- Email: [email protected]
Energy-angle distribution measurements for 0.8v020Ne and 209Bi ions penetrating thin carbon foils
Nuclear Instruments and Methods in Physics Research B32 (1985) 38-42 North-Holland, Amsterdam
38
E~RGY-ANGLE D~S~B~ON M~ASU~~~S PENE~~NG THIN CARBON FOILS
H. GEISSEL *, W.N. LENNARD, D. PHILIPS and D. WARD
FOR O.Sv, UtNeAND 209k IONS
H.R. ANDREWS, D.P. JACKSON, 1.V. MITCHELL,
Atomic Energy of Canada Limited Research Company, Chalk River Nuclear Laboratories,
Chalk River, Ontario, Canada KOJ IJO
Received 21 September 1984 and in revised form 14 January 1985
Energy-angle distributions have been measured for 0.8~9 ( v0 = Bohr velocity) Ne and Bi ions penetrating through carbon foils. Comparing the results with a Monte Carlo computer simulation that included an angle dependence only for the elastic collisions, we have observed for Ne projectiles an Anne-d~nd~t inelastic loss which, for small angles, is much larger than the elastic contribution in the case of thin foils. In the case of Bi, the energy loss dist~bution is dominated by elastic collisions. The calculations of Meyer, Klein and Wedell, and Ellmer and Wedell cannot describe the experimental results. The multiple scattering dist~butions are in agreement with both analytical and Monte Carlo calculations.
1. Introduction
In penetrating through matter, heavy ions lose energy and change their original direction of motion through collisions with the target atoms. Generally the stopping processes are described by an electronic interaction arising from the excitation of atomic or collective modes (electronic energy loss, A E,) and by elastic collisions with the target atoms (nuclear energy loss, A.&). The latter mechanism is mainly responsible for the angular scattering whereas its contribution to the stopping of heavy ions is only significant at low velocities. In a first approximation, the two slowing down processes were treated as uncorrelated events [1,2]. The validity of this basic assumption has been studied recently in new experiments [3-61 and theoretical investigations [7-91 treating simultaneously the energy loss and angular deflections of ions traversing the stopping medium. These studies are also of practical relevance. Most data on the stopping of heavy ions are derived from transmission experiments in which the energy loss of the ions after penetrating the stopping medium is measured within a restricted acceptance angle of the detector system. As will be seen later, the detection angle, the angular range accepted by the detector and the transmission foil thickness all influence energy loss distributions. We find that in the case of 0.8~~ Ne ions in carbon at small emergent angles (a), the cause of the angle-dependent energy loss is predominantly due to inelastic collisions. For Bi projectiles at the same veloc* On leave from GSI, Darmstadt. West Germany.
0~68-~83X/85/$03.30 @ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ity, elastic collisions dominate the increase in the energy
loss with increasing total scattering angle, (Y.The results demonstrate the correlation of electronic and nuclear stopping.
2. Experimental A low intensity, well-~llimated ion beam (angular divergence - 0.3 mrad) from the CRNL High Voltage Mass Separator was used to measure the angular and thickness dependence of heavy ion energy losses in thin foils. The energy losses were measured with a time-offlight (TOF) spectrometer in transmission geometry with and without the stopping foil in front of the detector system [lo], see fig. 1. The TOF spectrometer could be continuously rotated in the angular range a = - loo to + 37” relative to the incident primary beam direction (OO), with the axis of rotation intersecting the beam in the plane of the stopping foil. The detector system could be positioned reproducibly with a precision better than 0.05*, had an acceptance half-angle of 0.17O in the horizontal plane, and subtended a total solid angle of 0.03 msr. Since foil crystallinity can influence the scattering and energy loss of transmitted ions, we used the TOF spectrometer to survey metallic (polycrystalline) foils of Al, Cu, Ni, Ag, Au and Bi, as well as carbon foils. Multiply-peaked energy loss spectra were observed for Al, Au and Bi for 0.8~~ Ne ions measured at a! = 0’. From the variation of the relative intensities of these peaks as a function of a, we conclude that the highest energy component (lowest energy loss) of the distribu-
H. Geissel et al. / Energy-
angle distributions for Ne and Bi in C
Fig. 1. Experimental setup for energy loss measurements by time-of-flight. The stopping foil is positioned normal to the beam direction: Fl, F2 - time-of-flight detector foils, located on an arm that rotates about the target (a = - 10” to + 37”). The solid angle subtended by F2 is slightly larger than that subtended by Fl. The distance, D, was - 0.8 m.
tion was due to channeling. In those cases where the multiple peak structure could not be resolved at O’, systematic measurements of the energy loss straggling as a function of a proved to be a sensitive method of testing for channeling effects. For example, the strag-
32
*‘Ne--C
x
*ON,? -Al
.
