Equilibrium charge state distributions of fast Si and Cl ions in carbon and gold foils

Nuclear Instruments and Methods 204 (1982) 235-243 North-Holland Publishing Company

EQUILIBRIUM GOLD FOILS

CHARGE

STATE DISTRIBUTIONS

235

O F F A S T Si A N D CI I O N S I N C A R B O N

AND

Toyoyuki ISHIHARA, Kunihiro SHIMA, Takashige KIMURA, Satoshi ISHII, Tsuneo MOMOI, Hidenori YAMAGUCHI, Keiji UMETANI, Masao MORIYAMA, Mikio YAMANOUCHI and Takashi MIKUMO Tandem Accelerator Center, University of Tsukuba, lbaraki 305, Japan Received 30 March 1982

Equilibrium charge state distributions have been measured for 30-1 l0 MeV Si ions in carbon and gold foils and 25-142 MeV C1 ions in carbon foils. Obtained values of mean charge states have been well reproduced by the empirical formula by Shima et al. in both ion energy dependence and foil Z 2 dependence. Asymmetric charge state distributions are in fairly good agreement with the prediction of the chi-squared model by Baudinet-Robinet.

1. Introduction During the last decade, several experimental data have been reported concerning the distribution of charge states and the mean charge states of energetic heavy ions after the passage through foils. This is due, on the one hand, to the recent progress of heavy ion accelerator and detection techniques, and on the other hand, to the necessity of the application of ions of high charge state beams for injection into the post-accelerator. The data before 1973 are accumulated by Wittkower and Betz [1]. Following this review, data of charge state distributions of heavy ions with atomic number Z~, after the passage through foils (target atomic number Z2) have been reported: 72-123 MeV P ions by Deschepper et al. [2], 69-142 MeV S ions by Scharfer et al. [3], 3-20 MeV Ar ions by Knystautus et al. [4], N, O, Ne, S, Ar, Kr ions with various energies by Clark et al. [5], 373, 444 and 552 MeV Kr ions by Baron and Delaunay [6], and 40-120 MeV C1 and 120, 150 MeV Cu ions by Shima et al. [7]. Less data are reported for ions after the passage of foils other than carbon, Z 2 = 6. Several empirical formulae are proposed in order to reproduce the values of mean charge states, such as those of Nikolaev and Dmitriev [8], of To and Drouin [9,10], and the universal formula of Shima et al. [11]. In this paper are reported the fractions of equilibrium charge states, F(q), as well as the mean charge states, i/, of 28.7-108 MeV Si ions and 24.1-141.1 MeV C1 ions after passage through carbon foils. For 39.6-109 MeV Si ions, the F(q) data behind the gold foils have also been taken. Observed data of mean charge states are compared with existing empirical formulae. As for 0167-5087/82/0000-0000/$02.75

© 1982 North-Holland

the charge state distribution, the calculated prediction due to the application of the chi-squared distribution by Baudinet-Robinet [12] is tested.

2. Experimental procedure Si and Cl ion beams were produced by means of a sputter ion source and 12UD Pelletron accelerator at the University of Tsukuba. A well focused ion beam of 20-50 nA in intensity and less than 2 mm in diameter was introduced into a scattering chamber, at the center of which up to seven carbon or gold foils of different thicknesses were set. The foil thickness was determined using the elastic scattering of heavy ions and the energy loss of 241Ama-particles. Thicknesses measured by these two methods agreed within 10%. Fig. 1 shows the schematic setup of the experimental arrangement. Different charge states of a beam after passage through a foil were analyzed using a magnetic spectrograph, Enge split-pole spectrograph (ESP-90), and each current was measured by Faraday cup placed on the focal plane of the spectrograph. A potential of --300 V relative to the Faraday cup prevented the secondary electrons from escaping from the cup. The ion current was measured by a pico-ammeter and was integrated by a current integrator. On the other hand, a surface barrier semiconductor detector (SSD) was placed in the scattering chamber, and the determination of charge state fractions F(q) for each charge state q was done through normalization of the integrated beam current by the number of scattered ions detected by the SSD.

