Charge fraction of 6.0 MeV/n heavy ions with a carbon foil: Dependence on the foil thickness and projectile atomic number

$Page 1: Charge fraction of 6.0 MeV/n heavy ions with a carbon foil: Dependence on the foil thickness and projectile atomic number$
Charge fraction of 6.0 MeV/n heavy ions with a carbonfoil: Dependence on the foil thickness and projectile

atomic number

Y. Sato a,*, A. Kitagawa a, M. Muramatsu a, T. Murakami a, S. Yamada a,C. Kobayashi b, Y. Kageyama b, T. Miyoshi b, H. Ogawa b, H. Nakabushi b,

T. Fujimoto b, T. Miyata b, Y. Sano b

a National Institute of Radiological Sciences, Accelerator Physics and Engineering Division NIRS, 4-9-1 Anagawa-4-chome,

Inage-ku, Chiba-shi 263-8555, Japanb Accelerator Engineering Corporation (AEC), 2-13-1 Konakadai, 263-0043 Chiba-Inage, Japan

Received 18 September 2002; received in revised form 5 December 2002

Abstract

We measured the charge fraction of 6.0 MeV/n heavy ions (C, Ne, Si, Ar, Fe and Cu) with a carbon foil at the NIRS-

HIMAC injector. At this energy they are stripped with a carbon foil before being injected into two synchrotron rings

with a maximum energy of 800 MeV/n. In order to find the foil thickness ðDEÞ at which an equilibrium charge state

distribution occurs, and to study the dependence of the DE-values on the projectile atomic number, we measured the exit

charge fractions for foil thicknesses of between 10 and 350 lg/cm2. The results showed that the DE-values are 21.5, 62.0,

162, 346, 121, 143 lg/cm2 for C, Ne, Si, Ar, Fe, Cu, respectively. The fraction of Ar18þ ions was actually improved to

33% at 320 lg/cm2 from �15% at 100 lg/cm2. For Fe and Cu ions, the DE-values were found to be only 121 and 143 lg/cm2; there is a large gap between Ar and Fe, which is related to the differences in the ratio of the binding energy of the

K-shell electrons to an electron energy (3.26 keV) corresponding to the velocity of a 6.0 MeV/n projectile. The well-

known ‘‘two disjoint Gaussians (shell effect)’’ was also observed in the measured charge fractions of both Fe and Cu.

The results of the charge fractions were also compared with other data and to calculations of Rozet et al. [2], in which

there was a good agreement for light ions (C); however, a significant difference was observed for ion species heavier than

Ne.

� 2003 Elsevier Science B.V. All rights reserved.

1. Introduction

At the NIRS-HIMAC injector [1], we measuredthe charge fraction of heavy ions after passing

though a carbon foil at an energy of 6.0 MeV/n,

which corresponds to a velocity of 15.1 atomic

units. In this energy region, few data concerningthe charge fraction have yet been reported, par-

ticularly for ions heavier than Ne; data are neces-

sary not only to design and operate accelerators,

but also to improve model calculations for heavy-

ion beam interactions in solids. Accelerators

*Corresponding author. Fax: +81-043-251-1840.

E-mail address: [email protected] (Y. Sato).

0168-583X/03/$ - see front matter � 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0168-583X(02)02225-5

Nuclear Instruments and Methods in Physics Research B 201 (2003) 571–580

www.elsevier.com/locate/nimb

mail to: [email protected]

usually require the highest charge states (which

occur at the equilibrium charge state distribution)

with the thinnest foils, which minimize the energy

loss, and multiple scattering and energy straggling.The results were also compared with those obtained

at other facilities and calculated results using a

computer program (ETACHA), which was devel-

oped by Rozet et al. [2], based on data using the

10–80 MeV/n heavy ions at GANIL; this calcula-

tion is applicable to ions lighter than Ar. The

lifetime of the foils has been long (the order of

year) since the beginning of the HIMAC opera-tion, because the energy loss within the foil is very

small in the 6.0 MeV/n region.