3. Results
20 cc?
gling values showed a minimum for a-values near the critical angle for axial channeling, see fig. 2. Of the metallic targets, Cu and Ni foils showed the smallest influence of target texture. We concluded that, of the seven materials studied, only carbon films were suitable, viz. amorphous and elemental, as stopping foils for our energy loss measurements. The TOF spectra were analyzed for the most probable energy loss. A Monte Carlo computer simulation (MCCS) was used to calculate the contribution of elastic energy loss, relevant to the experimental geometry (i.e. the restricted nuclear loss) [ll]. The model assumed binary collisions in a random medium with the scattering process described by a repulsive Moliere potential. The electronic energy loss was incorporated on the straight path betweent two collisions using a modified LSS-formula adjusted to give agreement with the measured results at a = 0”. The calculated elastic energy loss was convoluted with a Gaussian to simulate the observed energy loss straggling measured at a = 0”. The calculated total energy loss was then derived from the most probable value of the convoluted distribution. The angle bin size in the simulation was chosen to equal that used in the experiment. The thicknesses of the stopping foils were determined by measuring the energy loss of - 620 keV 4He ions with the TOF spectrometer and using the stopping power values from the tables of Ziegler [12].
/
28
7 B
39
16
12
I
0
I
L
I
a
I
12
I
16
1
213
CI (degrees)
Fig. 2. Measured widths, 6,, of energy loss peaks for 0.80, *‘Ne + C and “Ne --t Al as a function of emergent angle, a. The values are obtained after correcting for the contribution of the timing foil, Fl in fig. 1. The C and Al foil thicknesses were 13.2 and 17.6 pg cmm2, respectively. The solid curves are to guide the eye.
The most probable specific energy loss as a function of the target thickness is shown in fig. 3 for 0.8~~ 20Ne and 209Bi ions in C at a: = 0”. The characteristic features of these results are: i) the specific energy loss, A E/Ax, increases with increasing target thickness, Ax, ii) in the thickness range studied (5 to 30 pg cme2), the saturation with increasing thickness is less evident for the heavier projectile. In a previous publication [13], we have addressed the question as to whether specific energy losses increase or decrease with increasing foil thickness. Especially for heavy ions, the interpretation of the thickness dependence must take account of the emergent angle selected by the detection system. Qualitatively the results in fig. 3 can be understood by the contribution of close impact parameter collisions through which projectiles are subsequently multiply scattered into the detector. These multiple scattering processes complicate the interpretation of thickness and angle-dependent results in terms of single collision phenomena. Because we have chosen the MCCS method to calculate the elastic energy loss contribution, we checked the reliability of the simulation by comparing the measured multiple scattering distributions with analytical STOPPING POWER WORKSHOP
40
rIf
I
x
H. Geissel et al. / Energv- angle distributions for Ne and Bi in C
.-------.--*09Bi-C
EXPERIMENT
----
MKW
I
/’
,I’
/’ /’
lot
Q
Idegrees)
Fig. 5. Experimental most probable energy losses ( X ) for 0.80, Ne + C and the corresponding MCCS results (0), as a function of emergent angle. The dashed curves show the path-dependent electronic energy loss, see text.
Fig. 3. Most probable specific energy losses as a function of the target thickness far 0.8~~ Ne and Bi ions. The solid curves are
potential.
The agreement
of the difference
results is
good. In fig. 5 we show the ex~~rnent~ energy loss and the corresponding MCCS results for O.Svu Ne ions in two carbon foils of different thickness as a function of the emergent angle. The electronic loss calculated in the MCCS for the straight path segments (AE~ccs) is
to guide the eye. See text for explanation of dashed curve. and MCCS results. In fig. 4, the experimental scattering intensities for Ne and Bi are compared with MCCS and analytical calculations [141 using the Lenz- Jensen
* EXPERIMENT -
I
I
2
4
I
I 6
8 LAB.
THEORY
(SW)
I 10
I 12
SCATTERING
I I 140
I
I
1
2
I 3
I
I
4
5
’
ANGLE, aldegreesl
Fig. 4. Measured scattering distributions (0) for 0.8~ Ne and Bi ions transmitted through 13.7 ng cm-’ calculations (solid curve) (ref. 1141)and Monte Carlo computer simulations (X) are also shown.
