PH YSICAL RE VIE% A VOLUME 22, NUMBER 2 AU GU S T 1980

Systematics of target and projectile K-x-ray production and radiative electron capture for20-80-Mev CP+ ions incident on 25-200-p g/cm' Cu targets

J.A. Tanis, ~ W. W. Jacobs, ~ and S. M. ShafrothDepartment ofPhysics and Astronomy, University ofNorth Carolina, Chapel Hill, North Carolina 27514

and Triangle Universities Nuclear Laboratory, Durham, North Carolina 27706(Received 5 September 1979)

A systematic investigation of K-x-ray production for 20-80-MeV Cl ions in collision with thin self-supporting Cu

targets has been conducted. Target and projectile characteristic x rays and radiative. electron capture (REC) have

been measured as a function of target thickness for incident charge states q (Zg 2 At 80 MeV data were ahoobtained for q = Z, —1. Large enhancements in both characteristic x-ray production and REC were observed

for q =Z, —1. Measured x-ray yields were parametrized versus target thickness using the model of Betz et al.,and least-squares fits to the data were performed. Target K-x-ray production for q (Z, —2 is described reasonably

well by the Coulomb perturbed-stationary-state relativistic plus electron capture relativistic (CPSSR+ECR)theory. For q =Z, —1 the enhancement in the x-ray yield is predicted quite well by the method of Gray et al.The mean fluorescence yield for the highly stripped Cl ions is determined and found to increase by a factor of about

6 over the range 20 —80 MeV, having a value ( —0.1) nearly equal to the single K-vacancy value at 20 MeV. The

radiative lifetime for the projectile ions is found to be —3 X 10 "sec, which is about three times longer than the

single-K-vacancy radiative lifetime calculated by Scofield. Parametrization of the REC yields versus target

thickness is used to normalize the measured REC intensity to the fraction of ions with K vacancies. Resulting RECcross sections are compared with the free-electron theory of Bethe-and Salpeter and good agreement is obtained if it

is assumed that each of the "loosely" bound electrons in Cu contributes equally to the REC process. By combining

the results obtained for the characteristic x rays and REC, the fluorescence yield for K-shell capture events may be

estimated, giving values in the range (2—4) X 10 for the beam energies studied.

I. INTRODUCTION

The dependence of heavy-ion induced x-ray pro-duction on foil thickness has been demonstratedin several recent experiments. ' ' This depend-ence has been attributed to the changing fractionof ions with K vacancies at a depth x in the foil,since it is found that a projectile with a K vacan-cy produces a large enhancement in the probabil-ity for K-vacancy production in the target. '4Hence, measured x-ray yields are strongly de-pendent upon whether or not the incoming beamhas a K vacancy. Experimentally it is found thattarget x-ray yields increase with foil thicknessfor incident charge states q «Z, —2 and decreasefor charge states q&Z, -2. The increase in x-rayproduction for q «Z, —2 can be understood quali-tatively from the fact that, as the foil thickness isincreased, a larger fraction of ions possesses Kvacancies, and these ions are more effective atproducing K vacancies in the target atoms. Sim-ilarly, the decrease in the target yields forincident charge states q & Z, —2 can be under-stood from the fact that, initially after entry intothe foil, projectile K-vacancy loss by electroncapture outweighs K-vacancy production in the.projectile by ionization, thereby reducing thefraction of ions with K vacancies for larger foilthicknesses.

These results imply that K-vacancy equilibriumis not reached until the ion travels many atomiclayers through the foil. Indeed, the works ofScharfer et al. ' hnd Gray et al. with sulfur ionsshow directly that the K-vacancy-bearing fractionof the beam is dependent on foil thickness. Inaddition, Gray et al. found that all charge statefractions of an ion beam moving in a solid dependon target thickness, and that this dependencecould be quantitatively understood in terms of thechanging fraction of ions with K vacancies. Onthe other hand, charge equilibrium for shellshigher than the K shell is reached very rapidly(in the first few atomic layers) after entry intothe foil as shown by the work of Cocke et al.o

Thus it is important to distinguish betweencharge-distribution equilibrium and charge-. .

state equilibrium.In order to describe these results quantitatively

a 'two-component" model proposed by Betz et al. ,'based on the formulation by Allison, " has beenapplied' ' in which the beam is considered to con-sist of two fractions of ions, those with a K vacan-cy and those without a K vacancy. For collisionsystems in which a significant fraction of the beamdevelops two K vacancies in passage through thefoil, Gardner et al. have shown that it is neces-sary to consider a "three-component" model'where the projectile may have zero, one, or two

22 1980The American Physical Society

J. A. TANIS, W. W. JACOBS, AND S. M. SHAFH, OTH

K vacancies. In this case target K-vacancy pro-duction is enhanced even more due to the presenceof the two projectile vacancies. Gray et al.4'have found that the enhancement in target K-vacancy production due to projectile K vacanciescan be described quite we11. in terms of a semi-empirical formula based on the works of Meyer-hof' and Taulbjerg et al. '

In order to compare heavy-ion induced x-rayproduction cross sections with theoretical calcu-lations, it is essential that target thicknesseffects be taken into account. It has been shown4

that measured target yields can vary by factorsof 8 or more depending on the foil thickness andthe incident charge state of the beam. Thusthe cross sections must be determined for van-ishing target thickness. The energy dependenceof target x-ray-production cross sections de-termined in this manner have been reported""and the results have been compared with theoreti-cal predictions of ionization and electron capture.

Measurements of target thickness effects havebeen reported for both target and projectile xrays, although most studies have concentratedon target x rays. These effects, however, havenot been measured for both target and projectilex rays in the same experiment nor has the sys-tematic beam-energy dependence of the pro-jectile collision parameters been investigated.Complicating the measurement of projectilex-ray yields for solid targets is the fact that it isnecessary to use self-supporting foils to ac-curately determine projectile x-ray productiondue to a single species of target atom.

In the present work we present the results ofa study examining both target and projectile K-x-ray production as a function of target thicknessfor 20-80-MeV Cl ions incident on thin self-supporting Cu targets. Radiative electron cap-ture (REC) by the incident Cl ions is also exam-ined. Preliminary reports of our results havepreviously been published. " Target and projec-tile x-ray yields are parametrized as a functionof target thickness using the model of Betz et al. 'Measurement of both target and projectile x raysenables us to obtain a single set of self-consistentfitting parameters to characterize all of the datasimultaneously. Values obtained for the fittingparameters are compared with theoretical re-sults where possible.

