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390 Charged Particle and Photon Interactions with Matter

between ∼10

−12

and (1–3) × 10

−10

s, and then decreases steeply to ∼2.2mM and 175μM at ∼10

−8

s, ∼165

and 15μM at ∼10

−7

s, and ∼17 and 1.3μM at the microsecond time scale, respectively. These predic-

tions of the track oxygen concentrations in fact compare very well with the experimental estimates

of Baverstock and Burns

(1976, 1981) and

Baverstock et al. (1978)

who found

that, for ∼100keV/μm

α-particles, [O

] would be 4.2mM at early times and 51μM after 10

−8

s.* These O

concentrations

provide clear evidence that supports the hypothesis that O

is engendered in substantial yields in the

tracks of densely ionizing radiation. As a consequence, the present calculations strongly suggest that

this excess production in situ of O

is a key intervening factor in the increased biological efciency

of radiations of high LET with, in turn, profound consequences in radiobiology, oxidative processes,

and other applications. In particular, they largely plead in favor of the “oxygen in the heavy-ion

track” hypothesis to account (at least in part) for the observed decrease of OER with LET.

14.6 ConCluding remarks

The Monte Carlo track structure simulations presented in this chapter strongly support the impor-

tance of the role of multiple ionization of water in the high-LET, heavy-ion radiolysis of pure,

deaerated liquid water. In particular, the mechanism of double ionization is found to largely pre-

dominate at high LET, whereas it is insignicant at low LET. Upon incorporation of the multiple

ionizations of water, a good overall agreement is obtained between the calculated yields and the

available experimental data. Most remarkably, Monte Carlo calculations quantitatively reproduce

the large increase observed in the

HO /O

2 2

i i−

yield with increasing LET, conrming a hypothesis

put forward several years ago by Ferradini and Jay-Gerin (1998) that MI of water should intervene

in the high-LET, heavy-ion radiolysis of water in the form of the production of

HO /O

2 2

i i−

radicals.

With the exception of protons, our simulations also simultaneously predict a maximum in the curve

for

H O

2 2

as a function of LET around 180–200 keV/μm, in accord with experiment (although there

are large uncertainties in measured H

yields for different kinds of radiation). In addition, for

each ion investigated, this maximum of

H O

2 2

occurs precisely at the point where

HO /O

2 2

i i−

begins to

rise sharply, suggesting, in agreement with previous experimental data, that the yields of

HO /O

2 2

i i−

radicals and H

are closely linked. In accordance with experiment, we nd that the maximum

observed in

H O

2 2

in the case of the radiolysis of 0.4 M H

solutions is more pronounced than

that found in neutral solutions and about 45% greater in magnitude. Further experiments on the

yields for LET above 1000keV/μm would be highly desirable to help clarify the question of

the

limiting value of

H O

2 2

at very high LET for both neutral and acidic liquid water.

Another point needing special attention in the problem at hand is the determination of reliable

“condensed-phase” multiple ionization cross-section data. In fact, existing heavy-ion cross sections

have

generally been obtained in water vapor but not in liquid water. To overcome these difculties,

we have adopted in our work a strategy consisting of inferring MI cross sections indirectly from

measurements (

G G

in the heavy-ion radiolysis of air-free aqueous FeSO

–CuSO

solutions

at pH ≈ 2.1) made in the liquid phase. Using these cross sections in our Monte Carlo simulations

allowed us to reproduce, among other things, the maximum in

H O

2 2

versus LET that is observed

experimentally. Other published reports have used cross-section data derived directly from gas-

phase measurements or from gas phase-based calculations with various theoretical adjustments to

take into account the effects due to the phase, but they could not reproduce any maximum in the

variation of

H O

2 2

with LET. More experimental and theoretical work is clearly needed in this area.

* Incidentally, another interesting remark that can be inferred from Figure 14.11b concerns the time dependence of

] for 300 MeV incident protons (LET ∼ 0.3 keV/μm). In fact, our calculated O

concentrations in the tracks vary in

the range ∼0.2–0.45 μM between 10

−12

and ∼2.5 × 10

−9

s and then fall to reach a value of ∼8.9 × 10

−4

μM at 10

−6

s. As

expected, these concentrations are too low to sensitize cells at low LET, based on the ndings of Millar et al. (1979),

who found that, for cobalt-60 γ radiation, sensitization of Chinese hamster cells (line V-79-753B) by oxygen occurs

progressively as the concentration of oxygen (present at the time of irradiation) is increased from ∼0.46 μM to 1.4 mM

(see also von Sonntag,2006).

