Title. Author(s)Date, H.; Sutherland, K.L.; Hayashi, T.; Matsuzaki, CitationRadiation Physics and Chemistry, 75(2): Issue Date

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1 Title Inelastic collis processes of low energy protons Author(s)Date, H.; Sutherland, K.L.; Hayashi, T.; Matsuzaki, CitatRadiat Physics and Chemistry, 75(2): Issue Date Doc URL Type article (author vers) File Informat RPC75_2.pdf Instructs for use Hokkaido University Collect of Scholarly and Aca

2 Inelastic collis processes of low energy protons in liquid water H. Date*, K.L. Sutherland 1, T. Hayashi 1, Y. Matsuzaki 2, Y. Kiyanagi 2 School of Medicine, Hokkaido University, Sapporo , Japan 1 Japan Science and Technology Agency, Tokyo , Japan 2 Graduate School of Engineering, Hokkaido University, Sapporo , Japan Abstract Product probabilities of and ited particle species along the proton beam track in liquid water are estimated around the Bragg peak reg, taking into account charge changing processes and energetic secondary electron (δ-ray) behavior. Ionizat and itat processes are divided into two categories in this study: primary processes associated with direct proton (or hydrogen) interact and secondary processes arising from the electrons ejected by the primary process. We show that the number of events in the secondary processes producing s and ited particles is larger than that of the primary processes around the Bragg peak while neutralized protons (i.e., hydrogen) with low energy have a large contribut to direct izat. Effects of charge changing processes on izat and itat are also discussed. Key words: proton Bragg peak, inelastic collis, δ-ray, charge transfer, cross sects, liquid water *Corresponding author: Department of Health Sciences, School of Medicine, Hokkaido University N12-W5, Kitaku, Sapporo , JAPAN Phone#: Fax#: date@cme.hokudai.ac.jp

3 1. Introduct When radiat particles interact with bio-materials, the particles transfer most of their energy to electrons. The resultant transformat of atoms and molecules in the material occurs through both electron colliss and direct interact with primary radiat particles (incident protons). The behavior of proton beams in material (specifically water) can be viewed as a canonical system in which incident protons and secondary electrons interact with bio-materials (Fig.1). A proton transfers a maximum of about 4m e /m p (m p : the proton mass, m e : the electron mass) of its energy to electrons through an izat collis. With such a large energy share, electrons generated through proton induced direct izat with water molecules have, therefore, sufficient energy and probability to induce further izat and itat processes with ambient molecules. The energetic secondary electron is the so-called δ-ray. In the energy range of interest, protons travel in essentially a straight line, loosing energy through colliss. At the Bragg peak reg of the proton track, low energy protons may be neutralized through the capture of electrons from water molecules. Conversely, hydrogen atoms arising from this neutralizat process may also undergo electron loss (electron stripping) as well. Both processes must be balanced in a dynamic equilibrium state. These charge changing processes take place along the proton's original straight trajectory. The tracks of the produced electrons spread out in a tree-branch structure (see Fig.1). Collis interact products (s and/or ited particle species) are also generated along the track within the branch structure. Although the density is lower, the number of the products is higher in the outer reg than around the original proton track due to the secondary electron processes. Conventally, the relative biological effectiveness (RBE) of radiat has been discussed based upon the energy deposit per unit length, that is, the stopping power (de/dx) or linear energy transfer (LET). However, from a microscopic point of view, the biological-cell mutat probability depends on the izat and/or itat rate, not the energy deposit itself. 2

