Cite this Article
Wu Xiao-Rui, Shen Li, Zhang Kai, Dai Chang-Jian, Yang Yu-Na. Branching ratio and angular distribution of ejected electrons from Eu 4f76p1/2nd auto-ionizing states. Chinese Physics B, 2016, 25(9): 093203  
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Branching ratio and angular distribution of ejected electrons from Eu 4f76p1/2nd auto-ionizing states
Wu Xiao-Rui1, 2, Shen Li1, 2, Zhang Kai1, 2, Dai Chang-Jian1, 2, †, , Yang Yu-Na1, 2
Key Laboratory of Display Materials and Photoelectric Devices, Ministry of Education, Tianjin 300384, China
School of Science, Tianjin University of Technology, Tianjin 300384, China

 

† Corresponding author. E-mail: daicj@126.com

Project supported by the National Natural Science Foundation of China (Grant No. 11174218).

Abstract
Abstract

The branching ratios of ions and the angular distributions of electrons ejected from the Eu 4f76p1/2nd auto-ionizing states are investigated with the velocity-map-imaging technique. To populate the above auto-ionizing states, the relevant bound Rydberg states have to be detected first. Two new bound Rydberg states are identified in the region between 41150 cm−1 and 44580 cm−1, from which auto-ionization spectra of the Eu 4f76p1/2nd states are observed with isolated core excitation method. With all preparations above, the branching ratios from the above auto-ionizing states to different final ionic states and the angular distributions of electrons ejected from these processes are measured systematically. Energy dependence of branching ratios and anisotropy parameters within the auto-ionization spectra are carefully analyzed, followed by a qualitative interpretation.

PACS: 32.80.Zb;32.30.–r;32.80.Ee
Keyword:velocity-map imaging;Eu 4f76p1/2nd auto-ionizing state;branching ratio;angular distribution
1. Introduction

For the last decade, spectra of highly excited states of rare-earth atoms[1–3] have attracted considerable attention. Although the position and width, as well as the line shape of an auto-ionizing resonance on both Eu and Sm atoms, have been reported,[4–6] they are only relevant to total cross section of auto-ionization, yielding no information on the dynamical process of auto-ionization, such as the final states of ions, and phases of the wave function of the ejected electrons. A more stringent test of future new theory on the rare-earth atoms is to measure the branching ratios (BR) of ions and the angular distributions (AD) of electrons ejected from auto-ionizing states, as the BR may provide the information of final ionic states, while the AD represents the differential cross section of auto-ionization, providing the information about phases of possible transition channels, which is important to the physical world.[7–9]

Systematic studies of the BR and the AD on the mp1/2nd auto-ionizing states of alkaline-earth atoms[10,11] have been carried out previously with the time-of-flight (TOF) method,[12,13] while similar investigations on the rare-earth atoms have been reported on the Eu 4f76p1/26d auto-ionizing state[14,15] until recently. Although the advanced velocity-map-imaging (VMI) method,[16–18] developed originally for the photo-dissociation of molecules, was employed there, to avoid rotating the axis of the polarizer, lack of systematic studies on the 4f76p1/2nd auto-ionizing states in terms of more n values is obvious. Additionally, there will be more final ionic states involved for the higher 4f76p1/2nd auto-ionizing states with n > 6, more challenge has to be faced than that for the 4f76p1/26d state. Based on the above facts, a systematic study of the spectra, the BR, and the AD of the 4f76p1/2nd auto-ionizing states, taking n = 7–9 for instance, with the VMI technique is a significant task.

In Section 2 the experimental setup and methods will be presented, while the results of the BR and the AD of auto-ionization process will be discussed in Section 3. In Section 4 some conclusions will be drawn.

2. Experiment setup and methods
2.1. Experiment setup

Since the experimental apparatus used for measuring the auto-ionization BR and the AD of ejected electrons from Eu auto-ionizing states have been described in our previous work,[9] only a brief description will be given here. As shown in Fig. 1, the experimental apparatus consists of three parts: a Eu atomic beam production system, a high energy laser system, and a signal collection system.

Fig. 1. Experimental setup, including an atomic beam production system, a laser system, and a signal collection system.

A Eu atomic beam is produced by a resistively heated production system inside a vacuum chamber, whose pressure is kept at 10−5 Pa.

