) could be well approximated byA(Z,H) « (Z1/3-l) .Vasilyev et al.48 have generalized expression (11) in the formA(Z1,Z2) =A(Z ,H) Z 1/3-l1 1__A(Z2,H) Z 1 '3-l2(11)(12)and compared its predictions with the Coulomb capture ratios available at that time. Equation (12), as shown in Table 1, approximated the experimental values much better than the Z-law (3) and somewhat better than (8).Another line of the descriptions of the atomic capture data has been initiated by Schneuwly, Pokrovsky and Ponomarev (SPP).53/54 They formulated a model where the p(E) efficiency of an electron in atomic capture depends on the electron binding energy E:P ( E )  =1 for E < E0 for E > E(rigid boundary53), or(13)(14)(smooth boundary54), where E0 and Ec are parameters. Following the idea of Gerstein ejt al.,41 after the meson has knocked off an electron, it is presumably trapped in an atomic or a molecular orbit. Thus the capture ratio is defined as(15)where rij and n2 are the effective electron numbers of atoms Z^ and Z2:ni = ^  °(E;Pnj • (16)Here Ej t*le ener8y an<l nj is the population of level j in atom Z^ ; and v2 are the corresponding valencies. w is the transition probability of the meson from the molecular orbit to the atomic orbit of atom Z lt and is assumed to have one of the following forms:OK =  (l +  Z z i z f 11 \  P i ' l l /for a long-lived mesic molecular state, or“ 2 = P 1 e i +  ( l - P i 0 r P 2 e2){l l(17)(18)for a short-lived mesic molecular state.54 The p^'s are the valence electron densi­ties expressed in terms of a, the ionicity of the Z i~Z 2 bond:(19)The transition from molecular state to atomic states is described by the quantities q and 8:q2 = 1 " 9] (20)1 for E < EP(E) = T /E-E\2"expL V ' V '  J fo r E > E on ,+ 2 v , ( i)A(Z1,Z2) =  I 1---n 2+ 2  v 2 ( l - u )INTRODUCTIONExotic (muonic and hadronic) atoms can be considered as new nuclear probes used in practically all fields of physical sciences, from particle physics to materials sciences and biophysics. However, the basic problem of exotic atoms, their formation via Coulomb capture of heavy negative particles, has not been solved yet. The experi­mentalist working in this field needs a simple calculation method for estimating the probability WM(Zk) of formation of an exotic atom ZkM“ when the M~ particle is stopped in a sample consisting of elements ZJt Z2, etc. (Zk denotes both the element and its atomic number). For that, several models have been suggested. A direct test of the models is the comparison of their predictions with the experimental values of the so- called Coulomb capture or atomic capture ratio:WM (Z1>TRIUMIF- 8 31 RAIF- C RU-Usually, that comparison is made for a more or less arbitrarily chosen group of binary compounds, in most cases a subset of the data on oxides. The aim of the present work is to compare the predictions of the various models with the 321 avail­able Coulomb capture ratios measured in simple binary gas mixtures, alloys, and com­pounds of composition (Zx)k(Z2) £• 1-38 First, we summarize the theoretical basis of the different models,39-59 then we make attempts to modify them by introducing adjust­able parameters and fitting their predictions to the experimental data. Finally, we compare the predictions of the different models. We do not give an exhaustive bibliography on exotic atoms here, the reader is advised to consult Ref. 60 for that.ATOMIC CAPTURE - GENERAL CONSIDERATIONSLet us summarize the common basis of the various descriptions of the atomic capture: the theoretical statements which seem to be supported by unambiguous experi­mental evidence or which most of the recently published theoretical works agree upon.A) The atomic capture process is similar for all negative particles, muons or hadrons.39-42)44-59 In the following we shall use the general term "meson".B) The slowing down and atomic capture of mesons are competing processes in the kine­tic energy region E^ < 10 keV, where their velocities approach those of the atomic electrons.40-42;46-47 However, in contradiction to the earlier assump­tions,39'41-42’44-45;49-52;58 the capture rates of mesons in atoms are not propor­tional to the atomic stopping powers. This has been predicted theoretically46; 56 and observed experimentally.35C) The Auger process (meson capture through electron ejection) is responsible for all the details of the meson capture because for almost every meson transition from the continuum to an atomic bound state the Auger cross sections dominate the radiative ones. 40-44; 46-47< 49-58D) In dense systems the mesons do not slow down to thermal velocities as they are captured at much higher energies, E^ ^ 10 eV. 40;43» 46-47’53< 56> 58- 7-OP = — —  ; e2 - — —  • (2i)n 1+2Vj n2+2v2It is shown in Ref. 54 that Eqs. (14-16) and (18-21), i.e. the smooth boundary approx­imations with w2 and parametersI Ex = 70 eV if Z < Z =18E. = 15 eV ; E- = ' E = ioo eV if Z > Z = 18 ’ (22)z Oo ccan describe the atomic capture ratios measured in oxides better than any of the simple relations (3-6), (8), (12). However, it is mentioned in Ref. 54 that the (22) parameter values are not optimized in the least-squares sense. Our attempts to opti­mize the SPP model are summarised in Table 1. We have tried to find an improvement for both the rigid- and smooth-boundary approximations, using both forms, (17) and (18), of the (u transition probability. The rigid-boundary model has only one para­meter, the E0 cut-off energy. The smooth-boundary model has been fitted with two different p(E) efficiency functions: the original Gaussian (14) and a Fermi functionP(E) = l+exp{(E-Eo)/Ec } • (23)In Table 1, if Z0 is not presented among the parameters, then we have used Ec = E1 with no change in the width. We also tried to find improvement in the