K-shell X-ray emission cross sections and ionization cross sections for light atoms and molecules by H+, H+2 and He+ impact at 30–145 keV

Physzcu 66 (1973) 16-32 0 North-Holland Pubbshmg Co

K-SHELL CROSS

X-RAY

SECTIONS

EMISSION FOR AND

LIGHT

CROSS ATOMS

He+ IMPACT

K G HARRISON*,

SECTIONS AND

AND

IONIZATION

MOLECULES

BY H+, H:

AT 30-145 keV

H TAWARA#

and F J DE HEER

FOM-Instrtuut voor Atoom- en Molecuulfysrca, Amsterdam. Nederland

Received 1 November

1972

Syn0ps1s

The cross sectlons for K-shell X-ray emlsslon have been measured for 30-145 keV H+, H: and He+ Ions mcldent on the gases CH4, CO, N2, Ne and Ar Usmg values for the fluorescence yrelds derived from slmdar electron impact experiments, m which the same gas targets were used, the lomzatlon cross sectlons for these K-shells by proton Impact have been deduced The valueb thus obtamed show reasonable agreement with the Auger-electron measurements of Stolterfoht for the gases CH4 and Nz m the energy range of overlap, 50-145 keV For the hghtest elements, C and N (m CH4 and Nz), the K-shell lomzatton cross sectlons agree reasonably with the Born theory for lomzatlon at the highest energies used For Ne and Ar, with larger K-shell bmdmg energies, and at low energies for C and N, the experlmental cross sectlons are much smaller than the ones calculated by the Born approxlmatlon These results are better described by the lomzatlon theory of Brandt mcludmg Coulomb rep&Ion, bmdmg and polarlzatlon effects, and the binary encounter theory of Garcia, which includes Coulomb repulsion effects The contrlbutlon of electron-capture processes to the K-shell lomzatlon cross sectlons IS dlscussed

1 Zntroductzon In a previous paper’), we presented the cross sections for K-shell X-ray emlsslon from gas targets by electron impact We compared these cross sections with correspondmg Auger-electron ejection cross sectlons of Glupe and Mehlhorn’), who used the same gas targets, and deduced fluorescence yields which are m excellent agreement with the recent calculations of Walters and Bhalla3) Here we descnbe measurements of the X-ray emlsslon cross sections for the same gases (excluding oxygen) by hght-Ion Impact In order to compare these cross sections with those measured m Auger-electron expenments4), Ionization * Present address School of Mathematical and Physlcal Sciences, Umverslty of Sussex, BrIghton, U K # Present address Department of Nuclear Engmeermg, Kyushu Umverslty, Fukuoka, Japan 16

X-RAY EMISSION

AND IONIZATION

CROSS SECTIONS

17

cross sections are derived using the fluorescence yields obtained previously m our electron experiments A direct comparison 1s then also possible with the bmaryencounter theory of Garaa5), the Born-approxlmatlon calculations of Khandelwal et al “) and McGmre’) and the theories of Bang and Hansteen*) and of Brandt et al “) The use of the same fluorescence yields for proton- and electron-induced K-shell vacancies 1s discussed We also compare our X-ray emlsslon cross sections for carbon with the expenmental results of Khan et al lo) and Terasawa”) who used thick graphite targets and Van der Weg et al 12) who used a target of a few monolayers of carbon on &con In a comparison of our He+ and H+ impact X-ray cross sections we observe the failure of the 2: scaling law predicted by the plane-wave Born approxlmatlon6) and the binary-encounter theory of Garaa5) (2, 1s the nuclear charge of the mcldent ion) This effect has already been reported m this energy range m solid-target experiments of Brandt and Laubert13) and of Shlma et al 14) All previous work on K-shell X-rays by light-Ion impact has been performed with solid targets Much of this work has been dIscussed by Brandt9), m a comparison with his theory (see section 5)

ton beam

wtndow proportlonal counter counter gas supply ’

Fig 1 A schematlc diagram of the apparatus

2 Apparatus and experimental method The apparatus 1s shown schematlcally m fig 1 A collimated, mass-analysed ion beam of 5-30 PA enters a colhslon chamber through a 2 mm aperture, and 1scollected by a Faraday cup Secondary electrons produced m the cup are prevented from escapmg by means of a strong transverse magnetic field. Target gases are introduced mto the dlfferentlallypumped collision chamber through a needle-valve The pressure m the chamber 1s measured by an iomzatlon gauge with a dlgltal meter; this gauge 1s calibrated for each gas against an MKS Baratron capacitance manometer In the operating region 10-3-10-4 torr, the repeatablhty of the lomzatlon gauge against the Baratron 1s better than 5 %. X rays are detected normal to the dlrectlon of the incident Ion beam by a Slemens flow-mode proportional counter The window transmls-

