PHYSICAL REVIEW A VOLUME 42, NUMBER 9 1 NOVEMBER 1990

M-shell x-ray production by 0.8—4.0-MeV "He+ions in ten elements from hafnium to thorium

M. PajekInstitute of Physics, Pedagogical University, 25-509 Kielce, Poland

A. P. Kobzev, R. Sandrik, and A. V. SkrypnikJoint Institute for Nuclear Research, Dubna, U SS R. . .

R. A. Ilkhamov and S. H. KhusmurodovInstitute ofApplied Physics, Tashkent State University, Tashkent, U SS R. . .

G. LapickiDepartment ofPhysics, East Carolina University, Greenville, North Carolina 27858

(Received 20 April 1990)

M-she11 x-ray production cross sections are reported for»Hf, »Ta, 74W, »Re, 760s, »Ir, »Pt,7/AU 83Bi, and»Th bombarded by 'He ions of energy 0.8-4.0 MeV. The measured cross sectionsare compared with the predictions of the semiclassical and first-order Born approximations and thecalculations of the perturbed-stationary-state (PSS) theory that accounts for energy-loss (E),Coulomb deflection (C), and relativistic (R) effects (ECPSSR). The ECPSSR theory gives the bestoverall description of the measured data, although systematical discrepancies are found in the low-

velocity region. Apart from deficiency of the available M-shell Coster-Kronig factors and fluores-cence yields near or above Z2 =74, where strong M4-MSN6 7 Coster-Kronig transitions become en-

ergetically forbidden, the increasing underestimation of the data by the ECPSSR theory with de-

creasing projectile velocities is genuine. In fact, we have found previously [Pajek et al. , Phys. Rev.A 42, 261 (1990)] the same discrepancy for identical target elements bombarded by protons at com-

parably low velocities.

I. INTRODUCTION

%hile over 10000 experimental cross sections concern-ing the K- and L-shell ionization by ion impact werecompiled and reviewed, ' only a few papers were relatedto the M-shell ionization by light ions of MeV ener-gy.

' Basic difficulties in M-shell x-ray measurementsare connected with an accurate efficiency calibration of aSi(Li) detector' for soft x rays (below 5 keV), where allM-shell —x-ray transitions occur. The high-purity carbontarget backings are desired in these experiments, so as toavoid any interference of measured M x-ray lines with theK x ray originating from typical light contaminationpresent in carbon foils. " Also, some target effects —suchas the projectile energy loss and strong M x-ray absorp-tion in the target —have to be properly accounted for'when M-shell x-ray production cross sections are extract-ed from x-ray yields.

M-shell x-ray production by He ions was measured us-ing high-resolution Si(Li) detectors, to our knowledge,only in four experiments. They were performed byThornton, McKnight, and Karlowicz who have mea-sured M-shell x-ray production cross sections for 65Tb,79Au, and 83Bi targets bombarded by e particles in the1 —5-MeV energy range; Mehta et al. ' ' who have donemore extensive measurements in 13 elements between~9Pr and 9zU using He+ beam of 0.25 —2.6 MeV; andfinally Gowda and Powers' who, using the thick target

method, reported M-shell ionization cross sections in 77Ir,78Pt, and „Pb by 0.4—2.2-MeV He+ ions.

M-shell ionization for strongly asymmetric systems(i.e., Z

~&(Z2, where Z, and Z2 denote the projectile and

target atomic numbers, respectively) proceeds mainly viadirect ionization. ' The competing mechanism of elec-tron capture to the projectile' is less important (electroncapture contributes' less than 3—S%%uo relative to directionization for the collision systems to be studied in thiswork). Theoretical M-shell ionization cross sections maybe obtained using the first-order Born approximation, i.e.,the plane-wave Born approximation (PWBA) for directionization and the Oppenheimer-Brinkman-Kramers ap-proximation ' of Nikolaev (OBKN) for the electroncapture. The ECPSSR accounts for the Coulomb-deAection, binding and/or polarization, relativistic, andenergy-loss effects for both electron-capture' and direct-ionization ' processes. The semiclassical (SCA) approachaccording to Hansteen et al. calculates only direct ion-ization and yields essentially identical results as theP%BA.