The three-step excitation in the experiment requires three pulsed dye lasers operated at 20 Hz, pumped by the 2nd or 3rd harmonic generation (at wavelength of 532 nm or 355 nm) of the same pulsed Nd:YAG laser. Each dye laser outputs laser pulses with a line width of 0.2 cm−1, pulse width of 5–8 ns, and pulse energy of 0.5 mJ. Having passed through three linear polarizers, the three dye laser beams are propagating collinearly, and crossed with the atomic beam perpendicularly in the interaction region to avoid the Doppler broadening effect. The laser pulses of the second and the third lasers are time-delayed properly, so that the three laser pulses are sequential in time. The laser polarization directions are set with three polarizers to be perpendicular to the electric field.

The signal collection system mainly includes an electron lens,[19] a position sensitive detector (PSD), a phosphor screen (PS), and a charge coupled device (CCD). Electrons produced in the interaction region are focused by a suitable electron lens and impacted onto the PSD. The fluorescence from the PS is captured by the CCD camera and transferred to a computer for the further data analysis.

2.2. Methods

To investigate the 4f76p1/2nd auto-ionizing states, it is preferable to use the three-step isolated core excitation (ICE) method,[20] which has been utilized extensively in studies of alkaline-earth and rare-earth atoms, and has several advantages: i) only low power is required for each excitation laser; ii) the spectrum obtained by ICE is simple, where interference effects can be reduced significantly for lower-n states; iii) the n values of the 4f76p1/2nd auto-ionizing states are determined by the 4f76snd states, which is the initial states of the third-step excitation, 4f76snd→4f76p1/2nd. However, since the 4f76snd states have been known for n = 6 and 7 only,[21] one has to begin with detecting the 4f76snd states (n > 6) for studying the 4f76p1/2nd (n > 6) auto-ionizing series.

To detect the 4f76snd states in the region of 41150–44580 cm−1, a two-color three-photon resonant ionization method[22] is employed. Furthermore, the three different paths, named Scheme I, II, and III, are designed, to uniquely determine the total angular momentum of 4f76snd states. According to the selection rule ΔJ = 0, ±1, the possible values of angular momentum J0 for the detected Rydberg states with Scheme I are 3/2, 5/2, or 7/2, with Scheme II are 5/2, 7/2, or 9/2, and the possible values of J0 are 7/2, 9/2, or 11/2 with Scheme III. For example, J=9/2 can be assigned to the states that can only be detected with Scheme III.

Scheme I:

Scheme II:

Scheme III:

As illustrated above, the wavelength of the first lasers, λ1, are fixed at 466.32 nm, 462.85 nm, and 459.53 nm to excite the Eu atom to three different 4f76s6p states, respectively. The wavelength of the second laser, λ2, is tuned over a certain range, to excite the Eu atom to many highly excited states, including some 4f76snd states, which can be detected by absorbing another λ2 photon, as shown in Fig. 2(a). Note that all wavelengths used in this paper are the values in a vacuum.

Fig. 2. The excitation schemes used in the experiment: (a) for detection of 4f76snd states; (b) the ICE scheme of the 4f76p1/2nd states.

As shown in Fig. 2(b), once the 4f76snd states are identified from the highly excited states, the 4f76p1/2nd auto-ionizing states can be populated with the ICE scheme. Comparisons among the spectra obtained with the above three excitation schemes can assign a unique J0 value to any 4f76snd state detected. However, there are only three highly excited states, which are shown in Table 1, that can be excited to auto-ionizing states through the ICE method.

Table 1.

Values of several parameters of the three highly excited states.

.

As shown in Table 1, EP represents excitation paths, δ denotes the quantum defect, and 4f76snl represents electron configuration. Since δ values of 4f76snd (n = 6, 7) states[21] are in the range of 2.79–2.90, two new electron configurations, 4f76s8d and 4f76s9d, can be identified.

In order to obtain the total cross section of Eu 4f76p1/2nd series states, this work uses three different intermediate states in the ICE excitation scheme, namely,

Scheme IV:

Scheme V:

Scheme VI:

where λ1 is fixed at 462.85 nm, 459.53 nm, and 459.53 nm, to excite the Eu atom from the ground state to different 4f76s6p states, respectively. The wavelength of the second laser, λ2, is fixed at 510.72 nm, 449.99 nm, and 442.22 nm for the Schemes IV, V, and VI, to excite the outer electron to three bound Rydberg states, respectively. Then, the third laser, whose wavelength λ3 is scanned in a wide range depending on the situations, the auto-ionizing resonance transition from 4f76snd state to 4f76p1/2nd state is carried out, as shown in Fig. 2(b). More interestingly, in these three excitation schemes, the Eu atom quickly decays to 4f75d+(7Do), 4f75d+(9Do), 4f76s+(7So), or 4f76s+(9So) ionic state with the ejection of an electron.