qj probability by fitting the exponent x in: t9 + ikf (24)It is quite clear from Table 1 that the best agreement is given by the SPP model in any form. Furthermore, the agreement between predictions and experimental values is much better for the smooth-boundary approximation. The best fits are obtained when using the original SPP model with modified parameters. The cut-off energy E0 tends to be zero in every case. The increase in the Ec width at Z > 18 suggested in Ref. 54 seems to be well established; its removal increases the Xr value, and the fitting changes the Z0 value only slightly (from Z0 = 18 to 15-17). The fitted values of exponent x in (24), x = 1.7-1.8, are not far from the original 2, and these changes do not affect the obtained x^  value very much. The goodness of fit is not sensitive to the actual form of the p(E) distribution, whether it is Gaussian or Fermian. It is, however, sensitive to the actual form of the transition probability of the meson from the molecular to atomic orbit, preferring the short-lived molecular state described by Eq. (18).In Tables 2 through 7 the experimental data are presented together with the theoretical predictions of five models from Table 1: the generalised Z-law (7) with a = 0.69 and b = 0.86; the modified model of Daniel (10) with a = 0.83 and b = 0.69; the model (12) of Vasilyev e£ al. and two versions of the SPP model with Gaussian efficiency function (14) and w2 probability. We did not feel any justification for the removal of experimental data from the comparison as removing a dozen of those with the biggest deviations does not affect the final picture.- 8 -In Table 8 the total x^values are presented for the six groups of binary sys­tems and the five chosen models. For the mixtures where no chemical effects are in­volved, formula (12) gives the best predictions; for the compounds the SPP model is the best. Therefore, we made an attempt to improve on formula (12) by including the terms of the molecular orbits from Eq. (15). With adjustable parameters a and b, it assumed the following form:Z1/3 - a + b(2v w)A(Z1,Z2) - zj/3 _ a + b(2v2(l-w)) ■ (25)For the probability u> of the transition from the molecular to an atomic orbit on Zj weused Eq. (18), the fast transition approximation. From the results presented in Table 1 it is clear that we got back the initial (12) form for the atomic capture in the mixtures, and including molecular effects does not improve the x| considerably.CONCLUSIONWe tested the various descriptions of the atomic capture of mesons against 321 experimental atomic capture ratios. The comparison shows that there is no adequate model for the atomic capture yet. The model proposed by Schneuwly, Pokrovsky andPonomarev gives the best agreement with the measured data, with zero boundary andslightly modified parameters:v - n . v - S Ei ” 86 eV for Z < 15o * c | E2 = 119 eV for Z > 15 * (26)For mixtures of elements (gases) the use of the (12) empirical formula is recommended. To facilitate the application of the SPP model for the estimation of atomic capture probabilities, we enclose a list of the effective electron numbers Ze^f, calculated by using models 4 and 5 of Tables 2 through 7 for the elements of the periodic system (see Table 9). The Zeff value listed in Table 9 corresponds to the effective numberof all electrons in the atom. The effective number of the core electrons, n, used inV9- (15)> can be obtained from Zeff by subtracting v, the actual number of valence electrons:n = Zeff - v . (27)This is a good approximation as the binding energies of the valence electrons are muchsmaller than those of the core electrons (i.e. v = vett'Finally, we emphasize the need for an adequate method of estimating the proba­bility of Coulomb capture of mesons in atoms. 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Schneuwly, "Exotic Atoms", Proc. 1st Course of Int. School of Physics of Exotic Atoms, ed. G. Fiorentini, G. Torelli (Pisa, 1977) p.255.54. H. Schneuwly, V.N. Pokrovsky and L.I. Ponomarev, Nucl. Phys. A312, 419(1978).55. H. Daniel, Z. Physik A291, 29 (1979).56. G.Ya. Korenman and S.I. Rogovaya, Radiat. Eff. 46 ,  189 (1980).57. J.S. Cohen, R.L. Martin and W.R. Wadt, Phys. Rev. A24, 33 (1981).58. V.S. Evseev, T.N. Mamedov, V.S. Roganov and N.I. Kholodov, Dubna report JINR-E4- 81-237, 1981.59. T. von Egidy and F.J. Hartmann, Phys. Rev. A26, 2355 (1982).60. D. Horvath and R.M. Lambrecht, Exotic Atoms. A Bibliography 1939-1982 (Elsevier,Amsterdam 1983) (in press).61. S.S. Gershtein, Zh. Eksp. Teor. Fiz. 43 (1962) 706; Sov. Phys. JETP 16 ,501 (1963).62. F. James and M. Roos, MINUIT, CERN Program Library.63. Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 1980) p.F-214.- 11 -Table 1. Comparison of atomic capture modelsFunctionDegreesoffreedomParametersTotalCHIsquareReducedCHIsquareModel Original Z-law 321 - 42152. 6 131. 32Model : Z-law A (Z11 Z2)=A*(Z1/Z2)**B320 A= 1. 00B— 0. 73 +/- 0. 00221837. 5 68. 24Model : Z—law A (Z1iZ2)=A*(Z1/Z2)»*B320 A= 0. 61 +/- 0. 001 B= 1. 0014418. 4 45. 06Model : Z-law A(Z11 Z2)=A*(Z1/Z2)**B319 A= 0. 69 +/- 0. 0004 B= 0. 86 +/- 0. 000812877 8 40. 37_n i “ _Model : Vasilyev et al W(Z)= Z**<l/3> - 1321 - 21905. 3 68. 24Model Vasilyev et al Modified version (eq. 25)319 A= 1. 00 +/- 0. 000 B= 0. 28 +/- 0. 00418145. 8 56. 88Model : Daniel W(Z)=Z**(l/3)*logCA*Z+B>321 A= 0. 57 Original B= 0. 00 values192280. 7 599. 01Model : DanielW(Z)=Z**(l/3)*log(A*Z+B>320 A= 1 28 +/- 0. 0015B= 0. 0020332. 9 63. 54Model DanielW< Z > = Z**(l/3)*log(A*Z+B)321 A= 1 B= 021166. 4 65. 94Model : DanielW<Z) = Z**<l/3)*log <A*Z+B>321 A= 1 B= 120621. 6 64. 24Model : Daniel W(Z)=Z**(l/3)*log(A*Z+B)319 A= 0. 83 +/- 0 009 B= 0. 69 +/- 0 00220202. 1 63. 33Model : SPP Rigid boundary Omega-1320 E0= 92. 13 +/- 0. 