Equilibrium charge distributions of lithium ions emerging from acarbon foil

A. Itoh a,*, H. Tsuchida b, T. Majima a, A. Yogo a, A. Ogawa b

a Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japanb Department of Physics, Nara Women's University, Nara 630-8506, Japan

Received 11 March 1999; received in revised form 8 June 1999

Abstract

Equilibrium charge distributions of lithium ions passing through a carbon foil have been measured in the energy

range 1±6 MeV. Average equilibrium charges �q are found to connect smoothly with previous high energy data above

6 MeV. It was found that the present results of both charge fractions and �q can be well reproduced by the empirical

calculations based on the independent electron model. We also found that available semiempirical formulae for �qcannot reproduce the present experimental data at all. A new semiempirical formula is presented for Li ions in the

energy range 0.8±30 MeV. Ó 1999 Elsevier Science B.V. All rights reserved.

PACS: 34.yKeywords: Ion±solid interaction; Equilibrium charge fraction; Lithium; Carbon foil

1. Introduction

When fast charged particles pass through con-densed matter, the ions may undergo repeatedelectron capture and loss collisions with targetatoms, and consequently, an equilibration of thecharge state distribution is attained for the movingions [1]. Information about such equilibriumcharge distributions is important for studies ofatomic collision physics and for its application tovarious ®elds of ion beam technologies. To date,

numerous experimental studies have been done fora variety of combinations between projectile ionsand target materials in a wide range of projectileenergy E. The experimental data are accumulatedin several review articles [2±6]. For lithium ions,Allison et al. [7] and Nikolaev et al. [8] made ex-periments using gaseous targets at E� 2±475 keVand 0.58±5 MeV, respectively. Pivovar et al. [9±12]made experiments quite extensively using varioustargets of vapors and foils in the energy rangebelow 150 keV. On the other hand, only a fewexperimental work have been performed for fastlithium ions in solid targets. Teplova et al. [13]made experiments for celluloid ®lms at E� 0.58±5MeV and Blair [14] for nickel foils at E� 2.9±3.8

Nuclear Instruments and Methods in Physics Research B 159 (1999) 22±27

www.elsevier.nl/locate/nimb

* Corresponding author. Tel.: +81-75-753-5828; fax: +81-

75-753-5845; e-mail: itoh@nucleng.kyoto-u.ac.jp

0168-583X/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 5 1 6 - 9

MeV. To our best knowledge, systematic mea-surements for carbon foils have been performedonly by Stocker and Berkowitz [15] using 5.8±16.4MeV 6Li ions. Since the data of charge fractionsfor a carbon foil are often used as standard dataamong solid targets, it is required to supplementdata in the MeV energy range.

In this work, we performed measurements ofequilibrium charge distributions for 7Li ionsemerging from a carbon foil in the energy rangefrom 1 to 6 MeV. The average charges obtainedare compared with calculated values using variousempirical and semiempirical formulae proposedpreviously. In Section 2 we describe brie¯y thepresent experimental method, results are discussedin Section 3 and concluding remarks are given inSection 4.

2. Experimental method

Experimental procedure for the measurementsof charge fractions is essentially the same as em-ployed by many previous researchers (see for in-stance [3]), and only a brief outline is given here.Lithium ions were produced from a 1.7 MeVtandem accelerator of Nara-Women's University.The incident energy was varied between 1 and6 MeV. A well-focussed beam was carefully colli-mated with two pin-hole slits (0.3 mm in diameter)separated by 2.3 m from each other. By usinganother hole slit (1.5 mm in diameter) located 110cm downstream from the second pin-hole slit,undesirable edge-scattered particles were removed.A carbon foil target was set at 30 cm downstreamfrom the hole slit. To select only such outgoingprojectiles that emerged into narrow forward di-rections, the beam was again passed through ahole slit (1.5 mm in diameter) located 62 cmdownstream from the target. The outgoing parti-cles were charge-separated with a magnet and de-tected by a position-sensitive-detector PSD(ORTEC P055-084-500). The incident beam ¯uxwas carefully adjusted so as to limit the PSDcount-rate to less than 300 cps.