Beams of 8 keV/n heavy ions are produced at

three ion sources before being accelerated up to

6.0 MeV/n by both the RFQ (8–800 keV/n) and

Alvarez (0.8–6.0 MeV/n) linacs. Regarding the

high energy of heavy ions, fully stripped ions are

desirable for synchrotrons, except for a part ofatomic physics experiments; for example, the

measurement of convoy electrons ejected from

foils through an electron-loss process of relativistic

H-like or He-like ions. Information concerning the

fraction of fully stripped ions is thus particularly

important. When designing the HIMAC 10 years

ago, or earlier, there were few data and little in-

formation concerning the stripping efficiency atsuch a high-energy region. Nevertheless, a rough

estimation was made to start the HIMAC opera-

tion, based on few data and calculations. Conse-

quently, a thickness of around 100 lg/cm2 was

found to be appropriate for light ions, such as

carbon and neon; hence, this fixed thickness has so

far been used for other ion species without any

optimization regarding the efficiency. Precise in-formation on both the exit charge fraction and its

dependence on the foil thickness has still been

important, particularly for ion species heavier than

Ne, though systematic measurements have not yet

been performed, except for light ions or at low

energies. The primary motivation in this work was

to experimentally obtain such information; an

additional motivation was to compare the ob-tained results to advanced calculations [2,3]. In

addition, the HIMAC injector can produce vari-

ous ion species having the same velocity, thus al-

lowing us to study the relation between the foil

thickness at the equilibrium charge state distribu-

tion and the projectile atomic number.

Along recent progress in research projects using

various ion species at HIMAC, another interesthas been focused on the quantitative charge state

distribution and its impact on the maximum in-

tensity, particularly for ions heavier than Fe; in

such cases, the fraction of fully stripped ions is

very small in the stripping process with foils at the

6.0 MeV/n region, and are generally not useful. It

is thus necessary to find the highest charge state

and the thinnest foil.The apparatus uses the existing beam line be-

tween the carbon stripper just downstream of the

Alvarez linac and the experimental cave with

6.0 MeV/n heavy ions. The main modification was

to develop an automatic sweeping system for all

magnets and the debuncher (DBC) in this beam

line, according to the different charge states. In the

summer of 2001, the apparatus began to worksuccessfully. The expected data for several ion

species have been obtained for a thickness range of

between 10 and 350 lg/cm2 with some new results,

which are presented and discussed in this article.

For example, an increase in the thickness from 100

to 320 lg/cm2 allowed us to improve the yield of

Ar18þ ions by a factor of 2 with no reduction in

their transmission efficiency or in the injection ef-ficiency into the synchrotron.

2. Apparatus and methods

2.1. Layout of the apparatus

Fig. 1 shows a schematic layout of the appa-

ratus. The carbon stripper foil (CSF) is attached to

a frame of 20 mm diameter, and is set just down-

stream of the Alvarez linac, where the beam spot

size is around 5 mm diameter. The momentumresolution of this beam line is 1=20; 000 at maxi-

mum, which allows us to clearly separate the iso-

topes of Xe and to adjust the linac beam energy

precisely to 6.0 MeV/n for injection into the syn-

chrotron. The beams after passing through CSF

generally have several fractions with different

charge-to-mass ðq=mÞ ratios. They are analyzed by20� pulsed switching and 70� DC analyzing mag-

572 Y. Sato et al. / Nucl. Instr. and Meth. in Phys. Res. B 201 (2003) 571–580

nets before being measured at a Faraday cup (FC-

2) regarding their peak intensity (current). Sweep-

ing of the magnetic field (B) is controlled by a Hall

detector in the 70� analyzing magnet, thus cover-

ing the various q=m values. The other elements in

the beam-transport line between CSF and FC-2,

such as the Q-magnets and steering magnets, are

also swept in the same way. Since the maximumq=m value is limited to 1/4 in this beam line, the

low-charge-state ions after stripping cannot be

measured; for example, Ar1þ–Ar9þ ions cannot be

measured for the case of Ar. However, such ions

generally have very small fractions at 6.0 MeV/n,

which are negligible at the equilibrium thickness

and are of little interest in this work.

There is a horizontal slit just upstream of FC-2,of which the width is usually set at 10 mm to

separate the adjoining charge states. Since the

beam size is of the order of a few mm, the beam

current of each charge state, when sweeping the

beam across FC-2, was measured to be a trapezoid

shape, and its flat peak value is proportional to the

product of each charge fraction and the charge

state. The charge fraction can thus be obtainedfrom both the charge state and the ratio of each

peak to the total of all peak values. Fig. 2 shows an

example of the measured charge state distribution.