27 X = 28342. 8 26. 07Model : SPP Rigid boundary Omega-2320 E0= 92. 60 +/- 0. 44 X = 28773. 1 27. 42Model SPP Smooth boundary Gaussian distribution Omega-1319 E0= 13. 11 +/- 0. 02 El= 75. 68 +/- 0. 44 X = 26267. 8 19. 65Model : SPP Smooth boundary Gaussian distribution Omega-1318 E0= 10. 59 +/- 0. 44 El= 79. 98 +/- 0. 51 E2= 73. 00 + /- 0. 74 ZO= 18 X = 26201. 4 19. 50Model : SPP Smooth boundary Gaussian distribution Omega-2319 EO= 00. 00 +/- 0. 01 El= 88. 76 +/- 0. 15 X = 25386. 3 16. 88Model SPP Smooth boundary Gaussian distribution Omega-2318 E0= 15 Original El= 70 parameters E2= 100 Z0= IB X = 24972. 5 15. 64Model : SPP Smooth boundary Gaussian distribution Omega-2318 E0= 00. 00 + /- 0. 12 El= 85. 24 +/- 0. 76 E2= 111. 86+/- 0. 94 Z0= 18 X = 24738. 8 14. 90Model : SPP 317 EO= OO. OO +/- 0. 19 El— 86. 12 + /- 0. 31 E2= 119. 06+/- O. 60 Z0= 15 (fitted) X = 24578. 6 14 44Smooth boundary Gaussian distribution Omega-2- 12 -Table 1. Comparison of atomic capture models <cont'd>FunctionDegreesoffreedomParametersTotalCHIsquareReduced CHI squareModel : SPP Smooth boundary Gaussian distribution Omega-2317 E0= El = E2= ZO= X *00. 00 +/- 0. 07 84. 74 +/- 0. 33 113. 65+/- 1. 53 181. 71 +/- 0. 034704. 9 14. 84Model : SPP Smooth boundary Gaussian distribution Omega-2316 E0= 00. 00 +/- 0. 02 4540. 3 14. 37E2= Z0= X =121. 09+/- 0. 56 15 (fitted) 1. 69 +/- 0. 01Model : SPP Smooth boundary Fermi distribution Omega-1319 E0= El — X =77. 37 18. 72 2+/- 0. 23 +/- 0. 136238. 1 19. 56Model : SPP Smooth boundary Fermi distribution Omega-1318 E0= El- E2= Z0= X =75. 64 20. 60 27. 18 18 2+/- 0. 57 +/- 0. 33 +/- 0 496185. 8 19. 45Model : SPP Smooth boundary Fermi distribution Omega-2319 EO= El = X =48. 21 38. 79 2+/- 0. 04 +/- 0. 025262. 2 16. 50Model : SPP Smooth boundary Fermi distribution Omega-2318 E0= El = E2= ZO= X =63. 90 33. 18 20. 53 18 2+/- 0. 22 +/- 0. 19 +/- 0. 275024. 7 15. 80Model : SPP Smooth boundary Fermi distribution Omega-2317 E0= E 1 = E2= Z0= X =63. 65 33. 98 19. 15 17 2+/- 0. 29 +/- 0. 16 +/- 0. 22 (fitted)4738. 0 14. 95Model : SPP Smooth boundary Fermi distribution Omega-2317 EO= El = E2= ZO= X =63. 8133. 38 20. 40 181. 89+/- 0. 41 +/- 0. 25 +/- 0. 33+/- 0 045017. 8 15. 83Model : SPP Smooth boundary Fermi distribution Omega-2316 E0= E1 = E2= Z0= X =64. 61 33. 29 18. 58 171. 84+/- 0. 39 +/- 0. 12 + /- 0. 42 (fitted) +/- 0 044728. 0 14. 96- 13 -CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SQUARESEXPERIMENTTARGETModels:1.) Modified Z-law: O. 69*<Z1/Z2>**0. 862. ) Z**(l/3)-l by Vasilyev et al.3.) Daniel's model modified: Z**<l/3)*log(O. 83*Z+0. 69)4. > SPP model: Omega-2 with Ouassian cutoff (EO-O, El-86 eV. E2-119 eV. ZO-15, q(Z)-Z**2>5. > SPP model: Omega-2 with Gaussian cutoff (E0=0. El-86 eV. E2-121 eV. ZO-15. q<Z)=Ze*l. 69)Table 2. Test of atomic capture models for simple binary mixturesName Z1 Z2 A<Z1/Z2> Ref. Model 1 Model 2 Model 3 Model 4 Model 5He+He-3 2 2 0.750 +- 0. 130 35 0.69 0.2 1.00 3.7 1.00 3.7 1.00 3.7 1.00 3.7N2+He—3 7 2 3. 520 +- 0. 230 10 2. 03 42. 2 3. 51 O. 0 3. 33 0. 7 2. 58 16. 7 2. 58 16. 7N2+He-3 7 2 3.740 ♦- 0. 160 35 2.03 114.7 3.31 2.0 3.33 6.7 2.58 52.7 2.58 52.702+He—3 B 2 4.680 +- O. 180 33 2.27 178.8 3.83 21.4 3.70 29.6 3.04 83.5 3.04 83.3Ne+He-3 10 2 4. 130 +- 0. 150 35 2.75 84.2 4.44 4.3 4.40 3.1 3.85 3.6 3.85 3.6Ar+He—3 18 2 4.340 +- 0. 160 35 4.57 0.0 6.24 112.3 6.69 181.1 4.22 4 0 4.23 3.7Kr+He-3 36 2 8. 000 +- 0. 230 35 8.29 1.6 8.86 13.9 10.49 117.2 7.25 10.6 7.33 8.6Xe+He-3 34 2 8. 660 +- 0. 310 33 11.74 99.0 10.69 43.1 13.41 234.3 B. 70 0.0 8.78 0.1N2+02 7 8 0. 834 +- 0. 031 28 0. 62 49. 8 O. 91 6. 5 O. 90 4. 4 O. 85 O. 3 0. 85 O. 3He+Ar 2 18 0. 150 +- 0.010 9 0.10 20.9 0.16 1.1 0.15 0.0 0.24 75 7 0.24 74.6He+Ar 2 18 O. 210 +- O. 040 27 0.10 7.0 0.16 1.5 0 15 2.3 0.24 0.5 0.24 0.4N2+Ar 7 18 O. 310 +- O. 020 9 O. 31 103. 8 0. 36 7. 1 0. 30 O. 4 0. 61 25. 6 0. 61 24. 8Ne+Ar 10 IB 0. 610 +- 0. 020 9 0. 42 93. 9 0. 71 26. 2 O. 66 5. 4 O. 91 227. 1 O. 91 223. 7Ne+Ar 10 IB 0.900 +- O. 120 13 0.42 16.3 0.71 2.4 0.66 4.1 0.91 0.0 0.91 0.0Ne+Ar 10 18 O. 710 +- O. 030 27 0. 42 93. 9 0. 71 0. O O. 66 3. 2 0. 91 43. 1 0. 91 44. 1Kr+Ar 36 IB 1. 340 +- O. 060 27 1.23 2.1 1.42 1.8 1.57 14.4 1.72 39.8 1.73 42.7Total chi-square for 16 points 910.3 247.3 610.6 388.8 383.314 -Table 3. Test of atomic capture models for simple binary oxidesTARGET EXPERIMENT CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SGUARESName Z1 Z2 A(Z1/Z2) Ref. Model 1 Model 2 Model 3 Model 4 Model 5Be O 4 8 O. 120 +- 0.040 8 0 3B 42.3 0.59 136.5 0.55 117.4 0.11 0.1 0.12 0.0B2 03 5 8 0.220 +- 0.050 8 0.46 23.2 0.71 96.0 0.68 83.5 0.16 1.5 0. IB 0.7CO 6 8 0. 766 +- 0. 030 28 O. 54 57. 4 0. 82 2. 9 O. 79 0. 7 0. 51 70. 2 0. 53 64. 0C 02 6 8 0. 430 +- O. 020 30 0. 54 29. 6 O. 82 374. 7 O. 79 326. 6 O. 30 43. 4 O. 32 31. 3NO 7 8 0.959 +- 0.030 28 0.62 131.4 0.91 2.4 0.90 4.0 0.77 40.7 0.77 38.0Mg 0 12 8 O. 830 +- 0. 070 8 0.98 4.5 1.29 43.1 1.36 57.2 1.03 8.5 1.02 7.1Mg 0 12  8 0.830 +- 0.040 24 0.98 13.7 1.29 131.9 1.36 175.2 1.03 26.2 1.02 21.6Mg O 12 8 0.800 +- 0.020 30 0.98 79.1 1.29 598.9 1.36 782.3 1.03 137.6 1.02 116.7Mg O 12 8 0. 890 +- 0. 050 33 0.98 3.1 1.29 63.8 1.36 88.1 1.03 8.4 1.02 6.4A12 03 13 8 0.650 +- 0.060 1 1.05 43.9 1.35 136.6 1.44 173.6 0.93 21.6 0.90 17.6A12 03 13 8 0.850 +- 0.060 8 1.05 10.8 1.35 69.8 1.44 96.8 0.93 1.7 0.90 0.7A12 03 13 8 0.840 +- 0.030 30 1.05 47.9 1.35 290.5 1.44 400.6 0.93 8.8 0.90 4.2A12 03 13 8 0.740 +- 0.040 33 1.05 59.1 1.35 233.6 1.44 306.6 0.93 22.3 0.90 16.3Si O 14 8 0. 960 +- 0. 050 33 1.12 9.8 1.41 81.1 1.52 124.9 0.93 0.3 0.91 1.0Si 02 14 8 0.570 +- 0.050 1 1.12 119.5 1.41 282.3 1.52 360.0 0.90 42.9 0.86 33.2Si 02 14 8 O. 790 +- O. 070 8 1.12 21.8 1.41 78.5 1.52 108.4 0.90 2.4 0.86 0.9Si 02 14 8 0. 860 +- 0. 