• Acta Photonica Sinica
  • Vol. 50, Issue 11, 1130002 (2021)
Xiaobin LIU1、*, Yinglong SHI1, Xiangbing LI1, Yuping WANG1, Hongwei HU2, and Yuee LUO3
Author Affiliations
  • 1Department of Physics,Tianshui Normal University,Tianshui,Gansu 741001,China
  • 2Department of Physics,Shangqiu Normal University,Shangqiu,Henan 476000,China
  • 3Department of Mechanical and Electronic Engineering,Jingdezhen University,Jingdezhen,Jiangxi 333000,China
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    DOI: 10.3788/gzxb20215011.1130002 Cite this Article
    Xiaobin LIU, Yinglong SHI, Xiangbing LI, Yuping WANG, Hongwei HU, Yuee LUO. Photoelectron Satellite Structure from the 2p Inner-shell Photoionization of Excited Sodium Atoms[J]. Acta Photonica Sinica, 2021, 50(11): 1130002 Copy Citation Text show less

    Abstract

    Based on multiconfiguration Dirac-Fock method, the high-resolution 2p photoelectron spectra and satellites originating from the corresponding shakeup transitions during the photoionization of neutral sodium atoms are theoretically studied. The main features of photoelectron spectra from the normal photoionization and strong shake-up transitions are presented and interpreted. It is shown that the electron correlations of the 2p hole affect the energy positions of photolines and give rise to considerable structures in the photoelectron spectra. The reasonable agreement between the measured results and simulated spectra confirms the reliability of the theoretical approaches and enables us to assign the observed photolines.

    Introduction

    Photoionization,i.e.,the emission of an electron after the absorption of a photon,is one of the most fundamental atomic processes in light-matter interactions,which has been studied for many years1-2. Thus,the photoelectron spectrum is a well-established method for studies of atomic structures in various forms of matter and is a powerful tool for estimating element abundances3-4. Moreover,rapid developments in the technology of modern light sources and the emergence of high-precision detectors have enabled experimentalists to obtain very accurate data on photoionization processes,and experiments on atomic photoionization have become possible by utilizing the high photon flux of third-generation synchrotron radiation sources,the photon-ion merged-beams technique5 and free electron lasers6,thereby facilitating measurements with unprecedented sensitivity and resolution.

    In most cases of inner-shell photoionization,the photoion will be left in a final hole state,where only one of the electrons is removed from the initial configuration. Much less likely,however,it is the formation of a final state of the photoionization system,which is associated with an excitation of one additional electron. Such photoionization with excitation requires a correlated motion of the electrons,and the corresponding transition matrix element will be nonzero only if the electron-electron interaction is taken into account7-8. From the shake theory9,shake-up satellites arise in the sudden approximation,where the photoionization causes a sudden change in the Coulomb attraction,i.e.,in addition to the photoemission of an inner-shell electron,a rearrangement of the residual electron density is likely to occur and leads to a satellite structure to the main photoelectron peaks. The 2p photoionization of excited and ground states of sodium atoms has been experimentally investigated using synchrotron radiation,and the corresponding analyses were performed with different approximations,such as many-body perturbation and multiconfiguration Hartree-Fock methods,and the results revealed the strong influence of electron correlation1810. It was observed that the shake-up process becomes more probable than the single photoionization as the principal quantum number of valence electrons increases11. The different spectrum structure arising from single photoionization and photoionization accompanied by excitation,i.e.,satellite photoelectron structure originating from the corresponding shake-up transitions during the 2p photoionization,were observed12. Motivated by the experimental photoelectron spectra,we performed a detailed Multiconfiguration Dirac-Fock(MCDF)calculation to understand the spectrum structure from the shake-up transitions during the 2p photoionization from excited states of sodium atoms. In this paper,the focus is on how shake-up satellites appear in the photoionization process by explicitly treating the electron correlation between photoelectrons and photoions. Atomic units are used throughout the paper unless otherwise specified.