Fig. 1 shows an example of the PSD positionspectrum obtained for 1.5 MeV Li ions emergingfrom a carbon foil of thickness 5.2 lg=cm

2. A total

number of particles Nq with a charge state q wasobtained by integrating the corresponding peakarea. Charge fractions Fq and an average charge �qof the outgoing particles were then obtained by,Fq � Nq=

P3q�0 Nq, and, �q �P qFq. Equilibration

of charge fractions was con®rmed by repeatingmeasurements using di�erent incident chargestates (1±3+) and di�erent carbon foils of thickness5.2, 13 and 20 lg=cm

2. For various combinations

between ions and foils investigated here, measuredvalues of Fq coincided fairly well with one another.Energy spectra of the detected ions were routinelymonitored by the PSD to ensure that no edge-scattering took place. Also, a noticeable peak shiftdue to projectile energy loss inside the target foilwas not observed. This was con®rmed by com-paring the energy spectra measured with andwithout a foil. Actually, the energy loss in a carbonfoil estimated with the TRIM code [16] was only1.6±3.1 keV/ lg cmÿ2 in the present energy range,giving rise to at most 60 keV for the thickest foil(20 lg=cm

2) at 2 MeV. Thus, the e�ect of energy

loss can be neglected in the present work. Experi-mental errors were estimated from the statistics ofcounts and the reproducibility of the repeatedmeasurements. Estimated maximum errors areabout a few percent for all fractions larger than

Fig. 1. PSD-position spectrum obtained for 1.5 MeV Li ions

emerging from a carbon foil (5.2 lg=cm2).

A. Itoh et al. / Nucl. Instr. and Meth. in Phys. Res. B 159 (1999) 22±27 23

3� 10ÿ3, and 20±30% for neutral fractions smallerthan 3� 10ÿ3.

3. Results and discussion

Equilibrium charge fractions of Li ions emerg-ing from a carbon foil are presented as a functionof the projectile energy in Fig. 2, where the chargefractions denoted by F0, F1, F2 and F3 are neutral,singly-, doubly- and triply-ionized components,respectively. The high energy data measured for6Li ions by Stocker and Berkowitz [15] are trans-formed to a 7Li energy scale as shown in the ®gure.Note that they measured fractions of only F2 andF3. Also shown are the data for a celluloid ®lm ofthickness 10±20 lg=cm

2[13] and F0 for a carbon

foil in low energy region [9±12]. The present valuesseem to have a good connection with the highenergy data [15], implying evidently a good con-nection also for the average charges �q since thefractions are dominated by F3 and F2 in this energy

range. Experimental data obtained for a celluloid®lm are also found to agree fairly well with ourvalues. The present fractions F0 and F1 decreaserather monotonically with increasing projectileenergy. In the energy range 1±6 MeV investigatedhere, the overall expressions for these fractions asa function of E (in MeV) were obtained as follows:

F0 � �1:2� 0:06� � 10ÿ2Eÿ�3:7�0:04�;

F1 � �0:33� 0:005�Eÿ�2:6�0:02� �1�A semiempirical method of calculation of

equilibrium charge fractions was suggested byDmitriev [17] for fast ions. He assumed that theprobability for removal of an electron in a pro-jectile is solely determined by the velocity ratiobetween the projectile and the electron considered.Using the experimental data for hydrogen projec-tiles as the universal function of the removalprobability, he obtained charge fractions for var-ious light ions. On the basis of this independentelectron model (IEM), systematic calculationswere made by Zaidins in a wide range of ion ve-locity for 2 < Z6 10, and the results are presentedgraphically in [18]. His calculations for Li ions(E� 0±8 MeV) are shown by ZMY in Fig. 2. Dueto large uncertainties in reading the data from agraph given in [18], we depict here only the frac-tions larger than 2%. As a whole, one can see aremarkably good agreement between his resultsand the present data. In particular, peak maximaand peak positions of Fq seem to be well predictedby his calculations. Note that for small fractions(Fq < 0:1) the theoretical values exhibit a commontendency of rather rapid decrease compared to theexperimental values.