II. EXPERIMENTAL

A. Procedure

The work described here was conducted atTriangle Universities Nuclear Laboratory usingthe FN tandem Van de Graaff accelerator. A

TO P Vl ENf

TARGETS

SURFACEBARRIER

DETECTOR

BEAM~

VIEWIWl NDO

FARADAYCUP

TATABLERGET ROD

SIDE VIEW

I I

1%

X/COLLIMATORS

MASK

MYLARWINDOW

X-RAYDETECTOR

FIG. 1. Schematic diagram of experimental arrange-ment.

schematic of the experimental apparatus isshown in Fig. 1. The incident ions struck thinCu target of varying thickness which were posi-tioned inside a hexagonal scattering chamberas shown. The incident beam was collimatedby means of graphite apertures of diameter 3. 2

rnm.Absolute normalization of the incident beam

intensity was accomplished by detecting elastical-ly scattered Cl ions in a silicon surface barrierdetector mounted inside the chamber at 60' tothe incident beam. Scattered ions were colli-mated with a mylar aperture of 3.2 mm diameterplaced in front of the particle detector. The in-cident beam intensity was also integrated bymeans of a Faraday cup as indicated in the figure.X rays were detected from below in air at 90' tothe incident beam with a Kevex Si(Li) detectorhaving a 25.4- p.m'Be window. The detectorviewed the target through a 25. 4-LILm Mylarwindow. An aluminum mask of thickness 3.2mm with a 3.2-mm-diameter hole was placedover the x-ray detector to preclude detection ofx rays near the edge of the detector, therebyimproving detector resolution. In order to)minimize pileup and dead-time effects a 12.7- p,maluminum, absorber was used to attenuate thex-ray intensity so that counting rates were& 400 counts/sec.

X-ray production for both target and projectilex rays was measured using self-supporting Cufoils with a range of thicknesses 60-220 pg/cm'.

SYSTEMATICS OF TARGET AND PROJECTILE K-X-RAY. . .

The target were prepared by vacuum evaporation.Target x-ray production for thicknesses & 60c 2

Wgicm was measured using Cu films evaporatedonto 20- p, g/cm' C backings. For target x-rayproduction it is, of course, not necessary to useself-supporting foils so long as the beam passesthrough the actual target material first. For agiven target the effective target thickness waschanged by rotating the target rod about a hori-zontal axis. Absolute target thicknesses meredetermined to about +5%%uo by measuring Coulomb-scattered 10-MeV oxygen ions. In addition, thesethicknesses were checked in some cases usingCoulomb-scattered protons with 3-MeV incidentenergy. For the range of target thicknesses usedthe targets can be considered "thin" since thebeam does not lose appreciable energy in passingthrough the foil and since the self-absorption ofthe measured x rays is negligible.

Since the Cl projectile x rays were attenuatedto a large degree (-99/o) due to the variousabsorbers, it was necessary to determineaccurately the absolute detector efficiency as afunction of x-ray energy. Detector efficiencywas determined in two ways: (1) calculated byusing tabulated photon absorption cross sections"for the known absorbers in the path betweentarget and detector and, (2) experimentally bymeasuring proton-induced x-ray production at 3MeV and comparing with tabulated values of pro-ton-induced x-ray-production cross sectionssuch as those found in Ref. 19. The results ofth ese detector efficiency measurements are shownin Fig. 2. The efficiencies obtained from thetwo methods agreed to within 10%%up and so thecalculated efficiency was used to correct all ofthe measured x-ray intensities.

10'

CI

Cu

o 5-

(g) 4—I-DO

Kq

0 ~ — '

2,0 4.0 6,0 8,0 10.0 128X - RAY ENERGY (keV)

FIG 3. 3. Typical x-ray spectrum resulting from 40MeV Cl ions incident on a thin solid Cu target.

B. Results

8P MeV

II l

1

Cl ~Cu

5400-

5000-

4600-

4200-

2000- 60

o 1800-

x 16QQ-1b

1400—

Target and projectile K-x-ray production masmeasured for Cl ions with energies 20, 40, 60,and 80 MeV. Data were obtained at each energyfor incident charge states q& Zy 2 At 80 MeVdata were obtained for charge state q=Zy 1 aswell. A typical x-ray spectrum for 40-MeV Clon Cu is shown in Fig. 3. Measured x-ray in-

10%

OZ.'QJ

U

10'—

ured

Uloted

I I

"40 Mev360-

320-

280-'" PPMeV

12—

10-

~ ~ ~

lp~0I I

2 4 6 8 10 12 14E ( keV)

FIG. 2. Absolute detection efficiency, equal to the pro-duct of detector solid angle and intrinsic detector ef-Qciency, for the geoinetry of Fig. 1. The solid angle wasequal to 6.7 && 10-4 sr.

I I I I I i I~ ~

0 40 80 120 160 200T( +g r'cm~)

FIG. 4. Target E-x-ray cross secti'on vs. target thick-ness for 20-, 40-, 60-, and 80-MeV Cl ions with initialcharge states q«& -2 incident on thin Cu foils. Thesolid curves are least-squares fits to the data using Eq.(3) with A=o.

486 J. A. TAXIS, W. W. JACOBS, AND S. M. SHAFROTH 22

20

18

16 480

14

12

~x 10m 520

lb—240(3

160

0 I I t I I I I I I I I

0 40 80 l20 160 200T (p, g /cm~)

80A =0

FIG. 5. Target K-x-ray cross section vs target thick-ness for 80-MeV Cl ' +=0) and Cl ' (A=1) ions inci-dent on thin Cu foils. The solid curves are the result ofa simultaneous least-squares fit to the data for A=0 and&=1 using Eq. (3). The dashed curve was calculatedfrom Eq. (3) for A=1 using results obtained for A=O(see text).

l i I i I'

i l

0 40 80 l 20 160 200T (p.g /cm~}

FIG. 7. Projectile K-x-ray cross section vs targetthickness for 80-MeV Cl ' Q= 0) and Cl ' (&= 1) ionsincident on thin Cu foils. The solid curves are the re-sults of a simultaneous least-squares fit to the data forA=O and A=1 using Eq. (6). The dashed curve was cal-culated from Eq. (6) for &=1 using results obtained for&=0 (see text).