Electrons ejected from the process of auto-ionizing are probed by the VMI method.[16–18] Figure 3 shows an example of VMI images acquired at a point of 4f76p1/27d state. Figure 3(a) displays that the two-dimensional (2D) distribution captured by the CCD is treated as the raw image, which could be reconstructed to a three-dimensional (3D) distribution of the ejected electrons by the inverted Abel transformation. Figure 3(b) shows that the 3D distribution is treated as the Abel-inverted image. The BR of ions and the ADs of electrons ejected from 4f76p1/2nd states can be derived by fitting the Abel-inverted images.

Fig. 3. The VMI images at the fixed energy of the 4f76p1/27d state: the raw image (a) and the Abel-inverted image (b).

As shown in Fig. 3, there are four rings in both the raw image and the Able-inverted image, corresponding to four different ionic states shown in Fig. 2(b). Namely, the four rings from the inner to the outer denote the ADs corresponding to the decays to the 4f75d+(7Do), 4f75d+(9Do), 4f76s+(7So), and 4f76s+(9So) final ionic states, respectively.

In the present study, several parameters of VMI will be adjusted in order to obtain the most accurate data. To ensure that the electrons ejected from the auto-ionization are located accurately, it is necessary for the spatial location of the image with VMI to be calibrated. Namely, the ejected electrons with zero kinetic energy should be in the center of the image. In addition, the brightness calibration of the VMI image leads to the uncertainty in boundaries within which angular integral is undertaken. In general, the uncertainty of this experiment is estimated to be 5%.

3. Results and discussion

Before describing the BR of ions and the AD of ejected electrons from 4f76p1/2nd states, the auto-ionization spectra of 4f76p1/2nd states will be discussed briefly. Eu atoms can be excited from the ground state to 4f76p1/2nd auto-ionizing states by absorbing three photons, while auto-ionization spectra of 4f76p1/2nd states are obtained by collecting the ions due to the instability of auto-ionization states.

For example, the auto-ionization spectrum (solid line) of 4f76p1/27d state together with the Lorentzian fitting result (dashed line) is shown in Fig. 4. The spectrum of 4f76p1/27d state is the standard Lorentzian profiles, indicating the success of the ICE method.

Fig. 4. Auto-ionization spectrum of 4f76p1/27d state in the energy range of 62800–64000 cm−1.

According to the above discussion, it is curious to know whether there is difference between 4f76p1/27d and 4f76p1/2nd (n = 8, 9) auto-ionizing states in terms of their spectra. As expected, the auto-ionization spectra of 4f76p1/28d and 9d states with the Lorentzian fitting results (dashed line) shown in Fig. 5 are also the standard Lorentzian profiles. With the assistance of Ref. [15], the three spectra of 4f76p1/26d auto-ionizing state are Fano-type line shapes, indicating that the ICE method is valid for Eu 4f76p1/2nd (n ≥ 7) auto-ionizing states.

Fig. 5. Auto-ionization spectra of 4f76p1/2nd (n = 8, 9) auto-ionizing states: (a) the spectrum of 4f76p1/28d state in the energy region of 65800–66600 cm−1, and (b) the spectrum of 4f76p1/29d state in the energy region of 66000–67000 cm−1.

Since λ3 is scanned across the or ionic transition, the spectra of the auto-ionizing states with 4f76p1/2nd configuration possess double-peak profiles.

With the combination of Figs. 4 and 5, the three spectra are all superimposed with some complex structures, manifesting the interaction among different auto-ionization series converging to different ionization limits. Because the line width of the auto-ionization spectrum is inversely proportional to (n*)3, the complex structures on the top of the main profile are the auto-ionizing states converging to 4f75d+ ionization limits, where n* is the effective quantum number. In addition, the wide complex structures are the configuration interaction between the 4f76p1/2nd auto-ionizing states and higher-n4f75d (7D) nl auto-ionizing states, while the narrow one converges to 4f75d+ (9D) ionization limits.

