The effect of 5f states on the nd → 5f transition energies and spectra of americium ions

The spectra originating from the electric dipole transitions of nd (n = 3 − 5) core excited states to the 5f valence states of Am2+ to Am8+ ions have been calculated using the Dirac-Hartee-Fock method, which are compared with the results from the Flexible Atomic Code for the explanation of accuracy. It is found that both the M4,5(3d→5f) and N4,5(4d→5f) spectra of these ions consist of two peaks that are well separated in energy respectively by 202.11 eV and 49.10 eV due to strong spin-orbit interaction of the 3d−1 and 4d−1 hole state, while the O4,5(5d→5f) spectra show a broad quasi-continuum profile.


Introduction
Americium (Am) is a radioactive element with atomic number Z=95. It is the third element past uranium and the fourth element discovered after curium. The main isotopes of Am are known as 243 Am (with a half-lifetime τ 1/2 =7,400 yr), 241 Am (τ 1/2 =433 yr), and 242 Am (τ 1/2 =152 yr). Am is the product of a series of successive neutron captures plutonium, and its most common use is focused on smoke detectors [1]. Due to the unique behavior of the 5f states of actinides which dominate its electronic structure, it have been of great interest in physics and chemistry [2][3][4][5][6]. Until the present, although a large number of studies have been performed on actinides [7][8][9][10][11][12][13], a lot of questions still remain nowadays [14].
Recently, Moore et al [14] studied the N 4,5 a short-hand notation for the  d f 4 5 transition spectra of Am metal by using the electron energy-loss spectroscopy (EELS). Butterfield et al [15] examined the O 4,5 (  d f 5 5 ) edge structure of the ground state α-phase of Am metal using the same experimental technique as in [14]. Furthermore, Buck and Fortner [16] have measured the absorption edge energies of Am also with the use of the EELS.
In the present work, the relative intensities of spectra originating from the electric dipole transitions from the nd (n = 3-5) core states excited to the 5f valence states of Am 2+ to Am 8+ ions have been theoretically studied by using the multiconfiguration Dirac-Hartee-Fock (MCDHF) method [17,18] and its corresponding computer code GRASP2K [19,20]. However, GRASP2K is not the only code that can do MCDHF. The Breit interaction, and the quantum-electrodynamic (QED) effect have been taken into account.

Theoretical method
As the details of the theoretical procedure of the MCDHF method have been explained in the [21] by Grant, therefore, in the present paper we only present the main points of it. The Dirac-Coulomb Hamiltonian of an atom or ion with N-electron can be given by Here, h D (r i ) denotes one-electron Dirac Hamiltonian. while the second term is the electron-electron Coulomb interactions. In the MCDHF method, an atomic state function (ASF) of the system with parity P, total angular momentum J and its component M is approximated by a linear combination of configuration state functions (CSFs) of the same symmetry PJM, in which n c is the number of CSFs and c r (α) denotes the configuration mixing coefficients corresponding to each individual CSF. The calculation is started from a single configuration Dirac-Fock solution with the nucleus described as an extended Fermi distribution. A single electron is excited from 3d, 4d, and 5d core hole-states to the 5f states. The trial radial wave functions are estimated by solving the Dirac equation either in the Thomas-Fermi potential or in the screened hydrogenic approximation. Furthermore, the contributions of the Breit interaction and QED effects are considered as a perturbation through relativistic configuration interaction (RCI) calculations.

Results and discussions
In  [24] are performed as well, which is also a fully relativistic package based on the Dirac equation for the calculations of atomic transition properties. Regarding the transition energies, the maximum relative discrepancies between the GRASP2K and the FAC results are 0.21%, 0.41%, and 3.34% for the M, N, and O transitions, respectively. As for the A-and gf-values, only relatively slight discrepancies between the GRASP2K and the FAC are found for most of the transitions, while for a few transitions such as the M 5 of Am 4+ and Am 8+ ions such a discrepancy is a little bit large. Since the same configurations have employed in both the GRASP2K and FAC calculations with an inclusion of the Breit interaction and QED 2725 Am 3+ d f 5 10 6 295 d f 5 9 7 3106 Am 4+ d f 5 10 5 198 d f 5 9 6 2725 Am 5+ d f 5 10 4 107 d f 5 9 5 1878 Am 6+ d f 5 10  effect, these discrepancies are mainly due to the difference of optimization techniques adopted by the two codes.
As can be seen from table 2, the transition energies corresponding to the same inner-shell hole-states are quite close in sequence to each other. For a specific ion, the corresponding transition energies decrease while the inner-shell hole moves towards outer shells. The energy difference between M 4 and M 5 , N 4 and N 5 as well as O 4 and O 5 indicates the splitting of the core states, i.e., the fine-structure splitting ofd 3 1 D ) spectra of Am 2+ -Am 8+ ions are shown, which are Gaussian line shapes and are obtained by convoluting the corresponding transition rates with the full width at half maximum (FWHM) 5 eV. However, since the separation of the 5f and 5d fine-structure energy levels is too small to be well separated, it appears like a quasi-continuum profile. With the decreasing number of the 5f spectator electrons, such a quasi-continuum profile changes gradually to be a two-peak-like characteristics especially for Am 7+ and Am 8+ ions, and the width of the corresponding transition peaks becomes narrower and the intensity becomes weaker. Moreover, for all of the spectra the peak center shifts towards higher-energy region. Moreover, the  N d f 4 5 4,5 ( )spectra of these Am ions as shown in figure 2 are studied. While these spectrum are obtained by the same convolution as in figure 1, the results are ultimately different from the ones of the O 4,5 transition. In the latter case, the core spin-orbit interaction is dominant over the electrostatic interaction of the 4d hole. Based on this fact, the two peaks are well separated in energies corresponding to the N 4 and N 5 . The energy difference between these two peaks is approximately 49.10 eV on average. Moreover, the N 4 and N 5 peaks witness a reduction in intensity from Am 2+ to Am 8+ . In figure 3, the ratio N 4 :N 5 is plotted versus the number of the 5f electrons. It is found that the ratio N 4 :N 5 increases with the decreasing number of the 5f vacancies. Also, it is found that the differences of the ratio N 4 :N 5 corresponding to the GRASP2K and FAC results are relatively small for most of the Am ions.
The 5 2,7 2 are well separated from each other, which arises from the spin-orbit splitting of 3d electrons. The energy separation of these two peaks is about 202.11 eV for all of the ions under study. Furthermore, the separation of energy levels are corresponding to the 3d 3/2 and 3d 5/2 states. Moreover, the peak intensity ratio M 4 :M 5 is plotted in figure 5 as a function of the number of the 5f electrons. It is found that the ratio M 4 :M 5 decreases as increasing number of the 5f spectator electrons.

Conclusions
The spectra originating from  =nd f n 5 3 5 ( ) transitions of Am 2+ -Am 8+ ions have been calculated by using GRASP2K code. While the obtained  O d f 5 5 4,5 ( ) spectra show a broad quasi-continuum profile, both  )spectra consist of two peaks that are well separated with respect to energy because of the strong spin-orbit interactions ofd 3 1 andd 4 1 hole state.