- Email: [email protected]
Channel interaction of Ba 6pnd (J = 1, 3) autoionizing states
Journal of Electron Spectroscopy and Related Phenomena 148 (2005) 11–16
Channel interaction of Ba 6pnd (J = 1, 3) autoionizing states Yan Zhang a, c, ∗ , Chang-Jian Dai b , Shi-Ben Li a a Physics Department, Zhejiang University, Hangzhou 310027, China Physics Department, Tianjin University of Technology, Tianjin 300191, China Institute of Information Engineering, China Institute of Metrology, Hangzhou 310034, China b
c
Received 21 November 2004; received in revised form 27 January 2005; accepted 29 January 2005 Available online 26 February 2005
Abstract The channel interaction of Ba 6pnd (J = 1, 3) autoionizing series has been investigated by means of unsaturation and saturation excitation methods, using a three-step isolated-core-excitation scheme with a proper polarization configuration of lasers. The physical manifestations of the observed interactions are analyzed by the cross-section and spectral density calculated from the multichannel quantum defect theory, whose results are quite satisfactory with experimental ones. © 2005 Elsevier B.V. All rights reserved. Keywords: Channel interaction; Autoionizing states; Isolated-core-excitation; Multichannel quantum defect theory
1. Introduction Autoionizing states of the alkaline-earth atoms consist of the configuration with two excited valence electrons, one is in the first excited state, and the other is in a high Rydberg state. In recent years, autoionizing Rydberg series of alkalineearth atoms have been extensively studied, including the line shapes of the transition [1–5], branching ratios and angular distributions of ejected electrons from autoionizing states [6,7], as well as their spectroscopic properties in electric and magnetic fields [8–11]. Since the channel interaction of autoionizing states can reveal the perturbation between the two valence electrons, it is desirable to extend analysis of autoionizing series for understanding the inner physical mechanism of the alkaline-earth atoms. Usually, the interaction among autoionizing states with different n and l leads to the complex spectra of autoionizing states. For the Ba 6pnd autoionizing states relevant to this work, Gallagher and coworkers have observed the interaction of the 6p3/2 10d (J = 3) autoionizing state with the higher n values of 6p1/2 nd (J = 3) autoionizing states [12,13]. Later, Li et al. observed the interactions between the 6p3/2 nd (J = 1) and the 6p3/2 ns (J = 1) series [14]. ∗
Corresponding author. E-mail address: [email protected] (Y. Zhang).
0368-2048/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2005.01.276
To our knowledge, only the fragmentary results are available on the channel interaction of Ba 6pnd autoionizing series converging to the 6p1/2 and 6p3/2 ionization thresholds, respectively, thus it is difficult to reveal the complex atomic properties. Further study of the properties of Ba atom motivates us to have a detailed investigation on the configuration interactions. Here we focus on the channel interaction of Ba 6pnd (J = 1, 3) autoionizing states, using a three-step isolatedcore-excitation (ICE) scheme with a proper polarization configuration of lasers. In addition, we use an alternative way to explore the channel interaction. Namely, the saturation spectra of Ba 6pnd autoionizing states are also measured with great care. On the theoretical side, the multichannel quantum defect theory (MQDT), which has been very successful in the study of Ba 6pns autoionizing states [1–3,6,7], is employed to analyze the channel interactions of 6pnd autoionizing states by calculating their cross-sections and spectral densities. For the J = 1 series, the MQDT parameters are obtained from the Rmatrix method, while for the J = 3 series, the MQDT parameters are from the fitting procedures. Since many additional channels are taken into account for J = 1 series, the theoretical analysis is greatly improved compared with previous works [12,13]. The MQDT analysis of the data allows us to explain the main features of the observed complex spectra.
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Y. Zhang et al. / Journal of Electron Spectroscopy and Related Phenomena 148 (2005) 11–16
The detailed descriptions of the experimental method and the theoretical treatment will be presented in Sections 2 and 3, respectively. In Section 4, the results and discussion will be provided, and the conclusion will be summarized in Section 5.