160-

140-

I I I l I I

8Q MeV

80—

80 MeV

120—

IOO-

80-

40—

60 MeV

60-

~100-Ib

80-

60 MevIb c,'

C3

60—

40 MeV

60-

40-

50-

4OMev-40—

20-~ ~

~ ~

20 I I 1

20 MeV

20 MeV

20 —.

~ ~

40 80t

120 160

g(P g /cfog }200

FIG. 6. Projectile K-x-ray cross section vs. targetthickness for 20-80-MeV Cl ions with initial chargestates q&&&-2 incident on thin Cu foils. The solidcurves are least-squares fits to the data using Eq. (6)with A= 0.

l I I060 180100 140 220

y (p.g /cm~)

FIG. 8. Differential BEC cross section (at 90') vs ..

target thickness for 20-80-MeV Cl ions with initialcharge states q& && -2 incident on thin Cu foils. Thesolid curves are least-squares fits to the data using Eq.(8) with A=O.

SYSTEMATICS OF TARGET AND PROJECTILE K-X-RAY. . . 487

1J

I I/

I

480-i

400

CA

520

~b clD 00 240

160—

80A =0

40 80 120

T (p.g ] cm')160 200

tensities were corrected for detection efficiency(Fig. 2) and experimental x-ray productioncross sections were determined for characteris-tic K x rays and REC.

The resulting x-ray-production cross sectionsare shown in Figs. 4-9 plotted as a function oftarget thickness. The smooth curves are theresults of least-squares fits to the data whichwill be discussed below. Figures 4, 6, and 8show the target x-ray production, projectilex-ray production and REC, respectively, forthe four beam energies studied for incidentcharge states q& Z, —2. The incident chargestates ranged from 3+ at 20 MeV to 10+ at 80MeV. For incident charge states q& Z, —2,K-x-ray production has been shown to be nearlyinsensitive to the precise charge state. ~4 Forq=Z, —2 the beam has a metastable component,namely, 1s2s'S, which results in slightly higherx-ray production due to the K-to-K electrontransfer made possible by this component of thebeam. In this work, we took no measurementswith this He-like beam, and so we need not beconcerned with this effect. The increase intarget x-ray production and REC as a function-of target thickness reflects the fact that the in-creasing fraction of ions with K vacanciesenhances the probabilities for these processes.

FIG. 9. Differential REC cross section (at 90') vstarget thickness for 80-MeV Cl ' (4=0) and Cl ~'

(A.=1) ions incident on thin Cu foils. The solid curvesare least-squares fit to the data using Eq. (8) with&=0 and A=1, respectively. The dashed curve was cal-culated from Eq. (8) for A=1 using results obtained for&=0 (see text).

Similarly, the decrease in the projectile x-raycross sections can be understood from the factthat K-vacancy loss (by electron capture orvacancy decay). outweighs K-vacancy production(by ionization) for the thicker foils.

Figures 5, '7, and 9 show the experimentalcross sections for target x-ray production,projectile x-ray production and REC, respec-tively, obtained from 80-MeV Cl ions with inci-dent charge state q=Z, —1 (2 =1), as well as therespective cross sections (from Figs. 4, 6, and8) for q & Z, —2 (A =0). X-ray production by 80-MeV Cl ions with q =Z, —1 is seen to be greatlyenhanced in each case over that for q& Z, —2.The enhancement in target x-ray production isin qualitative agreement with that of other inves-tigators'4 and is expected on the basis of themodel of Betz et a/. ' It will be shown below thatthe corresponding enhancements in the projec-tile x rays and HEC are also expected on thebasis of this same model and, in fact, the mag-nitude of the cross sections for A =1 can be pre-dicted quite accurately using the results for A =0.

III. ANALYSIS

A. Target x-ray yields

It is observed experimentally' that a projec-tile with a K vacancy produces a large increasein the measured target K-x-ray yield. There-fore, the measured target x-ray yield, writtenin units of a cross section, for a foil of thickness7.' is given by

1o„'(T)=— [o„'0(1—Y) +ct,Y]dx,TQ

(2)

In order to interpret the above results, thedependence of the respective x-ray yields onfoil thickness must be determined. To do thiswe use the two-component model of Betz et al. '

' in which the beam is considered to consist of twofractions of ions —those with a K vacancy andthose without a K vacancy. In this model thefraction of ions Y with a K vacancy at a depth xin the foil is given by

1'(x) =(o„/o)(1—e ~)+Be ~.In this equation A is the fraction of incident ionswith one K vacancy, and a =a„+o, + o„where 0„is the K-vacancy-production cross section forthe projectile, 0, the cross section for captureto the K shell, and p, the cross section for radia-tive or Auger decay. In principle, the possibilityof projectiles having two K vacancies should alsobe considered, but for the collision systemstudies here the two-component model has beenshown to be adequate. 4

488 J. A. TANIS, W. %. JACOBS, AND S. M. SHAFROTH 22

where 0„',is the target K-x-ray-production crosssection due to a projectile without a K vacancyand 0„',that due to a projectile with a K vacancy.(The superscript I denotes target x-ray crosssections. } Letting o'„',= no„'0where o( & 1 (o( is afunction of energy), Eqs. (1) and (2) give'

—"-A (1 —e')0'+ 0' (3)

This equation parametrizes the target x-rayproduction as a function of target thickness sub-ject to the validity of the assumptions inherentin Eq. (1).