4 Accordingly, the product rate of izat and itat particle species per unit volume in the track structure is essential for determining the radiat weighting factor (w R ) or quality factor of radiat (Q). In this study, we calculate the probability of izat and itat events by a proton incident in liquid water, in which secondary electron and charge transfer processes are also important. By taking into account event occurrences for both izat and itat by secondary electrons and charge changing react processes, we estimate the effective product rate of izat and itat around the Bragg peak reg per unit traveled of the incident proton. We also investigate implicit effects of the secondary electrons on the stopping power of protons. 2. Method of calculat In the present analysis, we estimate event probabilities for izat and itat of water molecules. Ionizat and itat occur in the course of proton transport and in subordinate processes associated with charge change and electron transport. Charge changing processes have an important role in proton energy degradat, particularly around the Bragg peak reg (e.g., Rudd et al., 1992, Uehara et al., 2000). Low energy protons may capture electrons from water molecules becoming neutral-hydrogen atoms. Electrons may also be stripped from a hydrogen atom. In a dynamic charge equilibrium state, the probabilities of both processes are given by Φ 0 = σ 01 σ 10 + σ 10,and where σ 10 and σ 01 are the cross sects for p + H 2 O H + H 2 O + (electron capture) and σ 01 Φ 1 = (1) σ01 + σ10 3

5 H + H 2 O p + e + H 2 O (electron loss). For an incident proton beam, the effective cross sects for izat and itat can be described by σ = σ Φ + σ Φ (2) (H) 0 (p) 1 and σ = σ Φ + σ Φ, (3) (H) 0 (p) 1 where σ, σ and (H) (p) σ, σ are izat and itat cross sects for hydrogen (H) (H) (p) and proton (p), respectively. Some electrons generated by the izat in Eq.(2) are energetic and have the ability to ize and ite other water molecules. However, the secondary electron energy after primary izat is below a few thousands ev. Accordingly, most of the electrons can move only less than 0.1-1μm in CSDA range (e.g., Atomic Data, 1972). Hereafter, we refer to these processes by electrons (namely δ-rays) "secondary processes", while we refer to the direct izat and itat by protons or hydrogen atoms "primary processes". The secondary processes are dominated by the energy spectra of electrons ejected in the primary izat. The probable energy distribut of the electrons is represented by the single differential cross sect dσ/de (differential in energy transfer E), dσ de = σ j d G j dw all j j, (4) where W j =E-I j is the secondary electron kinetic energy, I j is the izat energy of sub-shell j in liquid water and G j is the partiting factor (Rudd et al., 1992 and Dingfelder el al., 2000). If we consider the event counts for izat and itat in the electron processes from the initial energy W (just after the eject) down to the cutoff energy, as k (W) and k (W), the 4

6 effective cross sects for izat and itat by secondary processes are given by elec d = σ σ k (W)dW Wmin, de (5) and elec d = σ σ k (W)dW, Wmin, de (6) where W min, and W min, are cutoff energies equivalent to the izat and itat dσ (E) dσ (W) thresholds for the electron impact. It should be noted that the relat = de dw is sustained for the transfer energy E and the ejected electron energy W. Thus, the total cross sects for izat and itat including secondary electron processes become σ p+ s = (H) (H) elec (p) (p) elec ( σ + σ ) Φ + ( σ + σ ) 0 Φ 1 (7) and σ p+ s = (H) (H) elec (p) (p) elec ( σ + σ ) Φ + ( σ + σ ) 0 Φ 1. (8) Here, (K) σj denotes the cross sect for process-j (izat or itat) by the primary izat K (proton or hydrogen), and σ the cross sect associated with electrons (K) elec J generated by the primary izat K (proton or hydrogen). These are corresponding to Eqs.(5) and (6). Charge changing processes may also induce the izat and itat of water molecules. In the electron loss process, an electron departs from hydrogen and travels with the same speed as the proton. That is to say, it has the kinetic energy T/λ, where T is the proton energy and λ=m p /m e =1836 (m p : the proton mass, m e : the electron mass). This electron may cause izat and itat as well as the secondary electron mented above. Moreover, an (H 2 O + ) is produced in the electron capture process, which can also be regarded as an izat event. The equivalent izat and itat cross sects by the charge changing react 5