18

K G HARRISON,

H TAWARA

AND F J DE HEER

ston and detection efficrency of the counter are hsted for each X ray m table I. The pulse-herght analysts eqmpment is identical to that used m our previous expertmerits’))) Because of the small X-ray yrelds studted, two geometrical arrangements are used to collimate the X rays One of these 1s geometncally well defined (In = 2 56 x 10V2 sr, L = 1 05 cm, 9 1s the sohd angle subtended by the proportional counter, L IS the mteractron length vrewed by the counter), whtle the other 1s determmed expenmentally to have a geometrical efficiency (QL) 14 49 ttmes greater than this Under the latter (low) colhmatton condnrons, some X rays do not pass normally through the wmdow of the proportional counter, hence there TABLE I

X-ray wmdows and detectlon efficlencles

Gas target

(334

co NZ Ne Ar

X ray

C-K C-K N-K Ne-K Ar-K

Proportlonal counter wmdow

6 p Mylar 6 p Mylar 2 2 p tltamum 6 p Mylar 6 p Mylar

Wmdow transmlsslon (nommal)

Counter efficiency (at atmospheric pressure)

(%)

(%)

4 4

100 loo 100 100 55

I 3 87

1s a decrease in the effectrve transmtsston of the window Only m the case of mtrogen K-shell X rays (which have the lowest transmlsston) is such a change detectable m transmrssron measurements made m the two geometrtcal arrangements under hrgh colhmatron the transmrssron of nitrogen K-shell X rays 1s (1 23 + 0 06) %, whrle under low colhmatton tt 1s (1 14 f 0 05) % However, this effect IS eliminated as a source of expenmental error by usmg the value of the transmrssron appropriate to the geometry used Because of high neutrahzatton cross secttons for these ions, at low energies (x lo-l5 cm2, see ref 15), target-gas pressures are kept low at about 5 x 10e4 torr, except for neon where 1 x 10V3 torr 1s used. Nevertheless, correctrons of O-14oA have to be made for neutrahzation of the ion beam by the target gas; thus IS determined drrectly usmg the ratto of the current measured when the target gas IS introduced to that measured when the target chamber 1s evacuated under condtttons of a constant ion beam from the accelerator. In all cases the X-ray count rates vary hnearly wrth the target-gas pressure (and the corrected beam current).

X-RAY EMISSION

AND IONIZATION

CROSS SECTIONS

19

The cross section per atom 3. Evaluation of the cross sectlons. 3.1. General. for the lsotroptc emission of characteristic X rays is given by 4x 6,

=

-

L

f2 NnLT,T,A

’

where Z, is the number of characteristic X-ray counts from the proportional counter, Q is the sohd angle subtended by the proportional counter, N IS the density of target atoms, n 1s the number of mcident ions, L 1s the interaction length viewed by the proportional counter, T, IS the transparency of the wmdow supporting grid, T2 1s the transmission of the X-ray wmdow, A IS the fractton of characteristic X rays absorbed m the gases of the counter (counter efficiency) Q, L and TI are obtained from the geometry of the experimental arrangement, N follows from the target-gas pressure, and 12is derived from the integrated current measurement The X-ray wmdow transmission (T,) and the counter efficiency (A) are measured experimentally using techmques described prevlously1*16) The errors of measurement are estimated to be as follows. Z, 3 %, N 5 %, n 3 % ; QL 7 %, TI 4 %, T2 5 %. For the argon measurements the error m A may be about 8 ‘A Statistical errors (Z,) are always less than about 3 ‘A,although at the very lowest energies studied the background counts (which are always subtracted) sometimes approach lo-20% of the total counts; at high energies the background counts are always 2 % or less We beheve the probable errors m the H+ and Hz impact X-ray emission cross sections to be about 12 % for C-, N- and Ne-K X rays, and about 14 ‘A for Ar. The lowest energy results have errors greater than these For the He+-mduced X-ray emission cross sectrons we assume the same X-ray window transmission as, for H+-induced X rays There may be an error of 10-20x in this assumptlonwhich is discussed m the next section The ion-beam energies are accurate to 1 ‘A 3 2 Problems in the determination of T2 It is possible that the transmission T2 IS dependent on the romzmg particle and its energy, as these both mfluence the extent of simultaneous Inner- and outer-shell lomzatlon. Such processes give rise to shifts m the X-ray energies with respect to X rays from single K-shell lomzation”), consequently there are changes m T2 The magnitudes of these changes could only be measured for H+ ions over a hmlted energy range because of the relatively low X-ray yields for the other cases In the energy range 100-140 keV (75-140 keV for an Nz target), we could not detect any variations m T2 outside the experimental errors (5 “A. For He+, simultaneous Inner- and outer-shell lomzatlon of target gases is more ltkely than m H+ or H: bombardment because the outer-shell lomzatlon cross sections for the targets are larger for He+ Impact than H+ impact at the same ion velocity, and K- and L-shell iomzatlon can be treated as Independent processes (see refs 4 and 18) Therefore, T, can be expected to be different m this case