N'„(T)=I,Y(T)~~, (5)

where T is the foil thickness and u~ is the meanK-shell fluorescence yield for the highly ionizedprojectiles. Equations (4) and (5) are used toobtain an expression for the measured projectileK-x-ray yield o~(T) (in units of a cross section)as a function of target thickness

o~(T) =X,—"+ cr~, —X„l —Av„(0 1 &1-e '~

"V " I0 i OT

(6)

where F~=—(N„'+N„')/I, Te and o~, =to„a„.(Thesuperscript P denotes projectile x-ray crosssections. )

In this equation it is assumed that v~, does notdepend on the incident charge state for q& Z, —2,thereby requiring that electrons in shells higher

B. Projectile x-ray yields

For the characteristic projectile x rays, con-tributions to the measured intensity from decaysinside the foil and outside the foil must be con-sidered separately. In this analysis we assumethat the contribution to the x-ray intensity fromlong-lived metastable states is small so thatessentially all x-ray events occur within a dis-tance small enough to be viewed by the detector.Inside the foil the x-ray intensity dN„' resultingfrom an elemental thickness dx of the foil isgiven by

dN„'(x)=I,Y(x)X„dxe,

where I, is the total number of incident ions, X„is the radiative decay probability per unit pathlength {in units of cm') and & is the detectionefficiency. This equation may be integratedusing the expression for Y(x) from Eq. (1). Out-side the foil the x-ray intensity is

than the K shell charge-state equilibrium veryrapidly (in the first few atomic layers) afterentry into the foil. The recent work of Cockeet al. ' shows this to be a reasonable assumption.Thus 0~, is interpreted as the K-x-ray-produc-tion cross section for a projectile with no initialK vacancies and an equilibrium charge distribu-tion in the higher shells. The same equilibriumcondition for electrons in shells higher than theK shell is necessary so that X„and w~ will beconstant and not dependent upon the incidentcharge state.

From Eq. (6) it is seen that P„decreases withtarget thickness for both A =0 and A. =1 and thatfor A. =1 the cross section is greatly enhanced.Hence, this equation is in qualitative agreementwith the measured cross sections shown in Figs.6 and 7.

dN„„(x)=I,Y(x) ""~QZ dx,dQ (7)

where do'„«/dQ is the HEC cross section per Kvacancy. Integrating Eq. (7) over target thick-ness we get an expression for the measured RECyield Per incident Projectile:

d0'""(&)= ""—" ( ——(( —~"))dQ dA .g gT

(6)

where don«/dQ—= N«/I, TA Quand N«c is themeasured HEC intensity (at 90 ).

From Eq. (8) it is seen that do„«/dQ increaseswith target thickness for A =0. This is due to thefact that the fraction of ions with K vacanciesincreases as the target thickness increases. Incontrast, for A=1, dF„«/dQ decreases withtarget thickness since a smaller fraction of theions possess K vacancies for large foil thick-nesses. These features are in qualitativeagreement with the measured REC cross sectionsshown in Fig. 8 and 9.

D. Least-squares analysis

Equation (3) can be used to perform a least-squares fit to the measured target x-ray-pro-duction cross sections shown in Figs. 4 and 5

C. REC yields

In the case of REC, contributions to the mea-sured REC intensity can only come from insidethe foil. Since a K vacancy must be present forREC to occur, the REC intensity dN„«resultingfrom an elemental thickness dx of the foil in thesolid angle AQ„is given by

SYSTEMATICS OF TARGET AND PROJECTILE E-X-RAY. . .

giving values for the parameters v„'„n,o„andc. If, however, x-ray production is measuredonly for A =0 (q & Z, —2), then only e„'„oand theproduct (o. —1) v„canbe determined independ-ently. In the present work A =0 for the 20-,40-, and 60-MeV data while, for 80 MeV, datawere obtained for both A = 0 and A = 1. For the80-MeV data a simultaneous least-squares fitwas performed to the data for A =0 and A =1allowing the extraction of all four parameters.The solid curves shown in Figs. 4 and 5 are theresults of these fits to the data.

Similarly, Eq. (6) can be used to perform aleast-squares fit to the measured projectilecross sections, shown in Figs. 6 and 7, givingvalues for the parameters g~„X„,cr„and cr.

For A =0 only v~„aand the product X„cr„aredetermined. Equation (8) is used to fit the RECcross sections (Figs. 8 and 9) giving values fordo'0«/dQ, v„,and c. For A =0, only v and theproduct (de~»c/dQ) o„aredetermined, whilefor A=1 the intercept at T=O gives the valuesof dooasc/dQ directly.

It is noted that the parameters g„and o arecommon to each of the three cross-section for-mulations, i.e., Eqs. (3), (6), and (8), and hencetheir value should be the same for each case.In the least-squares analysis of the projectilex rays and REC, these parameters were con-strained to have values equal to those found forthe target x rays. There are three reasons forconstraining v„and o in this way. (i) Data wereobtained for smaller values of the target thick-ness (down to 25 p,g/cm') for the target x rays,providing measurements over the region wherethe cross section changes most rapidly. Targetx-ray production can, of course, be measuredfor arbitrarily thin target thicknesses by usinga backing foil. (ii} Target x-ray intensitiesare easier to determine accurately since thereis no interference in the spectrum from REC inthe region of the Cu x rays as is the case for the

Cl projectile x rays. (iii} When the target andprojectile x-ray production were fit separately[with Eqs. (3) and (6)], allowing v to vary freely,the values of v obtained were the same to within

The solid curves shown in Figs. 6-9 are theresults of the fits to the data using Eqs. (6) and

(8) under the constraint that o(and v„for 80 MeVand A =1) be equal to the values obtained fromthe analysis of the target x rays using Eq. (3).In this way a single self-consistent set of param-eters was obtained for all of the data.

IV. DISCUSSION

A. Target x rays

The results of the above least-squares analysisof the target x-ray production are summarized inTable I. Quoted errors include the fitting erroronly. The large decrease in 0 over the range ofenergies studied is due to decreases in the cap-ture cross section o, and the decay cross section

-0, with increasing velocity. The decrease in theproduct (a —l)g„is due to the large decrease in

n with increasing energy which outweighs theincrease in 0„.The decrease in n reflects thefact that the probability of electron transferfrom the target K shell to the K shell of the pro-jectile decreases with increasing projectilevelocity. More will be said about this laterThe increase in o„'0(the cross section for vanish-ing target thickness for 8 =0) is due primarily tothe increase in target K-vacancy production withincreasing projectile energy. A small contribu-tion may exist due to an increase in the fluores-cence yield with increasing multiple ionizationfor the higher beam energies.

Our results for 60-MeV projectile can be com-pared with the work of Gray et il.' These authorsfind values for v„'„o,and (n —1}o„of1180 b,1890 kb, and 2485 kb, respectively. From TableI it is seen that these values are all within 10%

TABLE I. Besults of least-squares analysis, using Eq. (3), of Cu target E-x-ray yieldsshown in Figs. 4 and 5.