7 are given as: CC σ = σ01φ 0k (T / λ) + σ10φ1 (9) and CC σ = σ Φ (T/ λ). (10) 01 0 k These cross sects are added to Eq.(7) and Eq.(8), respectively, to obtain a complete form of the effective total cross sects as a funct of the incident particle (proton or hydrogen) energy. Finally, we can express them in event counts per unit length: (H) (H) elec (p) (p) elec ( σ + σ + σ k (T / λ) ) Φ + N( σ + σ + σ ) total Nσ = N Φ1 (11) and (H) (H) elec (p) (p) elec ( σ + σ + σ k (T/ λ) ) Φ + N( σ + σ ) total Nσ = N 01 0 Φ1, (12) where N is the number of water molecules per unit volume. 3. Collis cross sects 3.1 Proton and hydrogen For the impact cross sects of proton and hydrogen in liquid water, we adopt the semi-empirical model following Dingfelder et al. (2000) as their analytical cross sects lend themselves to the present analysis. For clarity, we present the cross-sect here. For the itat cross sect for proton incident with energy τ, the analytic form for a single itat level k is given as Ω ν (p) σ0 (Za) ( τ E k ) σ,k ( τ) = (13) Ω+ν Ω+ν J + τ with sets of parameters for five levels in liquid water, a, J, ν, and Ω. Here, σ 0 is a constant (=10-20 m 2 ), Z the number of electrons in the target material, and E k the itat energy. The itat cross sects for neutral hydrogen impact are neglected in Dingfelder s paper, but 6

8 we consider them the same as protons ept the parameter a of Eq.(13) which is assumed to be 3/4 of the proton value, following Miller and Green (1973). The izat cross sect given by Dingfelder et al. (2000) is based upon the method by Rudd et al. (1992). The differential cross sects for five major izat processes are in the analytical forms with several specific parameters similar to the itat cross sects. We use the single differential cross sect dσ/de in the summat formula (Eq.(38) in their paper) with the parameters for liquid water. The differential cross sect for hydrogen is also presented by dσ de dσ = g( τ) ( H) de (p), (14) log10 ( τ) 4.2 where, g( τ) = exp , and subscripts (H) and (p) represent hydrogen and proton, respectively. Analytic forms for charge-changing cross sects for electron capture and electron loss mented in the previous sect are also taken from Dingfelder et al. (2000) and those curves fit well the other reported data (e.g., Toburen et al., 1968, Dagnac et al., 1970). All of the cross sects given above are shown in Fig.1. The total izat cross sect in Fig.2 was obtained by integrat of the single differential cross sect dσ/de over electron energy, which duplicates correctly the one shown in the paper by Dingfelder et al. (2000). 3.2 Electron In order to construct a Monte Carlo simulat of electrons generated by the primary izat process through proton or hydrogen impact, three types of electron colliss need to be considered for water molecules in liquid state: elastic, izat and itat. Electron impact cross sects of water have been reported by many authors (e.g., IAEA-TECDOC-799). 7

9 However, most of them are for water in vapor phase while the data for liquid water are scarce. Recently, some researchers have reported inelastic cross sects for liquid water, for example Emfietzoglou (2003) and Champ (2003). It seems to have been accepted that the izat and itat cross sects of water in liquid phase are significantly smaller than those in vapor phase especially for electron energy below 100eV. In the present study, we adopt the cross sects for total izat and total itat by Emfietzoglou, which are in good agreement with those of earlier work by Pinblott et al. (1996) and Dingfelder et al. (1998). As for the elastic collis cross sect, we use the experimental data in water vapor by Danjo and Nishimura (1985) with a multiplicat factor 1.4. The multiplicat factor has been chosen so as to fit the total cross sect due to the paucity of the elastic cross sect data. The elastic collis process is not so important in our calculat because the energy transfer in the elastic collis is minute and our aim is to focus on the inelastic event counts. The angular distribut of electrons after scattering is assumed to be constant ignoring angular anisotropy. We have confirmed that this assumpt causes negligible differences in the present analysis. The set of total izat, total itat and elastic cross sects is embedded into a Monte Carlo code. In order to determine the energy partit ratio of primary and secondary electrons after izat, we use the algorithm by Grosswendt and Weibel (1978) with some fitting parameters by Green and Sawada (1972). The electron transport calculat is performed in the same manner as that of a previous paper by Date et al. (2003). 4. Results and discuss Figure 3 shows stopping cross sects σ st (=S/N: S is the stopping power, N the number of water molecules per unit volume) which were deduced from the impact cross sects given in Fig.2 to check the validity for constructing the convental quantity. The stopping cross sect demonstrates the Bragg peak well, and the shape is quite similar to ICRU-49 data 8