20

K G HARRISON,

H TAWARA

AND F J DE HEER

However, we expect this difference to be qmte small because we have found that for the 6 v windows used here the value of T2 for neon K-shell X rays produced m Ne+ + Ne colhslons IS only 20% higher than the value of Tz for those produced m H+ + Ne colhslons (m the energy-range loo-140 keV) The degree of simultaneous Inner- and outer-shell lomzatlon m these heavy Ion-atom colhslons 1s known to be relatively large19) Hence we estimate that systematic errors m the low-energy H+ measurements (relative to the high-energy measurements) due to changes m T2 are not greater than lOoA and that the difference m T2 for H+- and He+-Induced X rays 1s about the same 4 Results, 4 1 X-ray emission cross sectlons The measured K-shell X-ray emlsslon cross sections ((T,) are given m table II The data for H+, H: and He+ are also compared m figs 2,3 and 4 It can be seen that for Nz and the atomic targets, Ne and Ar, a(H:) 1s almost equal to 2a (H+) at the same velocity This means that H: acts as two protons, and the remammg electron IS mslgmficant Deviations from this rule are observed for CO and CH*, which both show 10% smaller cross sectlons (per proton) for Hz at high velocltles (see fig 2) When we compare the cross sectlons by He+ and H+ Impact (figs 2-4), we observe the failure of the 2: scaling law predlctedm K-shell lomzatlon theorjes5*6), where Z, IS the nuclear charge of the incident ion In contrast to the theoretical factor of four, the X-ray emlsslon cross sections for He+ are generally only 30-60% higher than for H+ bombardment at the same velocity For CH4, the cross sectlons by He+ impact are actually lower than those by H+ impact by about 10% This deviation from the Zf scaling law 1s so large that It cannot be due to systematic errors m T2 (see section 3 2) or differences m the fluorescence

H'cl;

He’-40

CH‘

hcdmt m

-0”

Whmu

Fig 2 Carbon K-shell X-ray emlsslon cross sectlons for H +, Hi and He+ mcldent on the gases CO and CH4, scaled by Z; z The Hi cross sectlons have been dlvlded by two to normahze on atomtc values

X-RAY

EMISSION

AND

IONIZATION

CROSS

SECTIONS

21

TABLE II

Cross sectlons for the productlon

of K-shell X-rays by hght ions mcldent

on CH., , CO, Nz , Ne and Ar u (cm’/target (&

CK m CH4

CK m CO

atom)

NK m Nz

NeK m Ne

Ar, m Ar

1 H+ eons

-

2 69 x 1O-24

28

7 56 x 1O-24

31

2 02 x 10-23

9 72 x 1O-24

7 18

48

5 54

2 23 x 1O-23

181 x lO-23

141 x 1o-24

-

58

9 94

4 56

3 38

2 67

68

1 55 x 10-22

7 28

5 91

4 68

1 85 x lo-=

17

244

1 15 x 1o-22

9 19

7 83

3 01

87

3 32

1 65

1 26 x 1O-22

97

440

2 10

1 68

106

5 42

2 73

2 20

116

6 67

3 47

2 73

126

7 82

4 05

3 26

135

8 99

4 19

3 84

145

1 03 x 10-21

5 52

4 28

1 35 x 1o-23 -

6 58 x 1O-24

6 28 x 1O-24

68 77

3 94

1 89 x 1O-23

117 x 1o-24

-

87

-

2 86

179 x 10-23 -

97

8 88

4 14

3 92

1 26 x lo-=

5 78

5 54

260 -

-

2 H,+ cons 58

106

5 54 179 x 10-23

1 04 x 10-25

3 29

2 27

5 40

4 01

-

-

1 48 3 05

_

116

1 68

7 98

126

2 20

103 x 10-22

740 -

5 80 -

135

2 80

1 32

123 x 1O-22

9 94

145

3 34

1 65

1 46

2 11 x 10-24

1 36 x lo-”

