J . Phys. Chem. 1994,98, 4043-4049
4043
Track Effects in Water Radiolysis: Yields of the Fricke Dosimeter for Carbon Ions with Energies up to 1700 MeV1 Jay A. Laverne' and Robert H. Schuler Radiation Laboratory and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556 Received: December 27, 1993; In Final Form: February 10, 1994"
The radiation chemical yields of the Fricke dosimeter have been determined for carbon ions with energies up to 1700 MeV. These yields can be described by a general relation of the form Go = GB (G,-GB) (1 - EB/Eo)F where G, and GB represent the limiting yields a t high energy and at the Bragg peak, respectively, and F is a dimensionless factor given by a(E0 - E B ) ~ / ( ~a(Eo - E B ) ~ )The . initial value of the carbon ion energy is Eo in MeV while EB is the energy a t the Bragg peak, 3 MeV in the case of carbon ions. Taking G, as the yield observed with fast electrons (15.5 molecules/lOO eV) and GB as 2.65 molecules/lOO eV, the yields observed for aerated solutions are fitted very well for carbon ions by values of the empirical parameters a = 0.0258 and m = 0.520. It is shown that the differential yiefds are never more than 25% greater than the yields averaged over the track. Comparative measurements made in deaerated solutions provide information on the energy dependence of the hydrogen atom yield which increases from small values a t low energies to only -2 H atoms/100 eV for 1000-MeV carbon ions. Since the latter value is only 55% of the hydrogen atom yield observed for fast electrons, it is clear that intratrack reactions are still of major importance a t carbon ion energies of -1000 MeV where the L E T is -20 eV/nm, Le. only 10 times that of fast electrons.
+
+
Introduction It has long been recognized that the yield for oxidation of ferrous ion in the Fricke dosimeter by heavy ions is lower than that for fast electrons and is dependent on the linear energy transfer (LET, i.e. the stopping power; -dE/dx) of the ionizing particle.2 This dependence results from the increasing importance of intratrack reactions between the initial radicals as compared with diffusion into the bulk as the particle LET increases. Most early studies of the Fricke dosimeter were performed with protons, deuterons, or helium ions, and the results have been summarized previously.3.4 Because these particles have relatively low LETs (10-100 eV/nm), it is of interest to extend the measurements on this important dosimetric system to more massive and highly charged ions. Preliminary measurements with up to 102-MeV carbon ions have shown that the ferric ion yields are similar to those found with 10-MeV helium ions.5 More detailed studies with low-energy lithium, beryllium, boron, and carbon ions4 have demonstrated conclusively, as had been suggested earlier from a comparison of the yields produced by protons and helium ions? that the differential ferric ion yields are dependent not only on the LET but also on the charge of the ionizing particle. Because of this charge dependence, a coherent description of the effects of LET on the radiation chemical yield can be obtained only from measurements for a particular ion over a very wide range of energies. The present paper reports a comprehensive study of the Fricke dosimeter with carbon ions having energies up to 1700 MeV and includes parallel measurements on ferrous oxidation yields in the deaerated Fricke system which provides information on the LET dependence of the H atom yield. Experimental considerations require that appropriate studies be carried out a t a number of different accelerator facilities and with a proper comparison of absolute yields. Earlier measurements made at the tandem Van de Graaff of the Notre Dame Nuclear Structure Laboratory with carbon ions having energies up to 35 MeV3v4have now been extended to energies up to 200 MeV using the ATLAS linear accelerator at Argonne National Laboratory and up to 800 MeV using the K1200 cyclotron of the Michigan State University National Superconducting Cyclotron Laboratory (NSCL). Ad@
Abstract published in Advance ACS Abstracts. March IS, 1994.
0022-3654/94/2098-4043%04.50/0
ditional experiments with carbon ions having energies of 1700 MeV were carried out at the BEVALAC facility of the Lawrence Berkeley Laboratory. Because of the wide range of energies used, one obtains a consistent description of the energy dependence of the ferric ion yield which allows evaluation of the differential yield over the LET range of 20-1000 eV/nm. For the highest energy carbon ions (lowest LET), the differential ferric ion yield is still well below the yield of 15.5 ferric ions/ 100 eV found with fast electrons7 where the LET is only 0.2eV/nm. It is clear from this observation that, in general, intratrack reactions are of considerable importance for heavy particles having LETs even as low as a few eV/nm.