(MeV)

t b~~0 (~ -1)cr„b

(kh)

20406080

000

0, 1

7.0+ 0.2190 + 10

1100 + 203500 + 100

8200 + 30006300 + 6002600 + 2001600 + 100

12200 + 44005700 + 5002100 + 1001800 + 200

95'217.14.6 + 0.20

86300360350 + 20"

A is the fraction of incident ions with one X vacancy.Values obtained from least-squares fits to the data.Calculated from Eq. (9).From Bef. 4.

J. A. TAXIS, %. W. JACOBS, AND S. M. SHAFROTH

IO I I

CI + Cu

IO4

IOXl

0)C

IO

IOI

of the values obtained in the present work., The extracted values of o„',may be compared

with theoretical predictions of ionization asshown in Fig. 10. Single-vacancy fluorescence'yields were used to calculate theoretical x-raycross sections from the vacancy production crosssections. It is seen that the plane-wave-Born-approximation (PWBA)" and the binary-encounterapproximation (BEA)" overestimate the measuredcross sections by as much as an order of magni-tude. The solid curve ' labeled CPSSR+ ECR(K- L, M, . . . ) (Coulomb perturbed stationary-state relativistic plus electron capture relativistictheory) includes contributions from (1) directionization (CPSSR) given by the theory of Basbaset al.'4 with the relativistic treatment as devel-oped by Brandt and Lapicki" and (2) electroncapture (ECR} to the L and higher shells basedon the theory of Lapicki and Losonsky" modifiedfor radial cutoffs" and including the relativisticcorrections of Lapicki and McDaniel. " AlthoughRefs. 26-28 deal only with electron capture byfully stripped ions, it is possible to estimatecapture by a projectile with electrons by assum-ing that their only role is to occupy otherwiseavailable states on the projectile. " This, ofcourse, neglects the screening of the projectilenuclear charge which may be important. TheECR contribution tn the solid curve in Fig. 10is about 15%%uo of the total ionization cross sectionfor all energies investigated. Agreement withthe CPSSR+ECR theory is seen to be fair withthe agreement improving for higher incident

beam energies.These results indicate that target K-vacancy

production for the collision system studied here(Z,/Z2-0. 6) may be predicted reasonably wellwithin the framework of the CPSSR+ ECR theory.However, the present results tend to disagreewith those of McDaniel et al."in which it isconcluded that direct ionization alone accountsfor o„',for 0.44 ~Z, /Z, ~0.67. We find thatCPSSR+ ECR theory underestimates the dataeven with the 15%%uo contribution to the crosssection due to electron capture. This fact maysupport the contention by Gardner et al."thatelectron capture, to the L and higher shells ofthe projectile, plays a considerably larger rolerelative to direct ionization for Cl+Cu collisions.However, the discrepancy could also be due toinadequacies of the direct ionization theory forthis collision system. These questions clearlyneed further study.

We have also measured cross sections o„',forvanishing target thickness for Cl bombardmentof other targets in the range 19 &Z, +35." Wefind that agreement with the CPSSR+ ECR be-comes considerably worse as Z,/Z, —1. Thisresult is, of course, expected for more symmet-ric collisions. The importance of obtaining thecross section for vanishing target thickness incomparisons with theory should be stressed,however, since there can be sizable differencesbetween the zero thickness cross section a„',andthe equilibrium cross section P(~) Ifrom Fig. 4ot I o»(~}]

It is of considerable importance to be able todetermine the value of 0„,the K-vacancy-pro-duction cross section for the projectile, sinceknowledge of this parameter allows determinationof several quantities of interest concerning thehighly stripped projectile. In the present worko„is determined directly from the 80-MeV databy fitting Eq. (3) to the data for A =0 and A = 1shown in Fig. 5. For 60 MeV we can use thevalue of o. (= 8.1) found by Gray et al.» to deter-mine o„,giving a value of 360 kb which is con-sistent with the value found by those authors.Since n is simply the ratio o„',/o„'„its value canbe determined quite accurately when data is ob-tained for both A =0 and A =1. Furthermore,Gray eI; al.' find that the factor G can be calcu-lated quite accurately according to the formula(see also Gardner et al. ')

p IIO PO

I I- I

40 60E (Mev)

80 Q —1 =vsK&do„/o„o~

FIG. 10. Target X-x-ray-production cross section 0.„

for vanishing target thickness as a function of incidentbeam energy. Comparison is made with theoretical pre-dictions of direct ionization (Refs. 21-29).

where 0~ = mR' and R is the radius correspondingto the peak in the dynamic coupling elements asgiven by Taulbjerg et al. ," w is the Meyerhof"vacancy transfer probability, and are„is the

22 SYSTEMATICS OF TARGET A5 D PRO J ECTI LE K-X-RAY. . . 491

fluorescence yield' for Cu. The He-like bindingenergy" for the Cl K-shell was used in the cal-culation of ~. Values of o~ = 7.07 x 10 "cm' and

~c„=0.445 rvere usedIf the value of (n —1}given by Eq. (9) is calcu-

lated for the present 80-MeV data, we find avalue of 3.9 which is about 15% lower than ourmeasured value of 4.6, giving further evidencethat Eq. (9}provides rather reliable estimatesof n. If we use this calculated value of ~ alongwith the values of o„'„(a—1}o„,and o found froman analysis of the A. =0 data only, Eq. (3) can beused to predict the measured cross sectionso„'(T)for A =1. The result is shown by thedashed curve in Fig. 5. It is seen that the targetK-x-ray production for A =1 can be predictedquite well using results obtained for A =0 inconjunction with Eq. (9).

For 20- and 40-MeV Cl projectiles + was cal-culated from Eil. (9), allowing a determinationof o„.The values obtained for z and o„arelisted in Table I. The large decrease in a withincreasing energy reflects the fact that K-to-Kelectron transfer becomes less probable forhigher projectile velocities.