070 22 1.12 13.4 1.41 61. B 1.52 88.5 0.90 0.3 0.86 0.0Si 02 14 8 O. 960 +- 0. 040 30 1.12 15.3 1.41 126.6 1.52 195.1 0.90 2.4 0.86 6.5Si 02 14 8 0.840 +- 0.040 33 1.12 47.8 1.41 203.2 1.52 287.9 0.90 2.1 0.86 0.2P2 05 15 8 0. 930 +- O. 100 1 1. 18 6. 5 1. 47 28. B 1. 59 44. 1 O. 99 0. 4 O. 94 O. 0P2 05 15 8 0.870 +- 0.030 30 1.18 110.1 1.47 395.0 1.59 583 1 0.99 16.8 0.94 5.1 P2 05 15 8 1. OOO +- O. 050 33 1.18 13.7 1.47 86.9 1.59 141.3 0.99 0.0 0.94 1.6Ca O 20 8 1.360 +- 0.100 8 1.52 2.5 1.71 12.6 1.94 33.9 1.61 6.1 1.58 4.8Ca O 20 8 1.450 +- 0.090 18 1.52 0.6 1.71 B. 6 1.94 29.9 1.61 3.0 l'. 58 2.0 Ca O 20 8 1. 710 +- 0.090 37 1.52 4.6 1.71 0.0 1.94 6.6 1.61 1.3 1.58 2.1Sc2 03 21 8 2.780 +- 0.200 8 1.58 35.9 1.76 26.1 2.01 15.0 1.79 24.3 1.76 26.1Ti O 22 8 2.640 +- 0.190 33 1.65 27.3 1.80 19.5 2.07 9.0 1.97 12.6 1.94 13.7Ti 02 22 8 2.700 +- 0.200 8 1.65 27.7 1.80 20.2 2.07 10.0 1.99 12.7 1.94 14.4Ti 02 22 8 1.900 +- 0.100 18 1.65 6.4 1.80 1.0 2.07 2.9 1.99 0.8 1.94 0.2Ti 02 22 8 1.B70 +- 0.190 21 1.65 1.4 1. BO 0.1 2.07 1.1 1.99 0.4 1.94 0.1Ti 02 22 8 2. 170 +- 0. 110 30 1.65 22.6 1.80 11.2 2.07 0.8 1.99 2. B 1.94 4.3Ti 02 22 8 2. 700 +- 0. 130 33 1.65 65.6 1.80 47.7 2.07 23.6 1.99 30.1 1.94 34.1V2 03 23 8 2. 190 +- O. 180 IB 1. 71 7. 1 1. 84 3. 7 2. 13 O. 1 2. 14 0. 1 2. 10 0. 2V2 04 23 8 2. 280 +- O. 230 18 1. 71 6. 1 1. 84 3. 6 2. 13 O. 4 2. 15 O. 3 2. 11 0. 6V2 04 23 8 2. 700 +- O. 190 33 1.71 27.1 1.84 20.3 2.13 9.0 2.15 8.3 2.11 9.8V2 05 23 8 3. 100 +- 0. 200 8 1.71 48.2 1.84 39.4 2.13 23.5 2.17 21.8 2.11 24.4V2 05 23 8 2. 680 +- O. 140 18 1.71 47.9 1.84 35.7 2.13 15.4 2.17 13.5 2.11 16.5V2 05 23 8 2.860 +- 0.200 33 1.71 33.0 1.84 25.8 2.13 13.3 2.17 12.0 2.11 14.0Cr2 03 24 8 3. 000 +- O. 170 8 1.77 51.9 1.88 43.1 2.19 22.7 2.32 15.8 2 29 17.6Cr2 03 24 8 2. 040 +- 0.110 18 1.77 5.8 1. B8 2.0 2.19 1.9 2 32 6.7 2.29 5.0Cr2 03 24 8 2.630 +- 0. 130 30 1.77 43.3 1.88 32.9 2.19 11.4 2.32 5.5 2.29 7.0Cr2 03 24 8 3.450 +- 0.250 33 1.77 44.9 1.88 39.2 2.19 25.4 2.32 20.3 2.29 21.6Cr2 03 24 8 2. 650 +- O. 200 36 1.77 19.1 1.88 14.6 2.19 5.3 2.32 2.6 2.29 3.3Cr 03 24 8 2.960 +- 0.200 30 1.77 35.1 1. 8B 28.9 2.19 14. B 2.37 8 6 2.31 10.6Cr 03 24 8 3.520 +- 0.180 33 1.77 94.0 1.88 82.6 2.19 54.5 2.37 40.6 2.31 45.2Cr 03 24 8 3. 230 +- 0. 220 36 1. 77 43. 7 1. 88 37. 4 2. 19 22. 3 2. 37 15 1 2. 31 17. 5Mn 02 25 8 3.000 +- 0.170 30 1.84 46.7 1.92 40.1 2.25 19.5 2.38 13.2 2.34 15.1Mn 02 25 8 2. 600 +- O. 190 33 1.84 16.1 1.92 12.7 2.25 3.4 2.38 1.3 2.34 1.9Fe2 03 26 8 2.430 +- 0.240 21 1.90 4.9 1.96 3. B 2.31 0 3 2.57 0.4 2.54 0.2Fe2 03 26 8 3. 210 +- 0. 200 33 1.90 42.8 1.96 38.9 2.31 20.4 2.57 10.1 2.54 11.3Co2 03 27 8 3. 040 +- 0. 290 21 1.96 13.8 2.00 12.9 2.36 5.4 2.69 1.4 2.66 1.7- 15 -Table 3. Test of atomic capture models for simple binary oxides (cont'd)TARGET EXPERIMENT CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SGUARES Name Z1 Z2 A(Z1/Z2) Ref. Model 1 Model 2 Model 3 Model 4 Model 5S7 B 3 700 +~ 0.380 33 1.96 20.9 2.00 20.0 2.36 12.4 2.69 7 0 2 66 7 5 “ 84 2Z 8 3. 350 +- 0.250 33 1.96 30.7 2.00 29.2 2.36 15.5 2.69 6.9 2 66 7 6Cu2 0 29 8 3. 800 +- O. 900 8 2. 09 3. 6 2. 07 3. 7 2. 47 2. 2 2. 97 0 8 2 96 0 98u 8 o 6 140 +- 0.850 6 2.09 22.7 2.07 22.9 2.47 18.6 3.01 13.6 2 99 13 85|u 0 29 8 3. 600 +- 0. 400 8 2. 09 14. 3 2. 07 14. 6 2. 47 7. 9 3.01 2 2 2 99 2 48u 8 29 8 4. 060 +- 0.230 30 2.09 73.5 2.07 74.7 2.47 47.5 3.01 20.8 2 99 21 88u 8 29 8 3.260 +- 0.230 33 2.09 25.9 2.07 26.7 2.47 11.7 3.01 1 2 2 99 1 4Zn 8 ~ f 2. 220 +- 0.060 7 2.15 1.3 2.11 3.5 2.53 26.5 2.94 144.9 2 92 136 2Zn 8 22 2.660 +- 0.320 8 2.15 2.5 2.11 3.0 2.53 0.2 2.94 0.8 2.92 0 7 *n 8 30 8 2. 390 +- 0. 100 30 2. 15 5. 7 2. 11 8. 0 2. 53 1.9 2. 94 30. 5 2. 92 2S7 BZn 0 30 8 3. 060 +- 0. 240 33 2.15 14.4 2.11 15.8 2.53 4.9 2.94 0.2 2.92 0 3Ga2 03 31 B 2. 770 +- 0. 200 33 2. 21 7. 8 2. 14 9. 9 2. 58 0. 9 2 95 OB 2 92 O 622 8 2.900 +- 0.210 33 2.27 8.9 2.17 11.9 2.63 1.6 3.01 0.3 2 98 0 103 33 8 3 390 +- 0. 250 33 2. 33 17. 8 2. 21 22. 4 2. 69 8. 0 2. 99 2. 6 2. 97 2 9Se 02 34 8 2. 720 +- 0. 200 33 2. 39 2. 6 2. 24 5. 8 2. 74 0 0 3. 13 4. 2 3. 10 3' 6Sr 0 38 8 2. 120 +- O. 110 37 2. 64 21. 9 2. 36 4 8 2. 93 54. 3 2. 19 O. 4 2. 18 0 3Y2 03 39 8 1.830 +- 0.120 8 2.69 51.9 2.39 21.9 2.98 91.5 2.23 11.0 2.22 10 5Y2 03 39 8 2- 070 +- O. 130 IB 2. 69 23. 1 2. 39 6. 1 2. 98 48. 8 2. 23 1.5 2. 22 1 3Y2 03 39 8 2. 190 +- O. 160 33 2.69 9.9 2.39 1.6 2.98 24.2 2.23 0.1 2.22 0 0Zr 02 40 B 2. 380 +- 0. 160 8 2. 75 5. 5 2. 42 O. 1 3. 02 16 2 2. 30 O. 3 2. 28 0 4Z: 82 48 8 2. 620 +- 0.190 33 2.75 0.5 2.42 1.1 3.02 4.5 2.30 2.9 2.28 3.22 05 41 B 2. 950 +- O. 230 33 2. 81 O. 4 2. 45 4. 8 3. 07 O. 3 2. 49 3. 9 2. 47 4, 4Mo 03 42 8 3. 480 +- O. 230 8 2. 87 7. O 2. 48 19. 1 3. 12 2. 5 2. 71 11.3 2. 67 12 4Mo 03 42 8 3.600 +- O. 290 33 2.87 6.3 2.48 15.0 3.12 2. B 2.71 9.5 2.67 10^3Tc 02 43 8 3. 260 +- O. 310 33 2. 93 1.1 2. 50 6. O 3. 16 O. 1 2. 7B 2. 3 2. 76 2. 6Pd 0 46 B 3. 570 +- O. 440 33 3.11 1.1 2.58 5.0 3.29 0.4 3.24 0.6 3.23 0.6Ag2 0 47 8 3. 830 +- O. 320 33 3.16 4.3 2.61 14.6 3 33 2.4 3.17 4 2 3.16 4.3Cd 0 48 8 6.700 +- 1.500 8 3.22 5.4 2.63 7.3 3.38 4.9 3.21 5.4 3.20 5.4 Cd 0 48 8 2. 470 +- O. 220 18 3.22 11.7 2.63 0.6 3.38 17.0 3.21 11.5 3.20 11.2Cd 0 48 8 2. 500 +- O. 280 21 3. 22 6. 6 2. 63 O. 2 3. 38 9. 8 3. 21 6. 5 3. 20 6. 3Cd 0 48 8 3. 140 +- 0.250 33 3.22 0.1 2.63 4.1 3.38 0.9 3.21 0.1 3.20 0.1In2 03 49 8 2. 940 +- 0. 280 8 3.28 1.5 2.66 1.0 3.42 2.9 3.28 1.5 3.27 1.4In2 03 49 8 2.920 +- 0.310 33 3.28 1.3 2.66 0.7 3.42 2.6 3.28 1.3 3.27 1.3Sn 02 50 8 3. 170 +- O. 240 8 3.34 0.5 2.68 4.1 3.46 1.5 3.36 0.6 3.35 0.6Sn 02 50 8 3.020 +- 0.230 33 3.34 1.9 2.68 2.1 3.46 3.7 3.36 2.2 3.35 2.0Sb2 03 51 8 2. 790 +- O. 140 6 3. 39 IB. 6 2. 71 0. 3 3. 50 25. 8 3. 35 16. 2 3. 35 15. 9Sb2 03 51 8 3. 480 +- O. 350 8 3. 