2. Experimental observations The ICE scheme has already been proven to be very powerful and versatile in the study of atomic autoionizing states. One of its major advantages is that it enables one to obtain a spectrum with a line shape only determined by configuration interaction rather than any interference effects. Since the interpretations of observed spectra are noticeably simplified, it is easier to investigate channel interaction of the autoionizing states. The experimental arrangement used here was described in detail in previous works [4,5,15], so only the main features relevant to this work are included. The schematic diagram of the experimental apparatus is illustrated in Fig. 1. Three home-made dye lasers pumped by an Nd:YAG-pulsed laser are used to excite the Ba atom from its ground state to the 6pnd autoionizing states. A rhomb is used to rotate the polarization vector of the linearly polarized laser beam without reducing the laser power, and then the linearly polarized laser is calibrated by a polarizer. The Ba atomic beam is extracted from a stainless steel crucible vertically, and interacted with three laser beams. The atom in a 6pnd autoionizing state quickly decays into an ion and an electron. The ions are extracted by applying a pulsed electric field on the plates, and are detected by an MCP detector. Finally, the ion signals are first integrated and averaged with a boxcar, then stored in a computer for further analysis. A common method for studying the channel interaction of autoionizing states is to observe the normal spectra of these states. With the ICE scheme, the first two tunable lasers excite the Ba atom from the 6s2 ground state to the different 6snd Rydberg states, while the third laser excites the other valence
Fig. 2. The spectrum of the 6p1/2 22d (J = 1, 3) autoionizing state excited from 6s22d 1 D2 Rydberg state: (a) unsaturated case; (b) saturated case. The abscissa is the photon energy of the third laser.
electron from 6s to 6p ionic state. Noted that since the power of the third laser is kept at the lowest level possible and its frequency is tuned at the resonance line, excitation of the Rydberg electron can be neglected, which is an advantage over other excitation schemes. In this experiment, all the three exciting lasers are linearly polarized in the same direction, thus the spectra consisting of both J = 1 and 3 components are obtained. Most spectra show nearly Lorentzian profiles, but
Fig. 1. The schematic diagram of the experimental apparatus (PLD: pulsed-dye laser).
Y. Zhang et al. / Journal of Electron Spectroscopy and Related Phenomena 148 (2005) 11–16
some exhibits complex structures due to the channel interactions with other autoionizing states. An alternative way to study the channel interaction is to examine the saturation spectra, which are obtained by increasing the power of the third laser about 100 times than its usual level. In this case, the excitation of the Rydberg electron can no longer be neglected, thus many n values of the 6pnl autoionizing states are excited simultaneously. In other words, the weak satellite features of the main transition are enhanced significantly, providing a clear picture of channel interaction. Under the above consideration, the unsaturated and saturated spectra of Ba 6pnd (J = 1, 3) autoionizing states are systematically measured. Two typical examples are presented in Fig. 2, which illustrate the differences between these two cases. The unsaturated spectrum of Ba 6p1/2 22d state in Fig. 2(a) shows a normal Lorentzian profile, whereas there are many additional peaks make the saturation spectrum more complex, as shown in Fig. 2(b), from which the channel interaction can be analyzed by determining the energy level of each peak. More detailed analysis on the channel interaction, including the investigation on the spectral densities, will be discussed in the following sections.
In order to interpret the observations, it is necessary to calculate the cross-section and the mixing coefficient of relevant channels using the MQDT. Since the MQDT procedures have been well documented, only the main equations are included here. The partial cross-section σ Jc to a particular final ionic state and the total cross-section can be evaluated as: 2 4 Dρ exp(iπτρ )Aiρ σJc = π2 α¯hω3 (1) 3 ρ i
σ=
σJc
(2)
Jc
Here i and ρ refer to the open dissociation channel and the collision eigenchannel, respectively; h ¯ ω3 the photon energy of the third laser, and Dρ the corresponding reduced transition matrix element. Moreover, the mixing coefficient of the ith channel, which reflects the contribution from the ith channel to the final autoionizing spectrum, can be determined by: Aiρ =
1 Uiα cos[π(νi + µα )]Bα (ρ) Nρ α
Fig. 3. The comparison between the experimental spectrum (solid line) and the theoretical spectra (dashed line) of 6p1/2 20d (J = 1, 3) autoionizing state excited from 6s20d 3 D2 Rydberg state. The abscissa is the term energy.