The present results cannot be compared in ameaningful way with the vacancy sharing theoryof Meyerhof" since the conditions required forapplication of this theory are not satisfied in thepresent work. " There are basically two reasonsfor this. (1) Vacancy sharing is applicable onlyin the case where K vacancies in the heaviercollision partner result from transfer from the2Pv molecular orbital, i.e., direct K-vacancyproduction must be negligible. If the contribu-tion due to direct excitation is large, its effectmust be subtracted before comparing with thevacancy sharing model. In our case the vacancyproduction giving rise to 0„0is accounted foralmost totally (except possibly at 20 MeV) by the

direct ionization theory including electron cap-ture. " Hence. cr„'0 cannot be used to determinea meaningful value for the experimental vacancysharing probability w. (2) Vacancy sharingapplies to the outgoing part of the collision. "Hence the cross section 0„',cannot be used todetermine zo since it contains a large contribu-tion due to direct electron capture and this con-tribution cannot be separated experimentallyfrom the part due to transfer from the 2PO orbital.Furthermore, Winters et al."observed that ClK-vacancy production as a function of target Z,

. becomes monotonic for energies E~ 30 MeV,indicating that direct excitation dominates overvancancy transfer from 2Pcr for the energy rangeinvestigated here.

For similar reasons, our results cannot becompared with the universal scaling model ofLennard et al. '4 Furthermore, these authorsinvestigated collisions involving gas targetswhereas our work deals with thin foils. In addi-tion, they used projectiles in which there wereno initial 2p vacancies, a condition not nec'essar-ily satisfied in the work described here.

B. Projectile x rays and REC

The results of the least-squares analyses ofthe projectile x rays and the HEC are summar-ized in Table II. As in Table I, quoted errorsinclude only the fitting error. Since the valuesof o and o„were constrained to be the same asfor the target x-ray production their values arenot repeated in Table II.

The dashed curve in Fig. 7 was calculated fromEq. (6) using the values of of, (=&a~„),X,„v„,and

o found from the analysis of A, =O data and thevalue of v„determined from the product (c, —1)g„given in Table I after calculating n —1 fromEq. (9). As for target x-ray production, it is

TABLE lI. Results of least-squares analyses, using Eqs. (6) and (8), of Cl projectile E-x-ray and REC yields shownin Figs. 6-9.

E(MeV)

gv„b(kb2) (10-'4 sec)

do'REc0 b

v dg(kb2/sr)

d~REc0

dQ

(kb/sr)REC e

20406080

000

0, 1

11~ 189+ 3

151+ 3224 + 10

40300 + 800120 000 + 340086600 +420049400 + 9500

0.130.300.420.64 + 0.03

2.42.02.74.0

220 + 10280 + 10230 + 10160 + 10

2.60.930.640.47 + 0.03

2.52.04.53.2

A is the fraction of incident ions with one K vacancy."Values obtained from least-squares fits to the data.'Calculated from co~ ——0~0/0.„.(For 80 MeV ~E is determined directly. )~Calculated from r„=llnvh„where n is the atomic density (atoms/cm~} and v the incident velocity.'Calculated from uREc = OREc/o, where O'REc =-«O'REc(90')/dQ, and a, =cr-cr„-a (see text).

3

J. A. TAXIS, %. %. JACOBS, AND S. M. SHAFROTH

seen that the projectile x-ray production forA = 1 can be predicted quite well from the resultsobtained for A =0.

The increase in o~, (the zero-thickness crosssection for A =0) is due in part to the increasein vacancy production but is also due to an in-crease in the fluorescence yield of the highlystripped Cl ions. Values of the mean fluores-cence yield may be calculated from the relation&or=of,/v„. The results are listed in the table.(For 80 MeV, a&» was determined directly fromthe fitting. ) These values are plotted in Fig. 11as a function of the incident beam energy. Thesingle-vacancy fluorescence yield" is shownfor reference. It is observed that co~ has avalue (-0.1) nearly equal to the single-K-vacancyvalue for 20-MeV Cl and increases by a factor ofabout 6 over the range 20-80 MeV. The scalealong the top of the figure gives the averagenumber of L vacancies n~ corresponding to theenergy range investigated here. Values of n~were deduced by comparing observed Cl Kzenergy shifts with computed shifts obtained from

35Hartree-F ock- Slater calculations assuming afully stripped M shell.

The scaled theoretical estimate for ~~ shownin Fig. 11 was calculated using the scaling pro-cedure of Larkins. " The actual values for co~were computed from the formula of Greenberget al. ,

s' namely,

(10)

0,8

cl ~ cu

n,5

cl cu„

0.2—

0.0 ' l (

40 60E (MeV)

(

80

FlG. 11. Mean fluorescence yield for Cl projectileions as a function of beam energy. The solid line throughthe data is drawn to guide the eye. The single-vacancyfluorescence yield is from Ref. 20. The dashed curve isa scaled theoretical estimate of the fluorescence yieldQ,efs. 36 and 37). The scale along the top gives theaverage number of L vacancies at x-ray emission assum-ing a fully stripped M shell (Ref. 35).

where co, is the single vacancy fluorescenceyield. This formula assumes that both thex-ray and Auger transition-rates scale in pro-portion to the total number of remaining elec-trons. Qualitative agreement with the trend ofthe experimental data is obtained but the theo-retical curve differs systematically in magnitudefrom the experimental values, especially at thehigher energies. This is not unexpected and isprobably due to intrinsic inaccuracies in thescaling procedure used to calculate w~.

The values of A.„a„givenin Table II areseen to go through a maximum. This is due tothe fact X„decreases monotonically with increas-ing projectile velocity while v„increases. Usingthe values of v„from Table I to calculate X„,theradiative lifetime v„for K-shell decay for theprojectile ions may then be deduced from 7„= I/nvX„, where n is the atomic density (atoms/cm') and v is the incident velocity. The result-ing values of v„are listed in Table II. Uncer-tainties in v„are such that no systematic beam-energy dependence can be discerned. However,since the average equilibrium charge" for 20'-80-MeV Cl ions does not change appreciably (q= 10-12.5), it might be expected that r„wuol dnot vary greatly over this energy range. Theaverage of the values shown in the table is 7„=2.8&&10 "sec which is about three timeslonger than the theoretical single-K-vacancyradiative lifetime" of 1.1&&10 '4 sec. Quali-tatively such an increase in lifetime is expectedfor a highly stripped ion. These results are insubstantial agreement with the work of Betz etal. ' in which the radiative lifetime for -100-MeVsulfur ions in collisions with thin solid targetsis determined to be about 1.5 &10 "sec.

Finally, we consider the REC cross sectionsgiven in Table II. The peaked behavior of theproduct o'„(do'„«/dQ)is due to the fact thatdo'OEc/dQ decreases with increasing beam energywhile v„increases. In a manner similar to thatused for Figs. 5 and 7, the results of the A =0analysis can be used to predict the measuredcross sections Ch„sc/dQ for A =1 using Eq. (8).The dashed curve in Fig. 9 shows the predictedcross sections for 80 MeV which are seen to agreequite well with the measured cross sections aswas the case for the target and projectile x-rayproduction.

