L-subshell ionization by 14N ions

Nuclear Instruments and Methods in Physics Research B 86 (1994) 185-189 North-Holland

Beam Interactions withMaterials&Atoms

L-subshell ionization by 14N ions J. Semaniak a,+, J. Braziewicz a, T. Czy~ewski b, L. Glowacka b, M. Haller ‘, M. JaskC2a b, R. Karschnick ‘, A.P. Kobzev d, M. Pajek a, W. Kretschmer ’ and D. Trautmann e aInstitute of Physics, Pedagogical Uniuersity, Z-509 Kielce, Poland b Soltan Institute for Nuclear Studies, 05-400 Otwock-&ierk, Poland ’ Institute of Physics, Erlangen-Niirnberg University, Erlangen, Germany d Joint Institute for Nuclear Research, Dubna, Russian Federation e Institute of Physics, Uniuers~~ of Basel, CH-4056 Basel, Sw~tzerla~

L-subshell ionization cross sections for selected heavy elements between La and Au were measured for 14N ions in the energy range 1.75-22.4 MeV. The L-X-ray yields were corrected for a substantial projectile energy-loss in the target, being up to 20% for the lowest energies, and the X-ray absorption effect. The measured L-subshell ionization cross sections are compared with the predictions of the ECPSSR theory for direct ionization and electron capture processes and the SCA calcufations for direct ionization. Both theories underestimate the data for La-subshell for the lowest energies. This is attributed to the effect of intra-shell transitions not accounted for in both calculations. Systematic overestimation of measured L,-subshell cross sections by the theories is also found for higher scaled velocities 5 > 0.5, where the binding-polarization effects are expected to play an important role.

1. Introduction

Inner shell ionization by light MeV ions was studied extensively in last decades. From comparison of the available experimental results with existing theories one observes that, generally, the theoretical description of the ionization process fails in the low-energy regime, especially for the projectiles with higher nucIear charge Z,. It was evidenced that such discrepancies are related to the higher-order effects [l-4], not accounted for in the theories based on the first-order plane wave Born approximation (PWBA) and the semiclassical approximation @CA). For the L-she11 it was shown [5-8] that the effect of intra-shell vacancy transitions, caused by the Coulomb field of the projectile, can influence significantly the L-subshell ionization cross sections in the low-energy regime. Also, the binding and polarization effects [1,4], which are difficult to be fully described in calculations, are expected to contribute to the observed discrepancies for heavier ions due to a stronger perturbation of the initial electronic wave functions. In order to quantify these effects more systematically in the present study L-subshell ionization cross sections for selected heavy elements between La and Au were measured for 14N ions of energy 0.125-1.6 MeVfamu. With these data, covering a wide range of

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relative ion-electron velocities ul/uL = 0.08-0.3, a systematic comparison with existing theories of innershell ionization by charged particles can be performed. It should be noted that for the systems with Z,/Z, = 0.2 as in our case, where Z, is the target atomic number, the second-order effects in ionization process can be evidenced in a more pronounced way. The results are compared with the predictions of the ECPSSR theory of Brandt and Lapicki [l], which describes both direct ionization (DI) and electron capture (EC) processes and the SCA calculations of Trautmann and Kauer [4] for the DI process. An estimation of a contribution of the EC process, performed using the ECPSSR theory, shows that for low charge states q = 1 + , 3 + of nitrogen ions used in the experiment the EC process contributes less than 5% to the total ionization cross sections, This justifies a comparison of the data with the SCA calculations performed only for the DI process.

2. Experiments

The measurements were performed at two accelerators. For low energies 1.75-3.15 MeV a beam of 14N”’ ions from the Van de Graaff EG-5 accelerator at the Frank Laboratory of Neutron Physics, JINR, Dubna, was used, while for higher energies 4.8-22.4 MeV the measurements were performed using 14N3+ beams at the tandem accelerator at University of Erlangen-

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and data analysis

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Niirnberg, Erlangen. In both experiments thin targets (8-30 yg/cm2) of selected heavy elements were used. In measurements at low energies the targets of La, Pr, Tb and Ho were evaporated onto 0.2 mm Si wafers, while in high energy measurements, to avoid y-ray background from the nuclear reactions in target backings, the targets were evaporated onto thin (-20 kg/cm’) carbon foils. L-X-rays emitted from the targets were detected by a semiconductor Si(Li) detector (Dubna) and a HPGe detector (Erlangen). X-ray detectors were carefully efficiency calibrated following the calibration procedure outlined in ref. [9]. Experimental detector efficiencies were determined in two ways; first, by comparing the K-shell X-ray yields for 2 MeV protons with the reference [lo] K-X-ray cross sections for a set of thin calibrating targets, and second, by using absolutely calibrated X/y-sources. The measured efficiency was further fitted according to a detector model described in ref. [9]. The uncertaintics of the detector efficiency determined in this way, both for Si(Li) and HPGe detectors, were in the range of 3-S%. L-X-ray spectra were analyzed using a nonlinear least-squares code ACTIV [ 11) by fitting the Gaussians to the individual transitions L,, L, ,,*, L,,,Ls_, L, , b 2’ LP,.7,9,Ly5, L,,, L,z,,h and L_ and a polynomial background. For determination of L-X-ray cross sections the X-ray yields were normalized to a number of 14N ions elastically scattered into a Si surface barrier detector mounted at 0 = 135” relative to the beam axis. Due to a substantial energy-loss of nitrogen ions in the targets, as well as X-ray absorption, the X-ray cross sections were corrected for these effects. Consequently, the X-ray cross sections were obtained using the following formula:

Nx oede,~‘3% F(E, AE), ax(E) = F l(Ex) cl where N, and N,, are the numbers of X-rays and elastically scattered projectiles into the detector solid angle R,, respectively; crJ@, E) is the screened elastic cross section [12] and l(E,) is the X-ray detector efficiency. For substantial projectile energy-loss in the target, up to 20% in our case, the target thickness correction factor F( E, AE) was expanded up to the second order terms in AE/E, resulting in the following expression: F(E,

AE) = [l + t(2 +@)(AE/E)

where f = E cos y/S(E) cos S with y and 6 being the angles between a normal to the target and, respectively, ion beam axis and X-ray detector direction. In the formula above it was assumed that measured X-ray production cross section crx( E) and projectile stopping power S(E) vary with energy as E” and ED, respectively. The /3 parameter was calculated using the stopping powers of Ziegler et al. [13], while the a parameter was determined iteratively from measured data points. We checked that such iterative target thickness correction procedure was accurate within 5% for a cross section correction as large as 60% for the thickest target at low energy. From measured L-X-ray cross sections for Lo1,2,L,, and L72.,.6 transitions the L,., L,., and L,-subshell ionization cross sections were derived using the fluorescence and Coster-Kronig yields of Chen and Crasemann [14] and L-shell X-ray emission rates of Scoficld [15]. The overall experimental uncertainties of L-subshell ionization cross sections decrease with energy, being in the range of 25-10% for low energies (below 3 MeV) and about 10% for higher energies. An estimation of the influence of the collisional alignment [16,18] shows that this effect can contribute to the cross sections less than 2%. Similarly, the effect of the projcctile charge state equilibration in the target is not expected to play an important role, first, due to a relatively small contribution (below 5%) of the EC process to the ionization cross sections for the low charge states of 14N’+*s+ ion beam used in the experiment and, second, nearly the same (within 10%) L-shell ionization cross sections expected for 14N ions with and without K-shell electrons, as was measured by Andrews et al. [20] for similar systems, namely about 2 MeV/amu “C and I60 ion impact on heavy targets. Consequently, the effect of the ion charge equilibration in the target is expected to contribute below 5% for realistic charge state distribution. The influence of the multiple ionization increasing the L-subshell fluorescence yields is negligible for nitrogen ions below 2 MeV/amu impact energy for heavy target atoms. This effect was studied experimentally by Berindc et al. [21], who estimated the M-shell ionization probability in central collisions for similar systems to be less than 2% for ion energy below 2.5 MeV/amu. Following a simple estimation given in ref. [19], the fluorescence yields are expected to be changed by the same amount.

- :(2 + P)(3 +B)(AE/E)‘] x l-;(a-P+p?)AE/E [

3. Results and discussion

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Due to a limited number of experimental L-subshell ionization cross sections for nitrogen ions the present data are compared in Fig. 1 with other results only for gold, the target which was the most frequently studied

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.T.Smaniak

et al. / Nucl.

bastr.and A&h. in Phys.Res.B 86 (1994) .IW-189

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projectile is assumed to move on the classical trajectory and the ionization is described within the first-order time-dependent perturbai~on approach. ~onse~u~nt~~ the realistic ~oulombi~ trajectories are inherently accounted for in this theary. In present SCA calculations the relativistic hydroge~ic wave factions were used and the binding effect was simulated using the unitedatom limit f4b but the polarization effect was not included in cakulations. Present SCA ~lc~atio~s predict only the direct ionization cross sections, but a contribution due to the electron capture is negligible, as was estimated above using the ECPSSR theory. In Fig. 2 the measured L-subshell ionization cross sections are compared with the predictions of the ECPSSR tbcory versus the scaled velocity St8 = 2u,/ u~,&~, where L’~and vL, are the projectile and dec-

Fig. 1. Total L-shell ionization cross sections for gold versus the energy of i4N ions. The present data (m) are compared to the results of Sarkadi and ~~#yarna 1171(Q), P&&&s et af. 1181 Kl) and M&hi and Gray [22] (A 1. me curves are the theoretical predictions according to the ECPSSR theory (solid line) and the SCA calculations (dashed line).