nel quantum defect and the matrix elements of the unitary transformation, which contain the most important dynamical information. The sum over all relevant ρ to the square of the mixing coefficient is called the spectral density, i.e.: A2i = A2iρ (4) ρ
3. Theoretical treatments
and
13
(3)
where νi is the effective quantum number for a closed channel, and is replaced with −τ ρ for an open channel; Nρ the (ρ) normalization constant; Bα the coefficient of the wave function ϕα in the αth close-coupled eigenchannel. In particular, the MQDT parameters µα and Uiα represent the eigenchan-
For the J = 1 series of Ba 6pnd autoionizing states, the total cross-section can be calculated using a 13-channel model. These dissociation channels are 6s1/2 np1/2 , 6s1/2 np3/2 , 5d3/2 np1/2 , 5d3/2 np3/2 , 5d3/2 nf5/2 , 5d5/2 np3/2 , 5d5/2 nf5/2 , 5d5/2 nf7/2 , 6p1/2 ns1/2 , 6p1/2 nd3/2 , 6p3/2 ns1/2 , 6p3/2 nd3/2 and 6p3/2 nd5/2 , which converging to the 6s, 5dJ and 6pJ thresholds, respectively. The MQDT parameters can be obtained from the R-matrix calculation [16], which is superior to the empirical MQDT. On the other hand, a four-channel model is employed to calculate the cross-section of 6pnd states for the J = 3 series, whose parameters are the best fitting results so far [12]. In fact, we have made some efforts trying to improve the MQDT model by fitting our data to a new model with several additional channels, but there is almost no improvement in terms of the agreement between experiment and theory. By doing this, one has to deal with the new problem, that is when the amount of the fitting parameters increases rapidly, and the parameters are hard to be determined uniquely. Hence, we decided to use the four-channel model for the J = 3 series. The addition of these two calculated spectra for J = 1 and 3 components will yield the composite spectra for the 6pnd (J = 1, 3) states, to be compared with the experimental ones. An example of the spectra containing the experimental and theoretical profiles is shown in Fig. 3. It is obvious that the calculated spectrum of 6p1/2 20d state is in reasonable agreement with the experimental one, which means our MQDT model is reasonably good. Then we are ready to make a further step to investigate the channel interaction of Ba 6pnd (J = 1, 3) autoionizing states.
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4. Results and discussion Numerous experimental and theoretical data are available in this work. In particular, we are interested in those complex spectra, which are characterized by the channel interaction of Ba 6pnd (J = 1, 3) autoionizing states. The heavy configuration interactions are found on the 6p3/2 10d (J = 1, 3) state, whose transition profile exhibits sharp asymmetric structure in Fig. 4(a). This is due to not only the admixture with 6p3/2 12s autoionizing state, but also the interaction with 6p1/2 nd autoionizing series. Since the spectrum of 6p3/2 12s state shows complex configuration [2], the interaction between these two states results in the complexity of the profile of 6p3/2 10d (J = 1) state, as shown in Fig. 4(b). Otherwise, concern the energy range that the 6p3/2 10d state covers, it is easy to determine the mixing 6p1/2 nd (J = 3) states with n values ranging from 18 to 22, which have been marked in Fig. 4(c). This is reasonable that since the 6p3/2 10d autoion-
Fig. 4. Interpretation of the interactions of the 6p3/2 10d state with 6p3/2 12s state and 6p1/2 nd (n = 19–22) states: (a) the experimental spectrum of 6p3/2 10d (J = 1, 3) state excited from 6s10d 1 D2 Rydberg state; (b) the calculated spectrum of 6p3/2 10d (J = 1, 3) state for the J = 1 component; (c) the calculated spectrum of 6p3/2 10d (J = 1, 3) state for the J = 3 component.
izing state lies below the 6p1/2 threshold, its energy level degenerates with those of 6p1/2 nd states, which leads to the multi-peak profile of 6p3/2 10d (J = 3) state. Similarly, the spectrum of the 6p3/2 9d autoionizing state is found to display an additional feature, which is due to the admixture with the 6p1/2 13d (J = 3) autoionizing state, as shown in Fig. 5(a). Since the channel interaction is a mutual effect, this interaction must be also reflected in the spectrum of 6p1/2 13d state. In Fig. 5(b), it is apparent that the spectrum of 6p1/2 13d state exhibits a two-peak profile, and the left peak is identified to be contributed from the 6p3/2 9d state through the two-Lorentzian fitting procedure. Furthermore, the systematic investigation on the 6p1/2 nd autoionizing series shows that the higher 6p1/2 nd states (n ∼ 30) are almost unperturbed, whose spectra show the normal Lorentzian profiles. Now let us turn to discussion of Fig. 6, which are the typical saturation spectra of 6p3/2 25d and 6p3/2 19d autoionizing states. It is evident that the saturation spectra cover a much wider range, and several 6p3/2 n s (J = 1) autoionizing states are identified simultaneously, which indicates that the 6p3/2 nd (J = 1) states interact with the 6p3/2 ns (J = 1) states. This is
Fig. 5. Manifestation of the interaction between 6p3/2 9d state and 6p1/2 13d state: (a) the experimental spectrum of 6p3/2 9d (J = 1, 3) autoionizing state excited from 6s9d 3 D2 Rydberg state: (b) the experimental spectrum of 6p1/2 13d (J = 1, 3) autoionizing state excited from 6s13d 3 D2 Rydberg state (the solid line), together with the two-Lorentzian fitting results (the dashed lines).
