MIXED-STATE IONIC BEAMS: AN EFFECTIVE TOOL FOR COLLISION DYNAMICS INVESTIGATIONS

The use of mixed-state ionic beams in collision dynamics investigations is examined. Using high resolution Auger projectile spectroscopy involving He-like (1s2 1S, 1s2s 3,1S) mixed-state beams, the spectrum contributions of the 1s2s 3S metastable beam component is effectively separated and clearly identified. T his i s p erformed w ith a t echnique t hat e xploits t wo i ndependent spectrum measurements under the same collision conditions, but with ions having quite different metastable fractions, judiciously selected by varying the ion beam charge-stripping conditions. Details of the technique are presented together with characteristic examples. In collisions of 4 MeV B3+ with H2 targets, the Auger electron spectrum of the separated 1s2s 3S boron beam component allows for a detailed analysis of the formation of the 1s2s(3S)nl 2L states by direct nl transfer. In addition, the production of hollow 2s2p 1,3P doublyand 2s2p2 2D triply-excited states, by direct excitation and transfer-excitation processes, respectively, can also be independently studied. In similar mixed-state beam collisions of 15 MeV C4+ with H2, He, Ne and Ar targets, the contributions of the 1s2, 1s2s 3,1S beam components to the formation of the 2s2p 3,1P states by double-excitation, 1s → 2p excitation and transfer-loss processes can be clearly identified, facilitating comparisons with theoretical calculations.

In Figure 1, we show the surviving fraction of the 1s2s 1 S metastable state as a function of the ion 125 traveling distance s for various low-Z p elements and projectile energies of 0.25-2 MeV/u typical for 126 a TANDEM accelerator. It should be pointed out that the zero distance s = 0 may refer to either: (i) 127 the terminal inside the TANDEM tank, where the stripping of the incoming negative ion takes place, 128 or (ii) the post-stripper location when higher charge states are needed. Clearly, the 1s2s 1 S fraction is 129 considerably reduced, even for small distances (s < 20m), except for beryllium and boron, where larger For our ZAPS setup, currently operational at the Athens 5.5 MV tandem Van de Graaff accelerator 134 at the National Center for Scientiffic Research "Demokritos" under the atomic physics with accelerators: 135 projectile electron spectroscopy (APAPES) initiative [68], the interaction region is located at a distance 136 of s 1 = 25.4 m from the terminal stripper and of s 2 = 10 m from the post-stripper. The surviving 137 fractions of 1s2s 1 S metastable state are indicated in Figure 1 for the case of carbon. In addition, 138 assuming that the 1s2s 3 S and 1s2s 1 S states are statistically produced in a 3 : 1 ratio, the actual fraction 139 of the 1s2s 1 S beam compared to that of the 1s2s 3 S beam will be further reduced at the production 140 point by a factor of three.  The method is based on the assumption that the 1s2s2p 4 P state is exclusively produced by capture 190 to the 1s2s 3 S metastable state, while the 1s2p 2 2 D is primarily produced from the 1s 2 1 S by resonant method was also applied to low atomic number Z p elements with 4 ≤ Z p ≤ 9 [61].

199
In a similar approach, based on the same assumptions, Benis et al [62] proposed a different method that used the ratio of the yields of the 4 P and 2 D lines in the same spectrum, but did not involve any theoretical cross sections of the 4 P and 2 D states or any model calculations for the solid angle correction due to the long decay of the 4 P state. Actually, the critical assumptions are that the 4 P and 2 D lines result only from the 1s2s 3 S metastable and 1s 2 1 S ground states, respectively, without any additional conditions about the particulars of the population processes involved. Instead, the technique requires two independent measurements of the same electron spectrum at the same collision energy, but using mixed beams having quite different 1s2s 3 S metastable beam fraction in each. Then, the metastable fraction is determined only by the normalized yields Z of the 4 P and 2 D peaks as: where i = 1, 2 refers to the high and low metastable fractions, respectively. Thus, the method does 200 not suffer from uncertainties arising either from theoretical calculations or experimental parameters.