A capacitive pickup-type non-destructive beam

monitor (CTN) [4], also shown in Fig. 1, monitors

the beam intensity upstream of the Alvarez linac,

and is used to normalize the measured value at

FC-2. The fluctuation of the beam current is duemainly to that of the ion sources, which is nor-

mally on the order of �10%, and cannot be easily

reduced. The amplitude of signals from this CTN

is proportional to the peak beam intensity, be-

tween 5 and 1000 elA, while the actually used

beam intensity (50–500 elA in this work) was

within the limits. The width of the pulsed beam in

the HIMAC injector is 350 ls and its repetition

rate is 1–2 Hz. Since the response time of this CTNis faster than 1 ls, the precision in normalization

with this CTN should be satisfactory regarding

both the dynamic range and the response time.

The fluctuation in the transmission efficiency of

the Alvarez linac depends on neither the ion spe-

cies nor their intensity; it is normally constant at

92%, as long as the intensity is less than 500 elA.The use of CTN allows us to measure the chargefraction within an adequate accuracy.

2.2. Transmission efficiency (g) of beams in theapparatus

The transmission efficiency ðgÞ between FC-1

and FC-2 was measured in order to know the

beam loss in this beam line. Although this effi-ciency is independent of the charge fraction, it has

been an important parameter to study the beam

quality when using CSFs with different thicknesses

Fig. 1. Layout of the apparatus.

Fig. 2. Measured charge distribution for Ar with a carbon foil

(351 lg/cm2). The signal from the non-destructive current

monitor is also indicated, which represents the fluctuation in the

beam intensity.

Y. Sato et al. / Nucl. Instr. and Meth. in Phys. Res. B 201 (2003) 571–580 573

for various ion species. g was measured to be 90%

without CSF, and 85–88% with CSF, depending

on both the ion species and the thickness. The

beam loss ðDgÞ due to CSF can thus be evaluatedto be 2–5%, which is due mainly to an emittance

growth or an increase in the momentum spread

when using CSF. This Dg does not fluctuate

among fractions for one ion species using a par-

ticular thickness under an almost constant beam

intensity. Although the emittance value of the

beams from three ion sources varies widely, it is

always defined as being 150 pmm�mrad at theRFQ; this value is quite smaller than the accep-

tance of the Alvarez linac. The emittance of the

beams should thus be nearly constant at FC-1;

hereafter, a value of 90% ðgÞ should be applicable

to every ion species.

2.3. Measurement of the thickness of carbon strip-

per foils

Table 1 summarizes the thickness of the CSFs

used in this work. These CSF frames are attached

to a remote-controlled rotating device, with which

every thickness can be quickly selected. The

thickness of CSF measured by the maker was

compared to the measured value. Our method is to

measure the difference in the magnetic field (B)values of the 70� analyzing magnet between with

and without CSFs when tuning the N6þ beam on

the center of the multi-wire type profile monitor

just upstream of FC-2. B-values are precisely

measured by using a Hall detector, which is set

inside the analyzing magnet. Since the effective

curvature ðqÞ of the beam path through this

magnet is constant, we can know the difference inthe Bq-values ðDBq=BqÞ between with and withoutCSFs.

Since the Bq-value is proportional to the mo-

mentum of the beams (P ), we can finally know the

difference in the momentum of the beam DP=P .This difference is converted once into that of en-

ergy loss (2DP=P ¼ DE=E, E ¼ 6:0 MeV/n), and

then translated into thickness by using the stop-ping power table [5]. The precision of the profile

monitor is 0.1 mm, which corresponds to a reso-

lution in energy loss of 0.6 keV/n ðDE=E ¼1=10; 000Þ and in thickness of 2.9 lg/cm2. The

maker (Israel and Arizona) evaluated the thickness

by measuring the absorption of visible light for

foils thinner than �20 lg/cm2, or the weight for

thicker than �50 lg/cm2. The difference in thethickness between the two methods was �13 �þ19% for all used CSFs. Our method was carried

out under exactly the same condition in this work,

thus including some change in thickness, which

may have been produced in the processes of both

attachment to a frame and exposure to the actual

beams in the vacuum condition. The values mea-

sured by our method seem to be more reliable andare used for discussions in this work.

