Orbital and whole-atom proton stopping power and shell corrections for atoms with Z ⩽ 36

ATOMIC

DATA AND NUCLEAR

DATA TABLES

31,2X-297

ORBITAL AND WHOLE-ATOM AND SHELL CORRECTIONS

(1984)

PROTON STOPPING POWER FOR ATOMS WITH Z 4 36

JENS ODDERSHEDE Kemisk Institut, Odense Universitet 5230 Odense M, Denmark and JOHN

R. SABIN

Quantum Theory Project, Department of Physics University of Florida, Gainesville, Florida 326 1I

Stopping cross sections and shell corrections for atoms with 1 c Z d 36 have been evaluated using a technique based on Sigmund’s kinetic theory of electronic stopping. Results are tabulated for projectile velocities from 1 to 60 atomic units both for the whole atom and for the individual s&shells.

0092-640X/84 $3.00 Copyright 0 1984 by Academic Press, Inc. All rights of reproduction in any form reserved.

275

Atomic

Data and Nudear

Data Tabs.

Vol. 31, No. 2.3wtamtm

1934

J. ODDERSHEDE

and J. R. SABIN

Stopping Power and Shell Corrections

CONTENTS INTRODUCTION

........................................

276

Formalism ........................................... Accuracy of the Calculations ............................ Relation to Experiments ............................... EXPLANATION TABLE.

OF TABLE

276 277 279

...............................

281

Atomic Shell Corrections and Proton Stopping Cross Sections, 1 6 2 G 36 ............................ 282

INTRODUCTION

Formalism

v. Similarly the cross section can be related to the stopping number, L(v), by

The stopping of swift, charged particles has been of interest to experimentalists and theoreticians since the early work of Bethe’ and of Bohr2 and others. In the megavolt range of projectile energies, the stopping is primarily accomplished by elastic scattering of the projectile from target atom electrons having a particular velocity distribution, Early and successful introduction of quantum mechanics into the theory of Lindhard’ dealt with electronic stopping based on a linear response type of treatment of the electron gas. Recently Sigmund4 has treated stopping from the general point of view of momentum conservation. The theory is developed for an unspecified velocity distribution for the scatterers. In the present implementation we use a quantum mechanical atomic velocity distribution to compute stopping cross sections and shell corrections. We find’-’ that the stopping cross sections have large contributions from valence orbitals, while shell corrections are primarily determined by inner orbitals. Thus the tabulated cross sections are applicable to atomic-like systems, while the shell corrections are expected to have wider applicability. In the projectile energy range under consideration, we may ignore nuclear stopping and stripping (low-energy phenomena) and relativistic and density corrections (highenergy phenomena). Similarly, we shall, in this study, ignore the Barkas and Bloch corrections.4 In this case, one may write the stopping power or differential energy loss per unit length as

m)

=

4ae4Z:Z2 mv2

L(V)>

where Zr and Z2 are the projectile respectively, and e and m are the mass. It is conventional to consider to be composed of two terms, the the shell corrections,

(2)

and target charges, electron charge and the stopping number Bethe logarithm and

2mv2 C(v) L(v) = In -7- - - z2 , where I is the mean excitation energy obtained from the density of optical dipole oscillator strength per unit energy of excitation E above the ground state In I =

%lnE

dE

gf dE,

(4)

where $ indicates summation over discrete states and integration over continuum states. In the present implementation of Sigmund’s formalism5*’ we treat the atom on a shell-by-shell basis, so that W) = Iz Sk(v)

(5)

k

- dE/dx = nS(v),

(1) where n is the atom density and S(v) is the stopping cross section per atom as a function of the projectile velocity

and L(v)

276

Atomic

=

Data and Nuclear

z k

(6)

Uv)

Data Tables.

Vol. 31, No. 2. septm-bw

1334

J. ODDERSHEDE

4, s

where the summation L&l) = ?r

0

and J. R. SABIN

Stopping Power and Shell Corrections

where R is the Rydberg energy. From these, the Ok and Ik are determined as9

is over the atomic shells and

dvdvzdvz

nk

@k =

+

do)

2

(16)

and Ik = R Here the velocity distribution of the scatterers has been chosen as the kth shell electron velocity distribution, normalized as ml 47r p,,.(v2)v$dvz= 1. (8) s0

where nk are orbital occupation numbers fulfilling 2 nk = z2.

In order to generate the orbital velocity densities, we utilize a numerical Hartree-Fock wave function” produced on an exponential grid. As this is a numerical procedure, it should produce, within the limits of computational errors, the exact solution to the Hartree-Fock equations. As the Fourier-Dirac transformation of a Hartree-Fock wave function is isomorphic, we need only transform the orbitals, so that momentum space orbitals @‘&) may be obtained directly from the configuration space orbitals +‘,&) via

(9)

since Lg according to the Sigmund theory applies to target electrons at rest. Here, ak = (Ik/2m)“’

(10)

and the orbital weight factor, wk, is defined below. The Heaviside function, 6(v - (Yk), limits the range of integration to the range of validity of the Bethe formula. Thus, the shell corrections can be written on an orbital basis as

@‘,,(I?) = (-l)(i)“’

P&)

c

ok

In

cak=

nkfk

2-5.

The central quantities in the development of the theory outlined in the preceding section are the mean excitation energies, which were taken from the tabulation of Inokuti et al8 and thus are computed for atoms, The scattering cross sections depend critically upon the choice of the zk values, in particular at low velocities where S(v) is determined almost solely by the valence shell mean excitation energies. I3 Since the velocity distributions as well as the mean excitation energies are determined for atoms, the computed cross sections apply only to atoms or atomic-like systems where the valence velocity distribution is not much disturbed from the atomic case. We thus expect the cross sections presented here to apply to such systems as atomic gases, van der Waals and covalent

(13)

-

z do) k

(14)

and L(O) = Z2 In

cw

Accuracy of the Calculations

The orbital mean excitation energies and weight factors were derived from the Hartree-Slater calculations of orbital oscillator Stm@hSfk by Inokuti and coworkers.’ These authors calculated, for all atoms with Z G 36, the moments 2 k

d~dW.

Ik,

k

=

=

k

where the wk are orbital weight factors which, in a neutral atom, satisfy

s(o)

(19)

The machinery is now all in place and the orbital stopping numbers, cross sections, and shell corrections can be obtained directly from Eqs. (5)-(7) and (11) by numerical integration, Analyses of the numerical procedures utilized here, and their accuracy, have been presented elsewhere.7*‘2

In order to carry out the decomposition of L(v) into orbital terms [Eq. (a)] the mean excitation energy, I, must also be split into orbital terms. We have used the definition 2

% j@r)V,&)r2dr.

The transformations were carried out using the fast, accurate method of Talman. ” The momentum density is then simply obtained by

(11)

lnZ=+

(18)

k

For L&v) we use the Bethe formula 2mv2 Li (v) = 2 In 7 NV - ak) ( 1

eXp

(15)

277

Atomic

Data m3 Nucbaf

Data Tab!ss, Vol. 31. No. 2, Ss#embu

,334

J. ODDERSHEDE

and J. R. SABlN

Stopping Power and Shell Corrections

systems, and perhaps also, with prudent use of Bragg’s rule,14 to biological systems. On the other hand, for metallic systems, where the valence electrons are delocalized in bands, the valence I& are very different from the atomic val~es’~ that we have used here, and the present S(v) thus do not apply to solid metals. In fact, for metallic systems we expect to find a large gas/solid difference6 in 40) whereas one does not find such a difference for van der Waals solids such as argon. 16*17In order to estimate the accuracy of our calculated cross sections we have compared two sets of atomic-like data, namely, a calculation of McGuire et aLI8 for Al in Fig. 1, and in Fig. 2 to the experimental determination of S(u) for both gaseous” and solid” Ar. Both comparisons indicate that we obtain agreement to within a few percent. The disagreement is most pronounced at very low energy where we may be off by up to -25% (see also Table 2 of Ref. 6). In Fig. 1 we have included the semiempirical stopping power fit of Andersen and Ziegler” as well. Data points rather than curves are given in order to see the differences between the three sets of results. The present calculation and experimental gaseous proton stopping cross sections” for Ar are compared in Fig. 2. Besenbacher and co-workers have also measured S(u) for solid Ar16 and have found that for this atomic-like target, the gas/solid difference is small, in agreement with our expectations. However, the data for solid Ar are for stopping of He ions, and since for low velocities the factor (2:) in Eq. (2) actually must be viewed as a function of 11(see for example Fig. 23 of Ref. 17), the He data cannot be compared directly to our proton S(u) without properly scaling with (Z:). Nonetheless, it is expected that there would be only a small gas/solid difference for atomic-like targets and the present tabulation should thus apply to both gaseous and solid targets in such cases.

I

I

I-

.

Al

3

ff b

6 . 0 .

0 ‘? rFb b0 B

Q

O0

1

0

‘8

3

Ep(MeZV,

Figure I. Comparison of avemged experimental stopping cross sections for Al from Ref. 19 (squares) with calculated values from this work (open circles) and Ref. 18 (filled circles).

and the Walske results for the K-shell correction~O while our L-shell results am much larger than those of Wa.lske.*’ The origin ofthe latter discrepancy is that the hydrogenic approximation used by Walske works well only for the K shell. At large velocities the inner-shell contribution to the total shell correction dominates whereas at low velocities the penultimate shell gives a large fraction of C/Z2. Thus, our whole-atom shell corrections agree best with those of Walske at large velocities. The Bonderup C/Z2 cannot be split up in shellwise contributions and we can thus only compare whole-atom values. In most cases, we obtain good agreement with his results except at low velocities, where our values tend to be larger. Let us also point out that even though the mean excitation energy enters in the expression for the shell correction, we find that C/Z2 is almost invariant to the choice of total I provided that a reasonable decomposition into orbital Ik values is utilized. For instance, for Ne at u = 10 a.u. (EP = 2.5 MeV) the difference in C/Z2 is only 2% for a 10% variation in I. This variation decreases with increasing projectile velocity.

In contrast to S(u), the shell corrections C(u)/Zz are mainly dependent upon inner-shell mean excitation energies and velocity distributions,’ which do not vary much from atoms to molecules or solids. The present calculations should thus be applicable to any physical state of the stopping material. We have previously found that calculations with the present scheme yield shell corrections which compare favorably5*‘3 with both experimental gaseous and metallic data. Earlier theoretical estimates of C/Z* include work by Walske,20*2’ Bonderup, Khandelwak2’ Khandelwal and Merzbacher,24 and Bichse1. 25 These treatments are based upon either electron gas26 or hydrogenic models while our results are derived from Hartree-Fock atoms. Although there is some more recent work?‘*‘* most experimental workers are using the shell corrections by Walske and Bonderup and we have compared our calculations to Walske’s C/Z2 in Ref. 5 and to Bonderup’s results in Ref. 5 as well as in Ref. 13. We find, for Al, good agreement between our calculations 278

Alanic

Data andNuoiew Dam Teh~.

Vol. 31.

No.2.

Sqmmber

1284

J. ODDERSHEDE

Stopping Power and Shell Corrcction~

and J. R. SABIN

Ep (MeV) Figure 2. Comsuison of avuag#1 (Ref. 19. solid tine) and f@~eous (Ref. 17, dotsf experimental stopping values (da&d line).

-ions

with our calcu~ted

ulate further experimental investigations of the gas/solid difference for other types of systems. Finally, a consistent set of stoppiq cross sections for many atoms such as those presented here should be useful for investigating the validity of the Bragg rule.