116

5 3T x 10-24

4 50 x 1o-24

4 27

3 51

135

1 01 x 10-23

7 36

8 34

6 13

_ _ 3 82 x 1O-26

3 He+ eons 97

_

yields for K-shell vacancies produced by H+ and He+ (see section 4 2) The same devlatlon has been found by Brandt and Laubert13) and has been explamed by them as a consequence of two perturbmg effects, Coulomb repulsion and the bmdmg effect (see section 5) In table III we compare the ratios of X-ray cross sectlons by He+ and H+ impact measured by us (see also figs. 2-4), G (He+)/4a (H+), with preliminary calculations of ionization cross sections by Basbaszo) using the theory of Brandt’)

22

K G. HARRISON,

H TAWARA

AND F J DE HEER

H’ H; W-N,

VP4 0

I

20

M

60

Bo

UlO

120

lncldnt m nwgy

1LO

!a

keVlamu

Fig 3 Nitrogen K-shell X-ray emlsslon cross sectlons for H+, Hl and He+ Incident on Nz, scaled by 2;’ The Hz cross sectlons have been dlvlded by two to normahze on atomic values

. H’ x Hf .H

F

f

,0~~160 0 20

LO

60 lcadent

60 IO”

im energy

120

110

160

w,a mu

Fig 4 Neon K-shell X-ray emlsslon cross sectlons for H +, Hi and He+ Incident on Ne, scaled by 2; 2 The Hz cross sectlons have been dlvlded by two to normahze on atomic values TABLE III

Comparison of experlmental ratios of X-ray emlsslon cross se&Ions for He+ and H+ proJectlles of equal velocity with the loruzatlon calculations of BasbaszO) usmg Brandt’s’) theory

En+

Target

@eV)

0 U-Ie)Po (H) theory expenment

29 33 8

CHL

0 149 0 174

0 425 0 525

29 33 8

N*

0 342 0400

0425 0 502

33 8

Ne

0 426

0 383

X-RAY EMISSION

AND IONIZATION

CROSS SECTIONS

23

(mcludmg Coulomb repulsion, bmdmg and polarizatton effects) m the overlapping velocity region. Except for CH4, we see that the agreement between experiment and theory is reasonable The mclusion of a bmdmg as well as a Coulomb-repulsion correction is essential to get these theoretical ratios smaller than one It can be seen m fig. 2 that for proton impact the ratio of carbon K-shell X-ray emission cross sections for CO and CH, IS not constant, but varies from 0 46 at 37 keV to 0.54 at 145 keV Probably, because of the high-velocity equivalence of proton and electron cross sections*‘), at very high velocities (&+ k 1 MeV), this ratio approaches the value 0 64, which we measured m previous electron-impact expenments2*) and which was explanted by the difference m fluorescence yield for CO and CH4 For CO, there may be a contribution from oxygen K-shell X rays, which are not completely resolved by the proportional counter from carbon K-shell X rays. The detection efficiency for oxygen X rays is very low due to their exceptionally low transmission through the wmdow of the counter23) Nevertheless, the ratios quoted here (and also the carbon K-shell X-ray emission cross sections for CO) may be 5-10 % too high. The ratio measured m the electron-impact experimentsz2) IS corrected for the contribution of oxygen X rays A variation m the K-shell X-ray emission ratio is predicted by the theory of Brandtg), due to the bmdmg effect (section 5) and the difference m the carbon K-shell bmdmg energy, which for CO IS 296 eV and for CH* IS 290.5 eV24). Takmg the ratio due to the difference m fluorescence yield equal to 0.64, Basbas’s calculations20) give a variation of the CO/CH4 X-ray yield ratio from 0 56 at 37 keV to 0.59 at 145 keV This is, however, a smaller variation than found experimentally Because the Bohr radius of the K-shell of carbon IS about 0.1 A, collisions which result m K-shell lomzatlon generally have impact parameters of the order 0 1 A, and are therefore not sensttlve to the molecular environment of the atom. However, a Rutherford scattering calculation shows that the elastic energy transfer from a 25 keV H+-ion to a carbon nucleus m such a colhslon with an impact parameter of 0 05 A is about 8 eV* (for 0 1 A about 2 ev). This gtves the carbon nucleus a velocity of about IO6 cm/s As the hfetrme of the K-vacancy is of order lo-l4 s, the carbon nucleus can travel about 1 A and at the moment of the K-shell decay the molecule could be undergoing break-up or vibrational excttatton Such effects might mfluence the fluorescence yield and cause variations in the CO/CH4 X-ray yields as found experimentally The cross secttons for carbon K-shell X-ray emission m CH, can be compared with those made by Khan ef al lo) and Terasawa”), who used solid graphite targets (see fig. 5) and with those of Van der Weg et aLI*) who used a few mono* We are grateful to Dr F W Sam for pomtmg out ths effect