T. lshihara et al. / Equilibrium charge state distributions

236

Magnetic Spectrograph

dure was necessary to confirm that the data were taken at the foil thickness where the projectile charge states are already equilibrated. In figs. 2a, b and c, the dependence of F(q) on foil thickness is shown for 45, 65, 95 M e V S i + C , 31, 60, 94.5, 121 MeV C I + C , and 65, 90 MeV S i + A u collisions, respectively. For the present purpose, it is sufficient to confirm that the charge equilibrium of 31 MeV CI ions is attained after the passage through a 2 0 / ~ g / c m 2 thick c a r b o n foil, whereas f o r 121 MeV CI ions, the equilibrium is attained only after the passage through 100 / z g / c m 2 thick carbon. Considering the results of fig. 2, the foil thicknesses were properly selected so that the ions attain equilibrium but the a m o u n t of energy loss becomes small. F r o m the fractions F(q) of each charge state q, the m e a n charge state, E/, and the width of the distribution, d, have been deduced according to the following formulae,

ESP -90

C~rbon FoiL

SSD

Be o . m

Current

~

nteg ro.tor

~"~.~

-300V ~

Fcxrctdcty CuD

Fig. 1. Schematic experimental'arrangement.

q=~qF(q),

In advance of measuring the equilibrium charge states, the distribution d a t a as a function of foil thickness were taken for several ion energies. Such a proce-

(a) ~

I001

Si----C 45MeV Si 6+ -

(l)

q

3. R e s u l t s

~

:.

;.

11

95 MeV Si 9+ 13

31MeV CI5÷

1

z o

lO 13

Cl~C

(b)

65MeV Si 7÷ 12

10 -

The values of E/ a n d d together with F(q) are listed in

60 MeV CI 7 .

10

94 5MeV Cl 8+ ,_.,_14.

121MeV C110+ 15

11

11

14

'LtJ

w

~

q}

:.

~ 9.

io

-----L •

~o.1

i

60

17

14 H ,

120

,

i

i

,

,

60 120 180 CARBON THICKNESS (jug/crnZ)

i

J

120

180

~

i

Ol

0

i

,

40

i

,

80

40 80 40 80 CARBON THICKNESS (pg/cm 2)

40

L

80

,

L

120

,

h

,

160

Si--.-Au

(c) ~oo

65MeV Si7+

90 MeV SiO÷

11

12 11

12 9~

Z

2 I0 <

.~

13 ;

ud

g,

8

14

g 0.1 0

t

I00

i

,

~

i

t

200 300 0 100 GOLD THICKNESS (pgkm 2)

i

i

200

300

Fig. 2. Distribution of charge state fractions IF(q) in %] of ions after passage through foils of various thicknesses. (a) Si ions on C foils, (b) C1 ions on C foils and (c) Si ions on Au foils.

30 35 40 45

50 55 60 65

70 75 80 85 90 95

100 105 110

7+ 8+ 6+ 7+

7÷ 7+ 8~ 8+ 9÷ 9+

9+ 10 + 10 +

Incident energy (MeV)

5* 5+ 5+ 6+

Incident charge state

28.7 33.7 38.8 43.8 43.4 43.1 48.2 53.3 58.3 64.4 64.0 63.5 63.4 63.1 62.4 68.4 73.5 78.5 83.5 88.6 93.8 93.6 92.9 97.9 103.0 108.1

Exit energy (MeV) 68 68 68 68 98 108 108 108 108 37 68 98 108 127 167 108 108 108 108 108 98 108 167 167 167 167

Foil thickness ( p , g / c m2) 9.98 10.3 10.7 11.0 11.0 11.0 11.2 11.5 11.7 11.8 11.8 11.8 11.9 11.8 11.8 12.0 12.2 12.3 12.4 12.5 12.7 12.7 12.7 12.7 12.9 13.0

q

1.12 1.11 1.08 1.05 1.05 1.06 1.02 0.99 0.97 0.97 0.97 0.95 0.95 0.95 0.96 0.93 0.92 0.90 0.90 0.87 0.87 0.86 0.86 0.86 0.85 0.82

d

1.42 0.54 0.16 0.05 0.01 0.07

F7 +

0.02

0.02

8.72 4.38 2.25 1.07 1.09 1.15 0.49 0.22 0.08

F8 * 25.8 17.1 11.8 7.30 7.27 7.50 4.52 2.84 1.51 1.20 1.00 0.99 0.94 1.00 1.07 0.49 0.26 0.12 0.04

F9 *

C h a r g e state fraction F ( q ) (%)

