2. Results and Discussion

In Figure 1, the typical X-ray emission spectra of ₄₈Cd and ₄₉In produced by proton are presented as a function of the proton energy and well fitted by a nonlinear curve Gaussian fitting program. The structure of the spectra is similar for the two targets under different incident energies as a whole. It mainly consists of six distinct lines which are the L subshell X-rays arising from the relative deexcitation of target atomic L vacancies. The first five transitions are the same for both elements and identified as L _ι (3s_1/2-2p_3/2), Lα _1,2 (3d_5/2,3/2-2p_3/2), Lβ _1,3,4 (3d_3/2-2p_1/2, 3p_3/2,1/2-2s_1/2), Lβ _2,15 (4d_5/2,3/2-2p_3/2), and Lγ ₁ (4d_3/2-2p_1/2). Due to the difference in the electron configuration for the two elements, there is a small distinction for the sixth line. Electronic configuration of ₄₈Cd atom is 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰5s², but that of ₄₉In atom is 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰5s²5p¹. Therefore, the last peak is L _γ2,3 (4p_3/2,1/2-2s_1/2) and L _γ2,3,4 (4p_3/2,1/2/5p_1/2-2s_1/2) for ₄₈Cd and ₄₉In [Reference Thompson, Attwood and Gullikson25], respectively, and they are abbreviated as “Lγ ₂” in order to present the following discussion clearly and briefly.

Figure 1: Characteristic L X-ray spectra of (a) ₄₈Cd and (b) ₄₉In for proton impacting, which are normalized by the counts of Lα X-ray.

One can see in Figure 1 that although the spectrum of the two targets is similar for various proton energies, there is an obvious decrease in the Lγ ₂ X-ray emission with increasing incident energy, compared to Lγ ₁ X-ray emission. For further quantitative analysis, the relative intensity ratios of Lγ ₂ to Lγ ₁ X-ray are extracted from the original data after taking into account the detection efficiency of the detector and the self-absorption inside the target material. As shown in Figure 2, the ratios are larger than the theoretical data of single ionization which is calculated based on the ECPSSR theory [Reference Brandt and Lapicki26], and it decreases rapidly and is closer and closer to the atomic data as the proton energy increases, in the present experimental energy region. For example, the enhancement factor, namely, the ratio of the experimental result to the atomic data for Lγ ₂/Lγ ₁, is about 6 for ₄₈Cd and 7 for ₄₉In at the energy of 100 keV, but those drop approximately to 2 when the energy is 250 keV.

Figure 2: Lγ X-ray relative intensity ratios of (a) ₄₈Cd and (b) ₄₉In for proton impact. Circle dots are the experimental data and dotted lines are the theoretical calculation for the singly ionized atom (atomic data) [Reference Brandt and Lapicki26].

It is proposed that the enhancement effect of Lγ ₂ X-ray can be understood by the outer-shell multiple ionization. As mentioned in the Introduction, such multiple ionization can also occur for the impact of lower energy proton, except for the case of highly charged heavy ions. When it takes place, owing to the absence of outer-shell electrons, some of the nonradiative transitions, such as Auger transition, CK transition, and super CK transition, are restrained. Accordingly, the radiative transition probability of the X-ray emission is changed [Reference Czarnota, Banaś and Berset9–Reference Słabkowska and Polasik12]. As a result, the measured relative intensity ratio of subshell X-ray is altered. Figure 3 gives the experimental results of the intensity ratios of Lι and Lβ ₂ to Lα X-ray as a function of the proton energy, respectively, which are all larger than the atomic data [Reference Brandt and Lapicki26], decrease with the increase of proton energy, and present a similar trend as that of I(Lγ ₂)/I(Lγ ₁). Based on that result, an estimation can be deduced that the M and N subshell electrons of ₄₈Cd and ₄₉In are multiply ionized by lower energy proton impacting, as similarly discussed in our previous work [Reference Zhou, Cheng and Wang19].

Figure 3: L-subshell X-ray relative intensity ratios of (a) ₄₈Cd and (b) ₄₉In for proton impact. Circle dots are the experimental data and dotted lines are the theoretical calculation for the singly ionized atom (atomic data) [Reference Brandt and Lapicki26].

Lι and Lα X-rays originate from the main transitions for M₁ and M_4,5 electrons filling the same lower energy vacancy of L₃, respectively. The multiple ionization on M₁ subshell can be regarded as to be insignificant compared to that on M_4,5 shells because of three main reasons. The first is the large deviation of direct ionization due to the difference in binding energy and electron number between various subshells; for instance, the ionization energy of M₁ electrons is about 1.7 times larger than that of M₅ for ₄₈Cd element [Reference Crawford, Cohen, Doherty and Atanacio27–Reference Salem, Panossian and Krause29], and the single ionization cross section of M₅ electrons is higher than that of M₁ by almost one to two orders of magnitude in the present experimental energy region [Reference Brandt and Lapicki26]. The second is the high decay probability of M₁ vacancies via CK effects being promoted to higher M subshells. The last one is that the vacancy production in M₁ shell by CK rearrangement among the L subshells is energetically forbidden. One assumes that, besides the fluorescence yield, the X-ray emission intensity is proportional to the electronic number in the upper energy shell for filling the identical vacancy. The enhancement of ratios of Lι to Lα to the atomic data in Figure 3 indicates directly the multiple ionization in M_4,5 shells, and the diminished trend denotes that the extent of that multiple ionization decreases with the increase of proton energy. For example, the average number of multiple vacancies in M _4,5 shells is estimated using the relationship between the experimental ratios of Lι to Lα and the theoretical values [Reference Cipolla20, Reference Cipolla and Hill21, Reference Larkins30, Reference Ramakrishna, Rao and Raju31]. That is about 5.6 ± 0.8, 5.1 ± 0.7, 4.8 ± 0.7, 4.4 ± 0.6, 3.8 ± 0.5, 4.1 ± 0.6, 4.0 ± 0.6, and 4.1 ± 0.6 for ₄₉Cd and 6.1 ± 0.9, 4.8 ± 0.7, 4.2 ± 0.6, 4.0 ± 0.6, 3.9 ± 0.5, 3.9 ± 0.5, 3.8 ± 0.5, and 3.8 ± 0.5 for ₄₉In, with the proton energy of 75, 100, 125, 150, 175, 200, 225, and 250 keV, respectively.