The energies of the three 4f76p1/2nd auto-ionizing states are different, leading to 4f76p1/2nd auto-ionizing states interacting with different 4f75dnl states. Therefore, the three auto-ionization spectra have different complexity. Obviously, the spectrum of 4f76p1/28d state is the simplest one, while 4f76p1/29d state is the most complex.

Furthermore, the comparison between Figs. 5(a) and 5(b) shows that the line width of 4f76p1/28d state is smaller than those of the 4f76p1/29d state. This is because the line width is not only determined by the effective quantum number, but also affected by the interaction with the continuum channels.[4,14]

Because the energy of 4f76p1/29d state approaches the ionization limit, the spectrum of 4f76p1/29d may also be affected by these auto-ionizing states converging to the ionization limit. Specifically, the spectra of 4f76p1/28d and 9d auto-ionizing states further confirm the existence of 4f76s8d and 4f76s9d bound Rydberg states.

Since the spectra of 4f76p1/2nd states provide no information about the dynamical process of auto-ionization and energy conservation results in one-to-one correspondence between the energy of the ejected electrons and the final ionic states, the energy of the ejected electrons is analyzed instead to determine the final states.

Energy distribution of ejected electrons, which can be extracted from fitting the Abel-inverted image, is a key factor in the experiment. An example is shown in Fig. 6 for the energy distribution ejected electrons from 4f76p1/2nd states.

Fig. 6. Exemplified energy distributions of ejected electrons for (a) 4f76p1/27d state, (b) 4f76p1/28d state, and (c) 4f76p1/29d state.

As shown in Fig. 6(c), the fine structures of 4f76s+ ionic state cannot be resolved, while 4f76s+(7So) and 4f76s+(9So) ionic states can be resolved in Figs. 6(a) and 6(b), indicating that with the increasing energy of ejected electrons, the resolution becomes lower. Therefore, there are four auto-ionization channels for 4f76p1/27d state and 4f76p1/28d state, respectively. There are three auto-ionization channels for 4f76p1/29d state.

One of the primary objectives of the present work is to discuss the BR of the 4f76p1/2nd states, which can be extracted from the energy distributions of elected electrons based on the areas under different profiles. Let BR1, BR2, BR3, and BR4 be the BRs to the four different ionic states 4f76s+(9So), 4f76s+(7So), 4f75d+(9Do), and 4f75d+(7Do) in Figs. 6(a) and 6(b), while BR12 corresponds to 4f76s+ state in Fig. 6(c). The sum of BRs at any fixed point is equal to 1. An example is shown in Fig. 7 for the four BRs of 4f76p1/27d state and the auto-ionization spectrum.

Fig. 7. The spectrum and the BRs of 4f76p1/27d auto-ionizing state are illustrated: (a) auto-ionization spectrum, (b) BR1, (c) BR2, (d) BR3 and (e) BR4.

As shown in Fig. 7, BR3 is much larger than BR1, BR2, or BR4, meaning that Eu atoms mainly decay to 4f75d+(9Do) ionic state in the whole energy region. Nearly 40% of Eu atoms decay to 4f75d+(9Do) ionic state, leading to a population inversion between 4f75d+(9Do) and two 4f76s+ ionic states, which is significant for developing an ion laser. Meanwhile, all peaks in the spectra of BRs in Fig. 7 seem to have no correspondence to those in auto-ionization spectrum, which can be partially attributed to the configuration interaction between the 4f76p1/27d auto-ionizing state and the higher-n 4f75dnl auto-ionizing states.

Similar measurements and analysis are performed for 4f76p1/28d state, and the final results are presented in Fig. 8.

Fig. 8. The spectrum and the BRs of 4f76p1/28d auto-ionizing state are illustrated: (a) auto-ionization spectrum, (b) BR1, (c) BR2, (d) BR3, and (e) BR4.

The population inversion between 4f75d+(9Do) and two 4f76s+ionic states is still kept in the whole energy region. However, several differences between Figs. 7 and 8 can be found. For example, the BR1, BR2, BR4 of the 4f76p1/28d state vary remarkably in the vicinity of 66000 cm−1, corresponding to the auto-ionization peak on the left side.

The last example is shown in Fig. 9 for the auto-ionization spectrum and the BRs of 4f76p1/29d state in a short energy region of 66300–66900 cm−1, to compare with those shown in Figs. 7 and 8.