34.6 31.9 27.8 22.9 22.9 22.8 17.5 12.9 9.39 8.48 7.61 7.19 7.07 6.88 7.40 4.68 3.34 2.34 1.71 1.13 0.83 0.75 0.79 0.54

FI o' 22.1 30.9 35.0 35.2 35.6 35.4 34.5 31.0 28.2 27.2 24.5 23.8 23.1 24.8 24.4 20.6 16.8 13.5 11.3 8.76 7.77 7.21 6.88 6.32 4.27 3.60

Ft I +

Mean charge state q, width of charge state distribution d, and charge state fraction F ( q ) of Si ions after passage t h r o u g h C foils.

Table 1

7.05 14.3 20.7 28.8 28.5 28.4 35.2 41.1 42.7 43.2 43.4 45.2 45.0 44.2 44.7 44.5 43.1 41.3 38.9 38.5 31.0 31.7 32.5 30.2 26.0 2a,.8

FI 2 + 0.27 0.96 2.26 4.49 4.36 4.43 7.35 10.9 16.2 16.8 20.7 19.9 20.9 20.2 19.8 25.2 30.1 34.1 36.9 38.2 43.4 43.7 43.3 43.5 45.4 43.9

FI 3*

0.08 0.22 0.21 0.21 0.50 1.02 1.96 3.06 2,85 2.97 2.97 2.92 2.65 4.45 6.41 8.66 11.1 13.4 17.1 16.6 16.5 19.4 24.4 28.7

FI 4 +

..-.A

E

..-...

25 31

40 50 60

65 70 75 80 90 94.5

100 105 110 115 121

120 125 132 143

6+ 7+ 7*

6 ~ 8 + 7+ 7+ 8+ 8~

9+ 9+ 9+ 10 + 10 ~

11 + 11 + 11 + 11 + 12 ~

Incident energy (MeV)

5 ~ 5*

Incident charge state

24.1 30.5 30.1 29.3 37.9 48.0 59.5 59.2 58.5 58.1 57.9 62.4 68.2 72.6 78.3 87.7 94.1 93.8 93.2 92.9 92.7 97.8 103.2 107.9 112.9 120.6 120.4 119.9 119.5 119.4 119.1 118.1 123.0 130.0 141.1

Exit energy (MeV)

37 22 37 68 88 88 22 37 68 88 98 121 88 121 88 121 22 37 68 88 98 121 98 121 121 22 37 68 88 98 111 173 121 121 12l

Foil thickness (,tt g / c m 2 ) 10.2 10.7 10.7 10.7 11.5 12.1 12.6 12.6 12.6 12.6 12.6 13.1 13.3 13.4 13.6 14.0 13.8 14.0 14.2 14.2 14.3 14.4 14.6 14.7 14.8 14.2 14.6 14.8 14.9 15.0 14.9 14.9 15.0 15.2 15.3

1.17 1.15 1.16 1.14 1.15 t.15 1.11 1.15 1.17 1.16 1.17 1.11 1.13 1.12 1.11 1.05 1.00 1.03 1.05 1.05 1.05 1.05 1.01 1.00 0.98 0.93 0.94 0.98 0.97 0.97 0.97 0.98 0.97 0.95 0.96

d

0.72

FT+ 6.34 2.19 2.43 2.79 0.45

t"~, 21.2 10.8 12.0 9.23 3.82 1.02 0.26 0.24 0.26 0.28 0.28

F9 +

0.02

34.1 26.5 28.0 29.4 14.7 6.25 2.82 2.74 2.77 2.89 2.86 1.24 0.69 0.40 0.23

Fro+

C h a r g e state f r a c t i o n F ( q ) (%)

0.11

24.8 34.2 32.9 33.4 30.9 20.5 13.1 12.5 12.8 12.5 12.8 7.88 5.11 3.92 2.26 0.94 1.10 0.90 0.68 0.56 0.57 0.35 0.19 0.13

