Scaling rules for the ionization of biological molecules by highly charged ions
Alejandra M. P. Mendez, Claudia C. Montanari, Jorge E. Miraglia
aa r X i v : . [ phy s i c s . a t m - c l u s ] M a y Scaling rules for the ionization of biological molecules by highly charged ions
A. M. P. Mendez, C. C. Montanari, J. E. Miraglia
Instituto de Astronom´ıa y F´ısica del Espacio, Consejo Nacional de Investigaciones Cient´ıficas yT´ecnicas - Universidad de Buenos Aires, Pabll´on IAFE, 1428 Buenos Aires, Argentina
We investigate scaling rules for the ionization cross sections of multicharged ions on molecules ofbiological interest. The cross sections are obtained using a methodology presented in [Mendez et al.
J. Phys B (2020)], which considers distorted-wave calculations for atomic targets combined with amolecular stoichiometric model. We examine ions with nuclear charges Z from + + PACS numbers: 34.50Gb, 34.80Gs, 34.80DpKeywords: ionization, scaling, molecules, charged-ions, DNA, multicharged ions
I. INTRODUCTION
The interest in the ionization of biological molecules bymulticharged ions has increased due to medical and envi-ronmental implementations [1], including medical treat-ments [2–4] and contaminant recognition in biologicalmaterials [5, 6]. Many semiempirical [7] and theoreti-cal efforts are currently being undertaken [8–13] to getreliable values for the ionization cross sections of thesemolecular systems.In recent work [8], we combined the continuumdistorted-wave calculations (CDW) for atoms and thesimple stoichiometric model (SSM) to approximate theionization cross sections of complex molecular targets bythe impact of charged ions. The molecular ionizationcross section σ M was expressed as a linear combinationof atomic CDW calculations σ A , weighted with the num-ber of atoms for each specie n A , i.e, σ M = ∑ A n A σ A . TheCDW-SSM approximation showed consistent results forover a hundred of biologically relevant ion-molecule sys-tems. As expected, in the high energy range (i.e., above 5MeV/amu), the ionization cross sections of the molecularsystems follow the Z dependence predicted by the firstBorn approximation. However, at intermediate energies,the dependence with Z is not straightforward since non-perturbative models are mandatory.This contribution constitutes a follow-up to our previ-ous work [8]. We introduce here a two-folded scaling rulefor the ionization cross sections of complex molecules bycharged ions. Our approach considers the dependence ofthe cross section with the ion charge Z and incorporatesthe scaling of the ionization with the number of activeelectron n e of the molecular targets. Scaling rules aregenerally very useful since they can be used as first-orderapproximations in experimental measurements and mul-tipurpose codes. II. SCALING RULESA. Scale with the ion charge
In the development of our scaling rule, we examineforty collisional systems. The target-ion systems are com-posed of eight targets: the DNA and RNA nucleobases –adenine, cytosine, guanine, thymine, uracil–, tetrahydro-furan (THF), pyrimidine, and water; and five ion species:H + , He + , Be + , C + , and O + . We consider these sys-tems as a benchmark for the present rule.We found two types of Z -scaling laws in the literatureapplicable to the intermediate impact energy range. Therule suggested by Janev and Presnyakov [14] considers σ / Z versus E / Z to be the natural reduced form of theionization cross section σ and the incident ion energy E .More recently, Montenegro and co-workers [15, 16] sug-gested an alternative scaling by taking into account thatthe cross section is a function of Z / E at high energies.Their scaling, given by σ / Z α = f ( E / Z − α ) , (1)keeps the Z / E relationship for any value of the param-eter α . The authors proposed α = / by differently charged ions [15].Following the work of Montenegro and collaborators,we found that the parameter that best converges theCDW-SSM cross sections of the forty collisional systemsover the broadest energy range is α = .
2. The validity ofthis particular scaling is evident in Fig. 1, where –for eachtarget– the CDW-SSM curves corresponding to differentions lay one over the other. It is worth noting that ourtheoretical results are valid for impact energies above themaximum of the cross sections, which corresponds to animpact energy range from 50 keV for H + to 250 keV/amufor O + .We also examined the experimental data available forthe forty ion-target systems [17–28, 30–33] with the Z α -scaling rule. For targets with none or little experimental AdenineC H N H + He +2 Be +4 C +6 O +8 H + [17]C +6 [18]e − [34] CytosineC H N O e − [34] GuanineC H N O e − [34] ThymineC H N O e − [34] I o n i z a t i o n C r o ss S ec t i o n / Z α ( − c m ) UracilC H N O H + [19]C +4 [20]C +6 , O +6 , F +6 [21]O +6 , F +6 [21] PyrimidineC H N H + [22]e − [35] THFC H O H + [23]e − [35]e − [36]e − [37] Impact Energy/ Z − α (MeV/amu)WaterH O × H + [24,25,26,27]He +2 [28,29,27]Li +3 [30]C +6 [31,32]O +8 [33] FIG. 1. (Color online) Scaled ionization cross section σ / Z α as a function of the ion impact energy E / Z − α with α = .