Relation to Experiments The mean excitation energy is the central material constant in the Bethe theory of stoppmg power. It determines the stopping at large velocities where C/Z* vanishes.However, at the energiesat which most experiments are performed (keV to a few MeV range) the shell corrections are sizable. Experimental determinations of I thus require knowledge of shell corrections obtained from theoretical calculations.Since,asdiscussedin the previous section,our C/& most likely can beused for any physical stateof the target material, the presenttabulations should be useful for determining experimental mean excitation energies for gaseousas we11as solid targets. From an experimental point of view, it may also be useful that we have included data for ah shells of all atoms with 2 4 36, a feature which is not the case for previous tabulations. The applicability of the theory to all energy ranges of the projectile is a special characteristic of the present approach. Our resultscan thus be compared to both lowenergy (keV) and intermediate-energy (several MeV) experiments. Our calculations6~29 indicate that there should be a large gas/solid di&rence in 4u) for metals, in particular for the alkali metals where there may be as much asan order of magnitude difference. This prediction lacks experimental confirmation at present since experiments on vapor so far have been restricted to gaseswhich in their solid state are atomic-like (nobk gases,” oxygen, nitrogen, etc.). Perhaps the present tabulation will stim-

Acknowledgments

One of us (J.R.S.) is grateful to NORDITA for support and to the Kemisk Snstitut,Odense Universitet, for hospitality during the period that this work was done. The work was supported in part by National Science Foundation Grant DMR 8218498. References

1. H. Bethe, Ann. Phys. (Leipzig) 5, 325 (1930) 2. N. Bohr, K. Dan. Vidensk. Selsk.Mat. Fys. Medd. 18, No. 8 (1948)

3, J. Lindh&, K. Dan. Vidensk. Selsk.Mat. Fys.Medd. 28, No. 8 (1954) 4. P. Sigmund, Phys. Rev. A 26, 2497 (1982) 5. J. R. Sabin and J. Oddershede,Phys.Rev. A 26,3209 (1982) 6. J. Oddershede, 3. R. Sabin, and P. Sigmund, Phys. Rev. Lett. 51, 1332 (1983) 7. J. Oddershedeand J. R. Sabin, Chem. Phys.71, 161 (1982) 279

Atomtc Data Ivy1 Nudear

Oata Tabl.35, Vol. 31. NO. 2. %p(aMa

1982

J. ODDERSHEDE and J. R. SABIN

StoppingPower and ShellCorrections

8. J. L. Dehmer, M. Inokuti, and R. P. Saxon, Phys. Rev. A 12, 102 (1975); M. Inokuti, T. Baer, and J. L. Dehmer, Phys. Rev. A 17, 1229 (1978); M. Inokuti, J. L. Dehmer, T. Baer, and J. D. Hanson, Phys. Rev. A 23,95 (198 1); M. Inokuti, private communication

18. E. J. McGuire, J. M. Peek, and L. C. Pitchford, Phys. Rev. A 26, 1318 (1982)

9. See Ref. 5 for details.

20. M. C. Walske, Phys. Rev. 88, 1283 ( 1952)

10. C. Froese-Fischer, Comput. Phys. Comm. (1978); 4, 107 (1972); 1, 151 (1969) 11. J. D. Talman,

J. Comput.

19. H. H. Andersen and J. F. Ziegler, Hydrogen Stopping Powers and Ranges in all Elements (Pergamon, New York, 1977)

14, 145

21. M. C. Walske, Phys. Rev. 101,940 22. E. Bonderup, K. Dan. Vidensk. Medd. 35, No. 17 (1967)

Phys. 29, 35 (1978)

12. M. M. Pant and J. D. Talman, 1819 (1978)

15. E. Shiles, T. Sasaki, M. Inokuti Phys. Rev. B 22, 16 12 (1980)

Selsk. Mat. Fys.

Phys. Rev. A 17,

13. J. R. Sabin and J. Oddershede, Phys. Rev. A 29,1757 (1984) 14. W. H. Bragg and R. Kleeman, (1905)

(1956)

Philos. Mag. 10,3 18

23. G. S. Khandelwal,

Nucl. Phys. A 116, 97 (1968)

24. G. S. Khandelwal 144, 349 (1966)

and E. Merzbacher,

Phys. Rev.

25. H. Bichsel, University of Southern California Report, USC-136-120 (1967)

and D. Y. Smith, 26. J. Lindhard and M. ScharfX K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 27, No. 15 (1953)

16. F. Besenbacher, J. B&tiger, 0. Graversen, J. L. Hansen, and H. Sorensen, Nucl. Instrum. and Methods 188,657 (1981)

27. G. S. Khandelwal,

Phys. Rev. A 26, 2983 (1982)

28. H. Bichsel, Phys. Rev. A 28, 1147 (1983)

17. F. Besenbacher, H. H. Andersen, P. Hvelplund, and H. Knudsen, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 40, No. 3 (1979)

29. P. Sigmund, published.

280

J. R. Sabin, and J. Oddershede, to be

J. ODDERSHEDE and J. R. SABIN

Stopping Power and Shdl Corrections

EXPLANATION TABLE.

OF TABLE

Atomic Shell Corrections and Proton Stopping Cross Sections, 1 d Z d 36 Data are arranged in sets in order of increasing atomic number 2. In each set, the first line contains the atomic symbol and Z value, the orbital configuration used to form the Hartree-Fock determinant, and the LS configuration to which this corresponds. Beyond Ar, the completed orbital configuration of the n = 2 shell is abbreviated as (NE). Thus, (NE)3S2/3P6: IS refers to the ( ls)2(2s)2(2p)6(3s)2(3~)6 ‘S ground state of Ar. Within each set, atomic shell corrections and stopping cross sections for the whole atom and each orbital are arranged in blocks and listed as a function of the projectile velocity. The orbital designation and other relevant parameters are placed over each data block. ORBITAL W 1 W) ALPHA V C/Z S

(AU)

Heading designating either the whole atom or the individual orbital Orbital weight factors [wk in Eq. ( 16)] Orbital mean excitation energy Zk, in eV [Eq. ( 17)] Velocity parameter corresponding to Zk, in atomic units [Eq. (lo)]; 1 a.u. = arc = 2.19 X IO8 cm s-r. Projectile velocity in atomic units Shell correction for the whole atom and for each orbital [Eq. { 1 l)]. The latter sum to the whole atom value. Electronic stopping cross section in units of IO-” eV cm* for the whole atom and for the individual orbitals; the latter sum to the whole-atom value according to Eq. (5). The cross sections are evaluated for proton projectiles [Eq. (2), for ZI = 1J. The proton energy is given by Ep (keV) = 24.98 X V* (a.u.).

281

Atank

Oata m-d Nudur

Oata Tnbbs.

Vol. 31. No. 2. &@mbwr

1334

J. ODDERSHEDE and J. R. SABIN

Stopping Power and ShellCormtions

TABLE. Atomic Shell Corrections and Proton Stopping Cross Sections, 1 < Z G 36 See page 281 for Explanation of Table n

(Z=l

J

:

IS1

WHOLE

OREiITAL

--14.99 0.525

I(:“,

ALPHA(AJJ ” 1. 2. 3. 4. 5. 6. 7. a. 9. 2: I%: . E: 30. 35. 40. 45. 2:: 60.

c/z

S

I-",% . 0.136

5.677 7.270 3.565

0.072 0.044 0.030 oo'oo:I

:-:;o' 1:aes 1.008 0.813

0:013 0.010 0.007 0.005 0.004 0.003 0.003 0.002

0.670 0.563 0.416 0.321

2::: 0:001 0.000 0.000 0.000 0.000

0.066 0.052 0.042 0.035 0.029 0.02s

lfO500 14.99 0.525 C/Z

IS.2

1z=2

“E

2s

ATOM

ORBITAL

0.304 0.530

5.677 7.270

0.022

0.813 I .ooa

00'8:s 0:oio 0.007 0.005 0.004 0.003 0.003 X'%

0.670 0.563 0.416 0.321 0.255 0.209 0.174 0.118

0:001 0.001 0.000 0.000 0.000 0.000

8'::t. 0.052 0.042 0.03s 0.029 0.025

IS Y”CLE

It:“, ALPHACAU

---

ATOM

2!$00 38.83 0.845

38.83 0.645

” I. 2.

4.186 5.663 4.b17

2: 5. 6. 7.

8.

PXfX 0:021

::: 14. . :si.

20. 25. ii. 45.

. .

2: 60.

LX

3.455 2.615 2.034

0.097 0.069 0.052

9.

0.015 0.012 ;-x8':

0.547 0.439 0.361

0:005 0.003 ",'",",9 0:001 0.001 0.001 0.001

I

ItEVJ ALPHA(AU

---

s

4.188 5.663 4.617 3.455

0.069 2:;; . 0.052

"2-z: 1.626 1.330

0.040 0.032 0.021 0.015

i-E 0:703 :'5,*3 01361

z:: 0:152

8% 0:003

0.303 0.207 0.152

8' - :tx 0.075 0.063 0.053 0.045

E%: do01

0.092 0.,,6

8% 0:001

0.045 0:053

: WHOLE

C/Z

0.119 0.541 0.365 0.224

",%.

lS2/2Sl

(2=3) ORBITAL

S

8%

2s

ATOM

2!Zoo 109.32 1.417

J

,207 3.29 0.246

S

.0.410 0.260 0.374 ",*;:z . 0.170 0.126 8'82 . 0.059 0.040 0.028 0.021 0.016 0.013 o.ooe :'xooo $882' . ",-E. 0.001

25.295 11.464

-EE .

0.351

s-x:: . 3.972 3.099 2.483 2.035

z2: 0:164 0.122 0.093 0.072 0.057 0.039 0.028 0.021 0.016 0.013 0.008

:*:t': 1:077 0.838 0.673 0.553 0.463 00*X:27 0:178 0.141 0.115 0.095 0.081 0.069

0.087 0.04s 0.023 0.013 0.008 0.005 0.004

2.071 1.94s 1.673 1.404 1.177 0.994 0.560 0.443

0.000 0.000 0.000 0.000 o*oao 0.000 0.000 0.000

0.055 0.046 0.040

282

Atcmk

Data and Nudear

‘t%

5:24@

1.041 ;-;g. :'%:. 0.312 0.254 0.211 0.142 0.102 0.07R 0.061 0.049 0.041 0.034 0.029

Data Tab!m. Vol. 31. No. 2. SspMnba

1984

J. ODDERSHEDE

and J. R. SABIN

Stopping Power and Shell Corrections

TABLE. Atomic Shell Corrections and Proton Stopping Cross Sections, 1 < 2 Q 36 Seepage281 for Explanation of Table BE

<2=41

OYTM

I(EVJ ALPHA( AU)

152,252 UHDLE ATOM --C/Z

0.315 0.278 0.226 0.178 0.141 0.1*2 0.091 a.061 0.044 0.033 0.02s 0.020 0.012 0.008 0.006 0.00s 0.004 0.003

zx: 60.

C2=5)

C/L -0.383 0.025 0.200 0.272

2: 60.

C

lZ=6) ORBITAL

I. 2. 3. 4. 5. 6. 7. 8. 9. ::: ::: 18. 2 30. 35. 40.

22: tz..

ATOM

s 22.183 17.249 11.052 7.723 5.787 4.539

0O'fG 0:214 0.178 0.147 0.122 o.ofls 0.062 0.046

Xf 2:sse 2.185 1.651 1.294 1.043 0.061 0.723 0.498 0.36s 0.281

:*:i% 0:017 0.012 0.009 0.006 0.00s 0.004 0.003 0.003

:':f2. 0.151 :*::x .

152/252/2P2

5 0.364 0.723 0.997 1.101 1.077 0.986 0.A77 0.77r 0.678 0.597 0.470 0.379 0.311 0.261 0.222 0.156 0.116 0.090 0.072 0.059 0.050 0.042 0.037

s

C/Z

30.680 lS.158 8.618 5.603 3.954 2.951 P.293 1.838 I .509 1.264 0.927 0.711 0.565 0.460 0.3R3 0.259 0.187 0.143 0.112 0.091 0.075 0.063 0.054

0.202 ",*::7 8::;; . 0.021 0.015 0.01t O.O@A 0.006 0.004 z%: 0:oor 0.001 0.001 0.001 0.000 0.000 0.000 0.000 ?%t .