    Theory

    For open-shell atomic structures,the MCDF method has been found to be a very versatile tool for calculating photoionization cross sections and binding energies13-14. In this method,the Atomic State Functions(ASFs)of interest are generated as linear combinations from the relativistic jj coupled Configuration State Functions(CSFs)

    Ψ(PJM)=rcrψr(PJM)

    where the label(PJM)states that the linear combination is formed from the CSFs with the same parity P,same total angular momentum J,and one of its projections M. The coefficients cr describe the mixing of the corresponding CSFs at the ASF,and they represent the electron correlation. Numerical calculations were performed by applying the GRASP92 code15 together with the RELCI(relativistic configuration interaction calculation)extension16.

    The photoionization cross sections from the initial state(PiJiMi)to the final state(PfJfMf)can be written as17

    σifPI=4π2a02αdfifdε

    where α is the fine structure constant and a0 is the Bohr radius. Numerical calculations of Eq.(2) were performed using Relphoto081418-19. dfif/dεrefers to the oscillator strength density,and further details are available in Refs.[1418]. In the present work,the final state is the ionic one-hole state that is coupled to the continuum photoelectron to yield the opposite parity as the initial neutral atomic state.

    The 2p photoionization of excited states 2p63p1/2,3/2 of sodium atoms,which gives rise to the 2p54p monopole shake-up satellite states,can be written as

    2p63p(P2P1/2,3/2)+hυ2p54p(S1S0,P1P1,D1D2;S3S1,P3P0,1,2,D3D1,2,3)+εk(l=0,2)

    where the photoelectrons are assumed to escape by means of the partial waves |εκ and with kinetic energies ε. The energy ε=Ei+hυ-Ef is determined by the photon energy and the total energies of the atom in the initial and final states. The “photoion+electron” system then gives rise to the total final state αfN-1(Jf'Pf'Mf'),εk;αfN(JfPfMf) with total energy Et=Ei+ after the photon has been absorbed by the atom14. Here,we utilize the relativistic angular-momentum quantum number

    k=±(j+1/2) for l=j±1/2

    to denote the symmetry properties of the outgoing photoelectron,i.e.,its angular momentum j and parity(-1)l20.

    From the shake theory9,the corresponding transition matrix element is 2pôεl3p4p,the first term describes single photoionization in which the orbital of the 2p electron remains unchanged,and the second term accounts for the satellite excitation11. To estimate the shake-up cross sections,several overlap integrals between the initial-and final-state orbitals of the outermost electrons have been calculated. Therefore,the branching ratio between the satellite and main line is thus equal to 3p|4p2/3p|3p2. Shake-up satellites arise in the sudden approximation,in which the photoionization causes a sudden change in the Coulomb attraction,and the excited electron changes its orbital quantum number,which implies an exchange of angular momentum between the residual ionic core and the outgoing photoelectron. To compare the results of our calculations with experimental results,the theoretical spectra were convolved with a Gaussian function with a constant energy value to account for the finite experimental resolution.

    The most standard approach is to use the active space method. A single or minimal set of reference CSFs serve as a zeroth order basis,and by extending the configuration space stepwise to the limit where reasonable agreement with the experiment was obtained. For a better understanding of electron correlation,a comparison was performed between the single-configuration and multiconfiguration calculations. But it should be pointed out that the spectra structures can be predicted considerably better by multiconfiguration expansion than by single-configuration approximation because prominent electron correlation can be taken into account in the larger configuration set,so the discussion below is based mainly on multiconfiguration calculations. In the calculation of neutral-state wavefunctions,the configurations 1s2(2s22p63p+2s22p64p+2s2p63s3p+2s22p53p2+2s2p63s4p)were included. To reduce shifting of the average energy,the calculations were performed in two steps. In the first step,the wavefunctions of the sodium atoms were computed in a single configuration approximation,and in the second step,the wavefunctions of the Be-like core were fixed and the outer orbitals were generated. The single ionized state 2p53pwas computed in a similar way by including the configurations 1s2(2s22p53p+2s22p54p+2s22p6+2s2p63s+2s2p63d). For the final states 2p54pof the shake-up process,the configurations used were 1s2(2s22p53p+2s22p54p+2s22p54f+2s22p6+2s2p63s+2s2p63d)in the second step. In this case,the final-core wavefunctions were obtained from the single configuration calculation,and all outer orbitals were set to be free in a multiconfiguration iteration.