24

K G HARRISON,

H TAWARA

AND F J DE HEER

-ElO'o H+- C 2

1

10+ LO lncdmt

60

80

40" energy

1Oa

120

110

160

krV

Fig 5 Compartson of the present carbon K-shell X-ray emlsslon cross sectlons by H+ bombardment on CH4 with those of Khan et a/ lo) (“K”), Der et al lo) (“D”) and Terasawa”) (“T”), who used thick graphite targets and of Van der Weg et al I’) (‘TV”), who used a few monolayers of carbon on slhcon

layers of carbon on slhcon Our cross sectlons agree best with those of refs 11 and 12 and less well with those of ref 10 4 2 Relation between K-shell X-ray, Auger-electron and lonlzatlon cross sections For the K shells of atoms, a very simple relatlonshlp holds between the fluorescence yield (co& the K-shell Auger-electron ejection cross section (o,J, and the K-shell X-ray emlsslon cross section (CT,)This lsl) wK

=

ux/(ax+ uA)

This equation assumes that multiple decay processes are negligible Experimental evldencez5 26 “) Indicates that for the K shells of light elements only double Auger processes are of importance These occur m about 8 ‘A of the Auger transltlons m neonz6) Because of the uncertainty m the magmtude of these effects, no corrections for multiple decay processes are made here For hght elements up to neon, wK IS less than 0 02’7, it follows therefore that (T* = CJ,(the lomzatlon cross section) Alternatively, uI IS obtained usmg both the X-ray emlsslon cross sectlon and the fluorescence yield

This equation IS used for transferring our experlmental a, to cI for comparison of our expenmental results with available Auger measurements and theory (see figs 6-10) Here we use the fluorescence yields derived from electron-Impact experiments The use of the same fluorescence yields for proton- and electron-

X-RAY EMISSION

AND IONIZATION

CROSS SECTIONS

. x-rays {

25

Stotterloht

x present

o&J':

tw~:000271

150

2m

lnadent m

250

3ul

350

keV

energy

Fig 6 Comparison of the present carbon K-shell lomzatlon cross sectlons by H+ Impact with those deduced from Auger-electron measurements by Stolterfoht4) and Toburen”‘) and with the theones of Garcla5) (bmary encounter with Coulomb repulsion and deflectlon), Khandelwal et al 6, (- - PWBA, hydrogeneous wave fun&Ions), McGuu-e’) (--- PWBA, hfs wave functlons) and Brandt et alg*20) ( PWBA with Coulomb deflectlon, - - PWBA with Coulomb deflectlon, bmdmg and polanzatlon)

Induced K-vacancies can be Justified It 1s known that if outer-shell lomzatlon occurs simultaneously with inner-shell lomzatlon, this has some effect on the fluorescence yleld29), however, this influence 1s theoretically predicted to be

IO z'T 0

50

100

150

*ml

tnadent ton energy

I 250

300

I 350

keV

Fig 7 Comparison of the present mtrogen K-shell iomzatlon cross sections by H+ impact with those of Stolterfoht4) and Toburen31), and with the theories of Garclas), Khandelwal et aZ6), McGmre7) and Brandt et al g*20) See also figure caption 6

26

K G HARRISON,

H. TAWARA

AND F J DE HEER

rather weak for the K shellzg). Although there IS srmrlanty between the Auger spectra for electrons and protons30) It has been shown by Stolterfoht4) that outershell romzatron occurring simultaneously with inner-shell romzatron m H+ --t CH, and H+ --) N, colhsrons is more probable at low energies This indicates that there can be a difference m populations of multiply-excited and ionized states produced m K-rornzmg colhsrons for electron and proton Impact The fluorescence yields which we use here are listed m table IV The estimated experimental Table IV Fluorescence yields oK used m evaluation of the lonlzatlon cross se&Ions (from ref 1) Gas (334

co NZ Ne Ar

X ray C-K C-K N-K Ne-K Ar-K

WK

0 0027 0 0017 00047 0 0155 0 122

errors m these values are 14-17% Hence, the experimental errors m our lomzatton cross sections are probably about 20% (this estrmate disregards possible SIIIdl SyStematiC differences in wK for proton and electron impact). In fig 6 we show romzatron cross sections for the carbon K shell for H+ impact on CH, obtained by Stolterfoht4) and Toburen31) from Auger electron measurements together with the present results of 0,/m:’ Also some theoretical curves are displayed, these are discussed m the next section In fig 7 we show srmtlar data for the K shell of nitrogen In both these figures the present measurements he about 20% below the measurements of Stolterfoht m the energy region of overlap This confirms our assumption that the fluorescence yields we use (table IV) are quite close to the proper values for H+ impact 5 Comparison between experiment and theory. 5 1. Introductron When we measure the productron of X rays or of Auger electrons from the K shell by light ion Impact, two different colhston processes must be consrdered A+ +X+A+

+X2

A+ +X-tAO’*)+X,+

+e

(ionization), (electron capture)

These processes may occur with srmultaneous electron capture or romzatlon m the outer shell.