The vacancy produced in the M shell may be filled byhigher-shell electrons via three basic processes: x-rayemission, Auger-electron emission, or Coster-Kronigtransition. The rates for these processes were calculatedby McGuire and Chen et al. ; their values have agreat inhuence on the final comparison of the experimen-tal M-shell x-ray production cross sections with the

42 5298 1990 The American Physical Society

42 M-SHELL X-RAY PRODUCTION BY 0.8-4.0-MeV He+. . . 5299

theoretical results.In this work, we report systematic measurements of

M-shell x-ray production cross sections in selected ele-ments between 7zHf and 9OTh by He+ ions of 0.8 —4.0MeV. The analogous results measured by our group forthe proton impact were published recently. ' For heliumions, in precise conformation to what was observed forprotons (see Ref. 16), the increasing underestimation ofthe data by the ECPSSR theory is found for decreasingprojectile velocity.

II. EXPERIMENTAL METHOD

A He+-ion beam of 0.8—4.0 MeV from the Van deGraaff EG-5 accelerator of Joint Institute for NuclearRearch (JINR), Dubna, was employed in the presentmeasurements. Using the electron-gun evaporation tech-nique, thin targets (2.5 —35 pg/cm, see Table I) of 7zHf,73Ta, 74W, 75Re, 760s, 77Ir, 78Pt, 79Au, 83Bi, and 9OTh wereprepared by depositing a thin layer of element of interestonto a thin (-20 pg/cm ) carbon foil. The carbon foilsmade the M-shell x-ray experiments nearly contaminantfree the contamination of these foils by light elements(Al —Ca) was preliminarily measured using the particle-induced x-ray emission (PIXE) method with a 3-MeVproton beam.

For our data, M-shell x rays excited in thin targetswere collected into the Si(Li) detector positioned perpen-dicular to the beam axis, while the He ions were elasti-cally scattered into the silicon surface barrier detector fornormalization. More details concerning the experimental

setup and method may be found in Ref. 16. Consequent-ly, in this work only some basic features of the experi-mental method and data analysis mill be mentioned.

The low-energy Si(Li) detector efficiency was carefullymeasured by the PIXE method' using both 'H and He-ion impact to minimize any possible systematical errorsoriginating from the adopted "reference" K-shell ioniza-tion cross section. ' The measured efficiency was fittedin terms of a Si(Li) detector model' that incorporatedthe factors for absorption in the Be window, Au contactand Si dead layer as well as the effects of a growing icebuildup and an increased Si dead layer in the peripheralregion of the detector (called "edge effect "). This has ledto an essential modification in the energy dependence ofthe efficiency curve. ' The estimated Si(Li) detectorefficiency uncertainties in the x-ray energy region of in-terest (1.5 —4 keV) were 7 —3%, respectively (see Fig. 1 ofRef. 16.) It should be added here that the efficiency cali-bration of a Si(Li) detector by the PIXE method, usingthe same experimental setup, reduces the final experimen-tal uncertainties of the measured M-shell x-ray produc-tion cross sections due to a cancellation of errors con-nected with estimation of the particle detector positionangle (determining the elastic cross sections ) and itssolid angle.

Measured M-shell x-ray spectra were analyzed usingthe nonlinear least-square fitting program AcTIv, whichassumes a Gaussian line shape for the full-energy peaks.The fitted areas for dominating seven Mx-ray lines, i.e., M&(M4 5NQ 3 ) M3N / +M4E3,

TABLE I. The measured M-shell x-ray production cross sections (in barns), the total experimental uncertainties, target thicknesseshx, and the average M-shell fluorescence yields AM (see Ref. 16).

He-ionenergy(MeV)

0.81.01.21.41.61.82.02.22.42.62.83.03.23.43.63.84.0

7qHf

321513712957

1200145016401870210023802660312033903650

41904510

73Ta

284447624835

1040123014101610182020602280

31403140332035803770

304415591778974

115013501530174019602150248027603000316034203590

75Re

279452652886

1100133015201900197022002500285028603430351038304110

76OS

259415593791993

116013801560177019802220252027703020324033703520

77Ir

251406555745916

109013001430175019402180231026502750297032403530

78Pt

222355503652841990

12001310163017701990221025002530274031003270

79AU

210335473614796946

11201260157017101930211023602350263029503190

83Bi

120220303442557695775926

105012101350150016601740194021102240

9QTh

45.790.9

142209280354434518607700797880981

1070118012601390

Uncertainty (%)

Ax (pg/cm') 23 35

10

19

10

26 23 23 27 31 2.7

0.0176 0.0187 0.0197 0.0210 0.0225 0.0238 0.0251 0.0266 0.0325 0.0448

5300 M. PAJEK et al. 42

1.5PHOTON ENERGY (keV)

2.0 2.5 3.0 3.5

10'

O& 10'

at~NI + atoN~ M4N~ + at~Ne~

MINq + atqN~ at ~NO

M~oq~ + atgN4

at, o,

1080 100 120 140

CHANNEL NUMBER160 180

FIG. 1. The x-ray spectrum of 79Au for 3.6-MeV He+ ions. The M-shell x-ray lines resolved by the AcTIV program (Ref. 28) arelabeled in the figure.