Fig. 9. The spectrum and the BRs of the 4f76p1/29d auto-ionizing state are illustrated: (a) spectrum, (b) BR12, (c) BR3, and (d) BR4.

More interestingly, BR3 is much larger than BR12 in the energy region of 66552.4–66917.4 cm−1, and also BR4 is much larger than BR12 in the energy region of 66445.1–66532.8 cm−1. This means that population inversion is not only between 4f75d+(9Do) and 4f76s+, but also between 4f75d+(7Do) and 4f76s+ionic state. This phenomenon can be partially attributed to the fact that the J value of 4f76p1/29d is bigger than those of the other two auto-ionizing states. Furthermore, the BRs of the 4f76p1/29d auto-ionizing state to the 4f76s+, 4f75d+(9Do), and 4f75d+(7Do) ionic states fluctuate from 24% to 50%, 28% to 46%, and 16% to 44%, respectively.

After the partial cross section of 4f76p1/2nd auto-ionizing states, it is time to discuss the differential cross section. In addition, the AD of ejected electrons allows one to obtain more detailed information.

Both symmetry considerations and angular momentum selection rules constrain AD from the 4f76p1/2nd states to be of the form

where I0 = 4π α0 is the total cross section of the auto-ionization, αk/α0 is the anisotropy parameter, Pk(cosθ) is the kth Legendre polynomial and k is the fitting order of the AD. Furthermore, anisotropy parameters will be determined by fitting the AD to Eq. (1) for each energy point. As mentioned in Ref. [15], two limitations of the fitting order k are 0 ≤ k ≤ 2J and k = 2lmax, where l represents the orbital angular quantum. Considering the conservation of parity, we can determine that l is an odd number. Relationship of the bound Rydberg angular momentum J0, the total angular momentum J, and the fitting order k in this paper is presented in Table 2.

Table 2.

The values of fitting order in the experiment.

.

From Table 2 we can see that the highest value of k is 10. However, since the Legendre polynomials of higher orders play little role in the AD, the only anisotropy parameters up to k = 6 will be displayed here. In this experiment, let β = α2/α0, γ = α4/α0, and ɛ = α6/α0, whose varying with energy is of concern in this study. An example is shown in Fig. 10.

Fig. 10. Spectrum of the 4f76p1/27d state and spectra of the anisotropy parameters related to the 4f76s+(9So) ionization limit. (a) Auto-ionization spectrum, (b) β, (c) γ, and (d) ɛ.

As can be seen from Fig. 10, the anisotropy parameters β, γ, and ɛ fluctuate from −0.2 to 0.4, −0.2 to 0.1, and −0.1 to 0.05, respectively. The variation amplitude of the β parameter is as large again as γ and four times as large as ɛ, indicating that the higher orders offer some complementary contributions. In other words, the ADs of ejected electrons are well characterized by P2(cosθ). Therefore, it is very important to discuss the anisotropy parameter β of the AD. For example, the spectra of theβ parameters corresponding to the decays to the 4f76s+(9So), 4f76s+(7So), 4f75d+(9Do), and 4f75d+(7Do) ionization limits together with 4f76p1/27d auto-ionization spectrum are shown in Fig. 11.

Fig. 11. Spectrum of the 4f76p1/27d state (a) and β spectra of 4f76p1/27d state related to (b) 4f76s+(9So); (c) 4f76s+(7So); (d) 4f75d+(9Do); (e) 4f75d+(7Do) ionization limits.

As seen from Fig. 11, some peaks in β spectra seem to correspond to the auto-ionization spectrum. For instance, in the vicinity of the left auto-ionization peak β spectra in Figs. 11(b), 11(c), and 11(e) vary remarkably, while the β spectrum in Fig. 11(d) varies in a much smaller range. This means that the ejected electron is much slower for the 4f75d+(9Do) decay than for the other three decays.

Meanwhile, the AD diagrams should be of much interest, because they reveal more intuitive space distribution of ejected electrons. AD patterns may be generated in every energy point, but only some examples will be discussed below. For example, AD patterns of electrons ejected from 4f76p1/27d auto-ionizing state together with auto-ionization spectrum and one β spectrum are shown in Fig. 12.

Fig. 12. Spectrum of the 4f76p1/27d state (a), β spectrum of 4f76p1/27d state related to 4f76s+(7So) ionization limit (b), and AD patterns of 4f76p1/27d state related to 4f76s+(7So) ionization limit (c).