Experimental Section Solutions and Analytical Measurements. Fricke dosimeter solutions were 0.01 M in ferrous ammonium sulfate and 0.8 N in sulfuric acid. No chloride was presenf. The high ferrous ion concentration was used to minimize depletion problems. Solutions were either air-saturated or deaerated in the radiolysis cell by purging with helium before and during the radiolysis. Water was obtained from a conventional radiation chemical triple still employing alkaline permanganate and acidic dichromate. Final distillation was in an all quartz system. Quartz vessels were used to store the water until its use. The feed stock to the triple still was from a Millipore Milli Q system. Solutions prepared from this water gave blanks with absorbances less than 0.05 and were reasonably stable toward spontaneous oxidation in spite of the high ferrous ion concentration used. Absorption measurements were made at 304 nm with a Beckman DU2 spectrophotometer and were generally reproducible to -0.001, The ferric ion extinction coefficient at 304 nm was taken as 2174 M-1 cm-l at 23.7 'C, and corrections were applied for variations in the analysis temperat~re.~ Irradiation Cells. For the studies at the ATLAS facility and at the NSCL, irradiations were performed in cells similar to those used in previous studies at Notre Dame.4 These cells had a 1-cm optical cuvette and a magnetically driven pump which rapidly circulated the solution through the irradiation zone. Irradiation was through a -6 mg/cm* Mica window. The cells used at the ATLAS were 2 mm deep and had a total of 34 mL of solution. The cells used at the NSCL were 30 mm deep and contained a 0 1994 American Chemical Society
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total of 48 mL of solution. The cell used at the BEVALAC was a cylinder 3 cm in diameter and 1 cm in depth with 1.5 mm thick Supracil plates on the front and back surfaces. In this case, because of the high energy, the carbon ions passed through the cell and there was no provision for stirring the sample during the irradiation. Irradiations at the ATLAS. The measurements at the ATLAS were made with carbon ions having energies, after being passed through the window system, of 190,165,155,145,and 110 MeV. Aluminum absorbers were used to obtain energies between these values. The 110-Mevparticleswereattenuated to 50 MeV, which is comparable to the energy obtained using the Van de Graaff at the University of Notre Dame. Energy loss to the windows and the absorbers was determined using standard stopping power tables.8 At 190 MeV, the range of a carbon ion in water is 0.95 mm so that the beams were completely stopped in the irradiated solution. Beam energies, determined after acceleration, were from time-of-flight measurements in the beam handling system. In general, the particle energies were known to better than 0.5%. Magnetic analysis assured that the particles were fully stripped to the 6+ charge state. Current measurements were made with the target system previously described and shown in Figure 1 of ref 9. It had a 0.32-cm2 circular beam defining aperture and provided for magnetic suppression and measurement of low-energy secondary electrons emitted from the accelerator exit window. The particle beam current was collected from the sample and window system, which effectively acted as a Faraday cup. The total number of particles irradiating the solution was determined by integrating this current as previously described3.4and applying a 3% correction for electrons backscattered from the accelerator exit window, as measured with the magnetic suppression system. These experiments give an absolute value for the number of ferric ions produced per irradiating particle, which is expressed here as GO& in units of molecules/lOO particles where GOis the radiation chemical yield10 averaged over the particle track and Eo the incident particle energy in electronvolts. This quantity is known to the accuracy of the chemical and integrated current measurements and is good to a few percent. Uncertainties in EO do not contribute to the error limits assigned to thesemeasurements of G&o. Except for experiments near the end of the particle range, uncertainties in EOdo not contribute significantly to values of Go determined from these measurements. Beam currents in these studies were 0.5-1 .O nA. The particle flux, spread reasonably uniformly over 0.32 cm2, was 1.5-3.0 X IO9 particles cm-2 s-1. For a 190-MeV carbon ion with a range of 0.95 mm, the dose rate in the irradiation zone was of the magnitude of 6 X 1018 eV g1s-l (Le. 1 X 105 rad s-I). High stirring rates were required to avoid depletion of the sample. However, the average time the solution resided in the irradiation zone was estimated" to be only a few milliseconds so that less than 1% of the oxygen (G(-02) = 