Fil + l 1,2 20.3 18.9 19.8 32.2 34.2 29.8 29.1 28.2 29.0 28.7 22.1 18.0 15.1 12.3 6.45 7.67 5.93 5,29 4.69 4.5l 3.60 2.26 1.78 1.22 2.93 1.59 1.19 0.94 0.70 1.13 0.90 0.63 0.37 0.38

I-'12. 1.74 5.42 5.18 4.89 14.7 26.9 34.2 33.0 32.4 32.6 32.5 33.6 32.8 31.4 28.2 21.9 26.2 21.7 18.0 17.6 17.5 15.1 11.9 10.2 8.10 17.6 11.1 8.61 7.13 6.00 6.08 6.29 5.39 3.97 3.54

Fl~,

M e a n c h a r g e state (7/, w i d t h of c h a r g e state d i s t r i b u t i o n d, a n d c h a r g e state f r a c t i o n F ( q ) of C1 ions a f t e r p a s s a g e t h r o u g h C foils.

Table 2

0.58 0.56 0.47 3.07 9.52 16.4 17.8 18.3 17.9 17.8 27.9 29.2 31.2 34.3 35.0 39.0 36.7 35.4 34.3 34.1 30,9 29.8 29.1 25.1 38.5 32.0 28.1 24.7 24.3 23.9 22.7 21.5 17.7 14.5

FI4,

0.23 1.67 3.21 4.45 5.06 4.96 4.82 6.96 13.0 16.3 19.6 29.2 23.2 29.2 32.4 33.7 34.2 37.6 40.3 40.8 43.2 34.6 41.7 40.3 42.9 42.9 44.5 42.5 42.1 41.7 38.8

FI 5 ,

0.10 0.18 0.22 0.20 0.19 0.29 1.09 1.63 2.61 5.81 2.67 5.21 7.67 8.47 8.43 11.5 13.9 15.9 19.5 6.06 12.5 19.2 20.9 22.5 20.2 23.3 25.2 29.6 34.2

Fie÷

0.03 0.02 0,12 0.38 0. t l 0.35 0.57 0.72 0.74 1.07 1.60 2.06 2.90 0.30 1.20 2.56 3.52 4.50 4.01 4.36 5.14 6.70 8.64

Fw ,

2-

F:

t~

50 65

90

100 110

7+ 7+

8+

10 +

9+

40

Incident energy (MeV)

5+

Incident charge state

39.6 39.2 49.2 64.7 64.6 64.3 64.1 63.7 89.7 89.6 89.3 89.1 88.7 99.2 109.2

Exit energy (MeV) 76 148 148 55 76 148 185 266 55 76 148 185 266 185 185

Foil thickness ( # g / c m 2) 9.89 9.86 10.3 10.8 10.8 10.8 10.8 10.8 11.4 11.4 11.4 11.4 11.4 11.6 11.8

1.06 1.06 1.03 0.97 1.00 0.99 1.00 1.00 0.89 0.92 0.92 0.93 0.92 0.89 0.88

d

F(q) of

0.13 0.04 0.03

1.16 1.16 0.42

F7 . 8.33 8.29 2.97 0.9| 1.06 1.03 1.00 1.12 0.10 0.18 0.12 0.08 0.08 0.02

F~+ 26.7 26.9 17.1 7.29 8.60 8.41 8.25 8.90 1.45 2.03 1.99 2.08 2.03 1.05 0.58

F9+ 36.6 36.9 36.2 27.1 27.4 27.6 26.5 27.8 14.0 13.8 13.4 13.7 13.5 9.00 6.30

Flo, 21.6 21.5 31.3 40.0 37.5 39.4 38.8 38.2 38.1 36.4 36.4 36.2 36.2 31.1 27.7

Fi1,

Si ions after passage through Au foils.

Charge state fraction F ( q ) (%)

Mean charge state ~, width of charge state distribution d, and charge state fraction

Table 3

5.39 5.42 11.4 22.4 23.0 21.1 22.9 21.7 38.3 38.9 38.9 38.6 38.9 43.9 46.7

Fi2+

0.19 0.17 0.66 2.33 2.45 2.32 2.43 2.19 7.64 8.19 8.61 8.82 8.72 12.9 17.1

F13+

0.07 0.10 0.07 0.06 0.42 0.48 0.54 0.54 0.53 1.01 1.64

FI4+

e~ .,-....