Y. Zhang et al. / Journal of Electron Spectroscopy and Related Phenomena 148 (2005) 11–16
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Fig. 6. Typical saturation spectra of two series observed in the experiment: (a) centered at 6p3/2 25d (J = 1, 3) state excited from the 6s25d 1 D2 Rydberg state; (b) centered at 6p3/2 19d (J = 1, 3) state excited from the 6s19d 3 D2 Rydberg state. Several 6p3/2 ns (J = 1) autoionizing states are identified in the satellite features, indicating the admixture between 6p3/2 nd = 1 and 6p3/2 ns (J = 1) series.
not entirely surprising that since a 6p3/2 nd resonance occurs almost exactly midway between two adjacent 6p3/2 n s resonances. Meanwhile, the same investigation has also been carried out on the 6p1/2 nd (J = 1) autoionizing states. However, the results show that there are no additional peaks existing on the saturation spectra of the 6p1/2 nd states, indicating that the 6p1/2 nd (J = 1) states does not interact with the 6p1/2 ns (J = 1) states, which is very contrary to the case of 6p3/2 nd (J = 1) series. Further investigation of the channel interaction motivates us to calculate the channel mixing coefficient converging to the 6p1/2 and 6p3/2 thresholds. Fig. 7 shows the theoretical spectrum of 6p3/2 22d (J = 1) state excited from 6s22d singlet, together with the three spectral densities A211 , A212 and A213 . Since the 6p3/2 22d state lies above the 6p1/2 threshold, only the 6p3/2 ns channel may degenerate such complex spectroscopic structure. It is obvious that the main peak of the 6p3/2 22d spectrum is due to the contribution from the 6p3/2 nd3/2 and 6p3/2 nd5/2 channels, while the contribution from the 6p3/2 ns1/2 channel leads to the subsidiary peak on the right side. With the energy data of 6p3/2 ns series, the subsidiary peak can be attributed to the admixture of 6p3/2 24s state. In other words, the 6p3/2 ns channel has an important contribution to the 6p3/2 nd spectrum, which again confirms the interaction between 6p3/2 nd and 6p3/2 ns autoionizing series.
Fig. 7. The detailed information about the interaction between 6p3/2 nd and 6p3/2 ns autoionizing series: (a), (b) and (c) show the calculated results of spectral densities A2i with i = 11–13, corresponding to the 6p3/2 ns1/2 , 6p3/2 nd3/2 and 6p3/2 nd5/2 channels, respectively; (d) the theoretical spectrum of 6p3/2 22d (J = 1) state.
5. Conclusions In summary, the channel interaction of Ba 6pnd (J = 1, 3) autoionizing states has been systematically investigated using the ICE method, combined with a proper polarization configuration of lasers. It is found that the 6p3/2 10d autoionizing state, which lies below the 6p1/2 threshold, interacts with the 6p3/2 12s state and several 6p1/2 nd states with n values ranging from 18 to 22. Also, the 6p3/2 9d autoionizing state is observed to interact with the 6p1/2 13d state. Meanwhile, the study shows that the higher 6p1/2 nd autoionizing states with n ∼ 30 are almost unperturbed. Furthermore, it is found that the channel interaction between 6p3/2 nd and 6p3/2 ns autoionizing states is evident, whereas no interaction between 6p1/2 nd and 6p1/2 ns autoionizing states is observed. All the observations are well interpreted by calculating their crosssections and spectral densities from MQDT, the results of which are reasonably satisfactory with the experimental ones.
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Since all sorts of channel interactions of Ba 6pnd autoionizing states are presented for the first time, it is meaningful for further understanding the atomic properties of alkaline-earth atoms. Acknowledgements This work is supported by the National Science Foundation of China (Grant No. 10174065) and by the National High-tech ICF Committee of China. References [1] S.B. Li, C.J. Dai, W. Sun, P. Xue, J. Electron Spectrosc. Relat. Phenom. 127 (2002) 183. [2] S.B. Li, C.J. Dai, W. Sun, P. Xue, J. Phys. B: At. Mol. Opt. Phys. 34 (2001) 2123. [3] S.B. Li, C.J. Dai, J. Quant. Spectrosc. Radiat. Transfer 77 (2003) 345.