1) or of the ferrous ion (G(-Fe2+) = 10) would have been consumed while the sample was in the irradiation zone. With adequate stirring, no evidence for sample depletion was found in spite of the small volume in the irradiation zone. Samples of -34 mL were given total doses of -6 X 1017 eV g-1 (- 1 X IO4 rad). With repeated irradiations the ferric ion concentration was found to increase linearly with total dose. Irradiations at the NSCL. The target system and beam monitoring for the experiments at the NSCL were the same as at the ATLAS. Because the range of the particles was 13 mm at the maximum energy available, 830 MeV, an irradiation cell 30 mm long was used to ensure that the beam would be completely stopped in the sample. Carbon ions were accelerated to energies of 830 and 475 MeV. Since even small changes in particle energy required long times (hours) for the adjustment of cyclotron frequency and beam handling parameters, experiments were carried out at intermediate energies with aluminum absorber
-
-
'
LaVerne and Schuler methods similar to those used in our previous studies on HOz production.12 The energies of the particles incident on the solution were determined by correcting the initial beam energy for the energy loss in the absorbers and window system. As discussed in previous work on HOz production a t comparable energies,Iz above -200 MeV the TRIM91 stopping power tables used in making these corrections must be increased by 2%. In general, the use of absorbers was found to be reliable as long as the beam energy was not degraded by more than 50%. For the experiments at the highest energy, was extracted from the ion source, accelerated, stripped to C+6, and then magnetically analyzed. This procedure ensured that the beam was not contaminated with other ions. In the experiments with carbon ions accelerated to 475 MeV, was extracted from the ion source. Since this ion has virtually the same mass-to-charge ratio as 0+4,both ions will be similarly accelerated in thecyclotron, and after stripping, contamination of the beam with 0+8 ions is possible if the cyclotron and beam handling parameters are not carefully maintained. In order to avoid possible complications, an absorber was used to degrade the initial energy to 370 MeV after the ions were stripped so as to change the relative momentum of the carbon and oxygen ions sufficiently that subsequent magnetic analysis ensured beam purity. Several experiments were also conducted with the 475-MeV ions. Experiments with sufficient absorber to completely stop the beam confirmed that there was no 0+8 contamination. Beam currents were -0.5 nA (5 X lo8 particles/s) spread evenly over an area of 0.32 cm2 (particle flux of 2 X lo9 particles cm-2s-1). Totaldoseswere4 X 1019eVinabout48mLofsolution (- 1 X lo4 rad). The solutions were stirred rapidly throughout the radiolysis, and ferric ion production was found to be linear with dose. Corrections to the current measurement to account for backscattered electrons increase with energy and limit the accuracy at high energy. Measured corrections of 6 and 8%were applied at 475 and 830 MeV, respectively. Irradiations at the BEVALAC. The minimum usable energy of carbon ions available at the BEVALAC (- 1800 MeV) was attenuated to 1680 MeV after being passed through the accelerator exit window, several ion chambers, and the cell window. At this energy the residual range in water is -5 cm. Differential experiments were carried out in which the ferric ion yields were determined for carbon ions as they passed through 1 cm of sample. In addition to the measurements a t the full energy, experiments were performed with a 1- or 2-cm water column placed directly in front of the irradiation cell. Energy loss to the sample cell was determined from the TRIM9 1 stopping power tables.8 The beam profile was mapped with a wire chamber and particle currents determined from a sectored ion chamber placed directly in front of the irradiation cell. The ion chamber had been calibrated by the BEVALAC staff to give absolute currents and was crosschecked during these runs using a Faraday cage. These measurements provide information on the ferric ion yield averaged over an energy interval. The energy intervals (217, 267, and 332 MeV with 0, 1, and 2 cm of added water absorber, respectively) are sufficiently small that the measured differences closely approximate the differential ferric ion yields at the midpoints of 1570, 1190, and 890 MeV. Uncertainties due to scattering and fragmentation become increasingly important as the initial particle energy increases, but these effects should not be a major factor in the present determinations. It is estimated that in these experiments the measured differential yields could have errors of lo%, primarily because of uncertainties in determining particle flux.