201
The only requirement is that the two spectra have appreciably different fractions. Typical spectra The obtained fractions are summarized in Table 2. It is seen that the fraction obtained for carbon 208 is much smaller than that for boron. An explanation for this was proposed in Ref.
[61] considering 209 the K-vacancy sharing between the projectile and the target. Indeed, in the near-symmetric stripping 210 process (i.e. C 4+ traversing carbon foils) the K-vacancy transfer probability is close to 1/2 [77]. In 211 this case, the K-vacancy on an incident metastable C 4+ (1s2s 3 S) ion will be transferred to the stripper 212 carbon atom, leaving approximately half of the projectile ions in the ground state. For ions other than 213 carbon, the more asymmetric K-vacancy transfer probability for other He-like beams is about an order 214 of magnitude smaller and thus the reduction of the corresponding metastable fraction is negligible. We note that for GTS at low enough stripping energies, the metastable fraction can be quite small,  Be-like ions produced in TANDEM accelerators are delivered in the ground 1s 2 2s 2 1 S and the metastable 1s 2 2s2p 3 P J states. The metastable lifetimes are in the µs to s range depending on atomic number Z p and angular momentum J [79-81]. During collisions with H 2 targets, the needle ionization of the 1s electron [82] of the 1s 2 2s2p 3 P state results in the production of the 1s2s2p configuration. In the LS coupling scheme the 2s and 2p electrons interact strongly as parts of the same shell and are negligibly affected by the K-shell configuration. Thus, even after the 1s ionization, the L-shell electrons should maintain their 3 P coupling. In this spirit, the only viable states are the 1s2s2p 4 P and the 1s(2s2p 3 P) 2 P. This is very similar to what also occurs in photo-ionization of Be-like ions [81,[83][84][85][86]. Similarly, 1s ionization of the 1s 2 2s 2 1 S ground state results in the Li-like 1s2s 2 2 S intermediate state. Since the 1s needle ionization process is not expected to depend strongly on the L-shell configuration, the K-vacancy production cross sections from the ground state and the metastable state can be expected to be equal, i.e. σ 1s (1s 2 2s 2 ) = σ 1s (1s 2 2s2p 3 P) as also assumed by Lee et al [15]. In addition, the production population statistics of the 4 P and 2 P − states should result in the ratios σ( 4 P) : σ( 2 P − ) = 2 : 1, as is obvious from the multiplicity of the states. Consequently, the following ratios of the production cross sections should be valid, i.e. σ( 2 S) : σ( 4 P) : σ( 2 P − ) = 3 : 2 : 1. Then the metastable fraction f3 P is obtained as [87]: where Z denotes the normalized electron yields of the corresponding state in the Auger spectrum.

225
In Figure 3, we reproduce high resolution electron spectra obtained in collisions of 17.5 MeV O 4+ 226 and 6.6 MeV C 2+ with H 2 targets, initially reported in Ref.
[87]. The measurements were performed 227 with our ZAPS apparatus located at the tandem accelerator facility of "Demokritos". As can be seen, 228 the 4 P peak has an asymmetry towards the lower energy wing. This is due to the metastability of 229 the state that results in its decay all the way from the gas cell to the entry of the spectrometer. This 230 feature strongly affects the detection solid angle as compared to a prompt state that decays inside 231 the gas cell. We have studied in detail this behavior and results have been reported in the literature 232 [88,89]. In Figure 3, the reproduction of the asymmetry in Monte Carlo type simulations, using the 233 ion-optics package SIMION 8.1, is presented. Moreover, the small asymmetry in the peak near 425 eV, 234 evident in the oxygen spectrum, is due to the additional low-intensity 1s2s 2 2p 3 P Auger line.  respect to the target, the detection efficiency is large enough to avoid such difficulties.

264
Here, we followed this method for the spectra shown in Figure 4 (top). In more detail, due to the 265 different energy resolution of the two spectra, due to beam straggling for the FPS mixed-state spectrum, 266 we first convoluted the ground state spectrum with the slightly larger energy resolution width of the 267 mixed-state spectrum, and then normalized the two spectra with respect to the 1s2p 2 2 D peak, as shown 268 in Figure 4 (middle). Finally, after subtracting the two normalized spectra, the resulting spectrum 269 corresponding to the 1s2s 3 S metastable state is obtained. The result is shown in Figure 4 (bottom). with H 2 targets. The red squares correspond to the mixed-state (1s 2 1 S, 1s2s 3 S) beam, while the blue dots to the almost pure ground state 1s 2 1 S, as evident by the very small contribution of the 4 P peak. The high fraction spectrum was obtained with FPS, while the low fraction with GTS. (Middle) Same as in the top graph, but here the ground state spectrum was convoluted with the slightly larger energy resolution of the mixed-state spectrum and then normalized to the 1s2p 2 2 D line. (Bottom) Li-like Auger spectrum corresponding just to the 1s2s 3 S metastable state. The spectrum resulted from the subtraction of the two normalized spectra of the middle graph.
The first important result of this approach is the direct separation of the two beam component 2s2p 2 2 D and 2s2p 2 2D , respectively. These triply excited states, cannot be straightforwardly populated 278 by photo-ionization, thus they were studied by our group in ion-atom collisions for isoelectronic 279 projectiles with atomic number 5 ≤ Z p ≤ 9. This investigation also resulted in some of the first tests 280 of R-matrix calculations for open shells, eventually bringing them into good agreement [32,90,91].