39 O. 1 2. 71 4. 9 3. 50 O. O 3. 35 0. 1 3. 35 0 1Sb2 03 51 8 3. 520 +- 0. 280 33 3. 39 O. 2 2. 71 8. 4 3. 50 0. 0 3. 35 0. 4 3. 35 O. 4Sb2 05 51 8 1.730 +- O. 090 8 3.39 341.8 2.71 118.2 3.50 387.4 3.45 365.1 3.43 358.4Te 02 52 B 3. 220 +- O. 250 33 3. 45 0. 9 2. 73 3. 8 3. 54 1. 7 3. 48 1. O 3. 47 1. 0Ba 0 56 8 2.270 +- O. 220 8 3.68 41.0 2.83 6.4 3.70 42.3 2.77 5.2 2.78 5.403 0 56 8 1.450 +- O. 180 21 3.68 153.2 2.83 5B. 4 3.70 156.4 2.77 53.8 2.78 54.5La2 03 57 8 2. 210 +- O. 250 21 3. 73 37. 2 2. 85 6. 5 3. 74 37. 4 2. 78 5. 2 2. 79 5. 4La2 03 57 8 2. 730 +- O. 330 33 3. 73 9. 3 2. 85 0. 1 3. 74 9. 4 2. 78 O. O 2. 79 0. OCe 02 58 B 3. 700 +- O. 400 21 3. 79 O. 1 2. 87 4. 3 3. 78 O. 0 3. 01 3. O 3. 01 2. 9Ce 02 58 8 4. 500 +- O. 550 33 3.79 1.7 2.87 8.8 3.78 1.7 3.01 7.3 3.01 7.3Nd2 03 60 B 5.130 +- O. 350 33 3.90 12.3 2.91 40.1 3. B5 13.3 3.21 30.1 3.21 29.9Sm2 03 62 8 3. 090 +- O. 340 8 4. 01 7. 4 2. 96 O. 2 3. 93 6. 1 3. 44 1.0 3. 44 1.1Sm2 03 62 8 4.400 +- O. 740 33 4.01 0.3 2.96 3.8 3.93 0.4 3.44 1.7 3.44 1.7Eu2 03 63 8 3. 600 +- 0. 400 21 4. 07 1.4 2. 98 2. 4 3. 97 O. B 3. 55 O. O 3. 55 0. 0Eu2 03 63 8 4. 340 +- O. 460 33 4. 07 O. 3 2. 98 8. 8 3. 97 O. 7 3. 55 2. 9 3. 55 2. 9- 16 -Table 3. Test of atomic capture models for simple binary oxides (cont'd)TARGET EXPERIMENT CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SGUARESName Z1 Z2 ACZ1/Z2) Ref. Model 1 Model 2 Model 3 Model 4 Model 5Gd2 03 64 8 5.520 +- 0.330 33 4.13 17.8 3.00 58.3 4.00 21.2 3.55 35.6 3.55 35.5Dy2 03 66 8 4.700 +- 0.500 21 4.24 0.9 3.04 11.0 4.07 1.6 3.94 2.3 3.94 2.3Dy2 03 66 8 5. 790 +- O. 610 33 4. 24 6. 5 3. 04 20. 3 4. 07 7. 9 3. 94 9. 2 3. 94 9. 2Yb2 03 70 8 3. 180 +- 0. 340 8 4. 46 14. 1 3. 12 O. O 4. 21 9 3 4. 49 15. O 4 49 14. 8Yb2 03 70 8 6. B50 +- 0.420 33 4.46 32.5 3.12 78.8 4.21 39.4 4.49 31.4 4.49 31.7Lu2 03 71 8 4. 400 +- 0. 500 21 4. 51 O O 3. 14 6. 3 4. 25 0. 1 4. 60 O 2 4. 59 0. 1Lu2 03 71 8 5.310 1— 0.580 33 4.51 1.9 3.14 14.0 4 25 3 3 4.60 1.5 4.59 1.5Ta2 05 73 8 6. 000 +- O. 600 21 4. 62 5. 3 3. 18 22. 1 4. 32 7. 9 4. 89 3. 4 4. 88 3. 5Ta2 05 73 8 7.200 +- 0.730 33 4.62 12.5 3.18 30.3 4.32 15.6 4.89 10.0 4.88 10.1U 03 74 8 4. 700 +- O. 500 21 4. 67 O. O 3. 20 9. O 4. 35 O. 5 5. 06 O. 5 5. 05 O. 5W 03 74 B 5.750 +- 0.670 33 4.67 2.6 3.20 14.5 4.35 4.4 5.06 1.1 5.05 1.1T12 03 81 8 4. 000 +- 0. 500 21 5.05 4.4 3.33 1.8 4.58 1.4 4.28 0.3 4.31 0.4T12 03 81 8 4. 810 4— 0. 570 33 5. 05 O. 2 3. 33 6. 8 4. 58 O. 2 4. 28 O 9 4. 31 0. 8Pb 0 82 8 4. 560 +- 0. 530 6 5.11 1.1 3.34 5.3 4.61 0.0 4.00 1.1 4.03 1.0Pb O 82 8 5.800 4— 0.700 8 5.11 1.0 3.34 12.3 4.61 2.9 4.00 6.6 4.03 6.4Pb O 82 B 4.100 4— 0.400 21 5.11 6.3 3.34 3.6 4.61 1.6 4.00 0.1 4.03 0.0Pb O 82 8 4.880 4— 0.550 33 5.11 0.2 3.34 7 8 4.61 0.2 4.00 2.6 4.03 2.4Bi2 03 83 8 4.300 4— 0.500 8 5.16 3.0 3.36 3.5 4.65 0.5 3.90 0 6 3.93 0.6Bi2 03 83 8 3.100 4— 0.400 21 5.16 26.5 3.36 0.4 4.65 14.9 3.90 4.0 3.93 4.3Bi2 03 83 8 3. 770 +- 0. 430 33 5.16 10.4 3.36 0.9 4.65 4 1 3.90 0.1 3.93 0.1Th 02 90 8 2. 900 4— O. 400 21 5. 53 43. 3 3. 48 2. 1 4. 86 24. 1 3. 25 O. 8 3. 27 0. 8Th 02 90 8 3.570 4— 0.500 33 5.53 15.4 3.48 0.0 4 86 6.7 3.25 0.4 3.27 0.4U 02 92 8 3. 600 4— O. 400 21 5. 64 25. 9 3. 51 0. O 4. 92 10. 9 3. 65 O. 0 3. 66 0. 0U 02 92 8 4. 650 4— 0. 550 33 5. 64 3. 2 3. 51 4. 3 4. 92 0. 2 3. 65 3. 3 3. 66 3. 2U 03 92 8 6. 000 4— O. 500 8 5. 64 O. 5 3. 51 24. 7 4. 92 4. 6 3. 74 20. 5 3. 75 20. 3Total chi-square for 127 points 3005.6 5194.8 6265.4 1708.5 1642.8Models:1.) Modified Z-law: O. 69e<Zl/Z2)**0. 862. ) Z**(l/3)-l by Vasilyev et al.3.) Daniel's model modified: Z**< 1/3)*109<0. 83*Z+0 69)4. ) SPP model: Omega-2 with Guassian cutoff (EO-O. El-86 eV< E2-119 eV, ZO-15, q(Z)«Z**2)5. ) SPP model: Omega-2 with Gaussian cutoff (EO-O. El-86 eV. E2-121 eV, ZO-15, q(Z)=Z**1. 69)- 17 -Table 4. Test of atomic capture models for simple binary halidesTARGET EXPERIMENT CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SQUARESName Z1 Z2 A(Z1/Z2> Ref. Model 1 Model 2 Model 3 Model 4 Model 5Li F 3 9 0. 280 4~ 0. 030 8 0.27 0.2 0.41 18.6 0.38 11.6 0.17 13.3 0 17 12 6i-1 F 3 9 0 100 +- 0. 080 25 O. 27 4. 4 O. 41 15. O O. 38 12. 4 O. 17 0 8 O 17 OBNa F 11 9 1. 560 +- 0. 120 8 O. B2 38.0 1.13 12.6 1.16 10.9 0 91 29 4 0 91 29 6Na F 11 9 0.960 4- 0.050 25 O. B2 7.8 1.13 12.0 1.16 16.6 0.91 1 0 0 91 1 1Mg F2 12 9 0. 920 +- 0. 030 25 0.88 1.5 1.19 83.3 1.24 114.0 0.76 27 9 0 76 29 4Al F3 13 9 0. 900 +- 0. 300 16 0.95 0.0 1.25 1.4 1.31 1.9 0.60 1 0 0 59 1 1Al F3 13 9 0. 950 +- 0. 170 38 0.95 0.0 1.25 3.1 1.31 4 6 0.60 4.3 0^59 4 5S F6 16 9 1. 040 +- 0. 100 14 1. 13 0. 8 1. 41 13. 5 1. 52 23. 2 O. 75 8 2 O 73 9 4KF 19 9 1. 890 +- 0.180 23 1.31 10.3 1.54 3.7 1.71 1.0 1.15 16.8 1 15 16 9Ca F2 20 9 1.470 4— 0.260 25 1.37 0.1 1.59 0.2 1.77 1.3 1.18 1.3 1 17 1 3Ti F4 22 9 2.440 4— 0.310 38 1.49 9.4 1.67 6.2 1.89 3.2 1.31 13 4 1 30 13 6V F4 23 9 3.200 4- 0.290 38 1.55 32.5 1.71 26.5 1.94 18.8 1.43 37.4 1 42 37 8Mn F2 25 9 2. 160 +- 0. 210 38 1.66 5.6 1.78 3.3 2.05 0.3 1.72 4 4 1 72 4 4Fe F3 26 9 2.440 4- 0.390 25 1.72 3.4 1.82 2.6 2.11 0.7 1.80 2.7 1 80 2 7Co F2 27 9 2.380 4— 0.320 25 1.77 3.6 1.85 2.7 2.16 0.5 1.94 1.9 1 94 1 9Ni F2 28 9 3.090 4- 0.230 38 1.83 30.0 1.89 27.4 2.21 14.7 2.02 21.6 2 02 21 5Zn F2 30 9 3. 280 +- 0.200 38 1.94 44.7 1.95 44.2 2.31 23.7 2.16 31.1 2 17 30 9Rb F 37 9 2. 410 +- 0.180 38 2.33 0.2 2.16 1.9 2.63 1.5 1.76 13 1 1 77 12 5Sr F2 38 9 1. 830 +- 0.280 25 2.38 3.9 2.19 1.6 2.67 9.1 1.60 0.7 1 61 0 6Y F3 39 9 2.540 4- 0.190 38 2.44 0.3 2.21 2.9 2.72 0.9 1.53 28 0 1.54 27 6Zr F4 40 9 2.330 4- 0.490 25 2.49 0.1 2.24 0.0 2.76 0.8 1.51 2.8 1.51 2 8Ag F2 47 9 3.200 +- 0.230 38 2.86 2.2 2.42 11.6 3.04 0.5 2.32 14 5 2.33 14 3Cd F2 48 9 3. 980 4— 0. 540 16 2. 91 3. 9 2. 44 8. 1 3. 08 2. 8 2. 34 9. 2 2 35 9 2Cd F2 48 9 3. 