-
Results and Discussion
G.&(FG+): The Productionof Ferric Ion. In the experiments a t the ATLAS and at the NSCL, one, in effect, measures the total amount of product for a particle at a given initial energy,
The Journal of Physical Chemistry, Vol. 98, No. 15, 1994 4045
Track Effects in Water Radiolysis
1400 1200
E
fast electrons ,,'
fast electrons ,,'
z
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8ooo! 6000
I
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Particle Energy, E, (MeV)
Particle Energy, Eo (MeV)
fast electrons ,,'
fast electrons
1400
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o 6000
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50
100
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Figure 1. Production of ferric ions (GO&, molccules/lOO particles) as a function of initial carbon ion energy,EO,for aerated (top) and deaerated (bottom) solutions: (W) this work at the ATLAS; (0)ref 4; (v)ref 6; (X) ref 13; (+) ref 14. The dashed lines are the fast electron limits (G(Fe3+)= 15.45 in aerated solution (ref 6) and 8.22 molecules/100 eV in deaerated solution (ref 15). The solid line was obtained by the use of eq 2 with the appropriate values in Table 1.
Figure 2. Production of ferric ions (GO&, molecules/100 particles) as a functionof initial carbon ion energy, EO,for aerated (top) and deaerated (bottom) solutions. The symbols for this work at the NSCL are (k)for 830 MeV initial energy, (V)for 475 MeV initial energy, and (A)for 475 MeV initial energy attenuated to 370 MeV and (0)for this work at the ATLAS. The dashed lines and the solid lines are the same as in Figure
Eo.The results are reported in this section as G&o.IO The energy
the studies at the higher energies and at the ATLAS. In general, we conclude that absorbers can be used quite well to attenuate the particle energies by up to 50%. For higher attenuations one must carefully establish the particle range for the beam of interest using absorbers. In the studies at the BEVALAC, the energy loss to the sample at the highest incident energy (1680 MeV), as determined from the TRIM91 stopping power tables, is 217 MeV/cm. From the measured ferric ion production rate, a differential yield of 11.3 is calculated at an average energy of 1570 MeV. For the experiments with 1- and 2-cm water absorbers, differential yields of 10.8 and 10.2 are obtained at average energies of 1190 and 890 MeV, respectively. The energy transmitted by the 2-cm water column, 720 MeV, should produce a total of 5900 molecules/ 100 particles, as determined from the experiments a t the NSCL. Adding this value to the measured differential yields gives the values for G&o a t these energies, as indicated by the diamonds in Figure 3. A smooth transition is observed from the data obtained a t the NSCL to that obtained a t the BEVALAC. Ferric ion yields were not measured in deaerated solutions at the BEVALAC. Unfortunately, this instrument was decommissioned before the appropriate experiments could be performed. G(Fe3+): The Track-Averaged Yield. The track-averaged radiation chemical yields derived from the data of Figures 1-3 are given in Figure 4 along with data previously reported for protons6-15and helium ions.3~~ Even at the highest energy studied these observed yields are well below those for fast electrons, as indicted by the horizontal dashed lines. In the region of the inflection points in the figure, similar yields are observed for helium and carbon ions having energies 10- and 200-fold greater than for protons. At these energies the relative LETS are 1.0: 1.9:3.7, respectively, for protons, helium ions, and carbon ions.
dependences for carbon ions having energies up to 200 MeV, as determined at the ATLAS, are given in Figure 1 for both the aerated and deaerated Fricke systems. Also included in the figure are previously reported results for energies up to 35 MeV determined at the Notre Dame facility3.4 and earlier results on the aerated system for carbon ions in the 30-100-MeV region from studies at the Yale HILAC,5 at the 160-cm cyclotron of the Institute of Physical and Chemical Research a t Tokyo,13and a t the Lawrence Berkeley Laboratory 184-in. cyc10tron.l~ First it is noted that the present results smoothly extend those obtained a t the Notre Dame accelerator and for aerated solutions are in very reasonable agreement with the data obtained a t the other accelerators in the 30-100-MeV region. This agreement is quite gratifying, considering the very different types of accelerators and methods of energy determination. The solid curves represent the energy dependences given by the empirical expressions described below. The dashed lines in the figure correspond to the values of G&o expected if the yields were those observed for fast electrons (Go= 15.5 for the aerated system' and Go = 8.2 for the deaerated system's). The considerably lower yields observed for thecarbon ions reflect, of course, the relatively lower yields of radicals which escape the heavy-ion particle track as compared with fast electron radiolysis. The most extensive determinations at the NSCL were made with carbon ions having an initial energy of 830 MeV, but attenuated by absorbers down to 200 MeV. The resultant data, given in Figure 2, are reasonably consistent with the data at lower initial energies although there is somewhat more scatter than might be expected in the 300-400-MeV region for the data from the aerated system. The data in Figure 2 for carbon ions having initial energies of 475 and 370 MeV are consistent with
1.