2!:19 320.21 2.426

lTZ4S 16.33 0.548

C/Z

5

-0.720 -0.187 0.071 0.186 0.219 0.210 0.184 0.156

i-:3: . 0.537 0.652 0.700 0.694 0.656 0.604 0.549 0.496 0.404

Oo*t3: 0:076 0.055 0.042 0.032

0.332 0.277 0.234 0.201 0.143 O.IOR 0.084 0.068 0.056

0.026

0.016 0.011 0.008 0.006 0.005 0.004 0.003 0.003

8%. 0.034

lfF35 11.55 0.461

C/7

s

C/7

S

0.152 0.103 0.080 0.060 0.043 0.030 0.022 0.016 0.013 0.0‘0 0.006 0.004

13.966 10.204 6.249 4.21,

O.lP4 0.109 0.049 0.026 0.016 0.010 0.007 0.006 0.004 0.004 O.OOP 0.007

8.037 6.674 4.265 2.860 2.044 I.536 1.200 0.966 0.795 0.667 0.491 0.378

o,% 0:oor 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0O*z:: . 0.205 0.139 0.101 0.077 0.001 0.049 0.041 0.034 0.078

0:002 E83

?%F" . 1.915 1.468 1.214 1.02, 0.755 0.583 0.46S 0.380

0.001 0.001 0.001 :*",::

:*2":: 0:157 0.120 0.095

0:ooo 0.000 0.000

XX. 0.054 0.046

>

3P V”DLE

ATOM --61.95 1.067

It:,, ALPHAtAUI ”

C/Z -0.670 -0.042 0.205 O.PbI 0.24b 0.205 0.164 0.130 0.10. 0.084 0.057 0.041 0.031 0.024 0.019 0.012 0.008 0.006 0.004 0.003 0.003 0.002 0.002

50.22 0.961

1. 2. 3. 4. S. 6. 7. 8. 9.

2: 40. 45.

7f500 7.32 0.367

2P UHDLE

V

:,":

:* z: 0:721 0.605 0.415 0.304 0.233

I.54 ‘/252/2Pl

oRe:TAL

:"o: 2s.

I.060 1.397

:*::2.

I(EV) ALPHA(AUl

:20:

2fLl

203.78 1.935

s

-:‘E 0:zen

1:: 12. 14. 16. 18. 20. 25. 30. 3s. 40. 4s.

B

LS

38.62 0.842

V 1. 2. 3. 4. 5. 6. 7. 8.

:

C/Z

-PXg’f 0.188 . 0.242

00*:x: . 0.226 0.198 0.170

5

I!iYSS

c/z

S

c/z

S

8':E 0:314

0.080 0.102 0.078

7.291 7.570 5.100 x3

0.217 0.242 0.133 0.04s 0.074

8.073 8.938 6.582 3.440 4.679

2:011 L.599

0.030 0.021 0.016 0.012 0.010 0.007 0.005 0.004 9.003 0.002 0.001

2.62R 2.074 1.632 1.3q-4 1.174 0.570 0.673 0.538 0.44, 0.36A 0.251

Il.996 0.620

-0.691 -0.252 -0.022 0.104

5.113 6.503

8-E 0:176

Ez 0.472 0:474

f ' ::9" 2:904

0.160 0.141 0.122 0.090 0.067 0.051 0.039 0.031

0.454 0.427 0.396 0.33s 0.2A2 0.239 0.205 0.177

X*%E 0:009

0.097 0.128

:x’% *

0.14s 0.105 0.078

:**,",9" . 1.486 1.202

0:036 8'8:: 0.022 0.015

0.837 0.994 O.STB 0.425

0.006 0.005

0.212 0.177

:*x::.

t-:2": .

2P 2.217 20.91 0.621

I%28 27.57 0.712

451.34 2.880

8'82 o:os1 0.043 0.036 0.032

283

C/Z

5

0.000 0.000

0.072

0.001 0.001 0.000 0.000

2::: 0:111 0.090 0.075

:%ioo .

?858 0:043

0.000

0.054 0.063

Atomic

Data and Nwlee~

Dms Tablee. Vol. 31. NO. 2. sep(cVnb~

1994

J. ODDERSHEDE and J. R. SABIN

TABLE. N

Atomic

Shell Corrections and Proton Stopping Cross Sections, 1 Q Z 4 36 See page 281 for Explanation of Table

‘252/2P3

tz=7

:

C/Z

I. 2. 3. 4. 5. 6. 7.

-0.509 0.160

8. :20: 14.

8. EX 0:019 0.013 0.010

z'x: .

tz=BJ

1,IE”J ALPHAIAU

.

y:

OhOPAL IIEVJ ALPHA{ AU J ”

2: ::: ::: 20. iE: 2: 55. 60.

s 6.449 10.536 10.847 9.27' 7.573 6.191 5.::t 3:6.92 3.182 2.451 1.951 I.592

0.041 0.027 0.019

:':2f 0:7ea 0.580 0.448

"0'::: . 0.009 0.007 0.006

X*Z*G 0:245 0.206 0.179

7.009 9.240 7.7% 5.916

",-:i: 0:oas

:%i: . 0.314 0.26: 0.181 0.132 a.102 0.0831 0.066 0.055 0.046 0.040

C/L

0.097 0.144 0.188 0.224 0.251 0.267 0.274

0.059 0.042 0.031 0.024 O.Ol9 0.013 0.009 0.007 0.005 0.004

f .%S

0.003 0.002 0.00'

"o-321 . 0.197

FE5 1:903 1.611 1.202 0.934 0.749 0.615 0.515

o.oai 0.066 0.054 0.045 8-E 0:020

4fL3 46.64 0.926 s 2.336 3.R3R 3.362 2.491 1.903 1.500 1 r215 1.005

I 0;oss

-:-“,:z

"0% o.o,a 0:025 0.014

x*s:,' . 0.547

0.004 0.003 0.002 0.001

0.240 0.165 0.122 0.093

8%: 0:oor 0.000 0.000

"0% 0:oF.o 0.043 0.037

c/7

s

::%I

5.RFR

0:334 :-:3 0:100

"8%1: . 6.659 5.250 4.175

0.071

3.379

0.052 0.040 :-:2": 0:ots 0.01' 0.009

:*'3:3 L:PA7 I.402 1.165 0.937 0.772

0.001 :-:o": .

:-:a: 0.386 .

0.002

0.250

0.001

0.098

,ft27 74.04 1.166

I!:63 861.33 3.976

111.31 1.430 CIZ

f

0.137 0.347

2P

WHOLE _-- ATOM

1. 2. 3. 4. 5. 6. 7. 8.

C12

3.96’ 5.403 42% 2:214 I.726

0.049

0.265 0.272 0.242 0.215 O.lR9 0.166 0.146 0.108

:*x:x o:or3 0.010 0.007 0.006 0.005 0.004

:

JS2/252/2PS

I

1292 56.86 I.022 s

-0:111 0.003 0.075 0.116 0.136 O.t42 0.138 0.130 0.107 0.085 0.068 0.054 0.044

00*x:': o:*ro 0.327

0.016 0.012

(219)

1.1295 729.41 3.661 c/z

xx. 2.281 I.809 1.472 I.223 1.034

0.01 0.096 0.072 0.062 0.053 0.043 0.034 0.027 0.022 0.017 0.012 0.008 0.006

3P

18-g;:

2:::. 0.142 0.110

.

3::

X-E, 0:034 0.030

5

::-2:: 9:337 7.377 5.925 4.660 4.064

0:205 0.264 0.310 0.339 0.351 0.350 0.339 0.323 0.284 0.246 0.212 0.184 0.160

8'88," . 0.004 0.004

8.275

0:290 0.283 0.272 0.260 0.2-4 0.224

Oo’Et

s

C/2

S

8% 0:071 0.057

ATOM

c/z -g.

3%6 32.68 0.775

41.24 0.671

x:: 0:ooe

93.20 1.309

J

it: le.

JZ:

",'X,'f .

: “HDLC

1. 2. 3. 4. 5. 6. 7. 8.

F

:*xX8 l 0.480

152/252/2P4

Y

g:

0.100 0.077 0.060 0.047

:-:3: .

ORBITAL

$:

:*:5'5" 1:343 1.113

:-x 0:2*0 0.200

x:: 60.

0

0.044 0.114 0. I48

:-5536: 3:772 3.195 2.745

:-:;," . 0.057

:;:

l

-O.O?P

'f-Et 7:opo

:*;:x 0:1e9 0.165 0.125

9.

c/z :pgjg

11.039 14.781

t* zzxx 0:256 0.251

1559

l!Z25 590.00 3.293

76.79 I.lBA

V

1,".

45

WHOLE --- ATOM

oWB:TAL I(EVJ ALPHACAU

35":

Stopping Power and Shell Corrections

C/Z

s

-0.572 -0.208

.0.073 O.Obl3

x*8",: . 0.027 0.023

1.488 2.744 2.659 2.116 1.652 1.316 1.074 0.895 0.757 0.650

",-"0:; 0:ooe 0.006

:-3Ei 0:316 0.261

8-Z 0:oo: 0.001 0.00' 0.001 0.00, 0.001 0.000

"0%~ 0:112

Et: 0:047 0.042 2::: 0:126 0.189

0.015 0.011 X'% 0:006 0.005

.5&O 62.86 I.075

0.042 i?% 0:027

8%: 0:056 0.047 0.040 0.034

c/2 -;

. :*oz a:413 :-:z 0:1so 0.107 0.080 0.061 0.04R 0.032 0.023 0.017 0.013 0.01' 0.007 0.005 0.003 0.003 0.002 0.002 0.00, 0.001

S 4.925 7.719

3.046 iJ'$iE . 2.31? :':z 13107 0.914 ?Z% 0:390 lx:. :-::t 0:137 0.116

J. ODDERSHEDE and J. R. SABIN

TABLE. I2=10)

NE

lS2/2

Atomic Shell Corrections and Ptoton Stopping Cross Sections, 1 G 2 < 36 See page 28 1 for Explanation of Table

!52/2P6 WHOLE

OREkTAL

130.

I(EV) ALPHA

1. 2. 3.

tX. xx. 60.

NA

.

. .

(z=ll)

5

0:390 0.392 0.352

5.173 6.643 9.885 8.990 7.617

:* . E': 0.1*3

5'56"; . 2.696 2.081 1.703 1.422 1.206 0.644

"0-K o:r10 0.095 0.079 0.065 0.054 0.035 0.023

C/Z

1:: 12. 14.

::. .

t;:

. :*:2"3 0.102 0.084 0.054 0.036 0.026 0.019 0.014 0.011

ZX:

:-x:3 .

fk?: 38: 40.

(2=121

S

ORBiTAL I(EV) ALPHA4

1.

2. 3. 4. 5. 6. 7. 6. 9. ::: it: ia. 5:: 2: .

-1.177 -0.167 0.240 EXS 0:3se 0.326 0.296 0.269 0.244 L?::; 0:138 0.114 0.096 0.061 0.041 0.030 0.022 0.017 0.013

0.011 0.009

0.167 0.152 8'E 0:osr 0.074 0.059 0.046 0.040 kxt o:oes

0.080 0.014

0.052 0.044 0.037 0.032

C/7

s 4.133 6.791 7.660 7.075

-Ef . 0.466 0.383 0.284

“5’

E

4.209 l 3.543

:*:s: .

0.113 0.087

3.014

0.06R 0.045 0.037 0.024 0.019 0.015

2.593 1.976 1.558

1.262 1.044 O.RdO 0.609 0.449 0.346 0.276

:%z 0:oos 0.004 0.003 0.007 0.002 0.002

2s 1.613 119.24 1.480

c/z

s

-0.496 -0.270 -0.l40 -0.053 O.OOR 0.051 0.080 0.099 0.109 0.112 0.108 0.097 0.083 0.070 0.059 0.036 0.026 0.019 0.014 0.011 0.000

0.023 0.046 0.068

c/7 -0.122 0.034 0.060 0.052 0.04s 0.042 0.036 0.035 0.03, 0.028 0.021 0.016 0.012 0.009

0.089 0.108 0.124 :*:i; 0:154

0.157 0.156 0.148 0.137

X%2 0:159 0.137

0:oor 0.001 0.001 0.001 0.001 0.001

8%: 0:02e 0.025

s

c/z

S

-0.515 0.182 0.396 Cl.390 0.319 0.245 0.186 0.142 0.111 O.OAR 0.05R 0.041 0.031 0.024

2.312 3.990 4.930 5.065 4.665 4.091 3.527 3.034 2.621 2.280 1.764 1.404 1.145 0.952 0.806 0.562 0.416 0.322 0.957 0.210 0.176 0.149 0.128

0.56l 0.434 0.346 0.2R2 0.235 0.199 0.139 0.103

i’%3

T? 1.021 1.4C P..?,-?