    Results and discussions

    For the single photoionization 2p63p → 2p53p(1S01P11D23S13P0,1,23D1,2,3),10 fine-structure energy levels were constructed from the final ionic configuration 2p53p,as well as from the configuration 2p54p of the 2p63p→2p54p shake-up process. From the NIST database21 or our present calculations,for the final configuration 2p53p,the ascending energy order is 3S13D33D23D11D21P13P23P03P1 and 1S0,which are denoted by labels 1~10 in Figs.1 and 2,as shown in the following discussion. For example,the peaks labelled as 3 and 5 denote states 3D2 and 1D2 arising from the photoionization 2p63p→2p53p,respectively.

    2p photoelectron spectra arising from the single photoionization of initial state 2p63p(2P1/2)

    Figure 1.2p photoelectron spectra arising from the single photoionization of initial state 2p63p(2P1/2

    Same as Fig.1 but for the photoionization of initial state 2p63p(2P3/2)

    Figure 2.Same as Fig.1 but for the photoionization of initial state 2p63p(2P3/2

    To explore the influence of electron correlation effects on the spectra structure,we performed calculations within both the single configuration approximation and multiconfiguration approximation that accounts for more electron correlations in Eq.(2). The 2p photoelectron spectra arising from the single photoionization 2p63p(2P1/2)→2p53p of sodium atoms at the photon energy =54 eV are presented in Fig. 1. The solid(red dash)line in the right panel,which was generated with experimental energy resolution assuming a Gaussian instrument function,is the spectrum simulated with wavefunctions from the multiconfiguration(single)approximation. The vertical lines in the right panel indicate the calculated intensities and energy positions of the photolines with wavefunctions from the multiconfiguration approximation. As shown,the agreement of the simulated spectrum compared to the experimental one presented in the left panel is good22;in particular,the middle parts of the spectrum are well reproduced. For comparison,the calculated spectra are normalized to the dominant intensity of final ionic state 2p53p(3D2),and the calculated energies are shifted by +1.51 eV to coincide with the experiment. The peaks were identified by comparing the experimental spectrum to the present MCDF calculations.

    As shown in Fig. 1,the spectrum lines are separated into singlets and triplets,which are typical for LS-coupled systems,whereas the energy ordering of the lines deviates from Hund's rules. This deviation can be explained by the non-negligible spin-orbit interaction of the electrons. Our MCDF energy calculations in the jj-coupled basis show that peaks 1~6 arise from the 2p3/2 hole final states 2p53p(3S13D33D23D11D21P1),whereas peaks 7~10 correspond to final states 2p53p(3P23P03P11S0)having a hole in the 2p1/2 orbital. As expected,the contribution of electron correlation leads to a significant shift in the relative energy position,particularly for states 3S1 and 1S0,which are labelled as 1 and 10 in the figure,but it is not the same case for intensities.

    For sodium atoms,spin-orbit coupling is so strong that the 3p1/2 and 3p3/2 orbitals can be separated. According to the NIST database21 or the present calculations,the difference of the 10 fine-structure energy levels is 0.002 eV. To elucidate the influence of spin-orbit effects,the photoelectron spectra of sodium atoms from the initial excited 2p63p(2P3/2)are shown in Fig. 2. Of course,the solid(red dash)line in the right panel is the spectrum from the multiconfiguration(single)approximation,but the calculated spectra are normalized to the intensity of the final ionic state 2p53p(3D3). A similar theoretical analysis can be applied to this case. As shown,the spectrum structures are predicted by the calculations very well,even when the calculated spectra are shifted +1.51 eV to higher energies compared to the experimental results23. This shift is primarily caused by electron correlation;again,the peaks from the final states 3S1 and 1S0 are found to be very sensitive to the configuration basis used in the calculations.

    More importantly,it is well known that relativistic effects play only a fairly small role in low-Z elements. However,the present results show that the relativistic effects are strong for the spectra structure from the 2p inner-shell photoionization of sodium atoms. Comparison of Figs1 and 2 indicates that the total angular momentum J of the initial state 2p63p(2P1/2,3/2)has an obvious influence on the photoelectron spectra,whereas the structures clearly resemble each other. This result is not surprising because for 2p photoionization from excited states 2p63p(2P1/2,3/2),there are two open subshells,and special care must be taken to construct the wavefunctions.