20000
",
15000
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TABLE 1: Parameters Used in the Analytical Equations aerated deaerated EB particle (MeV) GB a m GB a m 5.00 0.2223 0.9037 4.00 0.1002 1.077 'H 0.1 3.80 0.04969 0.7516 3.20 0.05993 0.6225 'He 1.0 3.0 2.65 0.02578 0.5201 2.60 0.03237 0.4802 12C
-
7
X
E 2 10000-
*-
LaVerne and Schuler
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I
al
k
0
5000
-
01' 0
'
500
1000
I
1500
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Particle Energy, E, (MeV) Figure 3. Production of ferric ions (G&I, molecules/100 particles) as a function of initial carbon ion energy,EO,for aerated solution: (*) this work at the BEVALAC; (A)this work at the NSCL. The dashed lines and the solid lines are the same as in Figure 1. 16
fast.9kctrsns.......___. ......__ _ _ ..__.___ __ _ _. _ . I----.
'H
14t
respectively, and the empirical parameters a and m are used to fit the specific set of data. These limiting yields and parameters are expected to reflect the rather complex processes which involve both second and higher order reactions of the initial radicals within the track and their diffusion into the bulk medium. In order to weight the data properly, rather than use eq 1, one should fit the plots of G&o as a function of EO. In addition, at low energies the radiation chemical yield approaches a lower limit GBat energy EBcorresponding to the Bragg peakl6 (3 MeV for carbon ions) where the energy loss is at a maximum. Since very little is known about radiation chemical yields below the Bragg peak, it is assumed that the yield is constant at lower energies. Equation 1 can be modified to give G&o in the form G,(Fe3+)Eo = GBEO
+ (G,
- GB)(Eo- EB)F
(2)
where F is a dimensionless factor given by
F = U ( E 0 - E,)"/( 1
0 1 00
10'
1 02
o3
1
10'
Particle Energy, E, (MeV)
12
(2a) The values of G, are reasonably assumed to be given by the fast electron values of 15.457for aerated solutions and 8.2215 for deaerated solutions. Using a nonlinear least-square technique,I7 the solid curves in Figures 1-3 correspond to the best fit of eq 2 for the carbon ion data with the values of a and m given in Table 1. Similar fits to the data for protons6J5 and helium ions4 are also given in the figure. In all cases it is seen that the empirical fits describe the observed dependences very well. As will be shown in the next few sections, eq 2 is quite useful for describing a number of derived quantities. For example, the track-averaged radiation chemical yield is obtained directly as Go(Fe3+) = GB
0 100
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102
1o3
1 04
Particle Energy, E, (MeV)
Figure 4. Track-averagedferric ion yields (GO, molecules/lOO eV) as a function of initial particle energy, EO,for aerated (top) and deaerated (bottom) solutions. The symbols represent, for carbon ions, (*) this work at the BEVALAC, (A) this work at the NSCL, (M) this work at the ATLAS, and (0)ref 4; for helium ions, (X) ref 4; and for protons, (+) refs 6, 15. The dashed lines are the fast electron limits (G(Fe3+) = 15.45in aerated solution (ref 7) and 8.22 molecules/100 eV in deaerated solution (ref 15)). The solid lines were obtained by the use of eq 3 with the appropriate values in Table 1.
The limiting yield at low energies seems to be about 1 unit lower for carbon than for helium ions. As previously pointed out: this difference largely results from the lower yield of H atoms that escape from the spurs of carbon ions and the higher yield of HO2 produced within the track core. Analytical Description of the Energy Dependence. It is useful to describe the observed energy dependence by a n analytical function. The sigmoidal character of the data in Figure 4 suggests an energy dependence of the form
+
+
Co(Fe3+)= GL (G, - G,)[aEom/(l aEo")] (1) where GLand G, are the limiting yields at low and high energies,
+ a(E0 - E,)")
+ (G,
- GB)(1 - EB/Eo)F
(3)
The energy dependences predicted by eq 3 using the parameters in Table 1 are given by the solid lines in Figure 4. Equations 2 and 3 provide a very comprehensive way to describe the energy dependences of the H atom and net water decomposition yields and that of the differential yields which are appropriate for comparison with model calculations. The H Atom Yield. A comparison of the yields for aerated and deaerated solutions provides a measure of the H atom yield since H atoms oxidize three ferrous ions in the aerated solutions and only one in the deaerated solutions.2 This relationship can be written in the following form.