,00

T. lshihara et al. / Equilibrium charge state distributions

240 ~IOO

1 7

z 8

i 9

10

L.I~L. II 12 I[3

'

i 15 t

14 ~.~.[.

o

~ ~o < -r ij

g

1o

I ,'[

\/\

>,,.! :

,f",,I",,I F;,X'~ ~ '\ t

""[ b

N OJ

\

i

1o

?, !73o r

t\tlt

=:z r4; [J ' / ~ 2 L . " , [ . d ~:

o

0.01

(a)

3,o,

EI~

)%

:/ 6

~t~

*1 [

~V Y

16~ 1;

l

N.L t" [

f

o4

;

p,o,,, ,,,pT,Tvl-t _: _1 m

PI, oo p, ,? p,o),oo,

2.3 2.4 25 2.6 27 28 2.9 3.0 31 3.2 33

N

0011

,

,.

,J

,

h

,I

, ,,

,,

,

i,

,,.,

)Ol 24 2.5 2.6 2.7 2~ 2.9 3.0 3~ 3,2 3,a

,~,,~]

1.6 1.8 2.0 2.2 24 26 2.8 303-2 3.6 3.6 (b)

EV,

(e)

EV~

Fig. 3. Charge state fractions at equilibrium of ions of energy E after passage through foils. (a) Si ions on C foils, (b) CI ions on C foils and (c) Si ions on Au foils. In fig. 3b, experimental data by Almqvist et al. [15] are also shown with triangle marks. Solid lines are drawn only to guide the eye.

tables 1, 2 and 3, for the systems of Si + C, Cl + C and Si + Au, respectively. Since incident ions lose part of their kinetic energy during the penetration through a foil while the charge state fractions vary first and attain equilibrium, the charge state fractions observed behind the foil should be classified according to the projectile exit energy from the foil. Thus, the values of exit energy after correction for the energy loss [13,14] are also described in the tables. The reproducibility of the data a m o n g different runs was good and the errors in F ( q ) are estimated to be less than 3% for F ( q ) > 0 . 1 and less than 10% for F ( q ) < 0 . 1 . For systems of Si + C, C1 + C and Si + Au, the variations of F ( q ) in equilibrium are plotted in figs. 3a, b and c, respectively, as a function of exit energy E in MeV units or E I/4 according to the representation by Almqvist et al. [15]. The triangle marks in fig. 3b show the data of Almqvist et al. [15] with which the present data are seen to be smoothly linked up.

4. Mean charge state Fig. 4 shows the observed q values relative to Z mof Si and C1 ions plotted versus the "reduced velocity" which was defined by Nikolaev and Dmitriev (N D) [8] as X -- f)/( ~)tZ°45 ), where v is the ion velocity and ~' - 3.6 x 10 ~ c m / s . In the figure, ~ t / Z 1 data of P, S, C1 and Kr ions reported by other authors are also shown. In Pl0tting others' data, the data by Clark et al. [5] have been eliminated because, as was pointed out by Scharfer et al. [3], the 8 0 / L g / c m 2 thickness of the carbon foils used by Clark et al. may not be sufficient for the attainment of equilibrium at higher ion energies. The dashed line in the figure shows the empirical

formula by N - D for carbon foils expressed by

,~/z,(z~-6)=(1 The

N-D

+x

formula

,/o.~) o.~

(3),

which

(3)

reproduced

the

lower

energy data ( X < 1.5) for Z 2 - - 6 fairly well, underestimates the observed values at X > 1.5. This is because the N D formula was originally deduced from the data of Z~ >~ 17, Z z - - 6 and X < 1 ; I n s p i t e of this fact, all the

1.0

,

.

.

.

.

,

.

.

.

.

,

•

•

•

,

-Eq ( 5 ) ( S - l - M ) ----- Eq.(4)(T-D) Io-

0.9

....