250 +- 0. 370 38 2. 91 0. 8 2. 44 4. 8 3. 08 O. 2 2. 34 6. O 2 35 6 0Sn F2 50 9 2.300 4- 0.150 38 3.02 22.7 2.49 1.5 3.16 32.7 2.37 0.2 2 39 0 3Sb F3 51 9 3. 690 4- 0. 420 16 3. 07 2. 2 2. 51 7. 9 3. 19 1. 4 2. 35 10. 2 2. 36 10. 0Sb F3 51 9 2. 980 +- 0. 300 38 3. 07 0. 1 2. 51 2. 5 3. 19 O. 5 2. 35 4. 4 2 36 4 3Sb F5 51 9 4. 600 +- O. 710 25 3. 07 4. 7 2. 51 8. 7 3. 19 3. 9 2. 2B 10. 7 2. 28 10 7Cs F 55 9 3. 650 +- 0. 350 25 3. 27 1. 2 2. 60 9. 1 3. 34 0. 8 2. 20 17. 3 2. 21 16. BBa F2 56 9 3. 320 +- 0. 400 25 3. 32 O. O 2. 62 3. 1 3. 38 O. 0 2. 05 10. O 2. 07 9. 7La F3 57 9 3.930 4— 0. 2B0 38 3.37 3.9 2.64 21.3 3.41 3.4 1.97 48 8 1 99 48 OCe F3 58 9 5.400 4- 0.340 3B 3.43 33.7 2.66 65.0 3.45 33.0 2.14 92.1 2.15 91 2Nd F3 60 9 6. 720 4~ 0. 440 38 3. 53 52. 7 2. 70 83. 5 3. 52 53. O 2. 30 100. 8 2. 32 100 1Gd F3 64 9 7.300 4- 0.700 38 3.73 26.0 2.78 41.7 3.65 27.2 2.58 45.5 2.59 45.2Dy F3 66 9 6. BOO 4~ 0. 500 38 3.83 35.3 2.82 63.5 3.72 38.0 2.87 61.7 2.89 61.3Er F3 68 9 6. 800 +- 0. 500 38 3. 93 33. O 2. 85 62. 3 3. 78 36. 4 3. 10 54. 9 3. 10 54 6Yb F3 70 9 5. 100 4- 0. 600 38 4. 03 3. 2 2. 89 13. 6 3. 85 4. 4 3. 32 8. 8 3. 33 8. 7Ta F5 73 9 5.920 4- 0.410 38 4.18 IB. 1 2.94 52.7 3.94 23.3 3.42 37.2 3.43 37.0Hg F2 80 9 4.640 4- 0.330 38 4.52 0.1 3.06 22.8 4.15 2.2 3.32 16.0 3.35 15.2TI F 81 9 5.200 4— 0.600 38 4.57 1.1 3.08 12.5 4.18 2.9 3.14 11.8 3.17 11.4Pb F2 82 9 9.600 4- 1.400 3 4.61 12.7 3.10 21.6 4.21 14.8 2.92 22.8 2.96 22.5Pb F2 82 9 4.700 4- 0.400 8 4 61 0.0 3.10 16 1 4.21 1.5 2.92 19.8 2.96 19 0Pb F2 82 9 4. 170 +- 0. 470 25 4. 61 0. 9 3. 10 5. 2 4. 21 O. 0 2. 92 7. 1 2. 96 6. 7Bi F3 83 9 4.740 4- 0.450 5 4.66 0.0 3.11 13.1 4.24 1.2 2.76 19.4 2.79 18.8Bi F3 83 9 3.940 +- 0.360 38 4.66 4.0 3.11 5.3 4.24 0.7 2.76 10. B 2.79 10.2Th F4 90 9 2. 320 4- 0. 520 25 5. 00 26. 5 3. 22 3. 0 4. 44 16. 6 2. 24 O. O 2. 26 0. 0U F4 92 9 2. 800 4- 1.200 2 5.09 3.7 3.25 0.1 4.49 2.0 2.51 0.1 2.52 0.1U F4 92 9 6. 080 +- 0. 600 5 5. 09 2. 7 3. 25 22. 2 4. 49 7. 0 2. 51 35. 5 2. 52 35. 1Li Cl 3 17 0. 140 +- 0.020 7 0.16 0.6 0.28 50.0 0.24 25.4 0.16 1.4 0.16 1.6Li Cl 3 17 0. 190 4— 0. 080 32 O. 16 O. 2 O. 28 1. 3 O. 24 0. 4 0. 16 O. 1 O. 16 0. 1Be C12 4 17 0.056 4— 0.005 32 0.20 815.8 0.37 4040.8 0.32 2749.6 0.05 0 4 0.06 0.3- 18 -Table 4. Test of atomic capture models for simple binary halides (cont'd)TARGET EXPERIMENT CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SQUARESName Z1 Z2 ACZ1/Z2) Ref. Model i Model 2 Model 3 Model 4 Model 3C C14 6 17 O. 980 +- 0. 190 1 0. 2B 13. 3 0. 32 3. 9 O. 46 7 6 0. 06 23. 2 0. 09 22. 2Na Cl 11 17 1.050 +- 0.080 8 0.47 31.7 0.78 11.3 0.73 15.7 0.83 7.6 0.83 7.7Na Cl 11 17 O. 6B0 +- 0.040 13 0.47 26.4 0.78 6.1 0 73 1.8 0.83 13.9 0.83 13.8Na Cl 11 17 0.790 +- 0.030 18 0.47 110.6 0.78 0.1 0.73 3.6 0.83 1.7 0.83 1.6Na Cl 11 17 0.680 +- 0.060 22 0 47 11.7 0.78 2.7 0.73 0.8 O 83 6.2 0.83 6.1Na Cl 11 17 0.710 +- 0.070 23 0.47 11.3 0.78 1.0 0.73 0.1 0.83 2 9 0.83 2.9Na Cl 11 17 0.692 +- 0.019 29 0.47 131.0 O. 7B 21.0 0.73 4.7 0.83 32 0 0.83 31.3Na Cl 11 17 0.770 +- 0.130 32 0.47 3.2 0.78 0.0 0.73 0.1 0.83 0.2 0.83 0.2Na Cl 11 17 0.790 +- 0.030 32 0.47 110.6 0.78 0.1 0.73 3.6 0.83 1.7 0.83 1.6Mg C12 12 17 0.760 +- 0.040 32 0.31 38.6 0.82 2.3 0.78 0.3 0.69 2.8 0.69 2.7Al C13 13 17 O. 630 +- 0.210 16 0.33 0.2 0.86 1.2 0.83 0.9 0.53 0.2 0.33 0.2Al C13 13 17 O. 662 +- O. 016 22 0.33 30.9 0.86 153.2 0.83 108.0 0.53 68.8 0.53 64.9Al C13 13 17 O. 470 +- O. 230 32 0.35 0.1 0.86 2.4 0.83 2.1 0.53 0.1 0.53 0.1P CIS 13 17 0.830 +- 0.410 32 0.62 0.3 0.93 0.1 0.92 0.0 0.38 1.2 0.39 1.2P CIS 15 17 0.820 +- 0.040 32 0.62 25.1 0.93 8.0 0.92 5.9 0.38 118.9 0.39 116.3K Cl 19 17 1.160 4— 0.030 13 0.76 178.4 1.06 10.7 1.08 7.3 1.03 13.2 1.03 14.1K Cl 19 17 1. 160 +- 0.110 16 0.76 13.3 1.06 0.8 1.08 0.5 1.05 1.0 1.05 1.1K Cl 19 17 1.130 4— 0.030 18 0.76 61.1 1.06 3.1 1.08 2.0 1.05 3.9 1.03 4.2K Cl 19 17 1.190 4— 0.120 23 0.76 12.9 1.06 1.1 1.08 0.9 1.05 1.3 1.03 1.4K Cl 19 17 1. 140 +- 0.020 29 0.76 362.4 1.06 13.3 1.08 9.4 1.03 19.7 1.03 21.5K Cl 19 17 1.140 4- 0.130 32 0.76 6.4 1.06 0.3 1.08 0.2 1.05 0.4 1.05 0.4K Cl 19 17 1. 140 4- 0.060 32 0.76 40.3 1.06 1.7 1 08 1.0 1.05 2.2 1.05 2.4Ca C12 20 17 1.560 4— 0.170 8 0.79 20.3 1.09 7.6 1.12 6.8 1.08 7 9 1.08 B. 1Ca C12 20 17 1.270 4— 0.030 22 0.79 252.3 1.09 33.6 1.12 26.2 1.08 39.4 1.08 41.3Ca C12 20 17 1.370 4- 0.240 32 0.79 5.8 1.09 1.4 1.12 1.1 1.08 1.4 1.08 1.5Ca C12 20 17 1.410 4- 0.070 32 0.79 77.6 1.09 20.8 1.12 17.6 1.08 22.0 1.08 22.6V C13 23 17 1.960 +- 0.360 32 0.89 8.8 1.17 4.8 1.23 4.2 1.41 2.3 1.41 2.4V C13 23 17 2. 030 +- 0.110 32 0.89 106.3 1.17 60.6 1.23 33.3 1.41 31.3 1.41 32.2Cr C13 24 17 1.910 +- 0.350 32 0.93 7.9 1.20 4.1 1.26 3.3 1.55 1.0 1.54 1.1Cr C13 24 17 2.150 +- 0.100 32 0.93 149.3 1.20 90.4 1.26 79.3 1.53 35.7 1.54 36.9Mn C12 25 17 2. 290 +- 0. 320 32 0.96 17.2 1.22 11.1 1.29 9.7 1.63 4.3 1.62 4.3Mn C12 23 17 2.480 +- 0.140 32 0.96 117.7 1.22 80.4 1.29 71.8 1.63 36.9 1.62 37.4Fe C13 26 17 2. 010 +- O. 350 32 0.99 8.4 1.23 4.7 1.33 3.8 1.73 0.6 1.72 0.7Co C12 27 17 2.090 +- 0.290 32 1.03 13.4 1.27 7.9 1.36 6.3 1.85 0.7 1.84 0.7Ni C12 28 17 2. 340 +- O. 310 32 1.06 17.1 1.30 11.3 1.39 9.4 1.93 1.7 1.92 1.8Zn C12 30 17 2. 170 +- 0. 300 32 1.12 12.1 1.34 7.6 1.45 5.7 2.06 0.1 2.05 0.2Rb Cl 37 17 1.780 +- 0.110 18 1.35 13.3 1.48 7.2 1.66 1.2 1.62 2.0 1.63 1.9Rb Cl 37 17 1.750 4- 0.180 23 1.33 3.0 1.48 2.2 1.66 0.3 1.62 0.3 1.63 0.5Rb Cl 37 17 1.530 4— 0.190 32 1.33 0.9 1.48 0.1 1.66 0.5 1.62 0 2 1.63 0.3Zr C14 40 17 2. 060 +- 0. 430 32 1.44 2.1 1.54 1.5 1.74 0.6 1.48 1.8 1.47 1.9Nb C15 41 17 3.250 4- 0.580 32 1.47 9.4 1.56 8.5 1.77 6.6 1.58 8.3 1.36 8.3Mo C15 42 17 3. 220 +- 0. 580 32 1.50 8.8 1.58 8.0 1.79 6.1 1.71 6.8 1.68 7.0Pd C12 46 17 2. 730 +- 0. 