[4] Y. Zhang, C.J. Dai, S.B. Li, J. Electron Spectrosc. Relat. Phenom. 135 (2004) 63. [5] Y. Zhang, C.J. Dai, S.B. Li, J. Electron Spectrosc. Relat. Phenom. 136 (2004) 273. [6] J. Lu, C.J. Dai, X.H. Hu, S.B. Li, Chin. Phys. Lett. 18 (2001) 516. [7] Y. Zhang, C.J. Dai, S.B. Li, et al., J. Electron Spectrosc. Relat. Phenom. 128 (2003) 135. [8] R.R. Jones, B.J. Lyons, M.A. Baig, et al., Phys. Rev. A 62 (2000) 33408. [9] V.K. Dolmatov, A.S. Baltenkov, S.T. Manson, Phys. Rev. A 67 (2003) 62714. [10] S.B. Li, C.J. Dai, J. Electron Spectrosc. Relat. Phenom. 130 (2003) 43. [11] W.D. Dou, C.J. Dai, S.B. Li, J. Quant. Spectrosc. Radiat. Transfer 85 (2004) 145. [12] F. Gounand, T.F. Gallagher, W. Sander, et al., Phys. Rev. A 27 (1983) 1925. [13] C.M. Oliver, Y. Zhu, Y. Emily, et al., Phys. Rev. A 32 (1985) 2234. [14] S.B. Li, C.J. Dai, Y. Zhang, Chin. Phys. 11 (2002) 690. [15] S.B. Li, C.J. Dai, J. Electron Spectrosc. Relat. Phenom. 136 (2004) 247. [16] C.H. Greene, M. Aymar, Phys. Rev. A 44 (1991) 1773.
Channel interaction of Ba 6pnd (J = 1, 3) autoionizing states Yan Zhang a, c, ∗ , Chang-Jian Dai b , Shi-Ben Li a a Physics Department, Zhejiang University, Hangzhou 310027, China Physics Department, Tianjin University of Technology, Tianjin 300191, China Institute of Information Engineering, China Institute of Metrology, Hangzhou 310034, China b
c
Received 21 November 2004; received in revised form 27 January 2005; accepted 29 January 2005 Available online 26 February 2005
Abstract The channel interaction of Ba 6pnd (J = 1, 3) autoionizing series has been investigated by means of unsaturation and saturation excitation methods, using a three-step isolated-core-excitation scheme with a proper polarization configuration of lasers. The physical manifestations of the observed interactions are analyzed by the cross-section and spectral density calculated from the multichannel quantum defect theory, whose results are quite satisfactory with experimental ones. © 2005 Elsevier B.V. All rights reserved. Keywords: Channel interaction; Autoionizing states; Isolated-core-excitation; Multichannel quantum defect theory
1. Introduction Autoionizing states of the alkaline-earth atoms consist of the configuration with two excited valence electrons, one is in the first excited state, and the other is in a high Rydberg state. In recent years, autoionizing Rydberg series of alkalineearth atoms have been extensively studied, including the line shapes of the transition [1–5], branching ratios and angular distributions of ejected electrons from autoionizing states [6,7], as well as their spectroscopic properties in electric and magnetic fields [8–11]. Since the channel interaction of autoionizing states can reveal the perturbation between the two valence electrons, it is desirable to extend analysis of autoionizing series for understanding the inner physical mechanism of the alkaline-earth atoms. Usually, the interaction among autoionizing states with different n and l leads to the complex spectra of autoionizing states. For the Ba 6pnd autoionizing states relevant to this work, Gallagher and coworkers have observed the interaction of the 6p3/2 10d (J = 3) autoionizing state with the higher n values of 6p1/2 nd (J = 3) autoionizing states [12,13]. Later, Li et al. observed the interactions between the 6p3/2 nd (J = 1) and the 6p3/2 ns (J = 1) series [14]. ∗
Corresponding author. E-mail address: [email protected] (Y. Zhang).
0368-2048/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2005.01.276
To our knowledge, only the fragmentary results are available on the channel interaction of Ba 6pnd autoionizing series converging to the 6p1/2 and 6p3/2 ionization thresholds, respectively, thus it is difficult to reveal the complex atomic properties. Further study of the properties of Ba atom motivates us to have a detailed investigation on the configuration interactions. Here we focus on the channel interaction of Ba 6pnd (J = 1, 3) autoionizing states, using a three-step isolatedcore-excitation (ICE) scheme with a proper polarization configuration of lasers. In addition, we use an alternative way to explore the channel interaction. Namely, the saturation spectra of Ba 6pnd autoionizing states are also measured with great care. On the theoretical side, the multichannel quantum defect theory (MQDT), which has been very successful in the study of Ba 6pns autoionizing states [1–3,6,7], is employed to analyze the channel interactions of 6pnd autoionizing states by calculating their cross-sections and spectral densities. For the J = 1 series, the MQDT parameters are obtained from the Rmatrix method, while for the J = 3 series, the MQDT parameters are from the fitting procedures. Since many additional channels are taken into account for J = 1 series, the theoretical analysis is greatly improved compared with previous works [12,13]. The MQDT analysis of the data allows us to explain the main features of the observed complex spectra.
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Y. Zhang et al. / Journal of Electron Spectroscopy and Related Phenomena 148 (2005) 11–16
The detailed descriptions of the experimental method and the theoretical treatment will be presented in Sections 2 and 3, respectively. In Section 4, the results and discussion will be provided, and the conclusion will be summarized in Section 5.
