- Email: [email protected]
Equilibrium charge state fractions for 11.5 to 37.3 MeV 16O ions in carbon
N U C L E A R I N S T R U M E N T S A N D M E T H O D S 5 8 ([968) 274-276;
© NORTH-HOLLAND
PUBLISHING
CO.
E Q U I L I B R I U M C H A R G E STATE F R A C T I O N S F O R 11.5 T O 37.3 MeV 160 I O N S IN CARBON R. A. BROWN and G. D. SYMONS
A WRE, Aldermaston, England and I. HALL
Chadwick Laboratory, University of Liverpool, England Received 25 September 1967 The equilibrium charge state fractions for 160 ions in carbon have been measured by magnetic analysis of ions scattered from a gold target backed by a carbon foil. Charge state fractions and rms ionic charges are tabulated.
In the magnetic or electrostatic analysis of heavy ions it is often necessary to know the relative intensities of the various ionic charge states. The present measurements were prompted by a programme of Coulomb excitation which involved the measurement of crosssections for elastic and inelastic scattering of heavy ions by magnetic analysis of the scattered ions; this required an experimenta! determination of the energy dependence of the charge state fractions. In these measurements an oxygen beam of about 0 . 1 # A from the A W R E tandem accelerator was admitted through a 2 m m 2 collimator on to a target which comprised a 25-50/~g/cm z layer of gold evaporated on to a 20 #g/cm 2 carbon foil. The ionic charge of the incident beam was 4 +, 5 + or 6 + depending upon the energy required. The charge state distribution of the ions scattered by the gold but emerging from the carbon
foil was analysed with a 6l cm radius double-focusing magnetic spectrometer1). The spectrometer was set at an angle of 90 ° with respect to the incident beam and the plane of the target was at 45 °, in transmission geometry. The t 6 0 ions were detected in the focal plane of the spectrometer by a position-sensitive detector whose dimensions were 4.8 cm long (giving an energy acceptance of about 2%) by 0.8 cm wide (and thus much wider than the image of the target spot). With this arrangement the magnetic field could be readily adjusted so that the particular charge state desired was deflected on to the centre of the detector. A typical position spectrum is shown in fig. 1. The resolution of about 150 keV is due principally to the finite aperture of the spectrometer and to energy straggling in the target. After the field adjustment the intensity of the particular charge state group was measured by a
Position spectrum 18.7 MeV t60 ions
6C
•
FWHM ~- 150 keY
° e
ul
E • I
•
•
Q
4C •
E
•
•
•
oQ
e
• •
•
o• ~ e
•
e
• Q
•
e
•
•
o•
•
• •
•
eo oe •
20
i
o•
,
e I
•
•
o• • •
I
2o
i
e
•
l e
I
I
do
L
;o
~oe •
•
e ~ --
1;o
• e
• o ~ ~ le oo _.== %
12o
-~=
1t.0
Channel number
Fig. 1. Momentum spectrum of 18.7 MeV 160 ions recorded by a 4.8 cm × 0.8 cm position-sensitive detector in the focal plane of the spectrometer.
274
EQUILIBRIUM
CHARGE
275
STATE FRACTIONS
TABLE 1
Equilibrium charge state fractions of t~O ions in carbon. E and V are the energy and velocity, respectively, of the ions emerging from the carbon foil. The figures in parentheses are the errors in the last figures of the charge fractions q~i and are based only on counting statistics. The rms ionic charge Zrms carries a simple statistical error of about 0.1%. E (MeV)
V (10 s cm/sec)
~4
4)5
Charge state fractions ~bG
~b7
~b8