C foils. Results of analytical
H. Gei~.& et al. / Energy - angle d~tri~tions
shown by the dashed curve and is seen to be insensitive to angle. The quantities of interest are: (i) the difference between the total calculated energy loss and the path-dependent loss, A EMCCS - AEpCCS, and (ii) the difference between the experimental data and the pathdependent loss, A EexPt - A EMCCS. These differences show the angle-dependent eneriy loss. The lower panels in fig. 5 show the discrepancies between the calculations (elastic angle dependence only) and experiment. For small LT,the angle dependence of the inelastic loss is clearly observed, but there is suggestion that this effect saturates at a: L ~LY>,~,where (~r,,,~is the half-angle of the corresponding multiple scattering distribution. These Ne -+ C data show for the first time that the inelastic stopping processes are correlated. The results for the collision system Bi -+ C are shown in fig. 6, and are compared with MCCS. This comparison reveals that elastic collisions are mainly responsible for the increase of energy loss with a for all angles. Within the observed experimental and model uncertainties, the correlation between elastic and inelastic stopping is small or non-existent. Here we want to emphasize once more the measured energy losses are most probable values and that the MCCS results are analyzed in the same manner. For example, for Bi ions in the 13.9 pg cmm2 target, we obtained AE,, (a = O”) = 28 keV, whereas Krist et al. fl5] predict 62.5 keV. Their values
190'
I 1
170
?/2
$z 150 w Y 1 130 a" 110
LO i
1 X0 m
0 f
----.-.--_________
90 aif 70
I
1
sot
/
xQ I
300
.
* -_--_--_--__r____
1
2
3
L
0
12
3
4
for Ne and Bi in C
41
are presumably mean values and are therefore not applicable to our data. Jakas et al. [16] have recently observed and calculated energy-angle distributions for light ions (‘H, 4He) in C and Al foils. They derived the average inelastic loss in a single collision directly from their values for AE( a) -AE(O’), since the elastic loss is negligible in their case. The inelastic loss appears to saturate with increasing a: for these systems as well, a consequence of the monotonic decrease of electronic energy loss with increasing impact parameter from a finite value at zero impact parameter. With respect to the inelastic energy loss variation with angle, the light ion and heavy ion results bear a qualitative resemblance. A satisfactory theory that incorporate both scattering and energy loss is still lacking; however, Meyer, Klein and Wedell (MKW) [7] have described heavy ion energy loss as a function of emergent angle and target thickness in terms of most probable values. They assumed that an inelastic loss in a single collision has the same (quadratic) dependence on scattering angle as the elastic contribution, A~(~)=c~~+(c~~+c~~~~,
(1)
where B is a reduced angle, c, accounts for nuclear loss, and ccc is the electronic stopping at zero scattering angle. The parameters c,~ and c,~ can only be determined by fitting to experimental data. EBmer and Wedell (EW) have revised the MKW calculation in a recent work [S] but have dropped the correlation between elastic and electronic energy loss that was used in ref. [7]. With regard to both these treatments, three comments may be made. First, in the Ne -+ C data shown in fig. 5, we observe strong evidence for an angle-dependent inelastic electronic energy loss that is correlated with the elastic loss, contrary to the assumption of EW. Second, we have shown in fig. 6 that the nuclear loss dominates the angle-dependence for the Bi --f C case. However, when we use the MKW treatment with c,, = 0, as shown by the dashed line in fig. 3, we find that the observed thickness dependence is not reproduced by the calculation; this disparity suggests that the small angle approximation is not adequately fulfilled for this case. Third, for lighter projectiles, e.g. Ne + C, where the MKW elastic loss may be satisfactory, the experimentally derived values for c,, and cez (ref. [6]) from the thickness dependence at a = 0” cannot describe the angle-dependent data of fig. 5. This breakdown of the MKW description originates from the small angle appro~mation used in eq. (1).
CYidegfeesi
Fig. 6. Experimental most probable emergy losses ( X) for
0.80, Bi -+ C and the corresponding MCCS results (0). as a function of emergent angle. The dashed curves are path-dependent values only, as in fig. 5.