Here, we consider the energy reduction ratio

ðDE=EÞ between before and after CSFs, that is the

ratio of the energy loss of incident beams within

the foil to 6.0 MeV/n. The energy loss of a 6.0

MeV nitrogen ion within the foil was evaluated to

be 72 keV/n per 350 lg/cm2, which means an en-

ergy reduction ratio ðDE=EÞ of 1.2%; the energy is6.0 MeV/n before entering the CSFs, while it de-

creases to 5.93 MeV/n after passing through a CSF

with a thickness of 350 lg/cm2. The DE=E-valuesare roughly proportional to z2eff=m, where zeff is theeffective charge and m is the mass number. The

values of DE=E per 350 lg/cm2 are thus calculated

to be on the order of 1.0–3.5% for C–Cu ions,

where the zeff -values for C and Cu were estimatedto be 6.0 and 25.5, respectively. The effects pro-

duced by such energy reduction are included in our

data, though they are not significantly large to

discuss the charge state distributions of various ion

Table 1

Thickness of carbon foils used in this work (lg/cm2)

Catalog value Measured by the

maker

Measured in this

work

10 8.9 11

20 22.6 20

30 30.9 28

40 42.9 39

50 53.2 52

100 – 89

100 98.1 115

150 – 166

200 192 206

250 – 255

300 317 329

300 322 351


species having the same velocity. A similar esti-

mation was made in our previous work on electron

emission from foils [6].

At present, the overall error in the measurementof the charge fraction is dominated by the reading

error in determining each fraction at FC-2, which

is better than 1% in the maximum fraction values

observed for each ion species.

3. Results and discussion

3.1. Charge state distributions

Figs. 3–8 show the charge fraction versus

thickness of the CSFs for various beams (C, Ne,

Si, Ar, Fe and Cu) at 6.0 MeV/n. The calculations

of Rozet et al. [2] are also directly shown by the

solid lines. Table 2 summarizes the relation be-

tween the ion species and their charge fractions inthe equilibrium charge state distributions. As can

be seen from Fig. 3 (C) and Table 2, the fractions

of C6þ and C5þ reach an equilibrium state at a

thickness larger than �20 lg/cm2, and are 97.86%

and 2.10%, which agree well with both Shima�sdata of 97.67% and 2.33% at 5.983 MeV/n [7], and

the calculated values of 98.10% and 1.90% at 6.0

MeV/n.

Fig. 3. Charge fraction versus thickness of the carbon foils for

the impact of 6.0 MeV/n C2þ ions. The solid lines are from the

calculations of Rozet et al.


the impact of 6.0 MeV/n Ne4þ ions. The solid lines are from the



the impact of 6.0 MeV/n Si5þ ions. The solid lines are from the



For Ne–Ar ð106 z6 18Þ, however, the mea-

sured equilibrium charge state fractions of fullystripped ions were significantly smaller than those

of the calculated values in brackets: 83.50%

(86.80%) for Ne, 61.26% (70.31%) for Si and

35.15% (52.26%) for Ar. The differences between

our measurements and the calculations of Rozet

et al. [2] become large as the atomic number (z) ofincident ions increases. The fractions, except for

those of fully stripped ions, are also consistentwith these results. For Ar, Baudinet-Robinet�sanalysis [8] and Baron�s data [9] are quite differentfrom our data and the calculations of Rozet et al.

Concerning the mean charge ðhqiÞ of Ar, Baudi-net-Robinet and Baron showed that it is 16.71–

16.74, though our result (17.12) is smaller than the

calculations of Rozet et al. (17.40) by only 0.28.

Taking account of the good precision (<1%) in ourexperiment, the value of 17.12 should be the most

reliable for Ar. Generally speaking, for C–Ar the

calculations of Rozet et al. [2] are not very far from

our data, and his model calculation seems basically

correct, though the precision in the cross-sections

is somewhat unsatisfactory. Actually, his calcula-

tion was in good agreement with the data of 13.6

MeV/n Ar ions accelerated at GANIL; the prob-lem seems to be only in the precision of the cross-

sections.


the impact of 6.0 MeV/n Ar8þ ions. The solid lines are from the



the impact of 6.0 MeV/n Fe9þ ions. The solid lines are from the



the impact of 6.0 MeV/n Cu10þ ions. The solid lines are the



For Fe and Cu, the calculations of Rozet et al.[2] did not agree with our results regarding the

equilibrium charge fractions. For example, the

maximum charge fraction is 47.23% for Fe24þ in

the calculation, while it is 37.53% for Fe23þ in our

data; the charge state distribution is considerably

shifted to a higher charge state in the calculation.

hqi of our data is 23.09, while the calculated value

is 23.94; there is a big difference. A similar ten-dency can also be seen for the case of Cu. The

present calculation of Rozet et al. [2] cannot be

used for such heavy atoms.