The track-averaged H atom yields corresponding to the data of Figure 4 are given in Figure 5. As expected, these yields increase with increasing particle energy and are very dependent on the type of particle. The solid lines in Figure 5 are calculated from the differences given by eq 3. It is seen that for 10-MeV carbon ions the H atom yield is very small (-0.2) and approaches a limit very near to zero at the Bragg peak (LET = 1000 eV/nm), so it is clear that very few H atoms escape the dense track of lowenergy carbon ions. The data for helium ions and protons show similar energy dependences at roughly 1 and 2 orders of magnitude lower energy, respectively. Extrapolation of the available data, however, indicates that at their Bragg peaks (LETS of 200 and 80 eV/nm, respectively) there are small, but significant yields of H atoms which escape from the particle track. At the other end of the scale, it is seen that with 830-MeV carbon ions the H atom yields are about half those found with fast electrons. It is clear
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3,5 ....................................................... fast electrons
3.0
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4 t
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Particle Energy, E, (MeV) Figure 5. Track-averaged hydrogen atom yields (molecules/100 eV) as a functionof initial particleenergy, EO. The symbols represent, for carbon ions, (A)this work at the NSCL, (m) this work at the ATLAS, and (0) ref 4; for helium ions, (X) ref 4; and for protons, (+) refs 6, 15. The dashed line is the fast electron limit (3.62). The solid lines were obtained by the use of eq 3 with the appropriate values in Table 1.
1
.
.
, . ' ' . ' '
10
fast electrons ....................................
..............
x/
100
. .
' " " d
1000
Figure 7. Track-averaged net water decomposition yields (molecules/ 100eV) as a functionof initial particleenergy, EO. The symbolsrepresent, for carbon ions, (A)this workat theNSCL, (m) this workat the ATLAS,
and (0)ref 4. The dashed line is the fast electron limit (4.60). The solid line was obtained by the use of eq 3 with the appropriate values in Table ....................................
14 12 io -
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. . . . . . I
Particle Energy, Eo (MeV)
16 f . . ..!??!?!?F?ro?s..
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-
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.
. . . . . . . I
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. . . . . . .d
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Particle Energy, E, (MeV) Figure6. Ratioof track-averagedferricion yieldsinaeratedanddeaerated solutionsasa functionof initial particleenergy,Eo. Thesymbols represent, for carbon ions, (A)this work at the NSCL, (m) this work at the ATLAS, and ( 0 )ref 4; for helium ions, (X) ref 4; and for protons, (+) refs 6, 15. The dashed line is the fast electron limit (1.88). The solid lines were obtained by the use of eq 3 with the appropriate values in Table 1. from this that intratrack reactions are still of major importance a t carbon ion energies of -1000 MeV where the LET is -20 eV/nm, i.e. only 10 times that of fast electrons. Ratio of the Aerated to Deaerated Yields. Traditionally, the ratio of the ferricion yield in aerated solutions to that in deaerated solutions has been used as an indicator of the magnitude of the yield of H atoms which escape the particle track. For fast electrons this ratio is 1.88,'J5 which presumably represents an upper limit for very energetic heavy ions. If no H atoms escape the spurs, then the ratio is expected to approach unity at low energies. We have previously reported a ratio of 1.06 a t the carbon ion Bragg peak and extrapolated the observed values of a number of light ions to a limiting value of 1.01 for low-energy heavy ions.4 It is seen in Figure 6 that this ratio for carbon ions increases from -1.1 at 10 MeV to -1.7 a t 830 MeV. The solid curves in Figure 6 represent the ratio calculated from eq 3 using the parameters of Table l. The increase in the ratio with increasing carbon ion energy almost parallels that found with helium ions with only a displacement in the energy which is very nearly the same as the ratio of the particle LETS. If the observed trend for the ratio of the ferric ion yields continues to higher carbon ion energies, then one would expect to see values similar to that found with fast electrons when the carbon ions have energies of about 5000 MeV. This energy corresponds to an LET of about 10 eV/nm. Experiments at that energy would be very difficult to interpret because of particle fragmentation. Even though the ratios of the ferric ion yields in aerated and deaerated solutions observed with high-energy protons are similar to that found with fast electrons, the yield of H atoms is different
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The Journal of Physical Chemistry, Vol. 98, No. 15, 199'4
fast_electrons 16 . . . . . . _ . _ _ _ _ _ _ _ _ _ _ _ _ _-.-._ _ _ _ . _ _ _ _ _ _ _ _ _ _ .fast _ _electrons __....... ....................................................... 14
*\
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LET in Water (eV/nm)
Particle Energy (MeV) fast electrons
__________________________~____
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01 1
'
' ' ' . . I . /
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'
' " . . . "
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'
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LET in Water (eV/nm)
Figure9. Differential ferricion yield (Gi,molecules/lWeV) as a function of particle LET for aerated (top) and deaerated (bottom) solutions. The
data for carbon ions obtained at the BEVALAC are represented by diamonds for this work and by a long box for ref 18. The dashed lines and the solid lines are the same as in Figure 8.