10 (ICRU, 1993) ept for that the peak value of σ st in the present result is about 5% larger than that of the ICRU liquid data. The occurrence rates of izat and itat by electron impact as a funct of initial electron energy are shown in Fig.4, which were obtained by the Monte Carlo simulat of electrons. The number in the vertical axis represents the average cumulative event frequency during the electron track mot from an initial energy E down to a cutoff energy (typically itat threshold). Our results yield W-values in fairly good agreement with that of water vapor reported by Olivera et al. (1997). Figure 5 shows the probable izat counts per micrometer for the incident particle (proton or hydrogen), and Fig.6 the itat counts. These were derived from the terms given in Eqs. (p) (11) and (12). For example, the legend (p)- in Fig.5 represents Nσ Φ1 and (p)-e- is for Nσ Φ, etc. Here, N is the density of water molecules (= m -3 ), and we reduced (p) elec 1 all results to 1/μm units. As shown in Fig.5, the direct izat by protons occurs significantly in the energy reg higher than 10 4 ev and the count of izat by secondary electrons is larger than that of the direct proton izat. Contrary to this, the direct izat by hydrogen takes place mostly in the lower energy reg (<10 5 ev) and the contribut of izat by electrons generated by hydrogen is minor. In Fig.6, we can see that the secondary electrons generated by protons are the dominant particles for the itat process. The event counts for charge changing processes are shown in Fig.7. It is recognized that the electron stripping process from hydrogen to proton results in a steep peak of the itat probability by generated electrons between the hydrogen energy 10 4 and 10 5 ev. The total count ratios of the secondary process to the total process for izat and itat are plotted in Fig.8. Here, it should be recalled that the secondary process means izat or itat process by electrons generated by the direct izat with proton or 9

11 hydrogen impact and in charge changing processes. Figure 8 shows that the izat and itat events by electron collis processes are an important share of the total processes in the higher energy reg above 10 4 ev. Total counts classified into primary and secondary processes are presented in Fig.9. The curves in Fig.9 describe the interact processes of proton beam incident in water more precisely than the stopping cross sects in Fig.3. We illustrated the proton processes considering δ-ray behavior in Fig.1. In this figure, a narrow cylinder in the central reg represents the proton and hydrogen interact area and the outer co-axial cylindrical volume depicts the spatial area in which electron tracks are spreading out. Iwanami and Oda (1999) reported on the radiological act of heavy charged particles, in which they deal with the heavy charged particle as a two-component radiat including the processes of high LET heavy tracks of low fluence and low LET electrons of high fluence. Our results concerning protons also illustrate the two-component nature of the radiat, which may lead to more detailed evaluat of biological effects of radiat than with the LET approach. On the one hand, if we know the accurate interact radii "a" and "b" in Fig.1, we can estimate event densities for izat and itat, denoted as J n K (J: particle name, K: process type), then a ratio can be defined as R n (p) n + n e (p) + n + n e (H) + n (H). On the other hand, if we know the generat rates of single-strand breaks (SSB) and double-strand breaks (DSB) of a DNA chain through the izat and itat processes, the ratio R may be combined with the radiat weighting factor w R for protons. At least, from a physical point of view, the results in this paper support the recent recommendat of w R for protons approaching unity (ICRP-92, 2003). This tendency is attributable to the fact that the contribut of electron interact is considerably large in the inelastic processes of protons. The natural extens of the present analysis will likely be to heavier charged particles such as carbon. 10