X-RAY EMISSION AND IONIZATION

CROSS SECTIONS

27

When comparing experimental data with quantum-mechanical calculations, up till now, the first process only has been considered. Thts IS correct at sufficiently high impact energres, but may be not correct at low energies (see section 6). In the binary encounter theory, the K-shell ionization cross sections m&de the capture of K-shell electrons. For an extended review on different theoretical calculations and a comparison with experimental data of light-ion impact on sohds the reader is referred to the review paper of BrandtQ). Here we shall give a short summary of the different methods of calculation Of the quantum-mechanical calculations for ionization, the simplest IS the plane-wave Born approximation (PWBA). The work of HennebergJZ) and Merzbather and Lewis33) has been contmued by Khandelwal et al., and IS summarized m Atomic Data6) In then calculations, they use hydrogemc wave functions McGmre’) has carried out the same calculation with Hartree-Fock-Slater wave functions The PWBA has also been modified, Bang and Hansteena) have apphed a Born impact-parameter treatment and considered the effect of Coulomb repulsion (deflection) of the mcrdent ion by the target nucleus Brandt et al ‘) have developed the theory of Bang and Hansteen and have also included a correction for a second effect which they call bmdmg effect. The bmdmg effect is simply that the proximity of the incident ion to the target nucleus durmg the colhslon mcreases the effective nuclear charge of the target, such an effect is important for low Z targets The correction terms of Brandt’s theory are actually applied to the hydrogemc PWBA results. At relatively high energies, when U,&&J, (U, = bmdmg energy of the K-shell, aK = radius of the K shell, h = Planck’s constant and 2r1 = proJectlle velocity) is 2 1, BrandtQ) Introduces a third correction, due to the polarization of bound states m the quadrupole approximation by the projectile passing at large impact parameters. In the binary-encounter calculation Garcla5) considers the effect of Coulomb repulsion (deflection). 5 2 Experimental and theoretical data In fig 8 we show all the K-shell ionization cross sections by H+ impact deduced m the present experiments and in the PWBA of Khandelwal et al “) and McGmre’) and bmary encounter calculations of Garaa5) m a umversal form as indicated by Garcia5*34). ur Ut$Z: is a umversal function of E/U, (UK = bmdmg energy of the K shell, Z1 = atomic number of the proJectlle and E = impact energy). It can be seen that the experimental values all fall close to Garcia’s theory at high energtes, but are lower by a factor of between two and four at low energies. In particular the results deviate systematically from the umversal curve. the lower the value of Z, the greater is the deviation from Garcia’s curve at a given E/U,. This trend may be connected with Brandt’s theory which mdlcates the Importance of a bmdmg effect However, for carbon and nitrogen, where this trend is clearest we have used molecular targets, and it is possible that this is partly a molecular

28

K G HARRISON,

H TAWARA

AND F J DE HEER

effect Besides, this scaling 1s only an approxlmatlon m the bmary-encounter theory m the case of protons on low 2 targets (2, < 10)34) It 1s clear that at relatively low energes the PWBA overestimates the cross sectlon to a large extent Although Garcia’s calculations he much closer than the PWBA to all the experimental results, the Z:-scahng factor for He+, as shown m sectlon 4 1, appears to be incorrect m this energy range.

- - -

McGurc

-

Khmdelwal

-

-

et al

Garcs

, m

.,,,,I

40 -

I

al

BOXYI

mu

-I

LOO

WI

El&

Fig 8 The present lomzatlon cross sectlons by H+ Impact plotted on a umversal scale of qUi agamst E/o',, and compared with the theories of Garclas), Khandelwal et al 6, and McGulre’) (The scahng m some of the calculations IS not perfect, but devlatlons of up to 20% are seen m this range of 2, , the curve for mtrogen IS shown m each case )

In figs 6, 7, 9 and 10 the elements carbon, nitrogen, neon and argon are consldered separately In fig 6 for H+ + CH, we see that at high energies, expenment approaches theory, but that at low energies the experimental cross sections are smaller than all the theoretical ones In this region calculations mcludmg Coulomb repulsion, bmdmg and polarlzatlon corrections come closest to the experiment We reparked already that m the experiments molecular effects may play a role PWBA calculations with corrections for Coulomb repulsion only are

X-RAY EMISSION

AND IONIZATION

CROSS SECTIONS

--

Theory

Garcia itbndeiwal

x-rays

29

-}Brdt

(x

present

ox/w:

@I;‘= 0 0155)