2. Experimental observations The ICE scheme has already been proven to be very powerful and versatile in the study of atomic autoionizing states. One of its major advantages is that it enables one to obtain a spectrum with a line shape only determined by configuration interaction rather than any interference effects. Since the interpretations of observed spectra are noticeably simplified, it is easier to investigate channel interaction of the autoionizing states. The experimental arrangement used here was described in detail in previous works [4,5,15], so only the main features relevant to this work are included. The schematic diagram of the experimental apparatus is illustrated in Fig. 1. Three home-made dye lasers pumped by an Nd:YAG-pulsed laser are used to excite the Ba atom from its ground state to the 6pnd autoionizing states. A rhomb is used to rotate the polarization vector of the linearly polarized laser beam without reducing the laser power, and then the linearly polarized laser is calibrated by a polarizer. The Ba atomic beam is extracted from a stainless steel crucible vertically, and interacted with three laser beams. The atom in a 6pnd autoionizing state quickly decays into an ion and an electron. The ions are extracted by applying a pulsed electric field on the plates, and are detected by an MCP detector. Finally, the ion signals are first integrated and averaged with a boxcar, then stored in a computer for further analysis. A common method for studying the channel interaction of autoionizing states is to observe the normal spectra of these states. With the ICE scheme, the first two tunable lasers excite the Ba atom from the 6s2 ground state to the different 6snd Rydberg states, while the third laser excites the other valence
Fig. 2. The spectrum of the 6p1/2 22d (J = 1, 3) autoionizing state excited from 6s22d 1 D2 Rydberg state: (a) unsaturated case; (b) saturated case. The abscissa is the photon energy of the third laser.
electron from 6s to 6p ionic state. Noted that since the power of the third laser is kept at the lowest level possible and its frequency is tuned at the resonance line, excitation of the Rydberg electron can be neglected, which is an advantage over other excitation schemes. In this experiment, all the three exciting lasers are linearly polarized in the same direction, thus the spectra consisting of both J = 1 and 3 components are obtained. Most spectra show nearly Lorentzian profiles, but
Fig. 1. The schematic diagram of the experimental apparatus (PLD: pulsed-dye laser).
Y. Zhang et al. / Journal of Electron Spectroscopy and Related Phenomena 148 (2005) 11–16
some exhibits complex structures due to the channel interactions with other autoionizing states. An alternative way to study the channel interaction is to examine the saturation spectra, which are obtained by increasing the power of the third laser about 100 times than its usual level. In this case, the excitation of the Rydberg electron can no longer be neglected, thus many n values of the 6pnl autoionizing states are excited simultaneously. In other words, the weak satellite features of the main transition are enhanced significantly, providing a clear picture of channel interaction. Under the above consideration, the unsaturated and saturated spectra of Ba 6pnd (J = 1, 3) autoionizing states are systematically measured. Two typical examples are presented in Fig. 2, which illustrate the differences between these two cases. The unsaturated spectrum of Ba 6p1/2 22d state in Fig. 2(a) shows a normal Lorentzian profile, whereas there are many additional peaks make the saturation spectrum more complex, as shown in Fig. 2(b), from which the channel interaction can be analyzed by determining the energy level of each peak. More detailed analysis on the channel interaction, including the investigation on the spectral densities, will be discussed in the following sections.
In order to interpret the observations, it is necessary to calculate the cross-section and the mixing coefficient of relevant channels using the MQDT. Since the MQDT procedures have been well documented, only the main equations are included here. The partial cross-section σ Jc to a particular final ionic state and the total cross-section can be evaluated as: 2 4 Dρ exp(iπτρ )Aiρ σJc = π2 α¯hω3 (1) 3 ρ i
σ=
σJc
(2)
Jc
Here i and ρ refer to the open dissociation channel and the collision eigenchannel, respectively; h ¯ ω3 the photon energy of the third laser, and Dρ the corresponding reduced transition matrix element. Moreover, the mixing coefficient of the ith channel, which reflects the contribution from the ith channel to the final autoionizing spectrum, can be determined by: Aiρ =
1 Uiα cos[π(νi + µα )]Bα (ρ) Nρ α
Fig. 3. The comparison between the experimental spectrum (solid line) and the theoretical spectra (dashed line) of 6p1/2 20d (J = 1, 3) autoionizing state excited from 6s20d 3 D2 Rydberg state. The abscissa is the term energy.