4. Conchsions The angle dependence of the energy loss is clearly observed in our measurements. For both light and heavy STOPPING POWER WORKSHOP
42
H. Geissel et al. / Energy-angle
projectiles (Ne, Bi), elastic collisions dominate the angle dependence of energy loss. In the Bi case, the entire effect can be accounted for without invoking an angledependent inelastic loss, within the limits of uncertainty in both the experiment and computer modelling. This is not so for Ne projectiles. For angles a < 3a,,*,’ we cannot quantitatively describe our measurements with a model that includes only elastic and path-dependent electronic energy loss. Thus we infer the existence of a large angle-dependent inelastic loss. Neither MKW nor EW calculations can describe the experimental results. Multiple scattering distributions are in good agreement with analytical and Monte Carlo calculations. Since the angular distributions are determined mainly by the elastic collisions, the inclusion of an angle-dependent inelastic energy loss mechanism will have a negligible influence on the MCCS angular distribution results. We are grateful to G.A. Sims for technical assistance during the course of these measurements. One of us (H.G.) acknowledges the receipt of a research grant from the Deutsche Forschungsgemeinschaft and thanks the Chalk River Nuclear Laboratories for their kind hospitality.
References [l] N. Bohr, Kgl. Dan. Mat. Fys. Medd. 18 (1948) no. 8. [2] J. Lindhard, V. Nielsen and M. Scharff, Kgl. Dan. Mat. Fys. Medd. 36 (1968) no. 10.
distributions for Ne and Bi in C
131 R. Skoog and G. Hogberg, Radiat. Effects 22 (1974) 277. [41 G. Beauchemin and R. Drouin, Nucl. Instr. and Meth. 160 (1979) 519.
[51 R. Ishiwari,
N. Shiomi and N. Sakamoto, Phys. Rev. A25 (1982) 2524. [61 W.N. Lennard. H.R. Andrews, B. Dub& M. Freeman. I.V. Mitchell, D. Phillips and D. Ward, Nucl. Instr. and Meth. 205 (1983) 351. [71 L. Meyer, M. Klein and R. Wedell, Phys. Stat. Sol. (b) 83 (1977) 451. PI K. Ellmer and R. Wedell, Radiat. Effects 59 (1982) 169. J.C. Eckardt and V.H. 191 M.M. Jakas. G.H. Lantschner, Ponce, Phys. Stat. Sol. (b) 117 (1983) KL31. 1101 H. Geissel, W.N. Lennard, H.R. Andrews, D. Ward and D. Phillips, Proc. of Werner Brandt Workshop on Ion Penetration Phenomena, ed., R. Ritchie, ORNL CONF8404190 (1984). 1111 D.P. Jackson, J. Nucl. Mater. 93/94 (1980) 57. WI J. Ziegler, Helium Stopping Powers and Ranges in All Elemental Matter, vol. 4 (Pergamon Press, New York, 1977). 1131 H. Geissel, W.N. Lennard, H.R. Andrews, D. Phillips and D. Ward, submitted to Phys. Lett. P41 P. Sigmund and K.B. Winterbon, Nucl. Instr. and Meth. 119 (1974) 541. (151 Th. Krist, P. Mertens and J.P. Biersack. Nucl. Instr. and Meth. B2 (1984) 177. J.C. Eckardt and V.H. V61 M.M. Jakas, G.H. Lantschner. Ponce, Phys. Rev. A29 (1984) 1838.
38
E~RGY-ANGLE D~S~B~ON M~ASU~~~S PENE~~NG THIN CARBON FOILS
H. GEISSEL *, W.N. LENNARD, D. PHILIPS and D. WARD
FOR O.Sv, UtNeAND 209k IONS
H.R. ANDREWS, D.P. JACKSON, 1.V. MITCHELL,
Atomic Energy of Canada Limited Research Company, Chalk River Nuclear Laboratories,
Chalk River, Ontario, Canada KOJ IJO
Received 21 September 1984 and in revised form 14 January 1985
Energy-angle distributions have been measured for 0.8~9 ( v0 = Bohr velocity) Ne and Bi ions penetrating through carbon foils. Comparing the results with a Monte Carlo computer simulation that included an angle dependence only for the elastic collisions, we have observed for Ne projectiles an Anne-d~nd~t inelastic loss which, for small angles, is much larger than the elastic contribution in the case of thin foils. In the case of Bi, the energy loss dist~bution is dominated by elastic collisions. The calculations of Meyer, Klein and Wedell, and Ellmer and Wedell cannot describe the experimental results. The multiple scattering dist~butions are in agreement with both analytical and Monte Carlo calculations.