11.5 12.2 12.6 13.1 13.5 13.9 14.4 14.8 15.3 15.7 16.2 16.7 17.3 17.9 18.5 19.2 19.8 20.5 2 I. 1 21.8 22.3 22.6 23.4 24.0 24.6 25.3 26.0 26.8 27.5 28.1 28.6 29.2 29.9 30.7 31.4 32.2 33.2 33.8 34.1 35.1 36.2 37.3
11.8 12. I 12.4 12.6 12.8 13.0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.7 15.0 15.2 15.5 15.7 16.0 16.2 16.4 16.5 16.8 17.0 17.2 17.5 17.7 18.0 18.2 18.4 18.6 18.8 19.0 19.3 19.5 19.7 20.0 20.2 20.3 20.6 20.9 21.2
0.031(1 ) 0.023( 1) 0.023(1) 0.020( 1) 0.018( 1) 0.017( 1) 0.015(1 ) 0.014(1 ) 0.012(1) 0.010(1 ) 0.010(1) 0.008( I ) 0.008(I) 0.008( 1) 0.006(I) -
0.226(3) 0.213(3) 0.205(3) o. 196(3) O. 179(3) O. 169(3) O. 153(3) O. 151 (3) 0.140(2) o. 136(2) 0.121(2) 0.113(2) 0.106(2) 0.097(2) 0.091(2) 0.079(2) 0.075(2) 0.068(2) 0.063(2) 0.056(2) 0.044( 1) 0.049(I) 0.045(1 ) 0.042(1) 0.035( 1) 0.035(1) 0.027(1) 0.027(1) 0.025(1) 0.025(1) 0.021(1) 0.020(1) 0.019(1) 0.016(1) 0.013(1) 0.014(1) 0.0! 1(1) 0.009(1) -
0.563(5) o. 566(5) 0.558(5) O.557(5) 0.566(5) O.556(5) 0.560(5) O.541 (5) 0.543(5) 0.529(5) 0.526(5) 0.508(5) 0.493(5) 0.483(4) 0.462(4) 0.456(4) 0.442(4) 0.436(4) 0.409(4) 0.390(4) 0.421 (4) 0.365(4) 0.359(4) 0.348(4) 0.318(4) 0.315(4) 0.293(3) 0.275(3) 0.262(3) 0.259(3) 0.247(3) 0.231 (3) 0.233(3) 0.210(3) 0.202(3) 0.194(3) 0.173(3) 0.163(3) 0.168(3) 0.156(3) 0.142(2) 0.130(2)
O. 170(3) O. 185(3) 0.200(3) 0.210(3) 0.217(3) O.237(3) 0.248(3) 0.266(3) 0.274(3) 0.289(3) 0.303(3) 0.326(4) 0.342(4) 0.355(4) 0.375(4) 0.392(4) 0.402(4) 0.404(4) 0.428(4) 0.443(4) 0.432(4) 0.463(4) 0.460(4) 0.461(4) 0.487(4) 0.478(5) 0.492(5) 0.495(5) 0.490(5) 0.505(5) 0.498(5) 0.515(5) 0.498(5) 0.495(5) 0.497(5) 0.496(5) 0.492(5) 0.490(5) 0.494(5) 0.474(5) 0.484(5) 0.481(5)
0.010(1) 0.013( 1) 0.014(1) 0.017( 1) 0.020(1) 0.021 (1) 0.024(1) 0.028(1 ) 0.031(1) 0.036(1 ) 0.040(1) 0.045(1 ) 0.051(1) 0.057(2) 0.066(2) 0.073(2) 0.081(2) 0.092(2) 0.100(2) 0.111 (2) 0.103 (2) 0.123(2) 0.136(2) 0.149(3) 0.160(3) 0.172(3) 0.188(3) 0.203(3) 0.223(3) 0.211(3) 0.234(3) 0.234(3) 0.250(3) 0.279(3) 0.288(3) 0.296(3) 0.324(4) 0.338(4) 0.338(4) 0.370(4) 0.374(4) 0.389(4)
d i s c r i m i n a t o r a n d s c a l e r u s i n g t h e full e n e r g y p u l s e from the detector. Two silicon detectors, mounted in t h e s c a t t e r i n g c h a m b e r a t 90 ° a n d 150 ° , s e r v e d as monitors. At each energy the relative intensities of the different charge states were measured in turn and hence t h e f r a c t i o n s q5i s h o w n i n t a b l e 1 a n d fig. 2 w e r e d e d u c e d . I t will b e s e e n t h e r e t h a t v e r y little e r r o r is i n c u r r e d b y n e g l e c t o f t h e u n m e a s u r e d c h a r g e states. T h e e n e r g y o f t h e i o n s e m e r g i n g f r o m t h e c a r b o n foil w a s d e t e r m i n e d
Zrms
5.95 6.00 6.02 6.05 6.09 6.12 6.16 6.19 6.22 6.25 6.29 6.33 6.37 6.40 6.45 6.50 6.53 6.56 6.61 6.65 6.64 6.70 6.73 6.76 6.81 6.83 6.88 6.91 6.95 6.94 6.98 7.00 7.02 7.07 7.10 7.11 7.17 7.19 7.20 7.25 7.26 7.29
f r o m t h e m a g n e t i c field o f t h e s p e c t r o m e t e r w h i c h w a s calibrated with a Th e-source. I t is b e l i e v e d t h a t t h e c h a r g e s t a t e d i s t r i b u t i o n s reported here are indeed equilibrium distributions for 16 0 i o n s i n c a r b o n . I n t h i s r e g a r d we n o t e t h e f o l l o w i n g : 1. it c a n b e e s t i m a t e d f r o m t h e m e a s u r e m e n t s o f H u b b a r d a n d L a u e r 2) t h a t 5 ktg/cm 2 o f c a r b o n s h o u l d be enough to establish an equilibrium charge distribution;
276
R.A. BROWN et al.