Lβ ₂ and Lα X-rays mainly come from the transitions having the same lower energy level L₃ but different upper levels, i.e., N_4,5 and M_4,5 shells, respectively. When the outer-shell multiple ionization occurs, with the absence of some M and N shell electrons, the Auger transition ratio for filling L₃ vacancies will decrease, while the fluorescence yield ω ₃ will be enlarged [Reference Czarnota, Banaś and Berset9–Reference Słabkowska and Polasik12, Reference Crawford, Cohen, Doherty and Atanacio27–Reference Salem, Panossian and Krause29]. The Auger transition probability a ₃ of L₃ vacancies for Cd is almost a factor of 20 and 170 larger than the fluorescence yield of Lα (ω _Lα ) and Lβ ₂ (ω _Lβ2) X-ray, and that factor is about 18 and 149 for In, respectively [Reference Crawford, Cohen, Doherty and Atanacio27–Reference Salem, Panossian and Krause29]. Therefore, ω _Lβ2 will have a larger increase than ω _Lα ; as a result, the actual emission of Lβ ₂ X-ray will present an enlargement compared to that of Lα, namely, the measured relative intensity ratio of Lβ ₂ to Lα X-rays is enhanced than the atomic data of the singly ionized atom. Conversely, the results of Lβ ₂/Lα in Figure 3 illustrate the multiple ionization of M_4,5 and N_4,5 shells, and it decreases with the increase of incident energy.

Multiple ionization can be produced by concurrent direct Coulomb ionization, charge transfer, or subsequent excitation by CK and Auger transitions. The cross section for the loss of outer-shell electron due to charge transfer can be calculated on the basis of Oppenheimer–Brinkman–Kramer (OBK) approximation [Reference Nikolaev32–Reference Dewangan and Eichler35]. For ₄₈Cd impacted by proton with energy of 75–250 keV, this cross section is about 1.96 × 10⁻¹²∼3.92 × 10⁻¹⁰ barn for N shell and 2.57 × 10⁻¹²∼2.01 × 10⁻¹⁰ barn for O shell. For ₄₉In, that is about 8.49 × 10⁻¹²∼2.80 × 10⁻¹⁰ barn for N shell and 3.11 × 10⁻¹²∼1.43 × 10⁻¹⁰ barn for O shell. That is at least 19 orders of magnitude smaller than the direct ionization cross section. So, the multiple ionization results from charge transfer can be neglected for the present result. If leaving the subsequent excitation by nonradiative transitions and the effect of electron correlation out of account, the multiple ionization probability is positive to the single ionization cross section for the direct Coulomb collision. Single ionization is inversely proportional to the binding energy of the related orbital electrons. Besides, the bounding energy of outer-shell electrons is diminished with ascending energy level. So, in consideration of the above confirmed multiple ionization in M and N shells, it is easy to deduce that the O shell electrons of ₄₈Cd and ₄₉In are also multiply ionized by lower energy protons in the present work. That is just the reason for the enhanced emission of Lγ ₂ X-ray as shown in Figures 1 and 2.

In order to further clarify the dwindling trend of the multiple ionization reflected in Figure 2, the direct ionization cross sections of some outermost-shell electrons for ₄₈Cd and ₄₉In are simulated theoretically by binary encounter approximation (BEA) model [Reference McGuire and Richard36], in which the ionization cross section is proportional to the function of the scaled velocity G(V) ( $V=v_p/v_i$ , where v_p is the velocity of the projectile, v_i is the velocity of the ionized orbital electron) for a certain collision. Here, the v_p of proton is approximately 1.42–3.15 a.u. (a.u. is atomic units), and the v_i is about 1.10 and 0.73 a.u. for the 4d and 5s electrons of ₄₈Cd, and that is about 1.28 and 0.82 a.u. for the 4d and 5s electrons of ₄₉In and 0.59 a.u. for the 5p electron of ₄₉In, respectively. V is in the region of about 1.1∼5.3. The G(V) is diminished as a function of V. So, those cross sections decrease with the increase of proton energy as given in Figure 4. Taking into account the positive proportion between the single and multiple ionization, one can deduce easily the decrease of the extent for the multiple ionization from the above calculated result of single ionization, which leads to the change of ratios of Lγ ₂ to Lγ ₁ X-ray as in Figure 2.

Figure 4: Theoretical (a) ₄₈Cd and (b) ₄₉In outer-shell electrons ionization cross sections induced by proton.