Net Water Decomposition Yield. The yield for net water decomposition is given by the yield of ferric ions in the deaerated solutions less the H atom yield.2 For fast electrons the net water decomposition yield is 4.6 molecules/ 100 eV.7J5 The values for carbon ions calculated from the data and from eq 3 are given in Figure 7. Thenet water decomposition yields increase from about 2.5 at low energies to 3.3 molecules/ 100 eV at 1000MeV. There is considerably more scatter in the proton and in the helium ion data, but therangesofvaluesare 3.3-3.8 and 3.0-3.3, respectively. All of these data give water decomposition yields for heavy ions that are appreciably less than for fast electrons, indicating that there is considerable recombination of the initial radicals within the tracks of very energetic heavy ions. Of course, it is possible that the initial yields of water decomposition for heavy ions are somewhat lower than that for fast electrons. Track Segment or Differential Yields. Almost all experiments involve the determination of track-averaged ferric ion yields, and these measurements are very important for dosimetry studies. However, differential or track segment yields (Gi = d(G&o)/ dEo, i.e. the slopes of the dependences in Figures 1-3) are better for the comparison between different types of particles and with track calculations. Direct determination of the differential yields from the differences in the data of Figures 1-3 is not usually feasible because of the large scatter which would be introduced. More meaningful results are obtained by taking the derivative of the fitted curves. With the use of eq 2 it is possible to obtain the following equation for the differential ferric ion yields.
The differential ferric ion yields for protons, helium ions, and carbon ions are shown in Figure 8 as a function of particle energy. Included in this figure are the present results for the directly
0
d
1
10
Ino
1000
LET in Water (eV/nm)
Figure 10. Differential H atom yield (molecules/lOO eV) as a function of particle energy (top) and LET (bottom). The dashed lines are the same as in Figure 6 while the solid lines were obtained by the use of eq 4 with the appropriate values in Table 1.
measured differential ferric ion yields from the BEVALAC and those of Christman, Appleby, and JaykoIs also obtained at the BEVALAC. The present results are slightly lower than those of the other BEVALAC experiment and may be caused by fragmentation problems in the latter since that study started with 4500-MeV carbon ions whereas this work used initial 1800-MeV ions. Nevertheless, the agreement among all of the results is very good and indicates that fragmentation is not an extremely great problem. The combination of all the different results for carbon ions gives ferric ions yields over 3 decades of energy. Ferric ion yields in aerated solutions increase by about 3-fold as the carbon ion energy increases from 12 to 1000 MeV. Deaerated ferric ion yields are considerably less sensitive to carbon ion energy with an increase of a factor of 2 over the same energy range. Differential and track-averaged yields are by definition the same at low particle energy and are expected to approach one another at very high energies. A comparison of the calculations using eqs 3 and 5 for aerated solutions with carbon ions shows that the differential ferric ion yield is never more than about 25% greater than the track-averaged yield. The ratio of the two yields is actually very nearly constant in the range 1.25-1.20 for carbon ions of about 10-1000 MeV. The available proton and helium ion data do not extend to sufficiently high energies, but the data also suggest that the differential yields with these ions also are at a maximum value 20-30% greater than the track-averaged yields. For deaerated solutions the corresponding ratios are 1.1. Differential ferric ion yields are shown in Figure 9 as a function of particle LET. The data for carbon ions covers LETS in the rangeofabout 10-1000eV/nm. Thisrangeismorethansufficient to overlap the results with protons and helium ions. As previously discussed many times, the LET dependence of the differential ferric ion yields can be considerably different for two ions of the same LET. These experiments provide the magnitude of those differences for particles of widely differing charge. It is obvious
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Track Effects in Water Radiolysis that the local track structure determines product yields and this quality is not solely determined by LET. At LETs even as low as 10 eV/nm, the ferric ion yields in both aerated and deaerated solutions are only about 75% of that found with fast electrons. It is estimated that LETS of only a few eV/ nm are needed before the limiting fast electron value is reached. Figure 9 shows that the differences in ferric ion yields among the different types of ions begin to decrease with decreasing LET. The data suggest that if the radiation chemical yields with all heavy particles eventually reach the limiting fast electron yield, they do so at about the same LET. It is impossible to determine from the present results if the same limiting value is reached for all types of particles even though we have assumed as much in our choice of G,. Previous results on the production of HO219 had suggested otherwise, and such an outcome is still possible. Differential H atom yields are shown in Figure 10 as a function of particle energy and LET. Although the data for helium ions seem to be slightly high at low LETs, there appears to be a convergence of H atom yields with decreasing particle LET. At the highest LET for protons, the H atom yields are equivalent to those found with helium ions of 2 and carbon ions of 5 times greater LET. In summary, these experiments for carbon ions represent the largest range of LETS for which a product of the radiolysis of water has been measured for a single incident ion. They should bevery useful for the application and developmentof track models. They also give considerable insight into the effects of LET on product yields in the radiolysis of acidic water.