'

•

-

i

,

. , ~

~.~*~ - J

E q ( 3 ) (N-D)

. , ~ / ~

LLI (D rr

÷ ./

.-

_J---

/~ Z~>tj~

//

I ~ m~ 0.7

,, //

:::3~ O LIJ 0"6

÷Si~C 1 • CI ~ C / This work , Si~Au J

~:~

Deschepper (1979) ~S~C ° S ~ A u )JScharter(1977)

J ILl

0.5

X Kr~C ~ S~C o CI~C

0.4

.... 0.5

1.0

1.5

Baron (1975) Hvelplund (1972) Almqvist (1962) , . . . . . . 2.0 2-5

R E D U C E D V E L O C I T Y X = v / v ' z P ~5

Fig. 4. Relative equilibrium mean charge O/Zi of various ions of atomic number Z~ vs. reduced velocity X. Dashed, dot dashed and solid lines are those calculated using the formulae of Nikolaev and Dmitriev (N-D), To and Drouin (T-D) and Shima, Ishihara and Mikumo (S-I-M), respectively.

T. Ishihara et al. / Equilibrium charge state distributions

b r e a k d o w n of the relation, F(q + l ) / F ( q ) cc q- ~<,,~t seen beyond q = 11 (fig. 5a) a n d q = 14 (fig. 5b) indicates that the observed distributions deviate from the G a u s s i a n shape, which reflects the difference of electron loss and capture processes as a whole in between K shell a n d L shell. A n o t h e r illustration for this shell effect is s h o w n in figs. 6a, b and c, where the ratio F(q + 1 ) / F ( q ) is plotted as a function of projectile exit energy for systems of Si + C, CI + C and Si + Au, respectively. Solid lines in the figure indicate the tentative fitting of the following straight lines,

experimental data for c a r b o n foils are seen to cluster a r o u n d a single curve even in the higher velocity region of up to X = 2.5 when the data are plotted as a function of N D reduced velocity X. The To a n d Drouin formula ( T - D ) [9,10] which is applicable to Z 2 = 6 foils a n d is defined as

Et/Z. (Z2 = 6) =

-- exp( -- X ) ,

(4)

is also drawn with a d o t - d a s h e d line, which also deviates at high energies, although by a less amount, from the experiment. Shima, Ishihara and M i k u m o ( S - I - M ) [11] proposed a "universal empirical f o r m u l a " of El/Z t versus X;

El/Z, = q / Z , ( Z 2 = 6) [1 + g ( z 2 ) ],

ln[F(q+

--exp(--1.25X+0.32X

2 - 0 . 1 1 X 3),

g ( z 2) = - 0 . 0 0 1 9 ( Z 2 - 6) ~ / X + 0 . 0 0 0 0 1 ( Z 2 - 6)2X, which has the characteristics that the formula contains the Z 2 d e p e n d e n t term. The solid lines for c a r b o n and gold foils exhibit the formula (5) which is denoted by S - I - M . The agreement with experimental results is excellent in the reduced velocity d e p e n d e n c e as well as the Z 2 dependence of Z 2 = 6 and 79 foils.

5. Charge state distribution In figs. 5a and b, the ratio of charge state fractions

F(q + 1)/F(q) is plotted as a function of charge state q systems

Si + C

and

CI + C,

respectively.

100

The

100

5i-C •,

C[-C

¶ \

10

10

g LL

I.L ¸

7 u_

108.1MeV

LL

97.8 88.6 78.5 68.4 58.3

0.1

141.1MeV 1129 0.1

97.8 87.7 78.3 68.2

/-.,82 388 58.1

28.7MeV

0.01

6

l

~

,

,

~

7

8

9

10

11

i12

CHARGE STATE [i

i

,

13

14

(6)

where E is the projectile energy, a~, fl, and ~'i are constants which are d e p e n d e n t on the collision system, a n d i differs according to the groups q + 1/> Z I - 1 and q + 1 < Zj - 1. Clearly, the slope a, differs between two different groups, whereas within the same group, the data are roughly a p p r o x i m a t e d with F ( q + l ) / F ( q ) o : E % W i t h i n the limited data taken at present, fraction ratios are crudely expressed by eq. (6) whose ordinate intersections differ by 3'~ per every step of Aq = 1, which suggests that the distribution of charge states which are relavant to L shell electrons (q + 1 < Z~ - 1) is of Gaussian shape, although the centroid of the G a u s s i a n distrib u t i o n varies according to the projectile energy. In fig. 7, the widths of the distribution obtained for Si + C and C1 + C systems (listed in tables 1 a n d 2) are s h o w n as a function of reduced velocity X. We followed the choice of ordinate ( d / Z °'4) to the scale by B a u d i n e t - R o b i n e t [12] who analyzed the existing data of Z 1 + C systems for X > 1 and Z l/> 7, a n d found the