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by other gronps f17,18,22]. Fig. 1 shows that our total L-shell ionization for Au are in good agreement with

the results of P&link& et al. El81and recent data of Malhi and Gray [221. The law energy cross sections reported by Sarkadi and hlukoyama [171 are lower about 40%, which, in our opinion, can be partly attributed to the different target thickness correction procedure giving substantial corrections for the low energy data paints. The measured L-subshell ionization cross sections for La, Pr, ‘I%, Ho, Hf, Ta, Pt and Au by 14N ions of energy l-75-22.4 MeV are compared systematically with the theoretical predictions according to the ECPSSR and the SCA theories. The ECPSSR theory deveioped by Brandt and Lap&i [Xl describes both the direct ionization and the electron capture processes within the PWBA approximat~a~ for IX and the GBKN approximation [231 for EC. For both processes the corrections are made for the binding-plantation effects (treated within the perturbed stationary state (FSS) approx~mation~~ the Coulomb deflection (Cl, the relativistic fR) effect and the so-called energy-loss effect (El. For low charge states of nitrogen ions in the present experiment tq = 1 f , 3 + > and 2,/Z, m 0.2 the ECPSSR theory predicts that the EC process mntributes less thm 5% to the ionization cross sectionsThe semiclassical (SC_A> calculations presented in the present paper are described in details in refs. 14,241. We only recall here that in this approach the

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Fig. 2. Measured Lsubsheli ionization cross sections for *%I ions normalized to the predictions of the ECPSSR theory

plotted versus scaled velocity gL_= 2vt J’u~,~$ The points are marked as follows: La (open dircle), Pr fopen square), Tb (open diamond), Ho
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J. Semaniak et al. /Nucl. Instr. and Meth. in Phys.Res. B 86 (1994) 185-189

188

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tron velocities, respectively, and the reduced binding ener= 8,$ = n2E,i/Rz~j_ Here n = 2 for L-shelf, R is the Rydberg constant, Er+ is the electron binding energy and the screened atomic number Z,, = 2, 4.15. The scaled velocity measures the “adiabatkity” of the collision [l]. For instance, 5 < 1, as in our case, implies that the collision is slow, what justify the use of the united-atom limit for simulation of the effective electron binding energy in the SCA eafcufations. The most important observation found in Fig. 2 is the strong underestimation of the experimental cross section by the ECPSSR theory far L,-subshell for low energies (6 < 0.5), where a disagreement reaches a factor of 20. A similar trend is also found for L,-subshefl data, but its magnitude is much smatfer (see Fig. 2). On the other hand, the high energy data are systematically overestimated by the ECPSSR theory by a factor of about 3. The same general features are found in comparison of the data with the SCA calculations, as shown in Fig. 3. Here, however, a disagreement for low energy points for L,-subshell is reduced to a factor of S. Generally, the strong discrepancy observed for L, subshell for the low energies can be attributed to the

intra-shell transitions induced by the projectile Coulomb field f&6]. This effect was the subject of several theoretical studies ]25,26,7,27] where it was evidenced that it increases for higher Z, projectiles. The calculations of the intra-shell transition probabilities for studied systems are in progress, A reason for the substantial discrepancy seen between the data and theories for higher energies is not clear at the moment, bui it can be refated to a too simp~i~ed description of the binding-~larization effects for 5 < 1. This question, however, has to be further studied theoretically. For L,-subshell the experimental results agree with both theories within a factor of 2. For low projectile energies the experimental L,-subshell ionization cross sections are lower than the theoretica prediction partty due to the intra-shell transition mentioned above transferring vacancies mainly from L,- to L,-subshell. We found also that the ionization cross sections for L,-subshell are very sensitive to the atomic parameters (fluorescence and Coster-Kronig yields and X-ray emission rates) used to convert L-X-ray cross sections into Lsubshell ionization cross sections. In our opinion, further studies are needed to evaluate a new set of the atomic parameters for L-shell, because the available theoretical predictions of Chen and Crasemann [ 141 do not agree acceptably for many elements with the empirica] values of Krause 1281, and both are sometimes in disagreement with newer e~rime~ta~ data obtained using synchrotron radiatiation [29,30].

4. Conclusions L-subsheh ionisation cross sections for sefected heavy elements (57 I Z, 5 79) were reported for 14NQ ions of low charge states (q = 1 + , 3 + ) in the energy range 0.125-1.6 MeV/amu. Widely used theories of inner-shell ionization by charged particles, namely the ECPSSR and the SCA, show strong under~stima~on of the data, up to a factor of 20, in the low energy regime fc < 0.2). Observed disagreement is expected to be related to the intra-shell transitions not accounted for in the discussed theories. This calls for further calculation of L-subshell couphng effects using existing theoretical approaches [25,26,27]. Overestimation of the data by the ECPSSR and the SCA theories for high energies is not clear theoretieallyy, but is expeeted to be related to the binding-polarization effect. Further theoretical studies are needed to explain this observation.

111W. Brandt and C, Lapicki, Phys. Rev. A 20 (1979) 465; A 23 (1981) 1717.

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