0.702 1.439 1.124 I.575 1.313 1.079 0.897 0.648

0.007

0.046

7P 6.558 124.41 I.512

0.757

0.080

0.064 0.052 0.043 0.037 0.037

:*::;. 0.00.5 0.006 0.004 0.004 0.003 0.002 0.002

C/7

5

27.6?7 to .Ch5 5.63C -.5ee 3.4f.l 1 .a09 1 .TQP 1.107 0.003 O-75? 0.547 0.418 0.3?0 0.2-J?? 0.732 0.*4s O.lOR O.OA\ 9."64 0.052 0.043 0.036 0.011

A.075 0.011 0.004

0.002 0.001 0.001 0.001 0.001 0.000 9.000 o.olJo 0.000 0.000 -0.001 -9.601 -0.COl -0.001 -0.001 -0.001 -0.001 -9.00, -9.001 -0.001

1s

ATOM

1.490

c/z

8%: 0:01s 0.013 0.010 0.007 0.006 0.003 0.002 0.002 0.031 0.00, 0.001 0.001 0.000

:*:::. 0.1ao

0.006

:

1

0.178

0.007

:%: 0:215

--120.74 AU

V

:-"St; . 1.340 0.938 0.6% 0.539 0.431 0.353

“HOLE

0.153 0.166

1!Zo9 1110.36 4.517

30.b63 16.140 12.417 10.297 8.546 7.104 5.953 5.045 4.326 3.750 2.901 2.315

152/2S2/2P6/352

x: 0:134

1.011 1.995 2.140 1.604 1.444 1.164 0.957 0.801 0.6PZ 0.587 0.450 0.356 0.290 0.240 0.203 0.141 0.*04

25

ATOM

-1.106 -0.043 0.320 0.392 0.374 0.339 0.306 0.277 0.251 0.226 0.187

5

-0.093 0.051 0.060 0.049 0.044 0.040 0.036 0.032

0.057

0.012 0.010 0.008 0.006 0.005

X'3E 0:266 0.226 0.194

c/7

S

0.029

0.017

0.465

--123.14 1.504

1. 2. 3. 4. 5. 6. 7. 8.

X2

E-:3: . 4.523

:

V

60.

C/Z

-0.530 -0.276 -0.135 -0.04, 0.025

O-b27

Y”OLE

ALPHAtAUJ

2.

I. .x:1

152/2S2/2P6/35

OneiTAL I(EVl

NO

FP

6.606 e1.37 1.273

1'2:: 0:2se 0.234 0.212 0.173 0.140 0.113 0.091 0.075 0.047 0.032 0.023 0.017 0.013 0.011 0.009 0.007

,',:

2:

ATCW

-8%

4. 5. 6. 7. 8.

:8". 20. 25.

.-

C/Z

V

:::

Stopping Power and Shell Corrections

25

1.451 151.05 1.666

l!S90

1243.15 4.780 s

C/Z

0.019

-0.146

0.037 0.055 0.072 0.0% 0.102 0.114 0.123 0.129 0.134 0.135 0.131 0.123 0.114 0.105 0.063 0.066

0.014 0.055 0.054 0.047 S'E 0:037 0.034 0.031 0.024 0.019 0.014 0.011 O.OJ9 0.005 0.003

0.054 0.044 0.037 0.032

X%. 0.001 0.001

:-::a I

:-x:: .

285

7s

hPGl1 169.86 1.767 s 0.499 1.042 1.357 I.342 1.173 0.969 0.833 0.709 0.610 0.531 0.414 0.332 0.273 0.228 0.194 0.136 0.101 0.078 0.063 0.051 0.043 0.037 0.031

C/Z

-0.630 0.043 0.310 0.370 0.334 0.274 0.216 E-:3: 0:107 0.071 0.050 0,037 0.029 0.073 0.014 0.010 0.007 0.005 0.004 0.003 0.003 0.002

3.049 4.45 O.?P6 S 1.476 2.626 3.375 3.714 3.65, 3.360 2.996 2.637 2.316 :%2R . I.287 1.056 0.883 0.750 0.52b 0.391 0.303 0.243 ?:ziG 0:142 0.172

C/Z 0.065 O.O,S 0.01A 0.010 0.007 O.OOC 0.005 2x

l-l:003 0.003 0.001 0.001 0.000 0.000 0.000 0.000 -0.001 :;*g: -o:oo, -0.001 -0.00,

5

41.639 18.007 10.021 6.400 :%: e:sso 2.035 I.666 1.392 I.917 0.778 n.017 0 .s02 0.417 0.701 0.203 0.154 0.121 0.09P O.ORl 0.066 0 .OSR

286

J. ODDERSHEDE and J. R. SABIN

TABLE. AL

StoppingPower and ShellCorrections

Shell Corrections and Proton Stopping Cross Sections, 1 c 2 d 36 !3eepage 281 for Explanation of Table ,*2/2s2,*Pw3s2/3P, : 2P YWLE *ron --,573 I%77 6%5 123.67 1373.04 187.14 PZ1.15

tz=131

ORBITAL I,:“,

Atomic

ALPMA

1.507

5.023

” -0.4.0 -0.252 -0.144 -0.070 3%

1 Zlos 9.01 0.407

2.016

5

C/Z

I. 2. 3. a. 5. 6. 7. 8. 9.

1.654

2%;; . 8 I .060

C/Z

s

C,7

1.008 1.831

0.223

0.067 0.045 O.O2fJ

:-z,’ 0:291 0.240

x:: 6:OOS 0.007

I;-;:; .

I.125

. 0.053

‘,-z 03769

o:o9s 0.087 0.076 0.066

:-2: “,::;z

:-“0::. 0.027

2.298 2.054 I.R31 I..65 1.190 0.961 0.426 0.704

%F 40:

:-2: . 0.023 0.017

0:132 0.099 0.077 0.061 0.050

t-2: ;:“o”ot

“,-:‘7: 0:2a9

6.000 0.000 0.000

2:: 55. 60.

xi 0: 008 0.007

:-::; 0:031

:-“0% 0:003

0.231 0.190 0.159 0.136 0.117

“0-E:: 0:ooo 3.000 0.000

“0’ $

::: ‘1. it:

“O’BS ;g;

$2

ORB

,TAL

I,:“, ALPHA ”

5 19.364 x7”:: 3:soa :-‘Bxz I:413 L.129

C/Z 0.059 0.021 0.014 0.010 0.007 0.005 0.003

1. 2. 3. 4. 5. 6. 7. 6. 9.

8-8x: $WJ;

0.925

:x: 0:

001

:t!: i-o”:,” . 0.000 0.000 0.000 0.000 0.000 0.000

::: 3x 35: 2 59.

i?::: 0: 000

E:

51

(Z=l*l

,52/252,2P6/352/3P2

: WHOLE

--‘31.04 I.552

oRB:TAL TCE”, ALPHAl

C/Z

” 1. 2. 3. *. 5. 6. 7. 8. 9.

I;-;;: -0: -0.074

;- . i% 0.088 0.091 0.094

:z- .

:- :;a7 0: Obt) 0.048

:“,: . ::. 35.

:-2: o:o,s

2:

t::‘: 0:oos 0.007

2 60. ORBITAL 11:w ALPHAIAU

1 ” 1. 2. 3. . . 5. 6. 7. 8. 9.

:I? ‘4. :2 20. $3: .

2: 60.

113

-:-8:: 0:043

:20:

a:. 4s.

3P

ATOM

“,-tS$ 0:501 0.394

:-:2 . :-s: o:oa1

0:

005

0.001

s 79 .hB, ,3.L46 7.752 5.10a 3.6,o 3.705 3.106 : -s"g: . I.165 0.856 0.658 0 -52. O-.27 n -356 r).341 0.175 E-12* 0.085 0.070 0 -059 0.05,

J. ODDERSHEDE and J. R. SABIN

TABLE.

Atomic

287

StoppingPower and ShellCorrections

Shell Corrections and Proton Stopping Cross Sections, 1 G 2 4 36 See page 281 for Explanation of Table

P

t2=15, ORB

152/252/2P6/362/3P3

I TAL

I& ALPHA1

A”

:

l”oLE 1

--110.34 1.606

OS

ATOY *!:43 1616.33 6.453

”

C/Z

6

-0.394 1:.:::

1. 2. 3. 4. 5. 6. 7. 8. 9.

0.011 0.022 0.033

-0:077 -0.029

:-::3 0:062 0.070 0.077 0.003

:-“,x: 0:oss 0.070 0.080 0.091 0.09, 0.086 0.079 0.070 0.061 0.036 0.027 0.020

::: I$: . f2: 2: 2: 50.

: %3 0:094

i?::;: +‘,:

:%z 0: 0.33

I$;;:

0.215 0.152 0.664 :‘;E. 0.727 0.647 0.569 0.500 0.442 0.353 0.266 0.240

-0.796 -0.213 0.069 0.2PP 0.283 0.2Ob 0.263 :-:‘,: 0:162 0.1,3 0.06,

:‘:7”: 0:124 0.093 0.073 0.059 O.OQO 0.04, 0.035 0.030

;:,“o”z :*::7” 0: 048 0.040 0.031 0.029 0.025 0.022

“,‘Z 0:010 0.008

2;:

*

C/Z -0.102 -0.036 0.027 0.097 0.048 0.044 0.040 0.038 0.036

0:004 0.003 0.002 0.002 0.00, 0.00,

ORBITAL I,:“, UPHA ”

C/2

1. 2. 3. 4. 5. 6. 7. 8. 9.

6

0.157 0.096 0.060 0.0.7 0.036 0.027 0.02,

22.913 19.328 12. I.0 8.131 5.852 4.433 3..84 2.816

2% ;:ggt

:*z',: IL47

:,“: 0: 004 0.003

::: 4:: 5:: . i,“. :2 55. 60.

6

(Z=*6,

tl*. Ai::

2::: 0:001 0.001 0.001 0.000 0.000 0.000 0.000 0~000

:‘z’,: 0:4,2 0.299 0.228 0.180 0.1.6 0.12, 0.*02 0.088

L52/252/2P6/352/3PO

:

WHOLE

--151.26 1.667

oRB:TAL I(EV) ~LPHA~A”,

3P

ATOM

*!S30 1733.73 5.64.

”

c/z

1. 2. 3. 4. 5. 6. 7. 6. 9.

-0.3,O -0.225 I;‘;;: . 2’::: 0:027

::: 18.

:%z* :- ii:‘: 0:053 0.039

%: 30. 35. . 2. :“,: 60. ORBITAL ,I:“, ALPHA(A”, ” 1. 2. 3. 4. 5. 6. 7. 8. 1% 12. :2 IS. ::: :50: t:: 2 60.