nel quantum defect and the matrix elements of the unitary transformation, which contain the most important dynamical information. The sum over all relevant ρ to the square of the mixing coefficient is called the spectral density, i.e.: A2i = A2iρ (4) ρ
3. Theoretical treatments
and
13
(3)
where νi is the effective quantum number for a closed channel, and is replaced with −τ ρ for an open channel; Nρ the (ρ) normalization constant; Bα the coefficient of the wave function ϕα in the αth close-coupled eigenchannel. In particular, the MQDT parameters µα and Uiα represent the eigenchan-
For the J = 1 series of Ba 6pnd autoionizing states, the total cross-section can be calculated using a 13-channel model. These dissociation channels are 6s1/2 np1/2 , 6s1/2 np3/2 , 5d3/2 np1/2 , 5d3/2 np3/2 , 5d3/2 nf5/2 , 5d5/2 np3/2 , 5d5/2 nf5/2 , 5d5/2 nf7/2 , 6p1/2 ns1/2 , 6p1/2 nd3/2 , 6p3/2 ns1/2 , 6p3/2 nd3/2 and 6p3/2 nd5/2 , which converging to the 6s, 5dJ and 6pJ thresholds, respectively. The MQDT parameters can be obtained from the R-matrix calculation [16], which is superior to the empirical MQDT. On the other hand, a four-channel model is employed to calculate the cross-section of 6pnd states for the J = 3 series, whose parameters are the best fitting results so far [12]. In fact, we have made some efforts trying to improve the MQDT model by fitting our data to a new model with several additional channels, but there is almost no improvement in terms of the agreement between experiment and theory. By doing this, one has to deal with the new problem, that is when the amount of the fitting parameters increases rapidly, and the parameters are hard to be determined uniquely. Hence, we decided to use the four-channel model for the J = 3 series. The addition of these two calculated spectra for J = 1 and 3 components will yield the composite spectra for the 6pnd (J = 1, 3) states, to be compared with the experimental ones. An example of the spectra containing the experimental and theoretical profiles is shown in Fig. 3. It is obvious that the calculated spectrum of 6p1/2 20d state is in reasonable agreement with the experimental one, which means our MQDT model is reasonably good. Then we are ready to make a further step to investigate the channel interaction of Ba 6pnd (J = 1, 3) autoionizing states.
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4. Results and discussion Numerous experimental and theoretical data are available in this work. In particular, we are interested in those complex spectra, which are characterized by the channel interaction of Ba 6pnd (J = 1, 3) autoionizing states. The heavy configuration interactions are found on the 6p3/2 10d (J = 1, 3) state, whose transition profile exhibits sharp asymmetric structure in Fig. 4(a). This is due to not only the admixture with 6p3/2 12s autoionizing state, but also the interaction with 6p1/2 nd autoionizing series. Since the spectrum of 6p3/2 12s state shows complex configuration [2], the interaction between these two states results in the complexity of the profile of 6p3/2 10d (J = 1) state, as shown in Fig. 4(b). Otherwise, concern the energy range that the 6p3/2 10d state covers, it is easy to determine the mixing 6p1/2 nd (J = 3) states with n values ranging from 18 to 22, which have been marked in Fig. 4(c). This is reasonable that since the 6p3/2 10d autoion-
Fig. 4. Interpretation of the interactions of the 6p3/2 10d state with 6p3/2 12s state and 6p1/2 nd (n = 19–22) states: (a) the experimental spectrum of 6p3/2 10d (J = 1, 3) state excited from 6s10d 1 D2 Rydberg state; (b) the calculated spectrum of 6p3/2 10d (J = 1, 3) state for the J = 1 component; (c) the calculated spectrum of 6p3/2 10d (J = 1, 3) state for the J = 3 component.
izing state lies below the 6p1/2 threshold, its energy level degenerates with those of 6p1/2 nd states, which leads to the multi-peak profile of 6p3/2 10d (J = 3) state. Similarly, the spectrum of the 6p3/2 9d autoionizing state is found to display an additional feature, which is due to the admixture with the 6p1/2 13d (J = 3) autoionizing state, as shown in Fig. 5(a). Since the channel interaction is a mutual effect, this interaction must be also reflected in the spectrum of 6p1/2 13d state. In Fig. 5(b), it is apparent that the spectrum of 6p1/2 13d state exhibits a two-peak profile, and the left peak is identified to be contributed from the 6p3/2 9d state through the two-Lorentzian fitting procedure. Furthermore, the systematic investigation on the 6p1/2 nd autoionizing series shows that the higher 6p1/2 nd states (n ∼ 30) are almost unperturbed, whose spectra show the normal Lorentzian profiles. Now let us turn to discussion of Fig. 6, which are the typical saturation spectra of 6p3/2 25d and 6p3/2 19d autoionizing states. It is evident that the saturation spectra cover a much wider range, and several 6p3/2 n s (J = 1) autoionizing states are identified simultaneously, which indicates that the 6p3/2 nd (J = 1) states interact with the 6p3/2 ns (J = 1) states. This is
Fig. 5. Manifestation of the interaction between 6p3/2 9d state and 6p1/2 13d state: (a) the experimental spectrum of 6p3/2 9d (J = 1, 3) autoionizing state excited from 6s9d 3 D2 Rydberg state: (b) the experimental spectrum of 6p1/2 13d (J = 1, 3) autoionizing state excited from 6s13d 3 D2 Rydberg state (the solid line), together with the two-Lorentzian fitting results (the dashed lines).