Ag 9 Comparison of the present neon K-shell lomzatlon cross sectlons by H+ Impact with the theones of Garcla5), Khandelwal et al 6, and Brandt et al 9,20) See also figure caption 6

not displayed, because at 25 keV the correction IS only 10% and It is smaller at higher energies In fig 7 for H+ + Nz slmllar conslderatlons can be given In figs 9 and 10 protons are incident on the atomic targets Ne and Ar In Ar there IS agreement between experiment and PWBA calculations with Coulomb repulsion, bmdmg, polarlzatlon correctlons For Ne the agreement 1s not so good but the trend of this theory and experiment 1s the same

/ H*-Ar

-

/ Theory

i x-rays

Garcm Ktmdehval

-

-

-

->Bra”dt

{x pesent (4’

h/W:’

= 0122)

Fig 10 Companson of the present argon K-shell IonnatIon cross sections by H+ with the theones of Garcla5), Khandelwal et al 6, and Brandt et al 9*20) See also figure caption 6

30

K G HARRISON.

H TAWARA

6 Estzmatzon of electron-capture

AND F J DE HEER

cross sectzons

In section

5 we have remarked

that both lomzatlon and electron-capture processes can lead to the production K-shell vacancies With Gryzmskl’s35) bmary encounter theory, it 1s possible

of to

estimate

1s

neglected

then

relative

It IS known

Importance,

although

m this theory

that at high energies the lomzatlon

Coulomb

repulsion

cross sections are much

larger than correspondmg electron-capture cross sections, but at low energies this 1s no more the case The calculation 1s given for H+ incident on carbon at 25 keV The cross section

Qc = &

for a capture

3

process (QJ is given by [eq (39) of ref 351

G, (-$-,+)

cm’jelectron,

U;’ 1s the bmdmg energy of the electron to the target, Uf 1s the bmdmg energy of the electron to the ion after capture, G, 1s the capture function (see fig 17 of ref 35), Vl and Vf’ are the Bohr velocltles of the electron m its final and mltlal bound states, respectively For 25 keV H+ incident on carbon, UF = 13 6 eV, U,” = 290 eV, VG/ Vt = 0 22 and G, % IO-’ Hence Qc = 1 5 x 10m20 cm’/atom The lomzatlon cross section (Q,) 1s given by [eq (30) of ref 351 where o0 = 6 56 x IO-l4 eV2 cm’,

Q, = ($)

G, ($-)

cm’/electron,

where Gi 1s the lomzatlon function given by eq (32) of ref 35, U, 1s the bmdmg energy of the electron to the target, V, is the H+ impact velocity, V, is the Bohr velocity of the electron m the target For 25 keV H+ incident on carbon, this gives Qion = 8 x lO-2’ cm2/atom These calculations show that the electron-capture cross section from the K shell for H+ at 25 keV 1s even greater for a low-Z element than the direct K-shell lamzatlon cross section The same procedure shows that the importance of capture processes dlmmlshes as the H+ energy 1s increased A slmllar result was found by Volz and Rudd36) for L-shell lomzatlon of Ar by protons It seems, therefore, that for low-energy collisions, capture processes should not be arbitrarily disregarded m K-shell lomzatlon theory Also, it 1s possible that the capture of inner-shell electrons cannot be treated Independently of capture of outer-shell electrons 7 Concluszons Our measurements on the K-shell X-ray emlsslon from CH4 and N2 by H+ impact, when compared with correspondmg Auger-electron measurements m the energy range of overlap (50-145 keV), show that the fluorescence

X-RAY EMISSION

AND IONIZATION

CROSS SECTIONS

31

yields (oK) for these gases are slmdar to those measured by electron Impact We can detect no sigmficant energy dependence of u)~, a, and @Ahave a constant ratlo m this energy range The lomzatlon cross sections for low-Z elements approach the Born cross sectlons for values of E/U, between 400 and 600 At lower impact energies the behavlour 1s best described by the Born approxlmatlon of Brandt with Coulomb repulsion, bmdmg and polarlzatlon corrections and less well by the binary encounter theory of Garcia which Includes Coulomb repulsion (deflection) only Except for CH4 and CO, the ratios of X-ray cross sectlons for He+ and H+ impact measured by us are m reasonable agreement with the theory of Brandt m the overlappmg velocity region, devlatmg strongly from the Zf dependence It 1s found that H: proJectlles have cross sectlons about 2 times larger than H+ proJectlles at the same velocity Though m general at low energies Brandt’s theory 1s closest to the expenment, a problem stdl remains that m this comparison the theory does not consider the electron-capture processes which are Included m the bmary-encounter calculations of Garcia Using Gryzmskl’s formulas, It 1s estimated that the electron capture 1s very Important at low energies used m the present work Acknowledgements We are grateful to Drs N Stolterfoht, E J McGmre, M Terasawa, G Basbas and J D Garcia for provldmg us with tables of then experlmental and theoretlcal cross sectlons We also are thankful to Dr F W Saris for his comments on the manuscript The techmcal assistance of S Doorn and H Roukens m running the accelerator 1s much appreciated One of us (K G H ) IS grateful to the SRC (London) for the award of a NATO fellowshlp This work 1s part of the research program of the Stlchtmg voor Fundamenteel Onderzoek der Materle (Foundation for Fundamental Research on Matter) and was made possible by financial support from the Nederlandse Orgamsatle voor Zuiver-Wetenschappehjk Onderzoek (Netherlands Organization for the Advancement of Pure Research)