2. Colorsare associated with the incident ion labeled on top of the figure. Curves: present CDW-SSM theoretical results. Symbols:experimental data [17–28, 30–33]. Electron impact ionization values [34–37] are included with the corresponding equi-velocityconversion. data, we included electron impact ionization results [34– 37] at high velocity with the corresponding equiveloc-ity conversion. As can be noted, most of the data inFig. 1 confirm the present scaling, even for O + in wa-ter [33]. Only two data sets are off our predictions: theionization cross section of uracil by swift C, O, and Fions from Refs. [20, 21], and the values for Li + in wa-ter from Ref. [30] for E <
600 keV/amu. In the case ofuracil, recent CTMC calculations by Sarkadi [38] are alsoabove the experimental values by Tribedi and collabora-tors [20, 21].
B. Scale with the molecular target
The good results obtained in the scaling with the ioncharge encouraged us to further investigate a scaling lawthat could predict values for ionization cross sections ofany ion in any molecule. To this end, we considered thenumber of active electrons in each molecule n e proposedin Ref. [8] and combined it with the Z α -scaling from Sec-tion II A.In our previous work, we noticed that the CDW ion-ization cross sections σ A of atomic targets H, C, N, andO scale with the number of active electrons per atom ν A ,as σ e = σ A / ν A , where ν A is 1 for H and 4 for C, N, O,i.e., σ H ∼ σ C ∼ σ N ∼ σ O . (2)By means of the SSM, we define the number of activeelectrons per molecule as n e = ∑ A n A ν A . The n e val-ues for the molecular targets considered throughout thiswork are displayed in Table I. The scaling with the molec-ular number of active electrons proved to give excellentresults, as shown in Fig. 6 of Ref. [8]. C. Scale with the ion charge andthe molecular target
By incorporating the Z α reduction and the scalingwith the number of active electrons, we introduce thescaled and reduced ionization cross section of molecules˜ σ , which is expressed as a function of E / Z − α , and it isgiven by ˜ σ = σ e Z α = σ M / n e Z α , (3)where σ M is the ionization cross section for the moleculartarget, n e is the number of active electrons per moleculedisplayed in Table I, and the parameter is α = .
2. Fig. 2shows the theoretical and experimental values of ˜ σ (givenby Eq. 3) for all the systems displayed in Fig. 1. As can benoted, the scaling works very well and is independent ofthe ion charge or the complexity of the molecular target.Our theoretical curves lay in a narrow band valid for anycharged ion (reduced with Z α ) in any molecule (scaledwith the number of active electrons) with a dispersionof about ± Molecule n e Molecule n e Molecule n e H O 6 CO
12 C H N O 37N H O 28 C H N O H N
28 C H N H N O
36 C H N O 49TABLE I. Number of active electrons per target at intermedi-ate to high energies obtained from the CDW calculations [8]. the uncertainty of our scaling grows to ± + on water [30]. The discus-sion about these experimental values exceeds the presentwork.We consider the present scaling robust enough to bevalid for different ion-molecule combinations. We testedthe generality of our model by including in Fig. 1 severaldata sets of molecular targets not considered previously,such as the measurements by Rudd et al. [29, 39] for H + and He + in N , O , CH , CO and CO , and recent valuesby Luna et al. [40] for H + in CH .The good agreement shown in Fig. 2 summarizes themain result of this work and holds the validity of thepresent scaling for different ions and targets. Althoughthe theoretical CDW-SSM results are valid for energiesabove the maximum of the cross sections, the scalingof the experimental data extends even to lower impactenergies, as can be noted in Fig. 2. New measurementsfor other ions and molecules are expected to reinforce thepresent proposal. III. CONCLUSIONS
We present scaling rules for the ionization cross sec-tions of highly charged ions in biological targets. Thefirst scaling reduces the nature of the projectile by scalingthe cross section with the ion charge, Z α , as a functionof the reduced impact energy E / Z − α , with α = .
2. Thesecond scaling considers the molecular description of thetarget by taking into account the number of active elec-trons per molecule, n e . The last scaling law combinesthe Z α -reduction with the n e -scaling of the cross sec-tion, and it becomes independent of the ion charge andthe molecular target. The scalings are obtained by meansof CDW-SSM calculations for five different charged ionsin eight targets and tested with the available experimen-tal data. The generality of our independent scaling isproved to be valid in a wide energy range by consideringa significant number of experimental data sets for othercollisional systems. IV. ACKNOWLEDGMENTS
This work was finantially supported by Consejo Na-cional de Investigaciones Cient´ıficas y T´ecnicas (PIP
Impact Energy/Z − α (MeV/amu) − σ e / Z α ( − c m ) α = 1 . H + + C H N [17]H + + C H N O [19]H + + C H N [22]H + + C H O [23]H + + H O [24,25,26,27]He +2 + H O [28,29,27]C +6 + C H N [18]C +6 + H O [31,32]O +8 + H O [33]e − + C H N [34]e − + C H N O [34]e − + C H N O [34]e − + C H N O [34]e − + C H N [35]e − + C H O [35]e − + C H O [36]e − + C H O [37] H + + N [39]H + + O [39]H + + CO [39]H + + CO [39]H + + CH [39,40]He +2 + N [29]He +2 + O [29]He +2 + CO [29]He +2 + CO [29]He +2 + CH [29] FIG. 2. (Color online) Ionization cross section reduced with the ion charge Z and scaled with number of active electronsper molecule n e , given by Eq. (3) with α = .
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