Acknowledgment. We thank Argonne National Laboratory for the use of the ATLAS facility, the National Superconducting Cyclotron Laboratory at Michigan State University for the use of their facility, and Lawrence Berkeley Laboratory for the use
The Journal of Physical Chemistry, Vol. 98, No. 15, 1994 4049 of the BEVALAC facility. We thank Dr. B. Glagola of the Argonne staff, Drs. R. Blue and N. Anantaraman of the NSCL staff, and Dr. B. Ludewigt of the BEVALAC staff for their assistance with accelerator and beam transport setup. The ATLAS and BEVALAC facilities are funded by the U. S. Department of Energy and the NSCL is funded by the National Science Foundation.
References and Notes (1) The research described herein was supported by the Office of Basic Energy SciencesoftheDepartmentofEnergy. Thiscontributionis No. NDRL3625 from the Notre Dame Radiation Laboratory. (2) Allen, A. 0. The Radiation Chemistry of Water and Aqueous Solutions; Van Nostrand: New York, 1961. (3) Laverne, J. A.; Schuler, R. H. J . Phys. Chem. 1983.87, 4564. (4) Laverne, J. A.; Schuler, R. H. J . Phys. Chem. 1987,91, 5770. ( 5 ) Schuler, R. H. J. Phys. Chem. 1967, 71, 3712. (6) Schuler, R. H.; Allen, A. 0. J. Am. Chem. Soc. 1957, 79, 1565. (7) Schuler, R. H.; Allen, A. 0. J. Chem. Phys. 1956, 24, 56. (8) Ziegler, J. F.; Biersack, J. P.; Littmark, U. The Stopping and Range of Ions in Solids; Pergamon: New York, 1985. (9) Laverne, J. A,; Schuler, R. H. J. Phys. Chem. 1987, 91, 6560. (10) Radiation chemical yields, G values, are given in units of molecules per 100 eV. For consistency, the values of the total amount of product G&o are given in units of molecules per 100 particles so that the radiation chemical yield can be obtained by dividing by the particle energy in electronvolts. (11) Duncanson, I. B. Fusion 1989, 26. (12) Laverne, J. A.; Schuler, R. H. J. Phys. Chem. 1992, 96, 7376. (13) Imamura, M.; Matsui, M.; Karasawa, T. Bull Chem.SOC.Jpn. 1970, 43, 2745. (14) Jayko, M. E.; Tung, T. -L.; Welch, G. P.; Garrison, W. M. Biochem. Biophys. Res. Commun. 1976,68, 307. (15) Barr, N. F.; Schuler, R. H. J. Phys. Chem. 1959, 63, 808. (16) Collinson, E.; Dainton, F. S.; Kroh, J. Proc. R . SOC.London A 1961, 265, 407. (17) Bevington, P. R. Data Reduction and Error Analysis for Physical Sciences; McGraw-Hill: New York, 1969. (18) Christman, E. A.; Appleby, A.; Jayko, M.Radiat. Res. 1981, 85, 443. (19) Laverne, J. A,; Schuler, R. H. J . Phys. Chem. 1986, 90, 5995.