Average charges �q obtained from the abovefractions are shown in Fig. 3 together with otherexperimental data including gaseous targets[8,13,15]. The data for a nickel foil obtained byBlair [14] are not shown here because they areunreliable as stated by the author. As already seenabove, the present data are in fairly good agree-ment with higher energy data [15] and with thosefor a celluloid ®lm [13]. In comparison with gas-eous targets of He, N2, Ar and Kr [8], one can seeclearly that the average charges for solid targetsare higher than those for gases, while the Ar target

Fig. 2. Equilibrium charge fractions Fq as a function of 7Li

projectile energy. Data for 6Li ions [13,15] are energy-scaled.

IEM calculations by Zaidins [18] are denoted by ZMY.

24 A. Itoh et al. / Nucl. Instr. and Meth. in Phys. Res. B 159 (1999) 22±27

gives almost equivalent values of �q to a carbon foil.The higher �q for solid targets is consistent with ageneral trend recognized in atomic collision ®elds,and this gas±solid di�erence is usually attributedto the di�erence of the density e�ects in solids andgases [3]. It should, however, be pointed out thatthe �q for a given ion and a given energy exhibits ingeneral a Z2 oscillation when plotted as a functionof target atomic number Z2 [19,20]. A careful in-vestigation of the data in Fig. 3 also shows thisoscillatory behavior for lithium ions.

Until now various semiempirical formulae for �qhave been derived to obtain the most reliableuniversal expression as functions of projectileatomic number Z, its velocity v and Z2, as sum-marized in previous articles [3,21]. Here, we use thefollowing three representative formulae, whichmay be applicable in the present energy range. Itshould be noted that all these formulae were de-rived from the available experimental data, andthus, the range of validity of these formula islimited as shown below. Using the reduced velocityX de®ned by

X � 3:86Zÿ0:45����������E=M

p; �2�

for ions with energy E (MeV) and mass M (amu),the �q in carbon foils is expressed in the followingway:

ND : �q=Z � �1� Xÿ5=3�ÿ3=5;

for 0:3 < �q=Z < 0:7; Z P 16;

E > 0:5 MeV=amu;

TD : �q=Z � 1ÿ exp�ÿX �;for 0:26X 6 1:6; 56 Z6 18; �3�

SIM : �q=Z � 1ÿ exp�ÿ1:25X � 0:32X 2 ÿ 0:11X 3�;for X < 2:4; Z > 8:

Abbreviated letters ND, TD and SIM corres-pond to Refs. [22±25], respectively. In Fig. 4 arecompared the experimental results with these for-mulae. Obviously, any of these formulae cannotreproduce the experimental values in the wholerange of incident energy depicted. It should beemphasized that these formulae may be applicableonly for relatively high Z projectiles (Z > 5). Thus,large discrepancies observed indicate that thequantity �q=Z should contain Z- dependent termsexplicitly. This indication will be discussed again inmore detail below.

Fig. 4. Equilibrium average charge �q in comparison with var-

ious emirical and semiempirical calculations [16,18,22±25] (see

text). Also shown are the calculated results by Eq. (6) obtained

in the present work.

Fig. 3. Equilibrium average charge �q in comparison with other

experimental data obtained for solid [13,15] and gaseous targets

[8].