Radiation Chemistry of Liquid Water with Heavy Ions: Monte Carlo Simulation Studies 391

For four representative irradiating ions (

, and

), our results show, upon

incorporation of the mechanism of MI of water in the simulations, a substantial production in situ

of “track” O

that is available immediately after the passage of the ion, pleading in favor of the

radiobiological “oxygen in the heavy-ion track” hypothesis. Such an excess production of molecular

oxygen in high-LET, heavy-ion tracks is not observed with lower LET radiations. We have shown,

in particular, that the dissociation of doubly ionized water molecules is responsible, to a large extent,

for this O

production via the formation of oxygen atoms. The radiolytic formation, at high LET, of

substantial amounts of O

in heavy-ion tracks can have profound consequences in radiobiology and,

in turn, be of great practical relevance in radiotherapy. In fact, being immediately available after the

passage of the incident ion, this track oxygen can readily react, in cells, with adjacent potentially

lethal lesions formed by the same ionizing particle (e.g., the so-called O

xation of DNA damage)

to produce the observed reduction in the OER with increasing LET. Even if the present calculations

cannot exclude the possibility of other mechanisms that may also be involved to fully account for

the decrease of OER with LET (or equivalently for the increased efciency of high-LET radiations

for the inactivation of tumor hypoxic cells), they appear to clearly indicate that the excess produc-

tion in situ of O

in the high-LET tracks is a key intervening factor.

In contrast to

HO /O

2 2

i i−

H O

2 2

and

the incorporation of the mechanism of MI in the simu-

lations has almost no effect on the primary yields of

−

•

OH, H

•

, and H

(data not shown here)

(Meesungnoen and Jay-Gerin, 2005a; Gervais et al., 2006). As expected,

−

and

diminish

steeply as the LET is increased, and for the highest LET studied, there is almost no

−

and

•

surviving at the microsecond time scale. Our calculated primary H

•

atom yield values present a

slight maximum near 6.5 keV/μm before decreasing steeply at higher LET (similarly to the behavior

of other radicals). As for molecular hydrogen,

is found to rise monotonically with increasing

LET for the different impacting ions studied. The available experimental data are generally well

reproduced

by our calculated escape yields over the whole LET range studied.

a consequence of the fact that the LET does not exactly or uniquely dene the densities of spe-

cies in heavy-ion tracks and, therefore, the subsequent radiation–chemical effects, we observe, for

all the species formed during the radiolysis, an irradiating-ion dependence of the yields at a given

LET. In other words, two different incident ions of equal LET but different velocities produce dif-

ferent

yields due to differences in the effects of track structure on the radiation chemistry.

Finally,

under high-LET irradiation conditions, Equation 14.6 (traditionally given for low-LET

radiolysis

of water) should be rewritten as follows:

−

− + −

+ + + +

+ +

H O e H OH H OH

H OH H OH

H H O

2 2 2

 G G G G G

G G

i i

HH O HO /O O

HO /O

2 2 O

2 2

2 2 2

+ + +

−

G G

i i



(14.48)

(with the same conventions as before). The overall electroneutrality and stoichiometry equations

connecting

these product yields then are

G G G

e OH H

− − +

+ = (14.49)

G G G G G G G

e H

H O

HO /O

2 2

− −

+ + = + + + +

i i i i

2 2 3 4

2 2 2

, (14.50)

while the net yield of water decomposition is given by

G G G G G G

G G G

−

= + + − −

= + +

− −

H O

e H

HO /O

H O

HO /O

2 2

i i i

i i ii−

+ 2

(14.51)

392 Charged Particle and Photon Interactions with Matter

Of course, the material balance does not specify the source of

HO /O

2 2

i i−

and O

. Our present Monte

Carlo track structure simulations show that multiple ionization of water can successfully explain

both the large yields of

HO /O

2 2

i i−

and the excess O

produced in the heavy-ion radiolysis of water

high LET.

aCknowledgments

This work is dedicated to the memory of Professeur Christiane Ferradini, who together with her

colleague

Jacques Pucheault, was a pioneer in the study of the radiolysis of water with heavy ions.

The

authors are grateful to Dr. Norman V. Klassen for reviewing the manuscript. This work is

supported

by the Natural Sciences and Engineering Research Council of Canada.

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