Using the values of a„from Table I the RECcross section Per K vacancy doo»c/dA may bedetermined. %ithin the limits of validity of theexpression used for Y(x), ' the values shown fordooazc/dA in Table II are properly norma, lized tothe fraction of ions which develop K vacancies.This normalization is essential if REC cross

S YSTEMATIGS OF TARGET AND PROJECTILE E-X-RAY. . .

sections are to be compared with theoretical cal-culations.

We have compared our results for dooa«/dQwith predictions of the free-electron theory ofBethe and Salpeter. ' Other investigators havecompared REC cross sections with calculationsbased on the Born approximation. 4'4' The rele-vant parameter in determining the applicabilityof each theory is the Sommerfeld parameter,q =Ze'/hv, which is the ratio of the Cl K-shellvelocity to the incident projectile velocity. Ifg ~ 1 the disturbance of the atomic orbitals duringthe collision is large and the Bethe-Salpetertheory is applicable. For q & 1 the disturbanceis small and the Born approximation should bemore appropriate. In our case g& 1.7 for a11.

beam energies investigated, so we consider onlythe Bethe-Salpeter theory. Furthermore, pre-dictions based on the Born approximation ' havebeen shown to be in qualitative disagreementwith the trend of the experimental cross sections4'for collision systems similar to those investi-gated here.

Since the Bethe-Salpeter theory gives only thetotal REC cross section, theoretical differentialcross sections at 90' were calculated assuminga sin'8 dependence" "for the REC intensity.The results are shown in Fig. 12. Two theoreti-cal curves are shown. The lower dashed curveis calculated directly from the theory assumingthat each target atom has a single electron whichcan be captured. This curve underestimates theexperimental values by more. than an order ofmagnitude. However, a copper atom has several

)p5

O4Io&gb

C3 )p2

electrons which can be captured radiatively, andthese electrons should be included in the theoreti-cal calculations. The criterion to be used indetermining how many target electrons to includeis that the captured electron be essentially "free"with respect to the incident projectile. This con-dition may be expressed by

where E is the incident energy, M the projectilemass, U the target electron binding energy, and

m, the electron mass. This expression is, ofcourse, just the ratio of the incident projectileand orbital electron velocities. A simple calcu-lation for 20-80-MeV Cl using the binding ener-gies listed by Bearden and Burr4' shows that thiscondition is satisfied only for the ten M4, and oneN, electrons in Cu. If it is assumed that each ofthese electrons contributes equally to radiativecapture, then the upper solid curve is obtainedwhich is seen to be in excellent agreement withthe measured REC cross sections.

Finally, by combining the result& obtained forthe projectile x rays and the REC, the radiativeprobability for K-shell capture events may beestimated. Using the values obtained for &~ and

X„,the decay cross section o, =X„/~ris calcu-lated which, in turn, allows the total capturecross section a, =o —o„-cr, to be determined.Then, using the experimentally determined RECcross sections dc„'«/dA, the fluorescence yieldfor K-shell capture events is given by GREC=a„«/o,. ' We find values in the range (2-4)&& 10 ' as shown in Table II. Owing to the errorspropagated from the subtraction of large numbers(in the calculation of a,), uncertainties in &o„«are such that no systematic beam-energy depend-ence can be discerned. The average of the valuesshown is 3&&10 '. To our knowledge this is thefirst experimental determination of the radiativeprobability for K-shell capture events.

V. CONCLUSION

20 40E (Mev)

l

60t

80

FIG, 12. Differential BEC cross section (at 9{)')perE vacancy vs Cl ion energy. The dashed curve was cal-culated from the Bethe-Salpeter Qef. 40) free-electroncapture theory, corrected for the sin e angular distri-bution of REC efs. 43 and 44). The solid curve wasobtained by multiplying the dashed curve by the number(11) of "free" {i.e., loosely bound) electrons in Cu (seetext).

%e have presented a quantitative descriptionof target and projectile (including REC) x-rayproduction for Cl ions in collisions with thin Cutargets. '

By parametrizing the measured x-rayyields as a function of target thickness we ob-tained values for certain fundamental parameterswhich describe the collision dynamics. Simul-taneous measurement of both target and projec-tile yields gives a single self-consistent set offitting parameters which describe all of the data.X-ray production was found to be greatly en-hanced for incident charge states q = Z, —1 and it

J. A. TANIS, %. %. JACOBS, AÃO S. M. SHAFROTH 22

was shown that this enhancement could be pre-dicted quite reliably based on results obtainedfor q&Z~-2.

In summary, we have obtained the following'

results. (1) Target K-vacancy production byprojectile ions without a K vacancy is reasonablydescribed within the framework of direct (Cou-lomb) ionization, plus electron capture, for thecollision system studied here. The enhancementin target K-vacancy production by projectile ionswith a K vacancy is in quantitative agreement withthe prediction of Gray et al.» (2) The meanfluorescence yield for the highly stripped Cl ionsis determined and found to increase by a factorof 6 over the energy range investigated. (3) Theradiative lifetime v„for the highly ionized projec-tile is about three times longer than the theoreti-cal single-K-vacancy radiative lifetime. '9 (4) TheREC cross section, when properly normalized tothe fraction of ions with K vacancies, is in goodagreement with the free-electron theory of Betheand Salpeter. ' The fluorescence yield for K-shell capture events is determined and found to

have a value of -3 x 10 '. We know of no theoreti-cal calculation with which to compare this result.

In conclusion, measurements such as those pre-sented here provide information on the state ofhighly stripped ions moving in solids and alsoprovide an understanding of the systematics ofvacancy production in heavy ion-atom collisions.

ACKNOWLEDGMENTS

The authors wish to thank Professor W. E.Meyerhof for his comments concerning theapplicability of vacancy sharing. The assistanceof D. Schneider in the data acquisition is grate-fully acknowledged. G. Lapicki kindly providedthe CPSSR+ ECR calculations shown in Fig. 10.We thank Professor W. J. Thompson and Profes-sor E. Merzbacher for encouragement and con-sideration of this work. This work was supportedin part by the U. S. Department of Energy, Divi-sion of Chemical Sciences, and by a grant fromthe North Carolina Board of Science and Tech-nology.