12 5. Concluding remarks In the present study, we have investigated izat and itat processes at the Bragg peak reg of proton beams in liquid water. Primary processes by proton and hydrogen and secondary processes by electrons were separately treated in the estimat of izat and itat probabilities. The calculat results show that the contribut of secondary processes is more than 50% of the fract of total event counts in the upper energy reg of the Bragg peak and the primary izat processes with hydrogen are dominant in the lower reg. It is also shown that the product rates of and ited particle species are enhanced by charge changing processes between proton and hydrogen. In addit, we have discussed the implicat of primary and secondary processes suggesting a physical descript of the radiat effects contrary to the convental LET approach. 11

13 References Annals of the ICRP, Relative Biological Effectiveness (RBE), Quality Factor (Q), and Radiat Weighting Factor (w R ). ICRP Publicat 92, Internatal Commiss on Radiological Protect, Stockholm, Sweden. Atomic Data, Energy Loss, Range, and Bremsstrahlung Yield for 10-keV to 100-MeV Electrons. Atomic Data 4 (1), 1-127, Academic Press, New York and London. Champ, C., Theoretical cross sects for electron colliss in water: structure of electron tracks. Phys. Med. Biol. 48, Danjo, A., and Nishimura, H., Elastic Scattering of Electrons from H 2 O Molecule. J. Phys. Soc. Japan 54, Date, H., Ishimaru, Y., and Shimozuma, M., Electron collis processes in gaseous xenon. Nucl. Instr. and Meth. B 207, Dingfelder, M., Hanke, D., Inokuti, M., Paretzke, H.G., Electron inelastic-scattering cross sects of liquid water. Radiat. Phys. Chem. 53, 1-8 Dingfelder, M., Inokuti, M., Paretzke, H.G., Inelastic-collis cross sects of liquid water for interacts of energetic protons. Radiat. Phys. Chem. 59, Emfietzoglou, D., Inelastic cross-sects for electron transport in liquid water: a comparison of dielectric models. Radiat. Phys. Chem. 66, Green, A.E.S., and Sawada, T., Ionizat cross sects and secondary electron distributs. J. Atmosph. Terr. Phys. 76, Grosswendt, B., and Waibel, E., TRANSPORT OF LOW ENERGY ELECTRONS IN NITROGENS AND AIR. Nucl. Instr. and Meth. 155, Internatal Commiss on Radiat Units and Measurements, Stopping Powers and Ranges for Protons and Alpha Particles. ICRU Report 49. Internatal Commiss on Radiat Units and Measurements, Bethesda, Maryland. Internatal Commiss on Radiat Units and Measurements, Secondary Electron Spectra from Charged Particle Interacts. ICRU Report 55. Internatal Commiss on Radiat Units and Measurements, Bethesda, Maryland. Internatal Atomic Energy Agency, Atomic and Molecular Data for Radiotherapy and Related Research. IAEA-TECDOC-799, IAEA, Vienna Iwanami, S., and Oda, N., Can heavy charged particles really be regarded as high-let radiats with respect to their radiological acts? I: LETs and fluences of heavy charged particles and associated δ-rays. Phys. Med. Biol. 44,

14 Miller, J.H., and Green, A.E.S., Proton energy degradat in water vapor. Radiat. Res. 54, Olivera, G.H., Rivarola, R.D., Fainstein, P.D., LET AND w-values OF WATER VAPOR UNDER ANTIPROTON IRRADIATION. Radiat. Phys. Chem. 49, Pimblott, S.M., LaVerne, J.A., Mozumder, A Monte Carlo Simulat of Range and Energy Deposit by Electron in Gaseous and Liquid Water. J. Phys. Chem. 100 (20), Rudd, M.E., Kim, Y.-K., Madison, D.H., Gay, T.J., Electron product in proton colliss with atoms and molecules: energy distributs. Rev. Mod. Phys. 64, No.2, Toburen, L.H., and Wilson, W.E., Energy and angular distributs of electrons ejected from water vapor by MeV protons. J. Chem. Phys. 66 (11), Uehara, S., Toburen, L.H., Wilson, W.E., Goodhead, D.T., Nikjoo, H., Calculats of electronic stopping cross sects for low-energy protons in water. Radiat. Phys. Chem. 59,