10
15
20
Ion energy (MeV) 25 r
30
35
40
160 ions in Carbon 06 "
AAA
~ 7÷
a
0z~
o +
0.~
5 0"2
8÷ o
LLJ
O
O
O
O1 5* 0,
12
13
14
15
16
17
18
19
20
21
22
ion velocity (10a cmlsec) Fig. 2. Equilibrium charge state fractions ~ for 160 ions in carbon plotted against energy and velocity o f the emerging ions. This data are tabulated in table I.
2. there is no evidence o f any discontinuities in the d a t a for changes of the incident ion charge; 3. there is g o o d a g r e e m e n t between o u r d a t a a n d s o m e m e a s u r e m e n t s o f A r m i t a g e a n d H o o t o n 3) using 20-100 p g / c m 2 c a r b o n foils. O u r results do not, however, agree well with t h o s e o f B o o t h a n d Grant4), p a r t i c u l a r l y at their higher energies. Their rms ionic charge goes f r o m a b o u t 1.5% higher t h a n ours at 12 M e V to a b o u t 3.5% higher at 21 MeV. W e have no e x p l a n a t i o n of this d i s a g r e e m e n t ; on the o t h e r h a n d we note again the satisfactory c o m p a r i s o n o f the d a t a r e p o r t e d here with those o f 3). There is also r e a s o n a b l e a g r e e m e n t between o u r d a t a a n d the
semi-empirical curves of qS~ vs V d r a w n by ZaidinsS), W e are grateful to Mr. C. Parsons a n d Mr. A M u g g l e t o n for the f a b r i c a t i o n of the position-sensitive detectors. References 1) A. V. Cohen, J. A. Cookson and J. L. Wankling, Nucl. lnstr. and Meth. 10 (1961) 84. 2) E. L Hubbard and E. J. Lauer, Phys. Rev. 98 (1955) 1814. 3) B. H. Armitage and B. W. Hooton, private communication. 4) W. Booth and I. S. Grant, Nucl. Physics 63 (1965) 481. s) C. S. Zaidins, California Institute of Technology Report (unpublished) 1962.
© NORTH-HOLLAND
PUBLISHING
CO.
E Q U I L I B R I U M C H A R G E STATE F R A C T I O N S F O R 11.5 T O 37.3 MeV 160 I O N S IN CARBON R. A. BROWN and G. D. SYMONS
A WRE, Aldermaston, England and I. HALL
Chadwick Laboratory, University of Liverpool, England Received 25 September 1967 The equilibrium charge state fractions for 160 ions in carbon have been measured by magnetic analysis of ions scattered from a gold target backed by a carbon foil. Charge state fractions and rms ionic charges are tabulated.
In the magnetic or electrostatic analysis of heavy ions it is often necessary to know the relative intensities of the various ionic charge states. The present measurements were prompted by a programme of Coulomb excitation which involved the measurement of crosssections for elastic and inelastic scattering of heavy ions by magnetic analysis of the scattered ions; this required an experimenta! determination of the energy dependence of the charge state fractions. In these measurements an oxygen beam of about 0 . 1 # A from the A W R E tandem accelerator was admitted through a 2 m m 2 collimator on to a target which comprised a 25-50/~g/cm z layer of gold evaporated on to a 20 #g/cm 2 carbon foil. The ionic charge of the incident beam was 4 +, 5 + or 6 + depending upon the energy required. The charge state distribution of the ions scattered by the gold but emerging from the carbon
foil was analysed with a 6l cm radius double-focusing magnetic spectrometer1). The spectrometer was set at an angle of 90 ° with respect to the incident beam and the plane of the target was at 45 °, in transmission geometry. The t 6 0 ions were detected in the focal plane of the spectrometer by a position-sensitive detector whose dimensions were 4.8 cm long (giving an energy acceptance of about 2%) by 0.8 cm wide (and thus much wider than the image of the target spot). With this arrangement the magnetic field could be readily adjusted so that the particular charge state desired was deflected on to the centre of the detector. A typical position spectrum is shown in fig. 1. The resolution of about 150 keV is due principally to the finite aperture of the spectrometer and to energy straggling in the target. After the field adjustment the intensity of the particular charge state group was measured by a
Position spectrum 18.7 MeV t60 ions
6C
•
FWHM ~- 150 keY
° e
ul
E • I
•
•
Q
4C •
E
•
•
•
oQ
e
• •
•
o• ~ e
•
e
• Q
•
e
•
•
o•
•
• •
•
eo oe •
20
i
o•
,
e I
•
•
o• • •
I
2o
i
e
•
l e
I
I
do
L
;o
~oe •
•
e ~ --
1;o
• e
• o ~ ~ le oo _.== %
12o
-~=
1t.0
Channel number
Fig. 1. Momentum spectrum of 18.7 MeV 160 ions recorded by a 4.8 cm × 0.8 cm position-sensitive detector in the focal plane of the spectrometer.