and

for

1)/F(q)] =e~ilnE--(fli--,hq),

(5)

where

EI/Z,(Z 2=6)=

241

0.01

,

,

,

,

L

,

,

,

8

9

10

11

12

13

14

15

,

16 17

CHARGE STATE q

Fig. 5. Ratio of charge state fractions F(q + l)/F(q) vs. charge state q of Si and CI ions for (a) Si+C and (b) C I + C collisions.

7C lshihara et al. / Equilibrium charge state distributions

242 lOO

100

Si-C 8t7

918

lO19 n11o

~

1C

10C

C[-C 9/8 10/9 11110 12/11

12111

~" 10 LL

t,L. 13/12

÷ LI-

%" h

14/13

1

Si-Au 9/8

~3/12

10/9

14113

~LL

11110

15/14

~la.

12111

16/15

1

1 13112

17/16

"/

/

0-1

~/.

,

/

0.1

¢

/ //"

/

~ 10

2~o

, ION

i ....

~ ....

50

J

100

ENERGY

0.01

200

I

10

20

(MeV)

, ION

, 5~o . . . . . . . . .

~

100

ENERGY

200

0.01

10

2

'

0

(MeV)

ION

14113

/

/

Lo . . . . . . 100 ....

5

ENERGY

200

(MeY)

Fig. 6. Ratio of charge state fractions F(q + 1)/F(q) vs. ion energy for collision systems (a) Si ions on C foils, (b) Cl ions on (2" foils and (c) Si ions on Au foils.

empirical relation expressed by

d / Z °4 = 0.426 - 0.0571X.

(7)

Eq. (7) is drawn with a solid line in the figure. The figure indicates that the width becomes narrow at higher energies due to the absence of charge states q > Z~. C o n t r a r y to the linear decrease of the width with the increase of projectile energy for X > 1.3, the width shows the feature of almost a plateau for the region X < 1.3,

0.45

i

i

* Si ~ C ]This work •

C~C

0.40

which was not expected from eq. (7). The values of m e a n charge states in this energy region being less than 10.3 for Si ions and less than 12.6 for CI ions (see tables 1 and 2), the appearance of the plateau indicates that the widths become little affected by the K shell effect which provides the sudden decrease of charge state fraction at q ~> Z~ 1, and that the distribution a r o u n d the most p r o b a b l e charge state is d o m i n a t e d by those charges in which electrons are statistically distributed within the L shell. Recently, B a u d i n e t - R o b i n e t [12] applied the chisquared distribution for the fitting of asymmetric charge state distribution of heavy ions on carbon foils which is given by F(q)

= t ~/2

I exp(_t/2)/[2~

2i,(~/2)],

(8)

+

~

Or

•

*

0

•

+1

035

~.

÷

÷÷

0.30 --

0.25

•

4

d/z10

i"

10

.

,

÷

=0.426-0

,

,

i

.

,

,

~

1.5 2.0 X =v I v ' z 0a5

.

.

.

.

i

2.5

Fig. 7. Width of equilibrium charge state distribution, d, of Si and CI ions after passage through C foils• The ordinate and the abscissa are expressed by d / Z °4 and reduced velocity X, respectively. The solid line is the empirical relation given by Baudinet-Robinet [ 12].

where b o t h t and ~ are functions of mean charge state a n d standard deviation. Several F ( q ) data obtained in the present Si + C a n d C1 + C systems are shown in figs. 8a a n d b as well as the prediction by eq. (8) (solid lines). F o r that evaluation, the given formulae of eq. (4) and (6) in ref. 12 have respectively been used for the mean charge state and the standard deviation. The satisfactory agreement between observed values and prediction indicates that the "chi-squared model" is very promising in estimating the heavy ion charge state distribution especially of the asymmetric portions of high charge states.