*Present address: Lawrence Berkeley Laboratory,University of California, Berkeley, Calif. 94720.

/Present address: Indiana University Cyclotron Facil-ity, Bloomington, Ind. 47401.

H. -D. Betz, F. Bell, H. Panke, G. Kalkoffen, M. Welz,and D. Evers, Phys. Rev. Lett. 33, 807 (1974).F.Hopkins, Phys. Rev. Lett. 35, 270 (1975).K. O. Groeneveld, B. Kolb, J. Schader, and K. D. Sev-ier, Z. Phys. A277, 13 (1976).

T. J.Gray, P. Richard, K. A. Jamison, and J.M. Hall,Phys. Bev. A 14, 1333 (1976).F. Hopkins, J. Sokolov, and A. Little, Phys. Bev. A 15,588 (1977).R. K. Gardner, T. J. Gray, P. Richard, C. Schmiede-kamp, K. A. Jamison, and J. M. Hall, Phys. Bev. A 15,2202 (1977).U. Scharfer, C. Henrichs, J.D. Fox, P. Von Brentano,L. Degener, J. C. Sens, and A. Pape, Nucl. Instrum.Methods 146, 573 (1977).T. J.Gray, C. L. Cocke, and R. K. Gardner, Phys.Bev. A 16, 1907 (1977).

9C. L. Cocke, S. L. Varghese, and B. Curnutte, Phys.Rev. A 15, 874 (1977).S. K. A)lison, Bev. Mod. Phys. 30, 1137 (1958).

~~W. E. Meyerhof, Phys. Rev. Lett. 31, 1341 (1973).K. Taulbjerg, J.Vaaben, and B. Fastrup, Phys. Rev.A 12, 2325 {1975).H. Tawara, P. Richard, T. J. Gray, J. Newcomb,K. A. Jamison, C. Schmiedekamp, and J. M. Hall,Phys. Rev. A 18, 1373 (1978).T. J. Gray, P. Richard, G. Gealy, J. Newcomb, andH. Tawara, IEEE Trans. Nucl. Sci. NS-26, 1127(1979).T. J. Gray, P. Richard, G. Gealy, and J. Newcomb,

Phys. Rev. A 19, 1424 {1979).B. K. Gardner, T. J. Gray, P. Richard, C. Schmiede-kamp, K. A. Jamison, and J. M. Hall, Phys. Bev. A19, 1896 (1979).

~'J. A. Tanis and S. M. Shafroth, Phys. Rev. Lett. 40,1174 (1978); Phys. Lett. 67A, 124 (1978); Jpn. J.Appl.Phys. 17, Suppl. 17-2, 399 (1978); IEEE Trans. Nucl.Sci. NS-26, 1068 (1979).

~ E. Storm and H. I. Israel, Nucl. Data Tables A7, 565(1970).C. H. Butledge and B. L. Watson, At. Data Nucl. DataTables 12, 195 (1973).M. Bambynek, B. Crasemann, B.W. Fink, H. -U.Freund, H. Mark, C. D. Swift, B.E. Price, and P. V.Bao, Rev. Mod. Phys. 44, 716 (1972).G. S. Khandelwal, B.H. Choi, and E. Merzbacher, At.Data 1, 103 (1969).J.H. McGuire and P. Richard, Phys. Rev. A 8, 1374(1973).The CPSSR+ ECB curve in Fig. 10 was calculated byG. Lapicki (private communication).G. Basbas, W. Brandt, and R. Laubert, Phys. Bev. A17, 1655 (1978).W. Brandt and G. Lapicki, Phys. Bev. A 20, 465 (1979).G. Lapicki and W. Losonsky, Phys. Rev. A 15, 896{1977).F. D. McDaniel, J. L. Duggan, G. Basbas, P. D. Mil-ler, and G. Lapicki, Phys. Rev. A 16, 1375 (1977).G. Lapicki and F. D. McDaniel (unpublished);, also seeRef. 74 of Bef. 25.

SG. Lapicki (private communication).J. A. Tanis, B. L. Doyle, W. W. Jacobs, and S. M.Shafroth (unpublished) .R. L. Kelly and D. E. IIarrison, At. Data 3, 177 (1971).

SYSTEMATICS OF TARGET AND, PROJECTILE E-X-RAY. . .I

W. E. Meyerhof (private communication).L. Winters, M. D. Brown, L. D. Ellsworth, T. Chiao,E. W. Pettus, and J. R. Macdonald, Phys. Bev. A 11,174 (1975).W. N. Lennard, I. V. Mitchell, and J.S. Fbrster,Phys. Rev. A 18, 1949 (1978).F. Herman and S. Skillman, Atomic Structure Calcu-lations (Prentice-Hall, Englewood Cliffs, New Jersey,1963).F. P. Larkins, J. Phys. B 4, L29 {1971).

VJ. S. Greenberg, P. Vincent, and W. Lichten, Phys.Rev. A 16, 964 {1977).H. -D. Betz, Rev. Mod. Phys. 44, 465 (1972).J.H. Scofield, Phys. Bev. A 9, 1041 (1974).H. A. Bethe and E. E. Salpeter, Quantum Mechanics ofOne- and Theo-&lectron Atoms (Academic, New York,1957), pp. 320-322.

P. Kienle, M. Kleber, B.Povh, R. M. Diamond, F. S.Stephens, E. Grosse, M. R. Maier, and D. Proetel,Phys. Bev. Lett. 31, 1099 (1973).B.Schule, H. Schmidt-Bocking, and I. Tserruya, J.Phys. B 10, 889 (1977).

43H. D. Betz, F. Bell, H. Panke, and G. Kalkoffen, inProceedings of the Fourth International Conference onAtomic Physics, Abstracts of Contributed Papers,Heidelberg, Germany, 1974, edited by J. Kowalski andH. G. Weber (Heidelberg Univ. Press, Heidelberg, .

Germany. , 1974), pp. 670-673.4E. Spindler, H. -D. Betz, and F. Bell, Phys. Rev. Lett.42, 832 (1979).J.A. Bearden and A. F. Burg, Bev. Mod. Phys. 39, 125{1967).The total REC cross section is given by oRqg= (8m/3)daREc 90 )/d& (see Ref. 43).