3.2. DE-values at which the equilibrium charge state

distributions occur

The DE-values were derived by fitting a simpleexponential form of Fq ¼ Aq � Bq expð�t=tqÞ,where tq is the 1=e point of the curve, Aq equals the

equilibrium charge fraction of charge q, and Bq is

the fitting constant [10]. The equilibrium thicknessvalues, DE, are defined as the thickness t at whichFq equals 95% of its equilibrium value: Fq ¼0:95Aq. The obtained results of several fractions

show a similar value; for example for C, they were

calculated to be 21.5 and 21.4 lg/cm2 for 6þ and

5þ, respectively. In this case the average of these

two values was determined as the DE-value (21.5

lg/cm2). A similar technique was applied for otherion species. The finally determined DE-values are

listed in Table 2.

Fig. 9 shows the relation between the DE-values

and the atomic number, z, in which the obtained

DE-values from our data are 21.5, 62.0, 162, 346,

121 and 143 lg/cm2 for C, Ne, Si, Ar, Fe and Cu,

respectively, while those from the calculations of

Rozet et al. [2] are 26.1, 72.8, 212, 470, 147 and 147lg/cm2. A comparison between our data and the

calculation shows two clear tendencies: the DE-

values are smaller than those obtained in the

Table 2

Relation between the ion species (C, Ne, Si, Ar, Fe, Cu) and their charge fractions in the equilibrium charge state distributions

Ion species Charge fractions (%) hqi DE

C 4þ 5þ 6þThis work 0.04 2.10 97.86 5.98 21.5� 0.1

Rozet 0 1.90 98.10 5.98 26.1� 0.1

Shima 0 2.33 97.67 5.98

Ne 8þ 9þ 10þThis work 0.95 15.55 83.50 9.83 62.0� 0.3

Rozet 0.58 12.62 86.80 9.86 72.8� 1.4

Si 11þ 12þ 13þ 14þThis work 0 4.97 33.77 61.26 13.56 162� 1

Rozet 0 3.45 26.24 70.31 13.66 212� 15

Ar 13þ 14þ 15þ 16þ 17þ 18þThis work 0 0 1.55 19.27 44.03 35.15 17.12 346� 19

Rozet 0 0 0.51 11.12 36.11 52.26 17.40 470� 40

Baudinet-Robinet

model

0 1 9 26 46 18 16.71

Baron 0 0.81 6.99 29.94 42.08 20.18 16.74 75

Fe 19þ 20þ 21þ 22þ 23þ 24þ 25þ 26þThis work 0 0.78 5.36 20.76 37.53 29.15 5.66 0.76 23.09 121� 2

Rozet 0.69 5.35 24.35 47.23 20.13 2.25 23.94 147� 18

Cu 22þ 23þ 24þ 25þ 26þ 27þ 28þ 29þThis work 0.48 3.00 13.20 31.81 35.41 15.26 0.84 0 25.48 143� 9

Rozet 0.47 8.86 32.15 50.05 8.47 26.58 147� 10

The values listed above are the results from this work, other data and the calculated results by Rozet at 6.0 MeV/n, and Shima�s data at5.983 MeV/n. The mean charge ðhqiÞ and the DE-values (lg/cm2), at which the equilibrium charge state distributions occur, are also

listed.


calculation for C–Ar, though the tendency of the

curve is not very different; there is not a significant

difference for Fe and Cu. In the case of C, there is

a small, but meaningful, difference between 21.5

and 26.1 lg/cm2. Judging from both such a sig-

nificant difference and a good agreement in the

equilibrium charge state distribution, one can tell

that the ratio of cross-sections between the elec-tron loss (ionization and excitation) and capture

used in the calculation seems to be basically cor-

rect; however, their absolute values are slightly

small, thus requiring many interaction events

(large thickness) to reach equilibrium. This ten-

dency is somewhat true for Ne–Ar.