A. Itoh et al. / Nucl. Instr. and Meth. in Phys. Res. B 159 (1999) 22±27 25

In this ®gure, the experimental data are alsocompared with e�ective charges Zeff calculatedwith the TRIM code [16] which is widely used inion±solid collision experiments. The e�ectivecharge Zeff for lithium ions were obtained by theratio of stopping cross sections Se between lithiumand hydrogen ions at the same velocity;Z2

eff � Se�Li�=Se�H�. The results are denoted byTRIM in the ®gure. Compared to other semiem-pirical formulae the TRIM data are in much betteragreement with the experimental values. However,one can see somewhat large deviations at allincident energies outside 2 MeV region. Weshould, however, bear in mind that the e�ectivecharge used in the TRIM code is essentially adi�erent quantity from the equilibrium averagecharge �q. This is because the projectile electronsalso take part in the energy loss (stopping)processes via ionization and excitation of targetelectrons, and consequently the Zeff as de®ned inthe above formula would be higher than �q. Thisso-called antiscreening e�ect is well discussed inRef. [26].

On the other hand, the IEM calculation byZaidins, denoted by ZMY, is found to give per-fectly equivalent �q to the experimental values. This®nding is rather surprising, because in this IEMmodel, the probability for the loss of a givenprojectile electron is dependent only on the ve-locity ratio between the projectile and the orbitalelectron, and any physical quantity related to thetarget atom is not taken into consideration [17].Further investigations will be necessary to make asystematic evaluation of this model.

In order to obtain a semiempirical formula of�q for Li ions applicable in the MeV energy range,the experimental data of ours and Ref. [15] areplotted in Fig. 5 as a function of the reducedvelocity X, where the ordinate represents 1ÿ �q=Zin order to emphasize the variation in high veloc-ity region. One can see clearly that thelog�1ÿ �q=Z� is not a linear function of X, insteadit contains higher order terms as in the SIM for-mula. The best ®t to the data over the entirevelocity range is

�q=Z � 1ÿ exp�0:706ÿ 1:98X � 0:0883X 2�for 0:8 < X < 5: �4�

The ®tting formula seems to be applicable in awide range of incident energy ranging from 0.8 to30 MeV as can be seen in ®gure. This ®t is alsoshown in Fig. 4.

In Fig. 5 we depict also the experimental datafor light ions of He [27], Be and B [21] andcalculations by the SIM formula. There exists ob-viously a systematic deviation depending on Z.Namely, the ordinate increases with increasing Z.The data for B ions coincide faily well with theSIM formula, which is successfully applicablefor heavy projectiles of Z P 8, implying thatthe data for heavy ions of Z P 5 can be approxi-mated by this SIM formula. This deviationseems to be largest in the X range investigatedhere. This is due to the fact that the �q=Z mustapproach 0 at low velocity limit, while at highvelocities �X > 4� the �q=Z shows no longer Z de-pendence since the charge fractions are dominatedby fully stripped ions FZ and hydrogen-like ionsFZÿ1 as discussed in [21]. Thus, the systematic de-viation observed for low Z ions postulates a re-quirement of explicit Z-dependent terms inaddition to the parameter of X in the formula of�q=Z.

Fig. 5. The reduced velocity dependence of average charges of

low Z ions of He, Li, Be and B [15,21,27]. Calculations with the

SIM formula [25] are depicted for X < 2:4.

26 A. Itoh et al. / Nucl. Instr. and Meth. in Phys. Res. B 159 (1999) 22±27

4. Conclusions

Experimental results are reported for the ®rsttime for equilibrium charge fractions and for av-erage charges of 1±6 MeV lithium ions emergingfrom a carbon foil target. The present results are infairly good agreement with empirical calculationsby Zaidins [18]. On the other hand, availablesemiempirical formulae derived mostly for heavyions cannot reproduce the present results. The ef-fective charges obtained by the TRIM code arerather larger than the experimental �q, and this maybe due to the antiscreening e�ect arising from theprojectile electrons. The gas±solid di�erence due tothe density e�ect is observed in the present energyregion. Comparisons of �q for light ions (Z6 5)suggest strongly that the Z-dependent term shouldbe included explicitly to construct a more universal�q formula in the energy range 0.8±30 MeV.

Acknowledgements

The authors gratefully acknowledge Dr. N.Sakamoto and J. Karimata at the accelerator fa-cility of Nara Women's University and Dr. N.Imanishi for their valuable discussion.

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