1. Introduction
In penetrating through matter, heavy ions lose energy and change their original direction of motion through collisions with the target atoms. Generally the stopping processes are described by an electronic interaction arising from the excitation of atomic or collective modes (electronic energy loss, A E,) and by elastic collisions with the target atoms (nuclear energy loss, A.&). The latter mechanism is mainly responsible for the angular scattering whereas its contribution to the stopping of heavy ions is only significant at low velocities. In a first approximation, the two slowing down processes were treated as uncorrelated events [1,2]. The validity of this basic assumption has been studied recently in new experiments [3-61 and theoretical investigations [7-91 treating simultaneously the energy loss and angular deflections of ions traversing the stopping medium. These studies are also of practical relevance. Most data on the stopping of heavy ions are derived from transmission experiments in which the energy loss of the ions after penetrating the stopping medium is measured within a restricted acceptance angle of the detector system. As will be seen later, the detection angle, the angular range accepted by the detector and the transmission foil thickness all influence energy loss distributions. We find that in the case of 0.8~~ Ne ions in carbon at small emergent angles (a), the cause of the angle-dependent energy loss is predominantly due to inelastic collisions. For Bi projectiles at the same veloc* On leave from GSI, Darmstadt. West Germany.
0~68-~83X/85/$03.30 @ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ity, elastic collisions dominate the increase in the energy
loss with increasing total scattering angle, (Y.The results demonstrate the correlation of electronic and nuclear stopping.
2. Experimental A low intensity, well-~llimated ion beam (angular divergence - 0.3 mrad) from the CRNL High Voltage Mass Separator was used to measure the angular and thickness dependence of heavy ion energy losses in thin foils. The energy losses were measured with a time-offlight (TOF) spectrometer in transmission geometry with and without the stopping foil in front of the detector system [lo], see fig. 1. The TOF spectrometer could be continuously rotated in the angular range a = - loo to + 37” relative to the incident primary beam direction (OO), with the axis of rotation intersecting the beam in the plane of the stopping foil. The detector system could be positioned reproducibly with a precision better than 0.05*, had an acceptance half-angle of 0.17O in the horizontal plane, and subtended a total solid angle of 0.03 msr. Since foil crystallinity can influence the scattering and energy loss of transmitted ions, we used the TOF spectrometer to survey metallic (polycrystalline) foils of Al, Cu, Ni, Ag, Au and Bi, as well as carbon foils. Multiply-peaked energy loss spectra were observed for Al, Au and Bi for 0.8~~ Ne ions measured at a! = 0’. From the variation of the relative intensities of these peaks as a function of a, we conclude that the highest energy component (lowest energy loss) of the distribu-
H. Geissel et al. / Energy-
angle distributions for Ne and Bi in C
Fig. 1. Experimental setup for energy loss measurements by time-of-flight. The stopping foil is positioned normal to the beam direction: Fl, F2 - time-of-flight detector foils, located on an arm that rotates about the target (a = - 10” to + 37”). The solid angle subtended by F2 is slightly larger than that subtended by Fl. The distance, D, was - 0.8 m.
tion was due to channeling. In those cases where the multiple peak structure could not be resolved at O’, systematic measurements of the energy loss straggling as a function of a proved to be a sensitive method of testing for channeling effects. For example, the strag-
32
*‘Ne--C
x
*ON,? -Al
.
3. Results
20 cc?
gling values showed a minimum for a-values near the critical angle for axial channeling, see fig. 2. Of the metallic targets, Cu and Ni foils showed the smallest influence of target texture. We concluded that, of the seven materials studied, only carbon films were suitable, viz. amorphous and elemental, as stopping foils for our energy loss measurements. The TOF spectra were analyzed for the most probable energy loss. A Monte Carlo computer simulation (MCCS) was used to calculate the contribution of elastic energy loss, relevant to the experimental geometry (i.e. the restricted nuclear loss) [ll]. The model assumed binary collisions in a random medium with the scattering process described by a repulsive Moliere potential. The electronic energy loss was incorporated on the straight path betweent two collisions using a modified LSS-formula adjusted to give agreement with the measured results at a = 0”. The calculated elastic energy loss was convoluted with a Gaussian to simulate the observed energy loss straggling measured at a = 0”. The calculated total energy loss was then derived from the most probable value of the convoluted distribution. The angle bin size in the simulation was chosen to equal that used in the experiment. The thicknesses of the stopping foils were determined by measuring the energy loss of - 620 keV 4He ions with the TOF spectrometer and using the stopping power values from the tables of Ziegler [12].