281
Another clearly separated Auger line is the He-like hollow state 2s2p 3 P, the formation of which is 282 discussed in section 5.2 below.

283
The second and possibly even more important result is the separation of the contributions of 284 states that can be populated from both ground and metastable components. These states appear in 285 both the ground and the mixed-state spectra preventing a straightforward determination of their 286 production cross sections in a single measurement involving only mixed-state beams. However, in our 287 dual measurement approach, the two contributions can be separated and production cross sections for 288 the 1s2s 3 S metastable state and the 1s 2 1 S ground state, can be safely obtained. In our spectra shown in 289 Figure 4, these states include the Auger KLL lines 1s2s 2 2 S, 1s2s2p 2 P + and 1s2s2p 2 P − states, as well as 290 all the higher-lying KLn states with n≥3 mostly of the type 1s2s( 3 S)nl 2 L.

291
Moreover, such studies can also provide important information about secondary processes.  [57]. This new technique, similarly involves two independent measurements at the same collision 304 energy using mixed beams with different 1s2s 3 S metastable fractions. However, subtraction of the two 305 spectra is not viable, but rather extraction of the single differential production cross section of the Li-like 306 doubly excited states is obtained for both the ground and metastable components simultaneously.

307
Details are given in Ref.
[57]. behavior, i.e. that the yields for the 2 S, 4 P, 2 P − and 2 P + states, arising primarily from the metastable 319 component are reduced for the low fraction condition, as opposed to that for the 2 D state, arising 320 mostly from the ground state, where the yield is increased.

321
The above fraction-controlled measurements provide valuable information about the processes 322 involved in the production of the doubly excited 2s2p 1,3 P states. Indeed, as can be seen in Figure 5 (top), 323 the relatively small reduction of the metastable percentage results in a large reduction in the yield of 324 the 2s2p 3 P state, while the yield of the accompanied 2s2p 1 P state remains almost unaffected. This 325 behavior implies that the 2s2p 3 P state is populated primarily by the 1s2s 3 S metastable state. Indeed, the 2s2p 3 P state can be straightforwardly formed by 1s → 2p single electron excitation, a process of 327 large cross section due to its dipole character. On the other hand formation from the 1s 2 1 S ground 328 state would require higher order processes such as 1s → 2p excitation with spin flip and transfer loss 329 (2p transfer, 1s loss) which are much less probable at these collision energies compared to the direct 330 1s → 2p excitation.

331
At this point we should also consider possible contributions from the 1s2s 1 S state, so far not 332 discussed and assumed to be negligible. Even though its fraction is in general very small (< 5%) 333 and does not seem to appreciably contribute to the doubly excited KLL states, its contribution to 334 the 2s2p 1,3 P states should not be neglected. Indeed, the 2s2p 3 P could be populated from the 1s2s 1 S 335 state by direct 1s → 2p excitation with spin flip, reducing significantly its cross section. Therefore, 336 based on the data of Figure 5 (top), we may safely state that the 2s2p 3 P state is primarily formed 337 from the 1s2s 3 S state by 1s → 2p single electron excitation. Alternatively, the situation for the 2s2p 1 P 338 state is more complicated. The very small decrease of its Auger yield following the reduction of the 339 metastable part of the beam implies that the 1s2s 3 S state has just a small contribution. Indeed, 2s2p 1 P 340 can be populated from the 1s2s 1 S state by direct 1s → 2p excitation, but it may also be populated 341 from the 1s 2 1 S ground state via the second order processes of double excitation (1s → 2s, 1s → 2p) 342 and/or transfer loss (2p transfer, 1s loss). Transfer loss is also viable in the production of the 1s2s 3 S 343 state. These second order processes, although of smaller cross section compared to the direct 1s → 2p 344 excitation, have an increased weight due to the much higher ground state fractions they can arise 345 from. Therefore, the formation of the 2s2p 1 P state can most likely be attributed largely to the 1s → 2p 346 excitation of the 1s2s 1 S state and to a lesser extent to higher order processes involving the 1s 2 1 S ground 347 and 1s2s 3 S metastable states. Atomic orbital close coupling (AOCC) calculations in progress confirm 348 these observations. In Figure 5 ( is seen that the main population channel for the 2s2p 3 P state is still the 1s2s 3 S state, as evident by the 353 large change in its yield following the relatively small reduction of the metastable beam percentage.

354
The yield of the 2s2p 1 P state though seems essentially unaffected, implying that the second order 355 processes involving the 1s 2 1 S ground and 1s2s 3 S metastable states are now as significant as the 1s → 2p 356 excitation from the 1s2s 1 S state.