As can also be seen in Fig. 9, the DE-values

increase monotonically from 21.5 to 346 lg/cm2

with increasing the atomic number z from z ¼ 6

(C) to z ¼ 18 (Ar), while it rapidly decreases down

to 121 and 152 lg/cm2 for Fe ðz ¼ 26Þ and Cu

ðz ¼ 29Þ. In the former case ðz6 18Þ, an equilib-

rium (charge state) condition is obtained when all

electrons, including those in the K-shell, are bal-

anced regarding loss and capture; it is possible to

efficiently remove all of these electrons, due totheir small binding energies. In the latter, however,

there is little possibility to remove the K-shell

electrons due to their large binding energies. In

this case, the equilibrium condition should be de-

termined primarily by the behavior (loss/capture)

of the L- and outer-shell electrons. Since their in-teraction cross-sections are much larger than those

of the K-shell electrons in the 6.0 MeV/n region,

charge state equilibrium is obtained at a small

thickness. In the rest frame of the projectile, the

speed of a 6.0 MeV/n projectile corresponds to an

electron energy of 3.26 keV. The binding energies

of K-shell electrons are of 4.3 keV for Ar, 9.0 keV

for Fe and 11.2 keV for Cu, respectively [11]. Forthe case of Fe and Cu, the energy of 3.26 keV is

too small to effectively remove the K-shell elec-

trons. For Ar, it is comparable to 4.3 keV; there is

a significant possibility to remove the K-shell

electrons of the Ar atom by the impact of target

electrons, resulting in a 35.15% fraction of Ar18þ.

The large gap between Ar and Fe in Fig. 9

suggests that the binding energy plays an impor-tant role in the process of electron loss and cap-

ture. The binding energy of the 2s1 electron in the

L-shell of the Cu atom is 2.523 keV, which is close

to that (2.569 keV) of the 1s1 electron in the K-

shell of the Si atom [11]. Meanwhile, the DE-values

of Si and Cu are 143 and 162 lg/cm2; there is a

reasonable consistency in the relation between the

binding energy and the DE-values. Additional in-terest is focused on the information for K–Mn

ð196 z6 25Þ, though very few data have so far

been reported, as far as we know. We will try to

obtain them, though this depends strongly on the

capability of the ion sources used to produce me-

tallic ions. Fig. 10 shows the equilibrium charge

state distributions for Fe and Cu, in which the

well-known ‘‘two disjoint Gaussians’’ (shell effect)can be seen for both Fe and Cu [12–15]. The

measured charge fractions of Fe are 5.66 at q ¼ 25

and 0.76 at q ¼ 26, while those on the Gaussian

(left-side solid curve) are 9.96 and 1.49. For Cu,

the fractions are 0.84 at q ¼ 28 and 0.00 at q ¼ 29,

while those on the Gaussian (right-side) are 3.07

and 0.25, respectively. The measured charge frac-

tions of the K-shell electrons are thus significantlysmaller than those on the Gaussians obtained for

the L-shell.

As can seen in Figs. 7 and 8 (Fe and Cu), the

maximum charge fractions were found to be

Fig. 9. Projectile atomic number z versus equilibrium thickness

at 6.0 MeV/n. � indicates our data point and � the calculationsof Rozet et al.


37.53% and 35.41% for 23þ and 26þ (Li-likeions), at which the DE-values were 121 and 143 lg/cm2, respectively. According to these results, Fe23þ

ions are usually used for injection into the syn-

chrotron regarding the maximum intensity. Some

experiments require as large a momentum as pos-

sible, for which Fe24þ (He-like) ions are also used,

because their fraction is not small (29.15%). In the

HIMAC accelerator system, there is only onecharge exchange stripper at 6.0 MeV/n between the

Alvarez linac and the synchrotron rings. The mo-

mentum of the synchrotron beam is proportional

to q=m, thus depending on the charge state ðqÞafter CFS. From this point of view, Cu27þ ions are

also usable, of which the fraction is 15.26%.

4. Summary

We measured the charge fraction of heavy ions

after stripping with carbon foils at a projectile

energy of 6.0 MeV/n. The measured equilibrium

fractions of fully stripped ions for Ne–Ar

ð106 z6 18Þ were significantly smaller than those

of the calculations of Rozet et al. [2]. Althoughthese differences become large as the atomic

number ðzÞ of the incident ions increases, the cal-culations of Rozet are not very far from our data,

and his model calculation seems to be basically

correct. The precision in the cross-sections, how-

ever, is somewhat unsatisfactory at a projectile

energy of 6.0 MeV/n, except for C.