:-:z. 0.017 0.013 0.0, 0.009

s

c/z

0.010 0.019 0.029 0.038 0.046

-0.186 -0.046 0.016 0.042 0.047 0.049 0.010

:‘E’: 0:067

:* :z 0: 073 0.086

:20:

17507 308.23 2.300

L

“,%L: o:oe2 O.OBO 0.084 0.081 0.07, 0.066 0.065 0.046 0.038 0.033 0.028 0.024 0.021

0.030 0.026 0.022

0.006 0.004 0.003 0.002 0.002 0.002 0.00,

5 0.*73 0.362 0.539 0.652 0.683 0.652 0.693 0.528 0.468 0.416 0.336 0.270 “0%:. 0.168 0.,20 0.09* 0.071 0.057 :*::z. 0.034 0.029

0.236

5.037 5.976 4.049 7 .R96 9.164 I.671 L .37R 1 .OR, O.R99 0.760 0.567 0.140 0.353 0.79” Z’:zi: a:121 0 .‘)?T 0.074 0.060 :-“,:z 0:0X

J. ODDERSHEDE

and J. R. SABIN

Stopping Power and Shell Corrections

TABLE. Atomic Shell Corrections and Proton Stopping Cross Sections, 1 d 2 4 36 Seepage281 for Explanation of Table

* 0.143 0.298 0.446 0.552 0.595 0.584 0.542 0.490 0.439 0.392 0.317 0.261 O.P?O 0.187 0.161 0.116 :-:,"z . 0.05b 0.046 0.039 0.033 0.029

C/Z

5

0.138 0.193

18.374 Zi.260

0:077 rz2” 0.063 0.050 cl.010 0.03, 0.025 0.016 O.OLL 0.006 0.005 0.006

::*“o:: 8.15. -

b.278 ..99.9 4;osi :-f&T 2:147

0.003 0.002

:*x8: ;: fJJF . 0.626 0.457

:-E 0:001 0.001 0.00, 0.000

0.350 0.277 0.225 0.187 0.158 0. L35

(NE,352/3P6 Y”oLE

*Tot4 --175.35 I.795 0.122 0.25, 0.377 0.474 0.522 0.525 0.497 0.456 0.412 0.370 0.301 ",'E;: 0:1eo 0.155 0.113 0.066 0.067 0.054 0.045 0.038 0.032 0. om

c/z ~:-sil~ -0:046

t-i:: .

0.249 O.Pf3 O.?3R 0.213 :-:f:. 0.102 0.077 0.059 0.047 0.026 0.019 0.014 k%: 0:OOb 0.005 0.004

J. ODDERSHEDE

TABLE. Atomic

and J. R. SABIN

Shell Corrections and Proton Stopping Cross Sections, 1 G Z G 36 See page 281 for Explanation of Table : 25

WHOLE--- ATOM 168.20 1.758

l!X94

1% 429.39

2055.32 6.,46

2.809

C/Z

s

I",:::: -0.129 -0.079 -0.041 -0.012 0.012 0.030

:%: CL020 0.026 0.032 0.037 0.012

:*::: 0:072 0.079 0.080 0.078 0.073

0.062 0.056 0.018 0.041 0.035 0.030 0.026

i?oJ:z do34 0.026 0.020 0.016 0.0,3 0.011

:~% .

c/7

s

-0.194 -0.065 -0.004

s

0.105 O.Z,4 E-9”,: OhSO

L?::,' 0:041 0.039 0.037 0.034 0.033 0.030 0.028 0.029 0.022 0.019 0.013 0.009 0.006 0.004

C/Z

:*::'o 0:8X? 0.929 0.956 O.VSA 0.93e 0.859 0.762 0.66R 0.584 0.512 0.379 0.?90 :*:z.

0.47,

0.455 :*:;,’

0:350 0.2R7 0.239 ii?:“,: o:,so 0.10” 0.083 0.066

0.155 0.131 0.112 0.097

:e% 0:002 0.002

2:‘,8 0: 092 0.078

0.06s

: WHOLE. ATOM --163.52 1.733 5 6L.070

34.547 21.976 I8. ‘91 , . . 43. 0.310 1EJ-ZZ 0.349 . 0.36, 8.072 6.916 6.057 . . 7.4

0.*92

2.262 0.746

0.0..

0.033

i-2:: “,-2% 0:015

0.376 0:43s

3P 6.659 64.83 1.092

-:‘:x:

"0'2":: 0:24, 0.161 O.,ld 0.088 0.069 FE: 01039 0.033

1s

*!&I,

6.761

6:7,6 6.697

2.726

0:OOS

0.637 0:2tV

:-:E 0: 165 0.142

472.33

754.01 3.735

2.946

C/Z

s

-0.3*0 -0. ‘9. -0. L26 -0.079 -0.043 -0.0‘5 o.oo* 0.026 0.04, 0.052 0.066 0.075 0.078 0.077 0.073

z-:1”,” 0:ora 0.023 0.028 0.033 0.030 0.042 0.046 0.049 0.054 0.058 0.059

c/ 7

:-z o:os3

-0.182 -0.069 -0.010 0.021 0.036 0.040 0.039 0.037 0.014 0.037 0.030 0.028 0.025 0.022 0.019 0.013

2002 0:017

0.0.6 0.040 0.03. 0.029

:-ET 0:oos 0.004

0.0,. 0.01,

:-:z 0:020

Lx% 0:002

i?“,:,” o:oas

6233

I%,

2161.0, 6.302

0:223

0.062 0.052 0.036 0.025

:-“o!i: o:oo, 0.001

32.70, L2.182 6.364 3.955 2.718 L.992 1.528 1.213 0.988 0.822 0.596 0.454

:'5;6

::*:z? 5.510 :-t:: 3:175 0.018 :*::: :-:I% 0: 002 ET o:sS2

s

0.015 0.003 0.001 0.000 -0.001 -0.002 -0.002 -0.003 -0.003 -0.003 -0.003 :::;;4’ -0.001 -0.004 -0.004 1:’ !g: -0:oos ::-gi:. -0.005 -0.005

5 0.091 0. I.35 x,".

C/Z rp:zg -0:1CS -0.00, 0.101

s 0.165

0.320 0.456 OO’XX~ .

",'?E 0:4x< ",-2: 0:3x 0.274 0.229 0.194 0.167 0.145 0.106 0.081 0.064 0.052 0.0.3 0.036 0.03, 0.027

C/Z

0.202 0.390 0.552

1%8 L.60 0.17,

C/Z

289

Stopping Power and Shell Corrections

0.21, 0.199

0.164

O-L29 0.100

0.938

0.R32 O.,P, 0.705

-2’::; 4030

-

0.07, 0.027

1.016

0.012 0.010 :*:::. x:: $2," . 0.003 0.002 0.301 0.001 '3.001

0.000 0.000 0.000 0.000

290

J. ODDERSHEDE and J. R. SABIN

Stopping Power and ShellCorrections

TABLE. Atomic Shell Corrections and Proton Stopping Cross Sections, 1 s Z d 36 See page 281 for Explanation of Table :

t NE ,352,3P6/.62/3D‘

20

WHOLE--- *To* 171.63 L.776

11~78 2262.31 6..48

12L 5‘9.23 3.069

C‘Z

6

-0.296 IO”-:,“; -0: 075

EE 0.021 “:“‘a

::*g: 0:oos 0.022 0.037 0.048 0.“6. 0.072 0. “76 0.075 0.073 0.06‘

:-:5:. :*:3,’. 0.012 0.045 0.050 0.053 0.055 :‘:E 0:oso

EfS 0:OZP 0.023 0.0‘6 0.0‘5 0.012

0.044 0.038 0.033 0.029 0.025 0.022 0.019

1.192 * 5. ‘37 6.00, 6.675 7.595 6.165 4.983 4.095 3.426 ii-s’:: . I.922 1.521 1.235 L.02. 0.863 0.598 0.44, 0.340 0.270 0.22, 0.18. 0.156 0.13.

Es::; o:m* 0.3Rl 0.365 0.34,

0.032 0.030 0.026 0.026 0.023 0.020 0.014 0.0‘0 0.007 0.005 0.004 0.003 0.003 0.002

:*::2” a:220 0.167 0.161 0.**0 0.103 0.079 0.063 0.05‘ 0.012 0.036 0.03, 0.026

5 49.380 20.516 **.*3.

-0.002 -0.002

0.840 0.66. 0.5.0 0.4.e 0.30‘ 0.2‘7

-0.002 -0.002 -0.003 -0.003 -0.003 -0.003 -0.003 -0.003 -0.003 -0.003

2::: o:*os 0.067 0.073 0.062

0.222 0.290 0.330

5

C/Z

54.290 31.798 24.173 16.991

-0.289 -0.16. -“.‘22 -0.079 -0.04, -0.02, 0.000 0.01,

:z-,“z 10:,,9 6.56. 7.371 6.43” 5.0.. 3.371 4.077

!i- :*,I? OZ3.5 0.31. is::: 0:209 0. ‘52 0. L30

2.63, 2.423 1.719

0.095 0.070 0.053 O.O.1 :-:I:

:*z: 0:aos 0. ‘62 0.565 0.172

0:020

0.407

“,-Es. “0% 0:001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000

5

:‘:z.:.

6% 933.1. 4.141 s

C/Z

I;';;: o:os* 0.120 ".,C. 0.1*7 0.196 0.193 0.170 0.140 0.1‘3 0.090 0.072 0.044 :%Y 01015 0.0‘2 O.O,O 0.008 0.007

45 :*:i5

2%7

56.3, 1.017

0:25.

s .6.99. 19.818 LO. 5.5 6.660 ..769 3.527 2.72. 2.,72 1.776 1..62 , .o*i 0.626

C/Z -O.!+‘@ -0.423

l?:;: o:o*a 0.023 0.027 0.030 0.034

2::: . 0.019

C/Z

:'K .

:%: 0:057 0.047 0.039 0.033 0.028

0.005

0.0‘9 “.“,6 0.013

0.039 0.0*9 0.009 0.006 0~004 0.002 0.001 0.000 0.00” -0.00, -0.001 -0.001

"0-K. 0.0“ 0.009

,285

ix; 0:o.s 0.048 0.050 0.050 0.050 0.04, 0.042 0.037 0.032 0.028

6%2

:*::: ":?nn 0.191 0.133 : *s: . 0.060 0.049 O.0.‘ 0.035 0.030

~%: 0:0.1 0.077

582.70 3.272

0.031 0.0.2 0.058 0.068 0.072 0.073 0.07, 0.“6, 0.0.9 0.039 0.030 0.02.

PO.43 L .289

:-::: ;:;g': . 0.166 0.135 0.107

1.60” 2.346 2.266 I *A?* 1.506 1.204 0.977 0.606 0.676 0.575 0.432 0.337 0.271 0.223

“,% . 0.007 0.005 0.004

6.666 C/Z

-?E C:‘42

5

C/Z 0.00, 0.05, 0.0.. 0.030 0.020

‘!;iS7, 2433.00

-1.465 -0..25 -0.043 0.122

0:2*0

5 1.007 I.993 2.07. ‘ .669 1.346 1.104 0.917 0.770 0.654 0.562 0.427

C/Z -0-P35 -0.419 -0.184

30 t .258 42.69 0.066

C/Z 0.041 0.016 0.009

l?K7

0.0,7 0.033 Cl.038 0.0311 0.036 0.034

221, 3.15 0.2.0

.%O 77.32

5

C/Z

-0.16, -0.073 -0.0‘5

C/Z

-0.015 0.089 0.09,

5

2.243 3..60

0.068

3.669 3.228

:*::: 0:02. 0.016

:‘E 11795 I .495

0.013 0.010 0.007

:‘E! o:s*a

0.005 0.00. 0.003 Z’“,K

“,‘X Or.26 0.358

-0.002

:‘E: 0:*.1 0.29,

Io0-g;: -cl:003 -0.003

:-:i: 0:128 0.103

o:oo* 0.00, 0.00, 0.000

;‘:E “:I39 0.11, 0.090 0.075

~~‘~0”: -0: “03

0.065 0.072 0.06,

:-::: 0:000

:‘:z:.

,265 91.65 1.?98 5

“,-::c

C/7

-:*“,z . L

0:329 0.415 0.486

0.031 0.030 0.027

2%.

0.0‘7 0.022

28:;. 0.661

0.0,. 0.0,‘ 0.010

“O-22” 0: 5.7 0.191

0~007 0.00.9 0.006 0.005 0.00. 0.003 0.001 0.001 0.00, 0.00, 0.00‘ 0.000 9.000

5 0 .RSQ I.740 I .R7R I .?‘I? 1.2’19 1.06.