M p(M4~N67), My(M3N~), M304~+MzN4, Mz04,and M I Oz 3, shown in Fig. 1 for the gold target bombard-ed by 3.6-MeV He+ ions, were converted to the x-rayproduction cross sections, using the target thicknesscorrection procedure described in Ref. 16. Finally, theM-shell x-ray production cross sections were obtained bysumming up the individual x-ray cross sections forresolved M x-ray lines.

The uncertainties of measured M-shell x-ray produc-tion cross sections consist mainly of the uncertainty inthe determination of the Si(Li) detector efficiency (7—3%,see also Ref. 14) and uncertainties in the x-ray andelastic-scattering yields (1—2%%uo). The possible systemati-cal errors due to, for example, not fully resolved M x-raystructure or a nonisotropic M x-ray emission' ' are as-sumed to be 3% and they are combined linearly with thestatistical uncertainties. The overall uncertainties of themeasured M-shell x-ray production cross sections werefound to be nearly constant over the studied range of en-ergies; their average values are listed in Table I.

III. RESULTS AND DISCUSSION

M-shell x-ray production cross sections in Zz =72—79,83, and 90 targets were measured for He+-ion impact inthe energy range 0.8—4.0 MeV with an energy step of 0.2MeV. These experimental cross sections o.~z, correctedfor the x-ray absorption and the projectile energy lass ina finite target thickness (see Ref. 16), are summarized inTable I. Estimated overall experimental uncertainties,

the target thicknesses, and the average' M-shell fluores-cence yields co~ are also quoted in this table.

Our cross sections will be compared with predictions ofthe first-order Born approximation and the ECPSSRtheory' ' for both direct-ionization and electron-captureprocesses. In the first-order Born approximation, directionization is described in the plane-wave Born approxi-mation (PWBA) while electron capture in the OBKNapproximation. ' In the ECPSSR theory, these ap-proaches were further modified to include the higher-order effects: the projectile's energy loss and Coulombdeflection and the perturbed stationary state and relativ-istic nature of the target's M shell. According to thesetheories, for Z, /Zz of our experiments and only singlyionized helium, electron capture has small influence onM-shell ionization cross sections, i.e., its contribution isestimated to be less than 12% in the first-order Born ap-proximation, and less than 5% in the ECPSSR theory.The present data will be also compared with the predic-tion of SCA calculations of Hansteen, Johnsen, and Koc-bach, who evaluate direct ionization in a straight-lineapproximation for the projectile's trajectory.

In Figs. 2 —7, experimental M-shell x-ray productioncross sections are shown for selected elements coveringthe representative targets of our studies (from theZz=72 —90 range), including all elements for which ex-perimental results were reported by other authors. Crosssections of Mehta et al. ' for hafnium agree with ourswithin +20% (see Fig. 2). The data of Gowda andPowers' for iridium and platinum (see Figs. 3 and 4)

42 M-SHELL X-RAY PRODUCTION BY 0.8-4.0-MeV He+. . . 5301

410 t I I I I I I I I I I I I I I I I i f I I f I I I f I I I I ' I I I t '1 I

~ 1 Ii I I f t I I I I I I I; I

'i

' 't I I I I

+He Hf ~e ~

0

He --,Pt.

10

tft jt

f

Mehta et al, (1983)I ~ Present worl

SCAI

First BornECPSSR

l,'

l

l

I l t t I I I I I I I I I l li i I I I I I l i I I I. ! I I ,'. I

1 i

PROJECTILE ENERGY ( Me V)

0I

I/

/ t:owda and Powers {1985)Present work

SCAFirst BorttECPSSR

PROJECTILE ENERGY (M i')

I I I I I I I I t e I l I I I I I I I I I I I I I I t I I t I~t I I I I I I I i I I I

FIG. 2. M-shell x-ray production cross section for hafniumtarget vs He-ion energy. Other data are from Ref. 12. The pre-dictions of the ECPSSR theory (Refs. 18 and 19) ( ), thenfirst-order Born approximation (Refs. 20-22) (———) and theSCA theory ( ———

) of Hansteen, Johnsen, and Kocbach (Ref.23) are shown.

overlap within experimental uncertainties with our crosssections, but at higher energies (above 1.5 MeV) theystart to fall systematically below (by as much as 10%).For gold and bismuth (see Figs. 5 and 6) two groups havemeasured M x-ray production cross sections for He ionsin the energy range of interest. The data of Mehtaet al. ' are systematically 10—20% smaller than ours, al-

FIG. 4. M-shell x-ray production for platinum target vsHe+-ion energy. Other data are from Ref. 13. The curves are

as in Fig. 2.

though less than cross sections of Thornton et al. thatfall above 30—40% below the present measurements.The experimental errors, however, quoted in Ref. 7are —due to relatively thick (100—400 pg/cm ) targets-as high as 60%. Figure 7 shows the present data for tho-rium, our heaviest target for which we have found nodata in the literature.