/
28
7 B
39
16
12
I
0
I
L
I
a
I
12
I
16
1
213
CI (degrees)
Fig. 2. Measured widths, 6,, of energy loss peaks for 0.80, *‘Ne + C and “Ne --t Al as a function of emergent angle, a. The values are obtained after correcting for the contribution of the timing foil, Fl in fig. 1. The C and Al foil thicknesses were 13.2 and 17.6 pg cmm2, respectively. The solid curves are to guide the eye.
The most probable specific energy loss as a function of the target thickness is shown in fig. 3 for 0.8~~ 20Ne and 209Bi ions in C at a: = 0”. The characteristic features of these results are: i) the specific energy loss, A E/Ax, increases with increasing target thickness, Ax, ii) in the thickness range studied (5 to 30 pg cme2), the saturation with increasing thickness is less evident for the heavier projectile. In a previous publication [13], we have addressed the question as to whether specific energy losses increase or decrease with increasing foil thickness. Especially for heavy ions, the interpretation of the thickness dependence must take account of the emergent angle selected by the detection system. Qualitatively the results in fig. 3 can be understood by the contribution of close impact parameter collisions through which projectiles are subsequently multiply scattered into the detector. These multiple scattering processes complicate the interpretation of thickness and angle-dependent results in terms of single collision phenomena. Because we have chosen the MCCS method to calculate the elastic energy loss contribution, we checked the reliability of the simulation by comparing the measured multiple scattering distributions with analytical STOPPING POWER WORKSHOP
40
rIf
I
x
H. Geissel et al. / Energv- angle distributions for Ne and Bi in C
.-------.--*09Bi-C
EXPERIMENT
----
MKW
I
/’
,I’
/’ /’
lot
Q
Idegrees)
Fig. 5. Experimental most probable energy losses ( X ) for 0.80, Ne + C and the corresponding MCCS results (0), as a function of emergent angle. The dashed curves show the path-dependent electronic energy loss, see text.
Fig. 3. Most probable specific energy losses as a function of the target thickness far 0.8~~ Ne and Bi ions. The solid curves are
potential.
The agreement
of the difference
results is
good. In fig. 5 we show the ex~~rnent~ energy loss and the corresponding MCCS results for O.Svu Ne ions in two carbon foils of different thickness as a function of the emergent angle. The electronic loss calculated in the MCCS for the straight path segments (AE~ccs) is
to guide the eye. See text for explanation of dashed curve. and MCCS results. In fig. 4, the experimental scattering intensities for Ne and Bi are compared with MCCS and analytical calculations [141 using the Lenz- Jensen
* EXPERIMENT -
I
I
2
4
I
I 6
8 LAB.
THEORY
(SW)
I 10
I 12
SCATTERING
I I 140
I
I
1
2
I 3
I
I
4
5
’
ANGLE, aldegreesl
Fig. 4. Measured scattering distributions (0) for 0.8~ Ne and Bi ions transmitted through 13.7 ng cm-’ calculations (solid curve) (ref. 1141)and Monte Carlo computer simulations (X) are also shown.
C foils. Results of analytical
H. Gei~.& et al. / Energy - angle d~tri~tions
shown by the dashed curve and is seen to be insensitive to angle. The quantities of interest are: (i) the difference between the total calculated energy loss and the path-dependent loss, A EMCCS - AEpCCS, and (ii) the difference between the experimental data and the pathdependent loss, A EexPt - A EMCCS. These differences show the angle-dependent eneriy loss. The lower panels in fig. 5 show the discrepancies between the calculations (elastic angle dependence only) and experiment. For small LT,the angle dependence of the inelastic loss is clearly observed, but there is suggestion that this effect saturates at a: L ~LY>,~,where (~r,,,~is the half-angle of the corresponding multiple scattering distribution. These Ne -+ C data show for the first time that the inelastic stopping processes are correlated. The results for the collision system Bi -+ C are shown in fig. 6, and are compared with MCCS. This comparison reveals that elastic collisions are mainly responsible for the increase of energy loss with a for all angles. Within the observed experimental and model uncertainties, the correlation between elastic and inelastic stopping is small or non-existent. Here we want to emphasize once more the measured energy losses are most probable values and that the MCCS results are analyzed in the same manner. For example, for Bi ions in the 13.9 pg cmm2 target, we obtained AE,, (a = O”) = 28 keV, whereas Krist et al. fl5] predict 62.5 keV. Their values
190'
I 1
170
?/2
$z 150 w Y 1 130 a" 110
LO i
1 X0 m
0 f
----.-.--_________
90 aif 70
I
1
sot
/
xQ I
300
.