6. Conclusion

Charge state distributions are measured using Si and CI ion beams after passage through carbon foils. In

243

T. lshihara et a L / Equilibrium charge state distributions

Si-C 28.7 MeV

Z

108 MeV

I-U

IJJ

< LL m lC

10

(_'3 rr < '-r U ~E

D

n.. m

/

r~ .<

141.1 MeV

/

\

\

1 era EXP.

o ILl

29.3 MeV

z o p.-

0

rr LL

CI-C

o I00

°'~0 100

-0.1 6

i

7

Eq(8) I

8

"-3

/

CHI-SQUARED / I~

9

0

1

Ill

I

12

elmEXP. D1 Eq.(8) CHI-SQUARE -

W 13

14

0.1 8

-

9

CHARGE STATE q

, 10

,/, 11

12

, 13

,I

I

I

1

14

15

16

17

CHARGE STATE q

Fig. 8. Equilibrium charge state fraction F(q) vs. charge state q of (a) Si ions behind C foils and (b) CI ions behind C foils. Circle and square points are experimental values and curves are those calculated from the chi-squared distribution function given by Baudinet-Robinet.

order to verify the Z 2 dependence, gold foils are also used for Si ions. Since the data of 15P a n d ~6S ions have been reported [2,3] at energies c o m p a r a b l e to the present energy region, the addition of the present data of ]4Si and ~7C1 ions contributes significantly to the total i n t e r p r e t a t i o n of charge state distributions. In fact the values of m e a n charge state of these data have proved to deviate systematically from the well-known Nikolaev a n d Dmitriev formula in the high velocity region. On the other hand, empirical formula (5) giving the m e a n charge states of ions has reproduced all these data, not only in the wide range of ion energies but also in the foil Z 2 dependence. As for the charge state distribution, the present data agree fairly well with the prediction of the chiosquared model. Since the knowledge of the charge state distribution is of more practical signifiance in view of applications, the data presented in this work would be useful in deducing a more reliable universal function of the charge state distribution, because the accuracy of the prediction of the chi-squared model is attributed to the a b u n d a n c e of precise data for the o b t a i n m e n t of reliable functions of m e a n charge states a n d s t a n d a r d deviation. This work was supported in part by the Nuclear and Solid State Research Project of the University of Tsukuba. We are grateful to the staff of the T a n d e m Accelerator Center of University of T s u k u b a and to T. Miyoshi, K. N u m a t a a n d H. O h a r a for their help during the experiment. Y. Aoki offered m u c h useful advice with respect to the experimental arrangement.

References

[1] A.B. Wittkower and H.D. Betz, At. Data 5 (1973) 113. [2] Ph. Deschepper, P. Lebrun, J. Lehmann, L. Palffy and P. Pellegrin, Nucl. Instr. and Meth. 166 (1979) 53!. [3] U. Scharfer, C. Henrichs, J.D. Fox, P. von Brentano, L. Degener, J.C. Sens and A. Pape, Nucl. Instr. and Meth. 146 (1977) 573. [4] E.J. Knystautas and M. Jomphe, Phys. Rev. A23 (1981) 679. [5] R.B. Clark, I.S. Grant, R. King, D.A. Eastham and T. Joy, Nucl. Instr. and Meth. 133 (1976) 17. [6] E. Baron and B. Delaunay, Phys. Rev. AI2 (1975) 40. [7] K. Shima et al, to be published in Phys. Rev. A (1982). [8] V.S. Nikolaev and I.S. Dmitriev, Phys. Lett. 28A (1968) 277. [9] K.X. To and R. Drouin, Phys. Scripta 14 (1976) 277. [10] K.X. To and R. Drouin, Nucl. Instr. and Meth. 160 (1979) 461. {11] K. Shima, T. Ishihara and T. Mikumo, to be published in NucL Instr. and Meth. [12] Y. Baudinet-Robinet, Nucl. Instr. and Meth. 190 (1981) 197. [13] L.C. Northcliffe and R.F. Schilling, Nucl. Data Tables A7 (1970) 233. [14] F. Hubert, A. Fleury, R. Bimbot and D. Gards, Ann. Physique Suppl. 5 (1980) 1. [15] E. Almqvist, C. Broude, M.A. Clark, J.A. Kuehner and A.E. Litherland, Can. J. Phys. 40 (1962) 954.