0.141 “,-a:090 :z

0.R90 0.751 0.64‘ 0.551 0 ..22 0 -333 0.270 0.274 0.190 0.133 0.09, 0.0’5 t-23: o:o., 0.010.010

J. ODDERSHEDE

TABLE.

and J. R. SABIN

291

Stopping Power and Shell Corrections

Atomic Shell Corrections and Proton Stopping Cross Sections, 1 s 2 Q 36 See page 281 for Explanation of Table :

4F

lfZ66

,%7

2539.60 6.83, C/Z

s

-0.278 I;‘:;~

C/Z

s 0.060 0.121 0.,*2 0.23, O.Pe.0 0.30,

0.004 0.008 0.013

-0:079 -0.0.8 -0.023 -0.003 0.014 0.028

6%, 1011.46 4.3*3

625.00 3.3R9

0.034 0.034

0.055 0.039 O.Ob5 0.070 0.011

"0% 0:o.. 0.O.b 0.047

0.070 0.062 0.050 0.040 0.032 0.025 9.020 x:.

Xl 0:o.o 0.035 0.031 0.027 :*:;: o:o,s

0.026 0.02. 0.02,

0.17. 0.150 0.132

:?J:: 0:oos 0.006 0.005

E," 0:OSO 0.049 0.041

E% 0:002

0.03. 0.030 0.026

1 %o 102.2P L.371

s 0.,02

C/Z

-0.796 -0.422 -0.209

0.19s

0.286 0.36l

-:%: 0:101

0.485 0.478 0.?23 0.55, 0.58, 0.59. 0.590

z-:x. :*:88: 0:171 0.14. O.,lR 0.095 0.077 0.01, 0.031 0.022 0.016 0.013 0.010 0.008 0.007

-0.

to3 0.100

0.159 :*::: 0:09b 0.08b 0.078 :'::: 0: 0.5 0.033

5

5 2.::: .

6.095 5.813 4.978 ..13. s....

2*:2 3:.7.

:*::z 2:156 L.667

:-::: r:.sa 1.088 O.R,b O.b.6 0.525 0..36

2.685

0.001 0.00,

:':A;: o:oe7

0.00, 0.000 0.000

:%z 0:90.

EG 0:1s1 0.127

:%I: . 0.00. 0.00, 0.002 0.00, 0.00,

;*;:: 0:on 0.061

z*::: o:oo, 0.000

,!ZbO s 0.00. O.OOR 0.011

3.593 3.000 2.502 2.10. L.787 , .535 1 .lb, 0.919 :'I::. 0.517 0.357 :',':," . 0.161 0.13, 0.110 0.093 0.080

C/Z

s

-l? . % -0.03, 0.002

0:022 0.025 0.028

s-:,': 0:03.

0.024 0.035 0.051 0.062 0.06, 0.069 0.069

0.03, 0.033 0.037 0.040 0.043 0.044 0.0..

:*oo:: . 0.031

do.1

0.042 0.038 0.034

Z’:“,:

0.030 0.026 0.023 0.020 0.016

0.033

0.926 0.02,

:-x,',' 0:oes 0.024 0 .oz? 0.016 0.012 0.009 0.007 0.005 f?i%

C/Z

:*::: o:ooo -0.00,

-0.003

0.03. 0.029 0.025 6":., 65.38 1.096

0.24.

o.o** 0.007 0.002

0.640 0.040

0:003

lz.3 3.23

1051.66 4.454 0.051 0.104 0.,56 0.205 0.145 0.272 0.265 O..?RS 0.276 0.261 0.227 O.,Y. 0.16, 0.145 0.127 o.owi 0.07. 0.059

“0%~

-0"':::.

hfYA7

*IZ9* 692.8. 3.560

2652.59 6.982 C/Z

2.538 4.043 ..541 4.20.

0.031 0.02. 0.019 0.012 0.009

s 25.096 10.239 5.5b. 3.509 2.433 1.79b I.386 1.,05 0.903 0.753 0.549 0.419 0.332 0.269 0.22. :-:",fi o:oez 0.065 0.052 E2: 0:03,

C/Z

s

CIZ

x: 0:019 0.015 0.012 0.010

0. L65 0.13,

f

-0.05, 0.11. 0.135 o.**o 0.080 0.058 0.042

0:031 0.030

;'%: 0:006 0.005 0.005 0.003 0.00, 0.002

1.129

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-L?:::

k?",:s . 0.46. 0.417 0.320 ix .

3374 69.43 C/Z

t/7

5

-0.769

0.099

zJ*::: -0:07a 0.018 0.066 0.133 0.162 0.,,7

0.174 0.25, 0.3,R

",-:;: .

0.540

Z'Z. 0.099 0.00,

O..RO 0.51, 0.438 0.397

x3:.

0.712 0.30,

",-",:: 0:013 0.011 0.009 0.007

0.194 0.159 0.133 0.113 0.09, 0.085

i?.':," . 0.464

5 Ye::3 I:716 1 ..Q, ,.22R I .O?O 0.859 0.730 0.675 0.540 0.4,. 0.328 0.767 0.222 0.187 0.13, 0.097 ", *:rz 0:0.-2 0.04, 0 .osc 0.030

292

J. ODDERSHEDE and J. R. SABIN

TABLE.

Stopping Power and Shell Corrections

Shell Corrections and Proton Stopping Cross Sections, 1 d Z d 36

Atomic

See page 281 for .Explanation of Table MN

(2225)

:

6,s

OR8ITAL It:“, ALPHAi

AU)

5 O.O?P 00’:ii: 0:2az

C/7

”

-0.749 -0.Zl2 -0.219 -0.0.59 o.oo* 0.072 0.119 0.156 O.ICR 0.176 O.l?O 0.149

1. 2. 3. 4. 3. 6. 7. 8. 9. . :2”. it:

0.333 “,-::: 0:445 0.469 :-::z. 0.48, 0.451 0.415 0.37.3 0.296 0.234

0.126 0.10. 0.083

. ::. ‘J,“’ 35:

t-0”::. 0.025 0.018 0.010 0.01 0.009 O.OOB

. 2. 50. 28:

5%9

OYWITAL I

129.90 1.515

5 2.,14 x8: 4501 f-ES

0:021 9.017 3.014 0.0*2 0.009 O.OOR 0.007 O.“Orr Q.003 :-::: . 0.002 0.00, 0.001 “0-E 0:ooo

s 0.352 : -:2 1 :?I 1.124 0 .o*e 0.901 O.-.RP 0.593 0.51 0.401 “,-2;: o:n1c xi g:;:: o:oso 0.048 0.040 0.034 0.029

2:;90 4.57 0.290

* ::-::: . 10.153 6..?3 ..516 3.349

2:940 2.503

8. 9.

I

:-::z 0:1io 0.111 0.095 O-OR3

C/2 -0.051 “.OL!i 0.029 0.029 x’,:

EPI I :698

. ::. 1Q. 16. 0.425 0.286

:::

C/Z 2’:z

s 2.615 4.362 5.278 5.3,2 ..BJO ..206

0:202 o-*90 0. L53 O.ll? 0. ORR 0.067 0.051 0.040 0.02, :-%z 0:01 0.008

1-8:: 2:t&* 2.31 I.780

I

: .-::t 0.954 O.ROS 0.560

I

KE .

$9: 40. 45.

.

x-::: 0:124 0.100 0.003

2: 60.

:-,“z:.

:-::,”. 0.2s

:-::: “,:m:

XE . O-1.7 0.127

0:001 0.00‘

TS 1.691 792.34 3.816 C/Z -0.72. -0.404 -0.220

4. 5. 6. I. 8.

I:-$:: . 0.060 :-::o’ g::fz

9.

5 0.070 O-13(5

0.198 :-Ez. 0.339 0.374 0.402 :-1:;

.

“,k:

2.

. O.li?O 0.10, O.OA9 0.036 0.037 0.026 0.019

::: 18. f2 . $5”. 40.

:-::: 0:010 O.OOR

2%* ..92 0.301

Oh6 i?:::.

C/Z -0.036 0.010 0.027 O.O?P O-02? O.OP3 0.021 o.o,a 0.015 0.012 0.009 0.001) 0.007 0.006 3.005 0.00. :-:“,: 0:001 0.00, 0.001 0.001 0.00,

c: :-kx I :201 : -‘,:: 0:IW. 0 .,*7 0.662 g-2;: 0:3Ql “,-2:: . 8%:. 0.126 O.OQ4 0.073 0.05* :-2: 0:034 0.029

R

J. ODDERSHEDE and J. R. SABIN

TABLE.

293

Stopping Power and Shell Corrections

Atomic Shell Corrections and Proton Stopping Cross Sections, 1 c 2 Q 36 Se-epage 281 for Explanation of Table : .I= 3023.68

‘!L

,293 875.16

7.45. s

CIZ

s

43.270

-0.245 -0.16‘ -0.1‘1

xi,'

C/Z -1.6.9 -0.490 9.0‘8 :-‘,:z.

:x: ‘4.737 152 17:

“0’36: . 0.370

0:009 0.011

-0.077 -0.050

12.60‘ LO.796

2::: 0.019 * 0.02,

3’::: 0:003

i?::X 7: 133 5.65‘ 3.825 4.600

ii- . :,‘: 0.340 :*E. 0.2.. 0.2‘6 “0’ . E;: 0.09‘ 0.070

0.063

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E%: 0:053 0.0.. 0.036 0.030 0.02. 0.020 0.017

9.65‘ 9.555 0.400

0.035 0.036 “0%: 0:030 0.027 0.02. 0.072 0.019 0.017

-0.174 -0.088 -0.040

0.036 0.071 0.109 0.145

-:-8E 0:023 0.029 0.031 0.031 0.03, 0.028

s

x%: 0:003 0.002 0.001 0.000 -0.00,

Et a:‘83 0.1.. 0.112 0.080 0.070 0.046 0.032 0.02.

::‘g: -0:003

3227.87

0.360

s

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2% 0:371 x:0

Es: 712.7 5.758 4.696

o:rs,

3.9‘0 3.3‘0 2.8.1

l?;::. 0. ‘6. 0.*2. 0.095 Lxx

0:O.b

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0.031 0.030

C/Z -0.200 -0. -0.11, -0.078

C/Z

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vi:: 0.017 * 0.019 0.02, 0.023 0.026

0.033 0.033

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0.0‘7

5z3. 163.22 1.732

-0.207 0.017 0.102 0.116 0.102

s 0.003

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E:$. :’ Zf ,:200 0.967

:*:x 0:22, 0.179

“0%X 0:02cl 0.020 0.016 0.0‘2 0.010 O.OOR

2 :t: 0: 106 0.09‘ 0.079

s 2.462 4.25. 5.36. 5.736 5.500 ..9e, 4.396 3.8.. 3.359 2.9.5 2.30, 1.84, I .506 1.255 I.063 0.745 0.55‘ 0.426 0.34, 0.279 0.233 0.198 0.170

c/z

*

C/Z 0.031 0.010 0.009

S%S ,3*s.,s 4.916 5

-0.170 -0.007 -0.041 -0.011 i?E 0:ora 0.03, 0.031 0.030 0.028 0.026 0.025 0.023 0.022 0.0‘3

C/Z

0.034 0.069

-0.670 -0.380 -0.2*3 -0.099

0.10q 0.20. 0.212

-x% 0:09, o.,r. 0.146 o.*se

?I’::,”. 0.19, O.L6F 0. I.7 0.129 0.“.

i’:“,: 0:,34 0.1‘4 0.096

:*:::. 0.008

Ez: 0.055 0.0.5

:%: 0:029 0.02‘

:*:::. 0.00. 0.003

z-:3: 0:02tl 0.02.

:*::s o:o,, 0.009

2% 5.50 0.3‘8

1.37‘ 2.368 2.973 3.20. 3.07,

“,‘::: 01092

906.75 ..ORP

7.702

:‘,“,:f ‘I:513

:*;:: 0:310 0.342 0.370 0.392 0..09 0..25 0.421 O..“? 0.376

:*:,“:.

2s 1.694

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$5: 367

0.063 OS,24 0.180

I:‘;~;; -0:21.5 -0.097 -0.010 0.054 0.100 0.132

3l=

WHOLE--- *TOY

:’0:

“,‘::: 0:032 0.028 0.02.

z!:: 0:009 0.006 0.004 0.003 0.003 0.002 0.002 0.00,

$z”o; .