* -_--_--_--__r____
1
2
3
L
0
12
3
4
for Ne and Bi in C
41
are presumably mean values and are therefore not applicable to our data. Jakas et al. [16] have recently observed and calculated energy-angle distributions for light ions (‘H, 4He) in C and Al foils. They derived the average inelastic loss in a single collision directly from their values for AE( a) -AE(O’), since the elastic loss is negligible in their case. The inelastic loss appears to saturate with increasing a: for these systems as well, a consequence of the monotonic decrease of electronic energy loss with increasing impact parameter from a finite value at zero impact parameter. With respect to the inelastic energy loss variation with angle, the light ion and heavy ion results bear a qualitative resemblance. A satisfactory theory that incorporate both scattering and energy loss is still lacking; however, Meyer, Klein and Wedell (MKW) [7] have described heavy ion energy loss as a function of emergent angle and target thickness in terms of most probable values. They assumed that an inelastic loss in a single collision has the same (quadratic) dependence on scattering angle as the elastic contribution, A~(~)=c~~+(c~~+c~~~~,
(1)
where B is a reduced angle, c, accounts for nuclear loss, and ccc is the electronic stopping at zero scattering angle. The parameters c,~ and c,~ can only be determined by fitting to experimental data. EBmer and Wedell (EW) have revised the MKW calculation in a recent work [S] but have dropped the correlation between elastic and electronic energy loss that was used in ref. [7]. With regard to both these treatments, three comments may be made. First, in the Ne -+ C data shown in fig. 5, we observe strong evidence for an angle-dependent inelastic electronic energy loss that is correlated with the elastic loss, contrary to the assumption of EW. Second, we have shown in fig. 6 that the nuclear loss dominates the angle-dependence for the Bi --f C case. However, when we use the MKW treatment with c,, = 0, as shown by the dashed line in fig. 3, we find that the observed thickness dependence is not reproduced by the calculation; this disparity suggests that the small angle approximation is not adequately fulfilled for this case. Third, for lighter projectiles, e.g. Ne + C, where the MKW elastic loss may be satisfactory, the experimentally derived values for c,, and cez (ref. [6]) from the thickness dependence at a = 0” cannot describe the angle-dependent data of fig. 5. This breakdown of the MKW description originates from the small angle appro~mation used in eq. (1).
CYidegfeesi
Fig. 6. Experimental most probable emergy losses ( X) for
0.80, Bi -+ C and the corresponding MCCS results (0). as a function of emergent angle. The dashed curves are path-dependent values only, as in fig. 5.
4. Conchsions The angle dependence of the energy loss is clearly observed in our measurements. For both light and heavy STOPPING POWER WORKSHOP
42
H. Geissel et al. / Energy-angle
projectiles (Ne, Bi), elastic collisions dominate the angle dependence of energy loss. In the Bi case, the entire effect can be accounted for without invoking an angledependent inelastic loss, within the limits of uncertainty in both the experiment and computer modelling. This is not so for Ne projectiles. For angles a < 3a,,*,’ we cannot quantitatively describe our measurements with a model that includes only elastic and path-dependent electronic energy loss. Thus we infer the existence of a large angle-dependent inelastic loss. Neither MKW nor EW calculations can describe the experimental results. Multiple scattering distributions are in good agreement with analytical and Monte Carlo calculations. Since the angular distributions are determined mainly by the elastic collisions, the inclusion of an angle-dependent inelastic energy loss mechanism will have a negligible influence on the MCCS angular distribution results. We are grateful to G.A. Sims for technical assistance during the course of these measurements. One of us (H.G.) acknowledges the receipt of a research grant from the Deutsche Forschungsgemeinschaft and thanks the Chalk River Nuclear Laboratories for their kind hospitality.
References [l] N. Bohr, Kgl. Dan. Mat. Fys. Medd. 18 (1948) no. 8. [2] J. Lindhard, V. Nielsen and M. Scharff, Kgl. Dan. Mat. Fys. Medd. 36 (1968) no. 10.
distributions for Ne and Bi in C
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