Interspecies radiative transition in warm and superdense plasma mixtures.

Superdense plasmas widely exist in planetary interiors and astrophysical objects such as brown-dwarf cores and white dwarfs. How atoms behave under such extreme-density conditions is not yet well understood, even in single-species plasmas. Here, we apply thermal density functional theory to investigate the radiation spectra of superdense iron–zinc plasma mixtures at mass densities of ρ = 250 to 2000 g cm−3 and temperatures of kT = 50 to 100 eV, accessible by double-shell–target implosions. Our ab initio calculations reveal two extreme atomic-physics phenomena—firstly, an interspecies radiative transition; and, secondly, the breaking down of the dipole-selection rule for radiative transitions in isolated atoms. Our first-principles calculations predict that for superdense plasma mixtures, both interatomic radiative transitions and dipole-forbidden transitions can become comparable to the normal intra-atomic Kα-emission signal. These physics phenomena were not previously considered in detail for extreme high-density plasma mixtures at super-high energy densities.


Supplementary Information
Supplementary Figure 1: Convergence testing results with respect to number of atoms in supercell. Comparison of emission spectra of Fe-Zn plasmas at ρ=1000 g cm -3 and kT=100 eV, using different number of atoms in super-cell for DFT calculations.
Supplementary Figure 2: Convergence testing results with respect to number of bands. Comparison of emission spectra of Fe-Zn plasmas at ρ=2000 g cm -3 and kT=50 eV (32-atom super-cell), using different number of bands in ABINIT calculations.
Supplementary Figure 3: Convergence testing results with respect to number of cut-off energies. Comparison of emission spectra of Fe-Zn plasmas at ρ=2000 g cm -3 and kT=50 eV (32-atom super-cell), using different plane-wave cut-off energies in ABINIT calculations.
Supplementary Figure 4: Convergence testing results with respect to the cut-off radius of PAW pseudo-potentials. Comparison of emission spectra of Fe-Zn plasmas at ρ=2000 g cm -3 and kT=50 eV (32-atom super-cell), using different cut-off radius for all-electron PAW pseudo-potentials in ABINIT calculations.
Supplementary Figure 5: Convergence testing results with respect to exchange-correlation functionals. Comparison of emission spectra of Fe-Zn plasmas at ρ=1500 g cm -3 and kT=50 eV (32-atom super-cell), using different exchange-correlation functionals in ABINIT calculations.
Supplementary Figure 6: Testing results of non-dipole contribution to inter-atomic K α emission. The ratio of quadrupole to dipole contributions is plotted as a function of inter-atomic Fe-Zn distance.

Supplementary Note 1. CONVERGENCE TESTS
To obtain the converged emission spectra of super-dense plasmas, we have performed a variety of numerical tests on the number of atoms in super-cell, the number of bands, the planewave cut-off energy, and the cut-off radius of all-electron PAW pseudo-potentials. The convergence testing results are summarized in supplementary figures 1-4. In supplementary figure 1 we compare the results of emission spectra for Fe-Zn plasmas at ρ=1000 g cm -3 and kT=100 eV, using different number of atoms in super-cell for DFT calculations. It shows that the case of 32 atoms gives very similar result to the 16-atom case. Thus, the results presented in our paper had used 32-atom super-cell.
Supplementary figure 2 shows the convergence testing results on the number of bands used in our DFT calculations, for the emission spectra of dense Fe-Zn plasmas at ρ=2000 g cm -3 and kT=50 eV (32-atom super-cell). One can see that the calculation with 12000 bands give almost identical result as that of the 8000-band calculation. All of results presented in our paper were converged with a maximum of 18000 bands in ABINIT calculations (depending on the plasma density and temperature).
In supplementary figure 3 we plot the convergence testing results on the plane-wave cutoff energy used in our DFT calculations, for the emission spectra of dense Fe-Zn plasmas at ρ = 2000 g cm -3 and kT = 50 eV (32-atom super-cell). One can see that the calculation with E cut ≈ 95.2-keV give almost identical result as that of E cut ≈ 68-keV. All of results presented in our paper were converged with a maximum plane-wave cut-off energy varying from E cut ≈ 40.8-keV to E cut ≈ 95.2-keV in ABINIT calculations (depending on the plasma density and temperature).
Supplementary figure 4 shows the convergence testing results using different cut-off radius of all-electron PAW pseudo-potentials in our DFT calculations, for the emission spectra of dense Fe-Zn plasmas at ρ=2000 g cm -3 and kT=50 eV (32-atom super-cell). One can see that the calculation with r cut ≈0.25/0.30 4 Bohr for Fe/Zn give almost identical result as that of r cut ≈0.2 Bohr. All of results presented in our paper were converged with a minimum cut-off radius of r cut ≈0.2 Bohr in ABINIT calculations.

Supplementary Note 2. EXCHANGE-CORRELATION FUNCTIONALS
To verify if our results are insensitive to the choice of exchange-correlation functionals, we have performed two additional DFT calculations with both LDA-PZ (Perdew-Zunger) and . The results for Fe-Zn plasmas of ρ=1500 g cm -3 and kT=50-eV are shown by supplementary figure 5. One can see that these results are almost identical, except for a small (~10-15 eV) energy shift with each other. The inter-atomic K α signals and their amplitude relative to the normal K α emission are unchanged between LDA and PBE calculations.

Supplementary Note 3. NON-DIPOLE CONTRIBUTION
To examine the high-order electric quadrupole contribution to inter-atomic K α emissions, we have computed its relative amplitude to that of dipole contribution with the independentatom model. In supplementary figure 6, we plot the ratio of quadrupole to dipole contributions as a function of inter-atomic Fe-Zn distance. One clearly sees that as the interatomic distance increases the emitting entity gets bigger so that the quadrupole contribution rises. However, for the density range concerned, the maximum quadrupole term only gives less than ~3.2% of dipole contribution.