:

“0’::: 0:132 O*‘lC 0.088 0.069 0.055

C/Z -0.299 0.096 0.239

I;‘o”g +W:

24.592 41.596

“0% 0:,97

:-“,:t. 0.023 0.022 0.010 0.01. 0.0‘0 0.008 0.006 0.005 0.00. 0.003

0.032 0.0‘9 0.009

:pg: -0:002 -0.002

C/Z

ii*:3 o:21a 0.223

5

C/Z

30 9.783 L32.33 1.559

C/Z

:;‘gg 0: 0‘8

..a,9 5

C/Z

2% 5.17 0.308

25,

5%

“0’:~~ .

3.235

t- ~Z o:m

x5 0:035 0.028

1263.15

4.010

105:3, 149.45 , .h57 s :3%z . 9.659 t -::: 3:227

-0.00‘ I~‘~~~

1.006 0.6ll 0.770

-0:002

0..97 0.413 0.279

0.023 0.010

L .395 1.18.

-0.003 1;’ gj

:‘:z . 0.12,

0 .oo* 0.011 0.005 :*:::

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po’oo9e~ 0:oas 0.058

0:003 0.002 0.002

00-z: 0:rea 0.19i

,233 151.33 1.706

294

J. ODDERSHEDE and J. R. SAMN

Stopping Power and Sheii Corrections

TABLE. Atomic Shell Corrections and Proton Stopping Cross !%c.tions,1 d 2 Q 36 See page 281 for Explanation of Table cu

(2=29)

: lHOLE

O”YTAL l(W) ALPHA(

20

&TOM

,4&s 1010.46 4.309

I!:29 3362.26 AU,

7.86.

”

C/Z

5744 1336.95 ..95,

:p:34’ . iK+:: -0.109 o:oo, ~o”‘~~2’ . -0.032 2K 0:014

1. 2. 3. :: 6. 7. 6. 9.

-0.634 -0.361 -6.204 -0.096

ix% 0:019 0.021 0.024 0.027

:::

“0’:::

0: 190 0.227 “o-5: 0:x1 0.33,

8’::: 0:153

:*z . 0.366 0.358 0.339 0.3I6 0.257 0.207

x2 0:13*

ii: .

0.052

-:-2x . 0.086

-0.016

-X*88X.

s

C/2

s

0.060

:*:J’: 0: 031

32: .9. 45.

x2: 0:oss 0.038 0.031

0.031 0.030 0.028 0.025 0.023

k?d:,’ 0:022 0.01r

“0’::: $;;g

::: 60.

:*oDx: 0:01a

:*o”:: 0:OlS

x: . 0.009

g:g;: .

i?Ki. 0.06.

2250:

JO 12.404

11z45

OAEIT~L

5.52 0.318

la:“, ALPHA v

0.013 0.00, 0.002 0.00, 0.000 -0.001 -0.001

2.103 2.649 2.674 :*3’,3” . 2.18. 1.69‘ 1.643 1.439 1.132 0.916

:::

::‘:xx. ?E. ?g”EX . 1 .Sll 1.209 0.99,

I;‘::,’ +“o:

l?BzoX 0:46S 0.366

-0:ooa

::: 5: 52: 1:: 5::

ZH

:

(2=3&J, YH0l.E

oRB:TAL l(EVI ALPHAI

iv

”

--278.64 2.264

t Cl.?

8%; 01005 i?,“::*

:-x:: 01474 0.389 0.325

SJ::.

Z’Z8.

IS

2s

I f&6

1.697

1.962 s

C/Z

1372.04 4.474

s 0.002

C/Z

,541 ,7p..a4 c.eta

52771

LOR9.16

3449.96

s.021

s

-0.170

0.076

-0.092 -0.04A

0.052 0.079

%Z o:o29 0.027

5.930 :*:t: 0:294 0.262

31:

:*::% .

35:

:*:x 0:oao

4450:

“,-go’

:I? 69.

0: 041 0.033

-0.616 I;‘:;;:.

“O-:3: a:179

:*:“5: 31444 2.962

:-:2’: 9:023 9.022

?fi-: I:260 1.0*, 0.639 0.705 0.602 0.520

0.007

0.019

0.016

FE . 0.004

:*:::. 0:135 0.120 0.106 0.96, 0.064 0.052 0.043 0.036 9.031 0.027 O.OP3

2% 6.,9 0.33,

LA, ALPHAlAUJ ”

C/Z

1. 2. 3. 4. 5. 6. 7. E. 9. ii: ii: .

:*:5”: cl:159

:*:“,9

ORBITAL

::: 60.

:*1:3 1:0x2

-0”‘::: a:oa, 0.113

.

2:

5*::3 4:00fS 3.155 2.536 2.ORO

:*::r; 0:072 0.051

0.048 0.094 0.137

-‘).a96

1%:

:::

zu . 0.2,. O.l-?l

:~*;:4’ -o:oo* -0.004

-0.227

:2:

2:

0.302 0.3.5

x:8 0:072 0.01.

ATOH

1. 2. 3. 4. 5. 6. 7. 6. 9.

s 2.993 5.315 6.602 7.359 7.148 6.556 5.854

-:*dz .

:g*:g . -0.004 -0.00.

I:‘;:: -0:oos

I,“:

C/Z

s

C/Z

1.213

1. 2. 3. . . 5. 6. 7. 6. 9.

144.29 1.620

s

-0.196 0.003 0.085

1.06, L.666 2.31,

:*Kz o:os* 0.073

:-255 2:369 2.093

Cf.?

s

C/Z

s

:*;E. x5T 0:037 :*::I:. 0.01. 0.011 0,009

“,‘Ei 0:240 0.2‘7 0.290 0.309 0.325 0.345 0.350 0.342 0.326 0.306 0.25, :*:z. 0.138 0.116 9.099 0.066 0.075

C/Z -“,*E 0: 022 0.026 0.026 0.025 :*:‘3: ;:z;g . O.OIl 0.009 0.00.3 0.007 0.006 0.005 “0% 0:ooe :*::: 0:001 0.001

5 0.315 6.693 0.947 0.994 0.905 O.-m, 0.691 0.504 :*,‘z 0:366 0.296 “0% 0:173 0.122 :*2: 0:057 0.047 0.039 0.033 0 .OP9

J. ODDERSHEDE and J. R. SABIN

295

Stopping Power and ShellCormtions

TABLE. Atomic Shell Corrections and Proton Stopping Cross Sections, 1 d Z G 36 See page 281 for Explanation of Table

,!235 3642.55 8.18, C/L -1.804

Io,‘f2,gz

:;-go" . 0.210

-O:tO6 -0.076 -0.053

0.363 0.41. o:.,e z-t:?

:;-z: 8.52. 9.65. -

0.405 0.373 0.338

1.569 6.073 ..982 4.16.

0: 2.1 22: 0.182

3.042 3.536

:-:E 0: 085 :-:t:

,:297 1.017 0.864

",-2: 01049

,9:95 1100.06 4.496

s “,-“,“,:

0:OOS 0.008 0.010 0.012 0.013 0.015 ix8 0:021 0.023 0.025

:-z:

0:045 0.037

2z: 0:536

C/Z

s

-0.L64 -0.oe9 -0.047 -O.OLS 0.001 0.0'. 0.022

t-t%: . 0.077 0.102 0.125 0.1.. O-L59

0.027 0.029 0.029 0.027 0.025 0.024

;-:E 0:174 O-L65 0.150 0.133

0.023 0.022 o-o*9

:-:A: 0: 080

",-",:: o:o,o 0.008 0.006 0.005 0.004

0.063 0.05, 0.0.3 0.036 0.031 0.02‘ 0.023

C/Z

5

5

0.249 0.553 0.402 O.ACI 0.829 0.733 0.640 0.562 0.496 0.44' 0.352

-0.595 -0.3.3

0.044

-0.,9R -0.098

O:,S,

0.1.. 8-:x:

2:2': 0:2.6 0.267 0.286 0.30, 0.329 0.322

0:,3a 0.121 i';:t

0.32. 0.31, 0.293 0.243

0:0.7 0.033 0. "24 0.919

:-::I: 0:oor O-O"6 0.005

:-:t: 0:'s O-l,.

it?::," o:o,o

:-::: 0:073

",-I%: 0:ooi 0.002 0.00, 0.001 1.00,

i?G,”

-0.066 -0.005 o-o,9 i-z:: 0:024 0.023 0.021 z-z::

a:012

i-:% . 0.,9* 0.169 0.119 O.OR9 0.070 0 .OSh 0.046 0.039 0.033 0.029

4s

L-939 9.67 0.42,

.%a

L99.95 I.917 s 0.93’ L-6.2 2. ‘05

C/Z

-0.206 -0.009 0.076 0.103 0.099 0.066 0.075 0.068 0.062 0.058 0.05, 0.013

:-,"9,7 2:225 1.993 1.755 1.140 1.357 L.076 0.875 0.728 0.615

z-E% . 0.023 0.013 0.009 0.006 0.004 0.003

C/Z -0.60. -0.018 0.173 0.283 0.306 0.285 0.2.7 :-:"7: 0:141 0.096 0.068 :- z::: 0:030 L?::; 0:009 :- E 0:004 0.004 0.003

;-::2" a:002

C/Z

-0.073 -0.051 -0.033 ::-o";s" 0:005 0.015 0.030 0.0.0 0.048 0.053 0.057 :- :x4" 0:0.7 0.0*1 "0%: 0:024 0.020 59, 225.58 2.036

0.002

0.798 1.422 1.841 2.09, 2.157 2.06, 1.878 1.672 , ,478 0.710 0.602 0.516 0.369 0.277 O-2,6 0.113 0.143 0. *to 0.102 o.o**

-0.663 -0.148 0.11, 0.240 0.286 0.282 0.25. 0.219

71652 5.060 3.590 2.689 2.097 1.687 1.390 1.167 o.e.59 0.661 0.525 0.429

:-,","z . 0.004 0.004 0.003 0.002 0.001 o.oo* 0.000 0.000 0.000 -o*oo* -0.001 -0.001 -0.001 -0.001 -0.00, -0.002 -0.002 -0.002

C/Z

5

0.026 0.009 0.006 0.004 0.002 0.002 0.001 0.001 0.001 6.001

19.845 10.124

0.001 0 -00, 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

:-2345;7 0:175 0.134 0.105 0.085 0.071 0.060 0.051

:-::: 0:OOS 0.005 0.009 0.0'1 o-o,, 0.01. 0.016 0.017 0.020 0.022 0.024 0.025 0.026 0.027 0.025 0.023 O.OPl "o-8:; 0:016

C/Z

5

-0.163 ::-:g -0:021 -0.002 0.011 0.020 0.025 0.027

0.0*3 O-O.6 0.069 0.091 O-L'2 O-l.30 0.144 0.15. 0.160 0.16,

:-2;.

z-:7: 0:129

:-::z 0:0.72 0.021 0.019 0.016 0.013 0.010 O.OOR 0.006 0.005 0.004

"0.:;: . 0. OTB 0.062 0.050 0.042 0.035 0.030 0.026 0.023 I':,, L3.0, 0.506

s L-180 2.175 2.9,6 3.453 3.778

0.076 0.056 0.043 0.034 0.020

3.282 3.003 2.487 2.063 1.728 1.465 ‘-25.6 0.896

"0'::: 0:oos 0.006

0.525 0.673 0.422 0.348

C/Z

*

15.166 v.4:: 10.105 o:o,. 6.257 0.007 0.009

: .5::

0.006 0.005 0.00. 0.003 0.002 0.00, 0.001

: -:x:: 1:452 1.200 I.010 0.147 0.576

0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.001 :pg: . -0.001

",-:5x . 0.3'3 O-2,3 0.155 0.118 0.093 00-00~s n:o53 0.045

:-ET . :-",-:z . 1.453 1.161 0.951 0.794 0.58, 0.4.5 0.352 0.287 0.836 0.16, 0.116 0.088 :-"0"5: 0:oaa 0.039 0.033

2P 5.602 1434.2. 5.13.