Present M-shell x-ray production cross sections arecomprehensively compared with the ECPSSR theory in

n1U I I I I I I I I I I I I r f f I I I I I t I I I I I I I I I I t I I I I I I I I I I I I t I I I

1+ I I I I I I I I I !111I I I I I I I I I I I I I I I I I I I I I I I I~ I I I I 1 I I I I

H

10'—10

10 ':/iI

/,'

/'

//

/I

/

Jl

I/I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

1 2 4PROJECTILE ENERGY (MeV)

10 ':

0

Thornton et al (1o74&Mehta et al. (19821Present work

SCAFirst BornECPSSR

I /I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I t I I I I I I I I I I I

1 4PROJECTILE ENERGY (MeV)

FIG. 3. M-shell x-ray production for iridium target vs He+-ion energy. Other data are from Ref. 13. The curves are as in

Fig. 2.

FIG. 5. M-shell x-ray production for gold target vs He+-ion

energy. The other data are from Refs. 7 and 10; the cross sec-tions of Ref. 7 were reported for He + ions. The curves are asin Fig. 2.

5302 M. PAJEK et al. 42

n 41 U 1 1 I I 1 1 I 1 I I 1 I 1 I I I 1 I I I I I I I I I 1 I 1 I 1 I I I I I I I I 1 1 I I 1 1 1 I I

10':

4He „Bi

2.0

PROJECTILE; He

4~ ~

+g~ o

TARGETS:

o HfTRW

o Re+ Os

IrPt

~ AuBt

~ Th

0 2M SHELL

Cl 0CI ~X%aP

+ «jgg%a.+.+~ «

cable e@z~Vuga

10

ly&I

/ 0 Thornton et al. (1974)lQ Mehta et al. (1982)

~ Present work1'

I~ SCAl First Born

ECPSSR

kg

l 1111 I I 111111111I 111111111I 1111111I I I I I I I I I I I

4PROJECTILE ENERGY (MeV)

0.50

SCALED VELOCITY (M

FIG. 8. The cr M~/o. ,„~" ratios for all studied elements in

this work as a function of the average M-shell scaled velocityparameter fir—=2v, /v.„Me„. The symbols that mark diff'erent

elements are shown in the figure.

FIG. 6. M-shell x-ray production for bismuth target vsHe+-ion energy. The other data are from Refs. 7 and 10; the

cross sections of Ref. 7 were reported for He'+ ions. Thecurves are as in Fig. 2.

Fig. g, where the lrM~/cruz ratios are plotted versusscaled velocity (M

——2v, lv2MBM for all studied elements.Here v, and vzz are He-ion and target M-shell electronvelocities and eM denotes the ratio of the observed bind-

ing energy to the screened hydrogenic calculation. TheECPSSR theory underestimates systematically our data(with the exception of Hf, Ta, and W targets) in the low-

velocity region (below /M=1. 2), while at higher veloci-ties an excellent agreement (within the experimental un-certainties) is observed. When these ratios, averaged for

each element over scaled velocities gM ) 1.2, are plottedin Fig. 9 versus Z2 even at higher velocities, the ratios for72Hf, »Ta, and 74W (in contrast to heavier studied ele-

ments) appear to suggest that the ECPSSR theory overes-timates the data. This deviation may be, however, ex-plained in terms of ambiguities in the M-shell Auores-cence yields and Coster-Kronig factors entering in theconversion to theoretical 0.~~ cross sections, as wehave done it in Ref. 16. With such an explanation, gen-eral agreement of the present data (for all elements) withthe ECPSSR theory is indeed seen to be within a few per-cent for relatively high velocities (gM ~ 1.2). The sys-tematical discrepancies (up to a factor of 2) observed be-

n1 I 1 1 I 1 I 1 1 I 1 1 1 1 I I 1 1 I I I 1 1 I 1 I I I I I I I I I I I I I I I I 1 1 I I 1 1 1 1

He („~ 1.2

He „Th

10

liII J L

10

~ Present work

70

M SHELL FLUORESCENCE YIELDS

~ Chen. Craeemann. and Mark 1.9801McGuxre (19741Chen, Crasernann, and Mark to McGusre rat4o

1 I I i I I I & I II

75 80 85 C)0

TARGET ATOMIC NUMBER Z,

l

ll

10

SCAFirst BornECFSSR

1 1 I 1 I 1 I I I I I I 1 I I 1 I I I I 1 I I I I I I I I I I I I I I I 1 1

1 3 5P RO JECTILE ENERGY (Me V)

FIG. 7. M-shell x-ray production for thorium target vsHe+-ion energy. The curves are as in Fig. 2.