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1) 2) 3) 4)

32

K G HARRISON,

H TAWARA

AND F J DE HEER

8) Bang, J and Hansteen, J M , Matt Fys Medd Dan Vld Selsk 31 (1959) no 13 9) Brandt, W , m Atomic Physics 3, Proceedings of the Thud International Conference on Atomic Physics, August 7-l 1, 1972, Boulder Brandt, W , International Conference on Inner-Shell Iomzatron Phenomena, Atlanta, USA, 1972, ed R W Fink, U S Atomic Energy CornmIssIon, Oak Ridge, Tenn., 1973 Brandt, W , Laubert, R and Sellm, I , Phys Rev 151 (1966) 56. 10) Khan, J M , Potter, D L and Worley, R D , Phys Rev 139 (1965) Al735 Der, R C , Kavanagh, T M , Khan, J M , Curry, B P and Fortner, J , Phys Rev Letters 21 (1968) 1731 11) Terasawa, M , private commumcatlon, unpublished 12) Van der Weg, W F , Kool, W H , Roosendaal, H E and Saris, F W , to be published m Radiation Effects 13) Brandt, W and Laubert, R , Phys Rev 178 (1969) 225 14) Shlma, K , Saklsaka, M and Kokado, M , Jap J appl Phys 9 (1970) 1297 Shlma, K , Makmo, I and Saklsaka, M , J Phys Sot Japan 30 (1971) 611 15) Fedorenko, N V , Soviet Physics - Techn Physics 15 (1971) 1947 16) Saris, F W and Onderdelmden, D , Physica 49 (1970) 441 17) Larkms, F P , J Phys B4 (1971) 14 18) De Heer, F J , Schutten, J and Moustafa Moussa, H , Physlca 32 (1966) 1793, table IV 19) Kessel, Q C , McCaughey, M P and Everhart, E , Phys Rev Letters 16 (1966) 1189 and Phys Rev 153 (1967) 57 20) Basbas, G , private communication, unpublished 21) De Heer, F J , Schutten, J and Moustafa Moussa, H , Physica 32 (1966) 1766 22) Harrison, K G , Tawara, H and de Heer, F J , Chem Phys Letters 14 (1972) 285 23) Splvack, M A, Rev SCI Instrum 41 (1970) 1614 24) Slegbahn, K , Nordhng, C , Johansson, G , Hedman, J , Heden, P F , Hamrm, K , Gehus, U , Bergmark, T , Werme, L 0 , Manne, R and Baer, Y , ESCA Applied to Free Molecules, North-Holland Pub1 Co (Amsterdam, 1969) 25) Aberg, T and Utrlamen, J , Phys Rev Letters 22 (1969) 1346 26) Carlson, T A and Krause, M 0 , Phys Rev Letters 14 (1965) 390 27) LaVllla, R E , Phys Rev A4 (1971) 476 28) Bambynek, W , Crasemann, B , Fink, R W , Freund, H U , Mark, H , Swift, C D , Price, R E and Rao, P V ,Rev mod Phys 44 (1972) 716 29) Larkms, F P , J Phys B4 (1971) L29 and private commumcatlon 30) Ogurtzov, G N , Rev mod Phys 44 (1972) 1, see fig 10 31) Toburen, L H , contribution to International Conf on Inner Shell Ionization Phenomena, Atlanta, Georgia, USA (1972), ed R W Fink, US Atomic Energy Commlslon, Oak Ridge, Tenn , 1973 32) Henneberg, W , Z Phys 86 (1933) 592 33) Merzbacher, E and Lewis, H W , Encyclopedia of Physss, ed S Flugge, Springer-Verlag (Berlin, 1958) Vol 34, p 166 34) Garcia, J D , Phys Rev A4 (1971) 955 35) Gryzmskl, M , Phys Rev 138 (1965) A336 36) Volz, D J and Rudd, M E , Phys Rev A2 (1970) 1395