As the three excitation lasers apply an additional force on the electron cloud in the direction of the polarization axis, the expected propensity of the AD is the electrons that are mainly ejected along the direction of the polarization axis, such as the AD patterns marked with 2 and 4. However, the unexpected patterns of the ADs marked with 1 and 5 are also discovered in Fig. 12. This means that the excitations from nd to ɛp and ɛf continuum states are accompanied by the third-step excitation. Namely, it is the 6s electron that is initially excited by the third-step laser, after which the 6pnd resonance levels decay by auto-ionization into 6sɛp and 6sɛf continua. Due to the complex channel interactions, the ejection of electrons at some particular energy points that are not along the polarization axis appears.

In order to make a comparison, another example for the AD patterns of 4f76p1/29d state is shown in Fig. 13.

Fig. 13. (a) Spectrum of the 4f76p1/29d state; (b) β spectrum of 4f76p1/29d state related to 4f76s+ ionization limit; and (c) AD of 4f76p1/29d state related to 4f76s+ ionization limit.

What can be seen from Fig. 13 is similar to the case shown in Fig. 12, where some unexpected patterns of the AD are discovered. Some apparent differences can be seen if one examines Fig. 13 carefully. The patterns of several ADs here seem to be more complicated than those shown in Fig. 12, especially those marked by 1 and 2 in Fig. 13. On the other hand, when J value increases, a complex AD is observed.

As seen from Figs. 12 and 13, there is a link between the patterns of the AD and the spectrum of β parameter. Namely, the ADs are “unexpected” at some particular energies corresponding to the peak of the β spectrum, while most of the ADs are “expected” at the energies corresponding to the bottom of the β spectrum.

The last example is shown in Fig. 14 for the AD patterns of the ejected electrons from 4f76p1/28d state, to compare with those shown in Figs. 12 and 13.

Fig. 14. (a) Spectrum of the 4f76p1/28d state; (b) β spectrum of 4f76p1/28d state related to 4f75d+(7So) ionization limit; and (c) AD of 4f76p1/28d state related to 4f75d+(7So) ionization limit.

The relation between the AD patterns and the spectrum of β parameter can also be seen from Fig. 14. Furthermore, what can be seen from Fig. 14 is very similar to the case shown in Fig. 12, where the AD patterns are also less complex than those shown in Fig. 13. Note that the energies of the AD patterns at the bottom of Figs. 12–14 are listed in Table 3.

Table 3.

Energies marked in Figs. 12–14.

.

A comparison of Figs. 12–14 shows that the patterns of the AD correspond to the feature of the auto-ionization spectrum at some energy points. Namely, the patterns of the AD are more complex in the off-peak region of the auto-ionizing spectrum than those in the peak region. For example, those marked by 5 in Fig. 14 and marked by 3, 5 in Fig. 13 are much more diverse than those marked by 4 in Figs. 13 and 14. It is quite remarkable that the AD of electrons exhibits such dramatic variations across an auto-ionization resonance. The only logical explanation is that the Rydberg–continuum coupling is weaker at the peak than at other positions.[15] Namely, in the peak positions, the higher probability of auto-ionization may lead to weaker Rydberg–continuum coupling, thereby gaining simple patterns of the AD.

4. Conclusions

A detailed study of the auto-ionization dynamics of Eu atom, which consists of the auto-ionization spectra, the BRs of ions, and the ADs of ejected electrons, is undertaken. From the systematical study of the auto-ionization spectra of multiple d states, it is found that the ICE method is valid for the higher-n 6pnl auto-ionizing state of the Eu. Both the auto-ionization spectra and the BRs of the 4f76p1/2nd auto-ionizing states reveal the complex configuration interaction between 4f76p1/2nd auto-ionizing states and the 4f75dnl auto-ionizing series. The link between AD patterns and the β spectrum is a significant finding from the systematic study, indicating that the AD patterns are not only influenced by the Rydberg–continuum coupling but also by the complex channel interactions.

On the whole, 4f76p1/29d auto-ionizing state is a particular state that belongs to 4f76p1/2nd, but it is the different 4f76p1/27d state and 4f76p1/28d state in case of the auto-ionizing spectrum, the auto-ionization BRs and the ADs of ejected electrons. Furthermore, in view of the specificity of 4f76p1/29d state, 4f76p3/2nl auto-ionizing series states need to be investigated further.

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