    The spectra obtained from 2p63p(2P1/2,3/2)→2p54p(1S01P11D23S13P0,1,23D1,2,3)shake-up transitions at a photon energy of =48 eV are shown in Figs. 3 and 4. Then,the labels refer to the peaks for the ten final ionic states 2p54p,the calculated spectra are normalized to the intensity of the final ionic state 2p53p(3D2)in Fig. 3 but 2p53p(3D3)in Fig. 4. As clearly shown,our current calculations including full relaxation appear to provide fairly reasonable results. By comparing the experimental and simulated satellite structures from the single configuration approximation,it can be observed that the agreement is considerably worse than for the main spectra. For example,the calculated spectra are shifted by +3.75 eV to coincide with the experiment12,and some intensities are overestimated while others are underestimated,such as the leftmost intensities of the final ionic state 2p54p(1S0)in the figures. The large shift may follow partially from the uncertain factors,which depend on the geometry of the reaction volume. Subsequently,the other part most likely follows from the 4p wavefunction because the single configuration,and even the multiconfiguration approximation,was not able to produce the 4p radial wavefunction correctly. However,these results indicate that the energy splitting of the intensities is more difficult to calculate correctly,but more importantly,the satellites are caused by electron-electron interactions,which obviously makes the intensity calculations more difficult and sensitive to the correctness of the wavefunctions.

    Same as Fig.1 but for the 2p63p(2P1/2)→ 2p54p shake-up satellites

    Figure 3.Same as Fig.1 but for the 2p63p(2P1/2)→ 2p54p shake-up satellites

    Same as Fig.3 but for the 2p63p(2P3/2)→ 2p54p shake-up satellites

    Figure 4.Same as Fig.3 but for the 2p63p(2P3/2)→ 2p54p shake-up satellites

    As expected,the satellite spectrum shows that the spacing of energy levels decreases compared to the 2p63p→2p53p spectrum. The total width of the satellite spectrum is less than 1 eV,whereas that of the main spectrum is greater than 2 eV. The decrease in the energy spacing originates from the coupling change of the outermost electron,even though the jj coupled terms are completely the same in the two cases. For final configuration 2p54p,the ascending energy order is 3S13D33D21P13P23P03D11D23P1 and 1S0,which are denoted by labels 1~10 in Figs.3 and 4,i.e.,the energy order is adjusted compared to 2p53p and the singlet-triplet structure is obviously broken. The peaks corresponding to the final states 2p54p(3S13D33D2)are still at the three lowest binding energies,and 2p54p(3P11S0)are the two highest binding energies. The appearance of the jj coupled feature in the satellite spectra in Figs.3 and 4 shows that the spin-orbit interactions are more important in 2p63p(2P3/2)→2p54p shake-up transitions. It can be observed that the difference between the main and satellite spectra is significant,which means that the main spectrum structures divided by the coupling of 2p-1 holes also appear in the satellite spectra,but some of the structures are modified due to the changes in coupling of the outermost electron and mixing of configurations. In addition,the results demonstrate the sensitivity of satellite spectra to probe electron correlation in shake-up transitions and suggest that despite the large size of multiconfiguration expansion,the basis is still not sufficient to correctly account for the electron correlation.

    To more clearly illustrate the influence of the incident photon energy on the satellite spectrum,the spectra calculated with wavefunctions from the multiconfiguration approximation for different incident photon energies are shown in Fig. 5. The solid lines are the calculated results for a photon energy of =54 eV,and the(red)dash lines are for =48 eV. As shown in this figure,the calculations performed for the two photon energies yield virtually identical photoelectron spectra,whereas the differences between the leftmost intensities of the final ionic state 2p54p(1S0)cannot be regarded as negligible. This behaviour follows from the fact that while at different photon energies,the satellite photoelectron structures are mainly determined by the target atoms and the relative intensities of the photolines may not show any photon energy dependence over a certain energy range,as clearly emphasized in Ref.[12],even though the shake-up process is generally believed to be sensitive to the incident photon energy.