15 Figure capts Fig.1 Schematic illustrat of interact site for proton beam incident. Symbol "a" represents the radius of proton or hydrogen direct collis process reach and "b" the radius of electron track process reach. Protons can be changed to hydrogen in the vicinity of the endpoint. Dots represent izat or itat processes. Fig.2 Total cross sects for the different processes in liquid water: proton izat (thick solid curve), hydrogen izat (thick dashed curve), proton itat (fine solid curve), hydrogen itat (fine dashed curve), electron loss σ 01 (dotted curve), charge transfer σ 10 (dash-dotted curve), compared with izat cross sect by ICRU-49, 1993 (diamonds). Fig.3 Stopping cross sects σ st for liquid water: proton izat ((p)-), hydrogen izat ((H)-), proton itat ((p)-), hydrogen itat ((H)-), charge changing (CC), and total stopping cross sect, compared with ICRU-49 liquid data, 1993 (diamonds). Fig.4 Mean numbers of izat and itat events in liquid water by electron incident with initial energy E. These are referred to as k (W) and k (W) in the text. Fig.5 Ionizat counts for different processes per μm of proton (or hydrogen) flight: proton izat ((p)-), izat by electrons arising from proton izat ((p)-e-), hydrogen izat ((H)-), and izat by electrons arising from hydrogen izat ((H)-e-). Fig.6 Excitat counts for the different processes per μm of proton (or hydrogen) flight: proton itat ((p)-), itat by electrons arising from proton izat ((p)-e-), hydrogen itat ((H)-), and itat by electrons arising from hydrogen izat ((H)-e-). Fig.7 Ionizat and itat counts for the charge changing processes per μm of proton (or hydrogen) flight: izat by charge transfer ((p H)-), izat by electrons arising 14

16 from electron loss process ((H p)-), and itat by electrons arising from electron loss process ((H p)-). Fig.8 Ratios of secondary and primary processes for izat and itat: ratio of secondary izat to total izat (secondary/total-), and ratio of secondary itat to total itat (secondary/total-). Fig.9 Total izat and itat counts for the primary and secondary processes per μm of proton (or hydrogen) flight: primary izat (primary-), secondary izat (secondary-), primary itat (primary-), secondary itat (secondary-), and total count. 15

17 Liquid water electron proton a b Bremsstrahlung proton or hydrogen Fig.1 H. Date et al. 16

18 Cross sects (m 2 ) (p)- ICRU- (H)- (p)- (H)- σ 01 σ Incident particle energy, τ (ev) Fig.2 H. Date et al. 17

19 Stopping cross sects (evm 2 ) total (p)- (H)- (p)- (H)- CC ICRU Incident particle energy, τ (ev) Fig.3 H. Date et al. 18

20 Counts per track Ionizat Excitat Electron energy (ev) Fig.4 H. Date et al. 19

21 1500 Ionizat counts per μm (p)- (p)-e- (H)- (H)-e Incident particle energy, τ (ev) Fig.5 H. Date et al. 20

22 Excitat counts per μm (p)- (p)-e- (H)- (H)-e Incident particle energy, τ (ev) Fig.6 H. Date et al. 21

23 1000 Charge-changing counts per μm 500 (p H)- (H p)- (H p) Incident particle energy, τ (ev) Fig.7 H. Date et al. 22

24 Number ratio of electron processes secondary/total- secondary/total Incident particle energy, τ (ev) Fig.8 H. Date et al. 23

25 Counts per μm primary- secondary- primary- secondary- total- & Incident particle energy, τ (ev) Fig.9 H. Date et al. 24