274
EQUILIBRIUM
CHARGE
275
STATE FRACTIONS
TABLE 1
Equilibrium charge state fractions of t~O ions in carbon. E and V are the energy and velocity, respectively, of the ions emerging from the carbon foil. The figures in parentheses are the errors in the last figures of the charge fractions q~i and are based only on counting statistics. The rms ionic charge Zrms carries a simple statistical error of about 0.1%. E (MeV)
V (10 s cm/sec)
~4
4)5
Charge state fractions ~bG
~b7
~b8
11.5 12.2 12.6 13.1 13.5 13.9 14.4 14.8 15.3 15.7 16.2 16.7 17.3 17.9 18.5 19.2 19.8 20.5 2 I. 1 21.8 22.3 22.6 23.4 24.0 24.6 25.3 26.0 26.8 27.5 28.1 28.6 29.2 29.9 30.7 31.4 32.2 33.2 33.8 34.1 35.1 36.2 37.3
11.8 12. I 12.4 12.6 12.8 13.0 13.2 13.4 13.6 13.8 14.0 14.2 14.4 14.7 15.0 15.2 15.5 15.7 16.0 16.2 16.4 16.5 16.8 17.0 17.2 17.5 17.7 18.0 18.2 18.4 18.6 18.8 19.0 19.3 19.5 19.7 20.0 20.2 20.3 20.6 20.9 21.2
0.031(1 ) 0.023( 1) 0.023(1) 0.020( 1) 0.018( 1) 0.017( 1) 0.015(1 ) 0.014(1 ) 0.012(1) 0.010(1 ) 0.010(1) 0.008( I ) 0.008(I) 0.008( 1) 0.006(I) -
0.226(3) 0.213(3) 0.205(3) o. 196(3) O. 179(3) O. 169(3) O. 153(3) O. 151 (3) 0.140(2) o. 136(2) 0.121(2) 0.113(2) 0.106(2) 0.097(2) 0.091(2) 0.079(2) 0.075(2) 0.068(2) 0.063(2) 0.056(2) 0.044( 1) 0.049(I) 0.045(1 ) 0.042(1) 0.035( 1) 0.035(1) 0.027(1) 0.027(1) 0.025(1) 0.025(1) 0.021(1) 0.020(1) 0.019(1) 0.016(1) 0.013(1) 0.014(1) 0.0! 1(1) 0.009(1) -
0.563(5) o. 566(5) 0.558(5) O.557(5) 0.566(5) O.556(5) 0.560(5) O.541 (5) 0.543(5) 0.529(5) 0.526(5) 0.508(5) 0.493(5) 0.483(4) 0.462(4) 0.456(4) 0.442(4) 0.436(4) 0.409(4) 0.390(4) 0.421 (4) 0.365(4) 0.359(4) 0.348(4) 0.318(4) 0.315(4) 0.293(3) 0.275(3) 0.262(3) 0.259(3) 0.247(3) 0.231 (3) 0.233(3) 0.210(3) 0.202(3) 0.194(3) 0.173(3) 0.163(3) 0.168(3) 0.156(3) 0.142(2) 0.130(2)
O. 170(3) O. 185(3) 0.200(3) 0.210(3) 0.217(3) O.237(3) 0.248(3) 0.266(3) 0.274(3) 0.289(3) 0.303(3) 0.326(4) 0.342(4) 0.355(4) 0.375(4) 0.392(4) 0.402(4) 0.404(4) 0.428(4) 0.443(4) 0.432(4) 0.463(4) 0.460(4) 0.461(4) 0.487(4) 0.478(5) 0.492(5) 0.495(5) 0.490(5) 0.505(5) 0.498(5) 0.515(5) 0.498(5) 0.495(5) 0.497(5) 0.496(5) 0.492(5) 0.490(5) 0.494(5) 0.474(5) 0.484(5) 0.481(5)
0.010(1) 0.013( 1) 0.014(1) 0.017( 1) 0.020(1) 0.021 (1) 0.024(1) 0.028(1 ) 0.031(1) 0.036(1 ) 0.040(1) 0.045(1 ) 0.051(1) 0.057(2) 0.066(2) 0.073(2) 0.081(2) 0.092(2) 0.100(2) 0.111 (2) 0.103 (2) 0.123(2) 0.136(2) 0.149(3) 0.160(3) 0.172(3) 0.188(3) 0.203(3) 0.223(3) 0.211(3) 0.234(3) 0.234(3) 0.250(3) 0.279(3) 0.288(3) 0.296(3) 0.324(4) 0.338(4) 0.338(4) 0.370(4) 0.374(4) 0.389(4)