360 32 1.62 9.8 1.64 9.4 1.89 3.7 2.24 2.0 2.22 2.1Ag Cl 47 17 O. 800 4- O. 200 2 1.63 IB. 3 1.66 18.3 1.92 31.2 2.23 52.3 2.24 31.9 Ag Cl 47 17 2. 500 +- 0. 250 32 1.63 11.4 1.66 11.3 1.92 3.4 2.25 1.0 2.24 1.1Cd C12 48 17 2. 260 +- 0. 260 16 1.68 4.9 1.68 3.0 1.94 1.3 2.25 0.0 2.24 0.0Cd C12 48 17 2.220 +- 0.300 32 1.68 3.2 1.68 3.3 1.94 0 9 2.23 0.0 2.24 0.0Sn C14 50 17 2.360 +- 0.400 16 1.74 2.4 1.71 2.7 1.99 0.9 2.27 0.1 2.25 0.1Sn C12 50 17 1.980 +- 0.220 16 1.74 1.1 1.71 1.5 1.99 0.0 2.29 2.0 2.28 1.9Sn C12 50 17 2. 040 +- O. 310 32 1.74 0.9 1.71 1.1 1.99 0.0 2 29 0 6 2.28 0.6Sb C13 51 17 2.550 4- 0.390 16 1.77 3.9 1.72 4.5 2.01 1.9 2.30 0 4 2.29 0.4- 19Table 4. Test of atomic capture models for simple binary halides (cont'd)TARGET EXPERIMENT CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SQUARESName Z1 Z2 A(Z1/Z2> Ref. Model 1 Model 2 Model 3 Model 4 Model 5Sb C13 31 17 2.300 +- O. 430 16 1.77 1.4 1.72 1.6 2.01 0.4 2 29 0.0 2.27 0.0Te C14 32 17 2.070 +- O. 500 32 1.80 0.3 1.74 0.4 2.04 0.0 2.34 0.3 2.32 0.3Cs Cl 35 17 1.750 +- 0.090 7 1.89 2.6 1.78 0.1 2.11 15 6 2.03 9.6 2.03 9.9Cs Cl 55 17 2. 070 +- O. 210 23 1.89 0.7 1.78 1.9 2.11 0.0 2 03 0.0 2.03 0.0Cs Cl 55 17 2. 210 +- 0.230 32 1.89 1.9 1.78 3.4 2.11 0 2 2.03 0.6 2.03 0.6Ba C12 56 17 2. 670 +- O. 330 32 1.92 5.1 1.80 7.0 2.13 2.7 1.93 5.1 1.93 5.0Ta C15 73 17 3. 680 +- O. 620 32 2.42 4.2 2.02 7.1 2.48 3.7 / 3.35 0.3 3.32 0.3W C16 74 17 7. 200 +- 0.930 32 2.44 26.1 2.04 30.8 2.50 23.3 3.43 16.4 3.41 16.7Hg C12 80 17 3. 910 +- O. 440 32 2.61 8.7 2.11 16.8 2.62 8.7 3.19 2.7 3.20 2.6TI Cl BI 17 3. 690 +- 0. 370 32 2.64 8.0 2.12 18.1 2.63 8.1 2.98 3.7 3.00 3.3Pb C12 82 17 3. 160 +- 0. 240 8 2.67 4.2 2.13 18.3 2.63 4.3 2.81 2.1 2.83 1.9Pb C12 82 17 4. 230 +- 0.450 32 2.67 12.0 2.13 21.8 2.63 12.3 2.81 9.9 2.83 9.7Bi C13 83 17 2. 550 +- 0.410 32 2.70 0.1 2.14 1.0 2.67 0.1 2.70 0.1 2.71 0.2Na Br 11 35 0.372 +- 0. 013 29 0.26 81.0 0.54 164.9 0.46 43.6 0.44 24.9 0.43 22.6K Br 19 35 O. 420 +- O. 070 16 0.41 0.0 0.73 20 2 0.67 13.1 0.54 3.1 0.54 2.9K Br 19 33 0.590 +- 0.060 23 0.41 9.2 0.73 5.8 0.67 1.9 0.54 0.6 0.54 0.7K Br 19 33 0. 583 +- O. 014 29 0.41 136.2 0.73 117.3 0.67 41.8 0.54 8 3 0.34 9.3Cd Br2 48 33 O. 950 +- O. 120 16 0.91 0.1 1.16 3.1 1.21 4.8 1.13 2.3 1.12 2.1Li I 3 53 O. 770 +- O. 300 2 O. 06 3. 6 O. 16 4. 1 O. 12 4. 7 0. 08 3. 3 O. OB 5. 3Li I 3 33 O. 060 +- O. 010 4 O. 06 O. O 0. 16 100. 9 0. 12 32. 4 0. 08 3. 9 O. 08 3. 7Na I 11 53 0.290 +- 0.030 8 0.18 13.8 0.44 26.4 0.36 4.8 0.38 9.2 0.38 8.7Al 13 13 33 0.480 +- O. 180 16 0.21 2.3 0.49 0.0 0.40 0.2 0.21 2.3 0.21 2.2K I 19 53 O. 500 +- 0. 050 8 0. 29 18. 4 0. 61 4. 4 O. 32 O. 2 O. 47 O. 3 O. 47 0. 4K I 19 33 O. 500 +- 0.080 16 0.29 7.2 0.61 1.7 0.52 0.1 0 47 0.1 0.47 0.2K I 19 33 O. 540 +- 0.060 23 0.29 18.0 0.61 1.2 0.32 0.1 0.47 1.3 0.47 1.4Ag I 47 33 1.430 +- 0.230 8 0.62 11.0 0.93 4.1 0.93 4.3 0.97 3.6 0.97 3.7Cd 12 48 33 1.000 +- 0.200 8 0.63 3.4 0.96 0.0 0.94 0.1 0.97 0.0 0.97 0.0Cd 12 48 33 1.000 +- 0.120 16 0.63 9.3 0.96 0.1 0.94 0.2 0.97 0.1 0.97 0.1Pb 12 82 33 1.220 +- 0.110 8 1.00 3.8 1.21 0.0 1.29 0.4 1.22 0.0 1.22 0.0Total chi-square for 131 points 3897.6 6222.3 4129.7 1661.6 1633.0Models:1.) Modified Z-law: 0. 69*(Zl/Z2)**0. 862. ) Z**(l/3)-l by Vasilyev et al.3.) Daniel's model modified: Z**(l/3)*log(0. B3*Z+0. 69)4. ) SPP model: Omega-2 with Ouasslan cutoff (E0=0, El-86 eV, E2-119 eV, ZO-15, q(Z)=Z**2>5. ) SPP model: Omega-2 with Gaussian cutoff (EO-O, El-86 eV, E2-121 eV, ZO-15, q(Z)-Z**l. 69)Table 5. Test of atomic capture models for simple binary sulphidesTARGET EXPERIMENT CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SQUARESName Z1 Z2 ACZ1/Z2) Ref. Model 1 Model 2 Model 3 Model 4 Model 5Ca S 20 16 1. 370 +- O. 040 13 0.84 336.7 1.13 122.1 1.16 102 9 1.29 49.6 1.27 56.2 Fe S 26 16 3. 030 +- 0. 170 38 1.03 136.0 1.29 104.6 1.38 93.8 2.14 27.7 2.10 29.8Cu S 29 16 1. 890 +- O. 180 6 1.15 16.9 1.36 8.6 1.48 5.1 2.34 13.1 2.30 11.5Zn S 30 16 1. 820 +- 0. 360 7 1.18 3.1 1.39 1.3 1.52 0.7 2.50 3.6 2.46 3.2Z n S 30 16 2.690 +- 0.170 38 1.18 78.4 1.39 38.8 1.32 47.7 2.30 1.2 2.46 1 8As2 S3 33 16 2. 010 +- 0. 180 38 1.29 16.2 1.45 9.6 1.61 4.9 2.51 7.9 2.47 6 5Sr 8 38 16 1. 900 +- 0. 170 38 1.43 6.9 1.33 4.1 1.76 0.7 1.85 0.1 1.83 0 2Mo S2 42 16 2 700 +- O. 200 38 1.58 31.2 1.63 28.7 1.87 17.3 2.26 4.8 2.20 6 3Ag2 S 47 16 2. 280 +- O. 140 38 1.74 14. 7 1.72 16.2 2.00 4.0 2.73 10.3 2.69 8 7Cd S 48 16 2. 300 +- O. 160 38 1.77 20.3 1.73 23.0 2.02 8.8 2.79 3.3 2.74 2.3Sb2 S3 31 16 2. 460 +- 0. 130 6 1.87 13 5 1.78 20.4 2.10 5.8 2.91 8.9 2.86 7.1Sb2 S3 31 16 2. 430 +- 0.180 38 1.87 9.7 1.78 13.0 2.10 3.4 2.91 7.1 2. B6 5.7 Ba S 36 16 3.590 +- 0.200 38 2.03 61.1 1.86 74.9 2.22 47.0 2.37 36.9 2.35 38 6Pb S 82 16 2. 870 +- 0. 330 6 2. 81 0. O 2. 20 3. 7 2. 77 0.1 3. 50 3. 3 3. 48 3. 1Pb S 82 16 2. 670 +- 0. 160 38 2. 81 0. 8 2. 20 B. 6 2. 77 0. 4 3. 50 27. O 3. 48 25. 8Total chi-square for 13 points 747. 8 497.6 342.3 203.0 206.7Mo d e1s:1.) Modified Z-law: O. 69*<Zl/Z2)**0. 862. ) Z**( 1/3)—1 by Vasilyev et al.3.) Daniel's model modified: Z**( l/3)*log (O. 83*Z+0. 69)4. > SPP model: Omega-2 with Ouassian cutoff (EO-O. El-86 eV. E2-119 eV. ZO-15, q(Z)-Z**2)3. ) SPP model: Omega-2 with Gaussian cutoff (EO-O, El-86 eV, E2-121 eV, ZO-15, q(Z)»Z**l. 69)- 20 -- 21 -Table 6. Test of atomic capture models for simple binary alloysTARGET EXPERIMENT CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SGUARESName Z1 Z2 A(Z1/Z2> Ref. Model 1 Model 2 Model 3 Model 4 Model 5Ag Li 1.72 47 3 20. 100 +- 3. 840 6 7.35 4.8 3.90 5.9 7.96 4 3 11.51 2.2 11.54 2.2Cd Mg 0.18 48 12 3. 140 +- 0. 230 20 2.27 12.0 2.04 19.3 2.48 6.9 3.11 0.0 3.10 0.0Sn Mg 1.79 50 12 2. 730 +- 0.300 31 2.33 1.6 2.08 4.7 2.53 0.4 3.32 3.8 3 29 3.5Cu A12 29 13 3. 500 +- 0.360 3 1.38 34.8 1.33 29.8 1.72 24.5 4.02 2.1 3.93 1.4Cu A12 29 13 4. 