,‘,‘.a,

12%9 295.59 2.33, C/Z

0.015 0.009 0.006 0.005

0.021 0.012

1105.35 4.667 5

-0:103 :p:::

0.097 0.099 0.088

:-2: I:326 o-9.0 0.703 0.547 0.440 0.36, 0.363 0.258 0.223

5 ::-:I:

C/Z 0.030

,183, 3650.25 6.190

290.81 2.3'2

-0.220

5 L.55.

2.833 3.755 ..3*, 4.664 4.625 ..a79 4.038 3.672 3.3‘1 2.698 2.213

1.1e5 4.84 0.298

C/Z

5

0.0.”

I;-;:: -0:

,266 ?14.33 1 .a35

192

-0.095 -0.02. 0.030 0.072 0.103 O-,26 0.141 0.15. 0.151

0.079 0.,,6

:-::; O:?OS 0.230 0.350 :-:"Bt: 0: 304 0.312

:-::z a:107

0.310 0.299 0.283

0.0.9 0.072 0.03. 0.025 0.019 :-::x .

"0-E: 0:159 0.133 0.112 0.053 0.096

0.010

0.072

C/7 r;-$g “:o,R “.“P5 0.025 0.024 0.023 O-O?, 0.019 Z-,“i’ co,: o.oo* 0.007

0."06 0.005 0.00. 0.003 0.003 0.002 0.001 0.001 0.001

5 0.34, 0.573 0.756 0.94, O.-O* 0.714 0.626 0.550 0.4*7 0.,-T. 0.348 0 .PR. 0.235 0.lO-J 0.169 0.119 O.Or(9 0.070 :-Et o:ms 3 .",3 0.029

J. ODDERSHEDE

TABLE.

and J. R. SABIN

Stopping Power and Shell Corrections

Atomic Shell Corrections and Proton Stopping Cross Sections, 1 d 2 6 36 See page 281 for Explanation

~NE,352/3P6/30,0,452/4P3:

45

YHOLE

--300.39 2.3+9

1. 2. 3. 4. 5. 6. 7. 8. 9. :20: 14. :0: 20. $1: . 2: 2: 60.

of Table

ATOM

L%b 1202.15 4.700

I!:26 3852.74 &IL4

40.135 33.19‘ :;-z Is:ols 12.915 ‘~-Z a:771 ,.b.293 606 5.179 :-~~~ 3:160 2.292 :,:I01 -325

0.25, 6. L95 0.156 O-L16 ",- 2: ":061 0.050 0.042

0.002 0.003 0.005 0.00, kx;: 0:012 0.013 :';:B . "o-2: 0:072 :-,"ji: . 0.026 0.025 0.024 0.022 0.02" 0.019 0.017 0.015

0.910 0.7b.5 0.6.53 0.565

3P 4.946

11.79

219.60 2. **a ”

O-.66

C/Z

s

1. 2. 3. 4. 5. 6. 7. 8. 9.

O-b97

1.253 :-::s 1:971 1.920 1.777 ;-g; L:266

:2:

*

C/Z

. 0.056

z;-:g

Oo-:t; . 0.273 ",-z:!: 0.165 0: 195

L.016 :-t::

~-',~5' 0.063 .

0:591 0.506 0.364 0.214 0.214

0.0*5 0.030 0.023 0.015 0.011

2 ::: 0:119

0.007 0.008 0.005

0.101 0.056

E%:: .

:-:z. 1.929 1.626 I.387 1.194

::: :::

0.016 0.010 6.00, 0.605 0.00. 0.003 0.002 0.902

:2: 2: it:: 55. 60.

c2=34,

SE

~NE,352/3P6/3",0,452/4P4: W”OLE

--316.38 2.386

oRB:7*L I(W) ALPHAIAU)

::: :t: 16. 22:: 32:

C/L

0.294 0.355 0.436 O-.43 0.441 0.43, 0. a01 0.366 :-:x1 0: 263 0.200 0. ,!i5 ".L22

15.414 (3.152 :fJ-',::: CL692 7.920 6.394 6.269 3% 3:246

0.097 6.975 0."6.

b-t',: . 0.784

0.044 0.053

28% . 5x03 277.32 2.26,

-0.073 -0.052 -0.035 -0.021

0.002 0.003 0.065 0.006 0.008 0.009 0.011

-",-%': 0:010 0.024

0.012 0.013 o-o,5 O-Ok?

z-g; 0: 049

:-ET o:ata :-::a

!i*",:: . 0.9.l 0.035

0:024 0.023 0.021 0.020 0.018 0.016 0.015

0.022

2P

I%

C/Z

5

-0.156 -0.068 -0.049 -0.023

0.020 0.040 0.060 0.079

-"o-"0:: . ",-",::

Lx: 0:,27

0:025 0.02, 0.026 0.025 0.023 0."22 0.021 0.019 0.016 0.013 0.011 0.008 0.007 0.006 0.005

2::; 0:1r5 0.143 0.133 0.121 O.LOR 0.09, 0.075 0.059 0.04R 0.04" 0.034 KX 0:orr

C/I 0.015

6.725

:-::9 . 0.010 0.007 0.006 0.005 0.004

:-2:: 2:991 2.205 1.667 I.335 1.066

:-::: 0:oot 0.001 0.001 0.001 0.001 0.000

"O-4:: .

2: 36. :2 550:

:-i%: 0:""" 0.000 0.000 0.000

s

i-:4': 0:asa 0.29" 0.242 :-:t: 0.073 0:092 :-:z. 0.042 0.036

C/I -0.074 -0.014 0.01? 0.072

0.024 0.023 0.073 n-022 0.070 O.O,P 0.013 0.010 O.009 0.00, P-*07

“0’:z:

0.152

a:021 "-016

:-::I . 0.00' 0.001 :-Es 0:001 0.001

2:::.

15.21 0.529

1. 2. 3. 4. 5. 6. 7. 8. 9.

::15:

9

C/1

4763

,t:90 24.07 d-665

L23D362 4,5.65 2.76.

1% 264 .P7 2.106

5.502 1541.54 5.382

Y

:20:

%

:54”: 0:079 0.652 0.505 0.403 0.330 0.276 0. IRR 0.13, 0.104 0.063 0.06, 0.056 0.617 O-0.0

1286.55 4.662 s

-0.2"6

“5:. . 60.

I,:“, ALPHA,*“,

:-z:: ,:9as 1.551

ix: 0:002 0.001 0.00, 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.00,

If224 e022.64 6.596

:::

O”8ITAL

ix,' 0:s 05 0.407 0.336 0.262 0.241 0.206

0.02, 0.02" 0.0*5 0.010 0.00, 0.006 0.005 0.004

3P ATOM

” 1. 2. 3. *. 5. 6. 7. 6. 9.

0.92. 1.72" 2.329 2.764 3.101 3.263 3.246 3.125 2.939

5 ,0.*17 R-O** 5.153

C/Z

+ 0.171 0.376 0 -569 o.F1,4 0.67R 0.6?6 “.Sb!! n.997 0 444 0 .?-I?7

0.724 0 267 O.Y?PP O.IPP 0.16, 0.1!4 O-OR6 0.06, 0 -054 :-ES 0:033 0.02e

J. ODDERSHEDE and J. R. SABIN

297

StoppingPower and ShellCorrections

TABLE. Atomic Shell Corrections and Proton Stopping Cross Sections, 1 < 2 G 36 See page 281 for Explanation of Table

t/7 -0.074 -0.015 0.011 0.021 0.029 ?,"Z 0:022 0.020 0.018 0.0** O.O,l 0.009 0.00(1 0.007 0.006 0.001 0.003 0.003 "IOOZ 0.00% 0.001 0.001

C/Z -0..255 -“o-EEi . :-“,xs 0: 09, O.OE% 0.074 :- 2: 0: 056 0.049 0.043 0.036 0.030

s

5

0.516 0.949 1.260 I.473 L .595 1.614 L.547 *.*a,

0.60‘3 1.150

:-:% 0:9s, :-ET 0:564 0.487 0.353

:-::; 0: 008 0.006 0.005 0.004 0.003 0.00%

:-,‘“,x o:ra9 0.139 0.117 0.100 0. OBC

(NE)352/3P6/3”,0/QSZ/4Pd:

C/Z

:-E 2:177 2.356 2.442 :-22. 0.180 0. L36 0.100 0.07s 0.051 0.045 0.027 0.018 0.013 :-z 0:006 0.005 0.004

:-::: 2:x.* 1.97. 1.697 1.455 1.254 :-SE 0:bOO 0.472 0.382 0.3 Id 0.266 0.227 0.197

0.009 0.01, 0.014 0.010 0.007 0.006 0.005 0.005 0.004 0.003 2,“:: 0:001 0.001 0.001 0.00, :-:t% 0:ooo 0.000 0.000 0.000 0.000

5 0 -380 4 -922 3.451 8.491 I.863 I.437 1.113 0.933 0.778 0.660 0.993 0.381 0.308 0.253 0.112 0.145 0.106 0.08, 0.06. 0.052 0.043 0.037 0.032

s

CIZ 0.093 0.08, 0.057 0.044 0.032 0.023 0.018 0.014 0.012 0.011 0.009 0.00.9 0.006 0.005 0.004 0.002 0.001 0.001 0.001 0.001 0.000 0.000 0.000

26.611 26.W, 18.200 ‘i?-:z 7: “56 5.582 ..5%9 3.152 3. ,63 :-“8:: 1:451 1.,*9 0.999 0.678 0.49. 0.377 0.899 0.m3 0.201 0.170 0.146

IS

WHOLE

--329.59

ATOM

2.46,

C/Z

s

-1.887

29.75,

1;-:;9” . z-l%:

34.514 26.222 20.028 LB.219

0: 355 0.415 0.4*, 0.448 0.043 0.*,7

C/Z

S

c/z -0.149 -0.oe5 -0.049 -0.024 -0.006 0.006 0.015 o.o.%* 0.024 0.026 0.026

13.664 11.789 190-:3203 8:138 6.586

0.382 0.346 0.31, 0.279

:-2% 3:903 3.371

z-:2 0: 130 0.101 0.089

:-;*,x 1:*57 I.,,9 0.975

0.069 OS, 0. 0.048

2%: 0:607

125YEO 564.7, 3.222 C/L -0.263

C/Z

* :-2: ,:,a3

-0.793 -0.333 -:-:;:o:,se

0.076 0.084 :-:“,I 057 0: 0.05,

: -:z: ,:2*7 1.130

0:0x :-::z

FE 016.7 0.55. 0.479

0.020 0:007 :-:A:

00-1:: 0: 208

:-::,” o:ooa 0.002

C/I

S 0.018 0.03, 0.055 0.07% O.OPR 0.103 0.115

E:: . 0.022 0.021 0.019 O-O,6

:-::;: 0:134 0.133 0.125 0.115 o., 04 0.093 O.OTB 0.057

“0-E: 0:009 0.007 0.00‘ 0.005

i-z 0:033 0.028 0.025 0.022

-0.508 -0.300 -0.,,9 4.096 -0.033 0.016 0.054 O.OR3 0.106 0.123 0.14, 0.145 0.140 0.120 0.115 0.081 0.05, 0.0.0 0.030

0.029 0.057 0. OR. 0.109 0.132 0.153 0.171 0.188 :-:E 0:236 0.248 0.252 ix: 0:209 0.176 0.147 0.123

:-z::.

262 0: 07R O.“BR

“02x.

.t:,s 23.R, 0.66,

s 0.486 0.924 L.281 1.79, * -568

0.216 0.232 0.216

1.959 2.063 2.096

0.062 0.049

:-z; , :790 1.561 1.352 1.173 1.023

O.OPO 0.029

i-E .

FE: 0:oos 0.007 0.005 0.005

EH,” 0:302 0.2 0.218 O-,89

55

-0.074 -0.016 0.010 0.*?Z, 0.021 0.023 0.023 0.022 O.OIl 0.019 0.01s 0.01, 0.009 :-Ef 0:ooa 0.005 :-::I: C+$ . 0.001 0.00,

9 0.15, 0 -374 0.489 0.590 :-?I:: 0:5t, 0.467 0.410 0.37, i-2: . 0.215 “.lRP 0.156 0.112 O-OR, 0 -066 0.053 0 .O.d 0.037 0.03, 0 -027