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Fig. 6. Typical saturation spectra of two series observed in the experiment: (a) centered at 6p3/2 25d (J = 1, 3) state excited from the 6s25d 1 D2 Rydberg state; (b) centered at 6p3/2 19d (J = 1, 3) state excited from the 6s19d 3 D2 Rydberg state. Several 6p3/2 ns (J = 1) autoionizing states are identified in the satellite features, indicating the admixture between 6p3/2 nd = 1 and 6p3/2 ns (J = 1) series.
not entirely surprising that since a 6p3/2 nd resonance occurs almost exactly midway between two adjacent 6p3/2 n s resonances. Meanwhile, the same investigation has also been carried out on the 6p1/2 nd (J = 1) autoionizing states. However, the results show that there are no additional peaks existing on the saturation spectra of the 6p1/2 nd states, indicating that the 6p1/2 nd (J = 1) states does not interact with the 6p1/2 ns (J = 1) states, which is very contrary to the case of 6p3/2 nd (J = 1) series. Further investigation of the channel interaction motivates us to calculate the channel mixing coefficient converging to the 6p1/2 and 6p3/2 thresholds. Fig. 7 shows the theoretical spectrum of 6p3/2 22d (J = 1) state excited from 6s22d singlet, together with the three spectral densities A211 , A212 and A213 . Since the 6p3/2 22d state lies above the 6p1/2 threshold, only the 6p3/2 ns channel may degenerate such complex spectroscopic structure. It is obvious that the main peak of the 6p3/2 22d spectrum is due to the contribution from the 6p3/2 nd3/2 and 6p3/2 nd5/2 channels, while the contribution from the 6p3/2 ns1/2 channel leads to the subsidiary peak on the right side. With the energy data of 6p3/2 ns series, the subsidiary peak can be attributed to the admixture of 6p3/2 24s state. In other words, the 6p3/2 ns channel has an important contribution to the 6p3/2 nd spectrum, which again confirms the interaction between 6p3/2 nd and 6p3/2 ns autoionizing series.
Fig. 7. The detailed information about the interaction between 6p3/2 nd and 6p3/2 ns autoionizing series: (a), (b) and (c) show the calculated results of spectral densities A2i with i = 11–13, corresponding to the 6p3/2 ns1/2 , 6p3/2 nd3/2 and 6p3/2 nd5/2 channels, respectively; (d) the theoretical spectrum of 6p3/2 22d (J = 1) state.
5. Conclusions In summary, the channel interaction of Ba 6pnd (J = 1, 3) autoionizing states has been systematically investigated using the ICE method, combined with a proper polarization configuration of lasers. It is found that the 6p3/2 10d autoionizing state, which lies below the 6p1/2 threshold, interacts with the 6p3/2 12s state and several 6p1/2 nd states with n values ranging from 18 to 22. Also, the 6p3/2 9d autoionizing state is observed to interact with the 6p1/2 13d state. Meanwhile, the study shows that the higher 6p1/2 nd autoionizing states with n ∼ 30 are almost unperturbed. Furthermore, it is found that the channel interaction between 6p3/2 nd and 6p3/2 ns autoionizing states is evident, whereas no interaction between 6p1/2 nd and 6p1/2 ns autoionizing states is observed. All the observations are well interpreted by calculating their crosssections and spectral densities from MQDT, the results of which are reasonably satisfactory with the experimental ones.
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Since all sorts of channel interactions of Ba 6pnd autoionizing states are presented for the first time, it is meaningful for further understanding the atomic properties of alkaline-earth atoms. Acknowledgements This work is supported by the National Science Foundation of China (Grant No. 10174065) and by the National High-tech ICF Committee of China. References [1] S.B. Li, C.J. Dai, W. Sun, P. Xue, J. Electron Spectrosc. Relat. Phenom. 127 (2002) 183. [2] S.B. Li, C.J. Dai, W. Sun, P. Xue, J. Phys. B: At. Mol. Opt. Phys. 34 (2001) 2123. [3] S.B. Li, C.J. Dai, J. Quant. Spectrosc. Radiat. Transfer 77 (2003) 345.
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