d i s c r i m i n a t o r a n d s c a l e r u s i n g t h e full e n e r g y p u l s e from the detector. Two silicon detectors, mounted in t h e s c a t t e r i n g c h a m b e r a t 90 ° a n d 150 ° , s e r v e d as monitors. At each energy the relative intensities of the different charge states were measured in turn and hence t h e f r a c t i o n s q5i s h o w n i n t a b l e 1 a n d fig. 2 w e r e d e d u c e d . I t will b e s e e n t h e r e t h a t v e r y little e r r o r is i n c u r r e d b y n e g l e c t o f t h e u n m e a s u r e d c h a r g e states. T h e e n e r g y o f t h e i o n s e m e r g i n g f r o m t h e c a r b o n foil w a s d e t e r m i n e d
Zrms
5.95 6.00 6.02 6.05 6.09 6.12 6.16 6.19 6.22 6.25 6.29 6.33 6.37 6.40 6.45 6.50 6.53 6.56 6.61 6.65 6.64 6.70 6.73 6.76 6.81 6.83 6.88 6.91 6.95 6.94 6.98 7.00 7.02 7.07 7.10 7.11 7.17 7.19 7.20 7.25 7.26 7.29
f r o m t h e m a g n e t i c field o f t h e s p e c t r o m e t e r w h i c h w a s calibrated with a Th e-source. I t is b e l i e v e d t h a t t h e c h a r g e s t a t e d i s t r i b u t i o n s reported here are indeed equilibrium distributions for 16 0 i o n s i n c a r b o n . I n t h i s r e g a r d we n o t e t h e f o l l o w i n g : 1. it c a n b e e s t i m a t e d f r o m t h e m e a s u r e m e n t s o f H u b b a r d a n d L a u e r 2) t h a t 5 ktg/cm 2 o f c a r b o n s h o u l d be enough to establish an equilibrium charge distribution;
276
R.A. BROWN et al.
10
15
20
Ion energy (MeV) 25 r
30
35
40
160 ions in Carbon 06 "
AAA
~ 7÷
a
0z~
o +
0.~
5 0"2
8÷ o
LLJ
O
O
O
O1 5* 0,
12
13
14
15
16
17
18
19
20
21
22
ion velocity (10a cmlsec) Fig. 2. Equilibrium charge state fractions ~ for 160 ions in carbon plotted against energy and velocity o f the emerging ions. This data are tabulated in table I.
2. there is no evidence o f any discontinuities in the d a t a for changes of the incident ion charge; 3. there is g o o d a g r e e m e n t between o u r d a t a a n d s o m e m e a s u r e m e n t s o f A r m i t a g e a n d H o o t o n 3) using 20-100 p g / c m 2 c a r b o n foils. O u r results do not, however, agree well with t h o s e o f B o o t h a n d Grant4), p a r t i c u l a r l y at their higher energies. Their rms ionic charge goes f r o m a b o u t 1.5% higher t h a n ours at 12 M e V to a b o u t 3.5% higher at 21 MeV. W e have no e x p l a n a t i o n of this d i s a g r e e m e n t ; on the o t h e r h a n d we note again the satisfactory c o m p a r i s o n o f the d a t a r e p o r t e d here with those o f 3). There is also r e a s o n a b l e a g r e e m e n t between o u r d a t a a n d the
semi-empirical curves of qS~ vs V d r a w n by ZaidinsS), W e are grateful to Mr. C. Parsons a n d Mr. A M u g g l e t o n for the f a b r i c a t i o n of the position-sensitive detectors. References 1) A. V. Cohen, J. A. Cookson and J. L. Wankling, Nucl. lnstr. and Meth. 10 (1961) 84. 2) E. L Hubbard and E. J. Lauer, Phys. Rev. 98 (1955) 1814. 3) B. H. Armitage and B. W. Hooton, private communication. 4) W. Booth and I. S. Grant, Nucl. Physics 63 (1965) 481. s) C. S. Zaidins, California Institute of Technology Report (unpublished) 1962.