FIG. 9. The g Mz/g~~ ratios for all studied elements inthis work taken for each target as an arithmetic average of allratios with gM

~ 1.2 for two sets of the M-shell Coster-Kronigand fluorescence yields, i.e., from Chen, Crasemann, and Mark(Ref. 25) (~) and McGuire (Ref. 26) (U). The ratios of the aver-

age M-shell fluorescence yields QM calculated according toChen, Crasemann, and Mark and McGuire are joined using thesolid line to exhibit trends of these ratios with Z2.

M-SHELL X-RAY PRODUCTION BY 0.8 —4.0-MeV He+. . . 5303

10

PRO JEC

M SHE

production cross sections divided the average fluores-cence yields co~ that are based on the M4 and M5 sub-shell fluorescence yields and Coster-Kronig yields. As inRef. 16, we used values of Chen et al. to calculate B~.Nearly excellent universal character of measured crosssections (with exception of Hf, Ta, and W targets dis-cussed above) is visible in Fig. 10 throughout the wholescaled velocity region. This suggests that the possible im-provement of the theoretical description of studied crosssections at low velocities should probably depend on thescaled velocity g~. Further low-velocity data, however,preferentially for larger projectile charge (Z, ), are stillneeded to affirm this suggestion.

IV. CONCLUSIONS

I,1

1

SCALED VELOCITY

tween the present data and the ECPSSR theory for lowvelocities reflect probably some deficiency of the theoryin description of the binding or Coulomb-deflectioneffects. ' Similar discrepancies were reported in M x-rayproduction in Refs. 10 and 12 for He+ ions and in Ref.30 for Be+ ions; however, still more data are needed tovalidate these findings.

Finally, in Fig. 10, the reduced M-shell ionization crosssections o sr /o oxr, where o Oxr

—= 8na OZ ~ /Z2sr, are2 2 4

plotted —for all elements studied —versus scaled velocitygxr. Here Zz~ denotes the screened target atomic num-ber and ao is the Bohr radius. Experimental ionizationcross sections o.

M were obtained as the measured x-ray

FIG. 10. The universal M-shell ionization cross sectionso~/cr)~, where ooM =—8m.aoZ&/Zz~, for He+ ions and allstudied elements (the symbols used are explained in the figure),plotted vs scaled velocity parameter g~ =2U, /v2~6~. The pre-dictions of the M-shell ionization cross section (for 8~ =0.45)according to the ECPSSR theory (Refs. 18 and 19) ( ), thefirst-order Born approximation (Refs. 20—22) ( ———) and theSCA theory ( . ) of Hansteen, Johnsen, and Kocbach (Ref.23) are shown.

Using the accurately calibrated Si(Li) detector in thelow-energy region, the M-shell x-ray production crosssections, for all elements from hafnium to gold plusbismuth and thorium, were measured with He+ ions of0.8-4.0 MeV. The measured cross sections were com-pared with the predictions of the first-order Born approx-imation, the ECPSSR theory, and the SCA calculation ofHansteen et al. The best theoretical description of thepresent data is given by the ECPSSR theory, despite thesystematical discrepancies (up to factor of 2) observed atthe lowest velocities. The experimental M-shell ioniza-tion cross sections, obtained after the division of the mea-sured x-ray production cross sections by the average M-shell fluorescence yields according to Chen et al. , werefound to be highly universal with respect to the scaled ve-locity parameter g~. Observed systematical discrepan-cies between measured cross sections and the ECPSSRtheory for 72Hf, 7,Ta, and 74W as a function of Z2 mayoriginate from deficiency of the existing M-shell atomicrates ' near Z2 =74.

ACKNOWLEDGMENTS

We are indebted to the EG-5 Van de Graaff acceleratorstaff for their kind collaboration during the measure-ments. One of the authors (M.P.) wishes to acknowledgethe support provided by the Centralny Program BadanPodstawowich 01.09.

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