160 +- 0.300 5 1.38 31.0 1.53 27.6 1.72 23.9 4.02 0.1 3.93 0.2Cu Al 8.6 29 13 10.300 +- 0.430 7 1.38 430.7 1.53 415.6 1.72 398.3 4.02 213.1 3.93 219.4Cu Al 2.03 29 13 3. 560 +- 0.060 29 1.38 1323.3 1.53 1140.7 1.72 942.4 4.02 39.6 3.93 38.3Cu Al 0.17 29 13 3. 490 +- 0.110 29 1.38 369.4 1.53 316.3 1.72 259.5 4.02 23.5 3.93 16.1Cu Al 0.03 29 13 2. 520 +- 0.310 29 1.38 13.6 1.53 10.1 1.72 6.7 4.02 23.3 3.93 20.7Ni Ca O. 13 28 20 1. 640 +- O. 160 31 0.92 20.2 1.19 8.0 1.25 6.1 1.71 0.2 1.71 0.2Nb V 29. 3 41 23 1. 670 +- 0. 240 20 1.13 5.0 1.33 2.0 1.44 0.9 1.23 3.4 1.21 3.7Nb V 41 23 1. 070 +- 0.050 20 1.13 1.7 1.33 26.6 1.44 55.1 1.23 9.7 1.21 7.9Nb V O. 03 41 23 0. 980 +- 0. 170 20 1.13 0.8 1.33 4.2 1.44 7 4 1.23 2.1 1.21 1.8Nb V 21.74 41 23 1. 160 +- O. 090 26 1.13 0.1 1.33 3.3 1.44 9.8 1.23 0.3 1.21 0.3Nb V 3.49 41 23 1. 260 +- 0. 060 26 1.13 4.4 1.33 1.3 1.44 9.1 1.23 0.3 1.21 0.7Nb V 1.03 41 23 1. 170 +- 0. 050 26 1.13 0.3 1.33 10.0 1.44 29.4 1.23 1.3 1.21 0.7Nb V O. 25 41 23 1. 230 +- 0. 060 26 1.13 2.3 1.33 2.7 1.44 12.4 1.23 0.0 1.21 0.1Nb V O. 05 41 23 1. 110 +- 0.100 26 1.13 0.1 1.33 4.7 1.44 11.0 1.23 1.3 1.21 1.0Cu Ni 0.92 29 28 1.080 +- 0.050 20 0.71 34.4 1.02 1.6 1.02 1.3 1.08 0.0 1. OB 0.0Au Cu 5. 36 79 29 1.890 +- 0.180 6 1.63 2 0 1.59 2.8 1.82 0.1 1.65 I B 1.65 1.8Ag Zn 47 30 2. 200 +- 0.700 4 1.02 2.9 1.24 1.9 1.32 1.6 1.08 2.6 1.07 2.6Ag Zn 3.06 47 30 0. 970 +- 0.050 29 1.02 0.8 1.24 28.7 1.32 48 6 1.08 4.4 1.07 4.1 Ag Zn 0.17 47 30 1. 080 +- 0.170 29 1.02 0.1 1.24 0.9 1.32 2.0 1.08 0.0 1.07 0.0Ag Zn 0.03 47 30 O 970 +- 0.110 29 1.02 0.2 1.24 3.9 1.32 10.1 1.08 0.9 1.07 0.8Te Se 1.63 32 34 1. 020 +- O. 080 20 0.99 0.1 1.22 6.3 1.29 11.8 1.26 8.7 1.24 7.4Ni Y 0. 19 28 39 1. 300 +- 0. 1B0 31 0.52 18.8 0.83 6.2 0.81 7.3 1.23 0.1 1.24 0 1A u Ag 0.67 79 47 1. 270 +- 0.120 20 1.08 2.3 1.26 0.0 1.33 0.3 1.30 3.7 1.31 3.9Total chi-square for 27 points 2340.5 2087.2 1891.1 369.0 338.9Models:1. > Modified Z-law: 0. 69*(Zl/Z2)*e0. 862. > Z**( 1/3)—1 by Vasilyev et al.3. ) Daniel's model modified: Z**< l/3)*log (O. 83*Z+0. 69)4. ) SPP model: Omega-2 with Guassian cutoff (EO-O, El-86 eV, E2-119 eV, ZO-15, q(Z)-Z**2)3. > SPP model: Omega-2 with Gaussian cutoff (EO-O, El-86 eV. E2-121 eV. ZO-15, q(Z)«Z**1. 69)- 22Table 7. Test of atomic capture models for simple binary nitridesTARGET EXPERIMENT CALCULATED ATOMIC CAPTURE RATIOS AND CHI-SQUARESName Z1 Z2 A(Z1/Z2> Ref. Model 1 Model 2 Model 3 Model 4 Model 5BN 5 7 0.236 +- 0.012 17 0.52 346.9 0.78 2037.7 0.73 1836.7 0.28 16.0 0.31 37 9 B N diam 5 7 0.235 +- 0.020 IB 0.52 198.3 0.78 736.3 0.73 671.0 0.28 6.0 0.31 14 OB N graph 3 7 0.258 +- 0.020 IB 0.52 167.2 0.78 673.2 0.73 612.8 0.28 1.7 0.31 6 7B N cubic 5 7 0.233 +- 0.011 34 0.52 664 8 0.78 2451.9 0.73 2233.4 0.28 21.5 0.31 48 9B N hexag 3 7 0.275 +- 0.012 34 0.52 403.4 0.78 1754.8 0.73 1387.2 0.28 0.6 0.31 8.5Total chi-square for 3 points 1982.7 7653.9 6963.0 43.7 116.0Models:1.) Modified Z-law: O. 69*<Z1/Z2>**0. 862. ) Z**(l/3)-l by Vasilyev et al.3.) Daniel's model modified: Z**<l/3>*log(O. 83*Z+0. 69>4. ) SPP model: Omega-2 with Guassian cutoff (EO-O. El-86 eV, E2-119 eV, ZO-15, q<Z>«Z**2)5. > SPP model: Omega-2 with Gaussian cutoff <E0=0, El-86 eV, E2-121 eV, ZO-15, q<Z>-Z**l. 69)- 23 -Table 8. Total chi-squares for the groupsGroup Data • Model 1 Model 2 Model 3 Model 4 Model 3mlxtures 16 910. 3 247. 3 610. 6 588. 8 583. 3oxides 127 3003. 6 3194. 8 6263. 4 1708. 3 1642. 8halides 131 3897. 6 6222. 3 4129. 7 1661. 6 1653. 0sulphides 13 747. 8 497. 6 342. 5 203. 0 206. 7allogs 27 2340. 3 2087. 2 1891. 1 369. 0 338. 9nitrides 3 1982. 7 7633. 9 6963. 0 43. 7 116. 0All 321 12884 4 21903. 3 20202. 4 4378. 6 4340. 7Models:1.) Modified Z-law: 0. 69*<Zl/Z2>**0. 862.) Z**(1/3)— 1 by Vasilyev et al.3.) Daniel's model modified: Z**<l/3)*log(O. 83*Z+0. 69)4.) SPP model: Omega-2 with Guassian cutoff (E0*0» El*86 eV# E2*119 eV» Z0*1S» q(Z)*Z**2)3. ) SPP model: Omega-2 with Gaussian cutoff <E0=0» El=86 eV» E2=121 eV, Z0=13» q(Z)=Z**1. 69)Table 9. Effective Z-values calculated for SPP model with omega-2 and Gaussian cutoffZ Zl-eff Z2-eff Z Zl-eff Z2-eff Z Zl-eff Z2-eff1 0. 98 0. 98 32 14. 93 15. 04 63 18. 63 18. 772 1. 86 1. 86 33 14. 61 14. 74 64 18. 76 18. 903 2. 15 2. 15 34 14. 26 14. 39 65 19. 98 20. 114 2. 25 2. 25 35 13. 85 13. 99 66 20 69 20. 815 2. 96 2. 96 36 13. 47 13. 61 67 21. 43 21. 556 3. 89 3. 89 37 12. 52 12. 66 68 22. 20 22. 307 4 79 4. 79 38 11. 78 11. 92 69 22. 99 23. 098 5. 64 5. 64 39 11. 59 11. 71 70 23. 81 23. 919 6. 43 6. 43 40 11. 70 11. 80 71 24. 19 24. 2810 7. 14 7. 14 41 12. 24 12. 32 72 24. 53 24. 6111 7. 00 7. 00 42 12. 73 12. 80 73 24. 74 24. 8312 6 46 6. 46 43 13. 35 13. 41 74 24. 85 24. 9613 5. 68 5. 68 44 14. 00 14. 06 75 24. 75 24. 8914 5. 24 5. 24 45 14. 68 14. 75 76 24. 52 24. 6815 5. 34 5. 34 46 15. 61 15. 68 77 25. 10 25. 2616 6. 68 6. 74 47 16. 01 16. 09 78 24. 23 24 4317 7. 12 7. 16 48 16. 32 16. 40 79 23. 73 23. 9618 7. 84 7. 86 49 16. 43 16. 53 80 22. 58 22. 8319 8. 50 8. 52 50 16. 44 16. 56 81 21. 24 21. 5020 9. 10 9. 13 51 16. 42 16. 55 82 20. 05 20. 3221 9. 83 9. 87 52 16. 34 16. 47 83 19. 07 19. 3122 10. 54 10. 58 53 16. 25 16. 39 84 18. 40 IB. 6223 11. 21 11. 26 54 16. 15 16. 30 85 17. 98 IB. 1724 12. 16 12. 21 55 15. 50 15. 66 86 17. 80 17. 9725 12. 47 12. 54 56 14. 90 15. 06 87 17. 28 17. 4426 13. 06 13. 14 57 14. 65 14. 81 88 16. 86 17. 0227 13. 65 13. 73 58 15. 77 15. 93 89 16. 70 16. 8628 14. 20 14. 29 59 16. 27 16. 42 90 16. 64 16. 8129 15. 23 15. 31 60 16. 81 16. 96 91 17. 49 17. 6530 15. 32 15. 42 61 17. 40 17. 55 92 17. 95 18. 1131 15. 19 15. 29 62 18. 01 18. 16Parameters :Zl-eff : E0=0/ El=86, E2=119, Z0=15, X=2 Z2-eff : E0=0/ El=86, E2=121, Z0=15, X = 1.69

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