    Theoretical 2p photoelectron spectra arising from the 2p63p(2P1/2,3/2)→ 2p54p shake-up transitions

    Figure 5.Theoretical 2p photoelectron spectra arising from the 2p63p(2P1/2,3/2)→ 2p54p shake-up transitions

    To explore the main and shake-up processes with a unified standard and to obtain a deeper physical understanding,the 2p photoelectron spectra calculated with wavefunctions from the multiconfiguration approximation at a photon energy of =54 eV are shown in Fig. 6. The solid lines are the main spectra arising from the 2p63p→2p53p photoionization of sodium atoms,and the(red)dashed lines are the satellite spectra from the 2p63p→2p54p shake-up transitions. Again,the spectra from the initial state 2p63p(2P1/2)in the left panel are normalized to the intensity of the final ionic state 2p53p(3D2),and the spectra from the initial state 2p63p(2P3/2)in the right panel are normalized to the intensity of 2p53p(3D3). For the main spectrum from initial state 2p63p(2P1/2),the intensity of the final state 2p53p(3D2)is the highest. However,in the case of 2p63p(2P3/2),the intensity of the final state 2p53p(3D3)becomes the highest. Therefore,the spectra from the initial state 2p63p(2P1/2)are normalized to the dominant intensity of the final ionic state 2p53p(3D2),and the spectra from the initial state 2p63p(2P3/2)are normalized to the intensity of 2p53p(3D3). As discussed above,these satellites primarily arise from the rearrangement of electron density during the course of photoionization,which gives rise to a finite shake-up probability for the 3p valence electron. By comparing the main and satellite spectra in Fig. 6,one can observe that the overall intensities of the 2p63p→2p54p shake-up transitions are smaller compared to the 2p63p→2p53p photoionization,i.e.,shake-up transitions are weak compared to normal photoionization transitions,as generally expected1324. This result is due to the smaller overlap between the initial-and final-state orbitals of the outermost 3p and 4p electrons,as described 2pôεl3p4p,respectively.

    Theoretical 2p main and satellite photoelectron spectra of sodium atoms

    Figure 6.Theoretical 2p main and satellite photoelectron spectra of sodium atoms

    However,as shown in Fig. 6,the relative intensities of the shake-up transitions are quite obvious compared to the main spectra. According to the present calculations,some shake-up intensities are found to be more than 50% of the corresponding main transitions. This result tends to indicate a strong orbital relaxation because of the removal of a 2p electron and the importance of shake-up processes in the case of sodium. The physical model used for the monopole shake-up transition is a simultaneous dipole transition and an electron excitation into the higher orbital. In this simple picture,these originate exclusively from the substantially larger overlap 3p|4p between neutral 3p and ionic 4p radial wavefunctions. The present calculations show that the atomic 3p mean orbital radius is 5.99a0,the ionic 4p mean orbital radius is 8.02a0,and the 3p mean orbital radius is 3.71a0. Note that the orbital relaxation may lead to an increase in the overlap between neutral 3p and ionic 4p radial wavefunctions compared to the overlap 3p|3p between neutral and ionic 3p radial wavefunctions,i.e.,to an increase in the satellite intensities compared to the main ones,even though the single photoionization is still the strongest process.

    Conclusion

    The 2p photoelectron spectra of sodium atoms from the initial states 2p63p(2P1/2,3/2)and the satellite spectra originating from the corresponding shake-up transitions during the 2p photoionization have been investigated using MCDF method. In our theoretical analysis,special emphasis was placed on the influence of electron correlation on the photoelectron spectra. It has been shown that the theoretically predicted photoelectron spectrum is in good agreement with the experimental results,allowing us to identify the photolines.

    It is also shown that the spin-orbit effects have an important role in forming the photoelectron spectra. As expected,the main photoelectron spectrum spans a considerably broader energy region than the 2p63p→2p54p satellite spectrum,and the shake-up transitions are weak compared to the normal transitions. However,the relative intensities of shake-up transitions are very obvious compared to the main spectra. The reason is the strong relaxation effects due to the collapse of 3p orbital after the emission of 2p photoelectron,which leads to an increase in the shake-up intensities.

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    Xiaobin LIU, Yinglong SHI, Xiangbing LI, Yuping WANG, Hongwei HU, Yuee LUO. Photoelectron Satellite Structure from the 2p Inner-shell Photoionization of Excited Sodium Atoms[J]. Acta Photonica Sinica, 2021, 50(11): 1130002
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