For C–Ar ð66 z6 18Þ, the thickness of theequilibrium charge state increased monotonically

from 21.5 to 346 lg/cm2 with increasing atomic

number, z, while it rapidly decreased to 121 and

143 lg/cm2 for Fe and Cu (z ¼ 26 and 29). In the

latter two cases, the equilibrium condition should

be determined by the behavior of the L- and outer-

shell electrons (shell effect); there is little possibility

to remove the K-shell electrons due to their largebinding energies (9 and 11 keV), compared to the

relative energy of the target electrons (3.26 keV) in

the rest frame of the projectile.

Acknowledgements

The authors would like to thank Prof. K. Shima(Tsukuba University), Dr. F. Soga (NIRS) and the

staff in the Division of Accelerator Physics and

Engineering (NIRS) for fruitful discussions on

atomic physics. This work was part of the research

project with heavy ions at NIRS-HIMAC.

References

[1] Y. Sato, T. Honma, T. Murakami, A. Kitagawa, M.

Muramatsu, S. Yamada, H. Ogawa, T. Fukushima, C.

Kobayashi, Proc. 20th Int. Conf. on Linac, Monterey in

CA, 2000, 654.

[2] J.P. Rozet, C. Stephan, D. Vernhet, Nucl. Instr. and Meth.

B 107 (1996) 67.

[3] J.P. Rozet, A. Chetiou, P. Piquemal, D. Vernhet, K.

Wohrer, C. Stephan, L. Tassan-Got, J. Phys. B: At. Mol.

Opt. Phys. 22 (1989) 33.

[4] T. Katoh, T. Murakami, S. Yamada, J. Yoshizawa, C.

Kobayashi, Y. Honda, S. Hara, in: Proc. 11th Symp. on

Accel. Sci. and Technology, Harima in Japan, 1997, p. 249.

[5] J.F. Ziegler, Hand Book of Stopping Cross-Sections for

Energetic Ions in All Elements, NY 10598, 1980, p. 93.

Fig. 10. Equilibrium charge state distributions for Fe and Cu.

Symbols of � and � indicate the fractions of L-shell electrons,

and � and j K-shell electrons for Fe and Cu, respectively. Two

disjoint Gaussians can be seen between the L-shell and K-shell

electrons for both Fe and Cu. The measured fractions of Fe are

5.66 at q ¼ 25 and 0.76 at q ¼ 26, while those on the Gaussian

(solid curves) are 9.96 and 1.49. For Cu, the fractions are 0.84

at q ¼ 28 and 0.00 at q ¼ 29, while those on the Gaussian are

3.07 and 0.25, respectively.


[6] Y. Sato, A. Higashi, D. Ohsawa, Y. Fujita, Y. Hashimoto,

S. Muto, Phys. Rev. A 61 (2000) 052901.

[7] K. Shima, N. Kuno, M. Yamanouchi, Phys. Rev. A 40

(1989) 3557.

[8] Y. Baudinet-Robinet, Phys. Rev. A 26 (1982) 62.

[9] E. Baron, IEEE Trans. Nucl. Sci. NS-19 (1972) 256.

[10] S.K. Allison, Rev. Mod. Phys. 30 (1958) 1137.

[11] T.A. Carlson, C.W. Nestor, J.N. Wasserman, J.D. McDo-

well, Atomic Data 2 (1970) 63.

[12] K. Shima, T. Mukoyama, T. Mizogawa, Y. Kanai, T.

Kambara, Y. Awaya, Nucl. Instr. and Meth. B 53 (1991)

404.

[13] H.O. Funsten, B.L. Barraclough, D.J. McComas, Nucl.

Instr. and Meth. B 80–81 (1993) 49.

[14] L. H€aagg, O. Goscinski, J. Phys. B: At. Mol. Opt. Phys. 26

(1993) 2345.

[15] L. H€aagg, O. Goscinski, J. Phys. B: At. Mol. Opt. Phys. 27

(1994) 81.


Documents

Charge fraction of 6.0 MeV/n heavy ions with a carbon foil: Dependence on the foil thickness and projectile atomic number