Citation: | Li X., Rosmej F. B.. X-ray transition and K-edge energies in dense finite-temperature plasmas: Challenges of a generalized approach with spectroscopic precision[J]. Matter and Radiation at Extremes, 2025, 10(2): 027201. doi: 10.1063/5.0235418 |
The capacity to predict X-ray transition and K-edge energies in dense finite-temperature plasmas with high precision is of primary importance for atomic physics of matter under extreme conditions. The dual characteristics of bound and continuum states in dense matter are modeled by a valence-band-like structure in a generalized ion-sphere approach with states that are either bound, free, or mixed. The self-consistent combination of this model with the Dirac wave equations of multielectron bound states allows one to fully respect the Pauli principle and to take into account the exact nonlocal exchange terms. The generalized method allows very high precision without implication of calibration shifts and scaling parameters and therefore has predictive power. This leads to new insights in the analysis of various data. The simple ionization model representing the K-edge is generalized to excitation–ionization phenomena resulting in an advanced interpretation of ionization depression data in near-solid-density plasmas. The model predicts scaling relations along the isoelectronic sequences and the existence of bound M-states that are in excellent agreement with experimental data, whereas other methods have failed. The application to unexplained data from compound materials also gives good agreement without the need to invoke any additional assumptions in the generalized model, whereas other methods have lacked consistency.
[1] |
R. J. Taylor, The Stars: Their Structure and Evolution, 2nd ed. (Cambridge University Press, 1994).
|
[2] |
R. P. Drake and P. A. Norreys, “Focus on high energy density physics,” New J. Phys. 16, 065007 (2014).10.1088/1367-2630/16/6/065007
|
[3] |
G. Chabrier, “Plasma physics and planetary astrophysics,” Plasma Phys. Controlled Fusion 51, 124014 (2009).10.1088/0741-3335/51/12/124014
|
[4] |
R. Helled, J. D. Anderson, M. Podolak, and G. Schubert, “Interior models of Uranus and Neptune,” Astrophys. J. 726, 15 (2011).10.1088/0004-637x/726/1/15
|
[5] |
J. Lindl, “Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain,” Phys. Plasmas 2, 3933 (1995).10.1063/1.871025
|
[6] |
C. S. Reynolds and M. A. Nowak, “Fluorescent iron lines as a probe of astrophysical black hole systems,” Phys. Rep. 377, 389 (2003).10.1016/S0370-1573%2802%2900584-7
|
[7] |
D. R. Inglis and E. Teller, “Ionic depression of series limits in one-electron spectra,” Astrophys. J. 90, 439 (1939).10.1086/144118
|
[8] |
G. R. Griem, Principles of Plasma Spectroscopy, 1st ed. (Cambridge University Press, 1997).
|
[9] |
D. Salzmann, Atomic Physics in Hot Plasma (Oxford University Press, 1998).
|
[10] |
M. S. Murillo and J. C. Weisheit, “Dense plasma, screened interactions, and atomic ionizations,” Phys. Rep. 302, 1 (1998).10.1016/S0370-1573(98)00017-9
|
[11] | |
[12] |
J. C. Pain, “A model of dense-plasma atomic structure for equation-of-state calculations,” J. Phys. B: At., Mol. Opt. Phys. 40, 1553 (2007).10.1088/0953-4075/40/8/008
|
[13] |
D. J. Hoarty, P. Allan, S. F. James, C. R. D. Brown, L. M. R. Hobbs et al., “Observations of the effect of ionization-potential depression in hot dense plasma,” Phys. Rev. Lett. 110, 265003 (2013).10.1103/physrevlett.110.265003
|
[14] |
C. R. Stillman, P. M. Nilson, S. T. Ivancic, I. E. Golovkin, C. Mileham et al., “Picosecond time-resolved measurements of dense plasma line shifts,” Phys. Rev. E 95, 063204 (2017).10.1103/physreve.95.063204
|
[15] |
A. Unsöld, “Zur Berechnung der Zustandssummen für Atome und Ionen in einem teilweise ionisierten Gas,” Z. Astrophys. 24, 355 (1948).
|
[16] |
G. B. Zimmermann and R. M. Moore, “Pressure ionization in laser fusion target simulations,” J. Quant. Spectrosc. Radiat. Transfer 23, 517 (1980).10.1016/0022-4073(80)90055-2
|
[17] |
J. Stewart and K. Pyatt, “Lowering of ionization potentials in plasmas,” Astrophys. J. 144, 1203 (1966).10.1086/148714
|
[18] |
G. Ecker and W. Weizel, “Zustandssumme und effective Ionisierungsspannung eines Atoms im Inneren des Plasmas,” Ann. Phys. 6, 126 (1956).10.1002/andp.19564520210
|
[19] |
G. Ecker and W. Kröll, “Lowering of the ionization energy for a plasma in thermodynamic equilibrium,” Phys. Fluids 6, 62 (1963).10.1063/1.1724509
|
[20] |
M. Belkhiri, C. J. Fontes, and M. Poirier, “Influence of the plasma environment on atomic structure using an ion-sphere model,” Phys. Rev A 92, 032501 (2015).10.1103/physreva.92.032501
|
[21] |
L. B. Fletcher, A. L. Kritcher, A. Pak, T. Ma, T. Döppner et al., “Observations of continuum depression in warm dense matter with x-ray Thomson scattering,” Phys. Rev. Lett. 112, 145004 (2014).10.1103/physrevlett.112.145004
|
[22] |
B. J. B. Crowley, “Average-atom quantum-statistical cell model for hot plasma in local thermodynamic equilibrium over a wide range of densities,” Phys. Rev. A 41, 2179 (1990).10.1103/physreva.41.2179
|
[23] |
S. X. Hu, “Continuum lowering and Fermi-surface rising in strongly coupled and degenerate plasmas,” Phys. Rev. Lett. 119, 065001 (2017).10.1103/physrevlett.119.065001
|
[24] |
T. R. Preston, S. M. Vinko, O. Ciricosta, H.-K. Chung, R. W. Lee et al., “The effects of ionization potential depression on the spectra emitted by hot dense aluminium plasmas,” High Energy Density Phys. 9, 258 (2013).10.1016/j.hedp.2012.12.014
|
[25] |
C. Lin, G. Röpke, W. Kraeft, and H. Reinholz, “Ionization-potential depression and dynamical structure factor in dense plasmas,” Phys. Rev. E 96, 013202 (2017).10.1103/physreve.96.013202
|
[26] |
X. Li and F. B. Rosmej, “Spin-dependent energy-level crossings in highly charged ions due to dense plasma environments,” Phys. Rev. A 82, 022503 (2010).10.1103/physreva.82.022503
|
[27] |
F. B. Rosmej, V. S. Lisitsa, and V. A. Astapenko, Plasma Atomic Physics, Springer Series on Atomic, Optical and Plasma Physics (Springer, Heidelberg, 2021).
|
[28] |
B. Deschaud, O. Peyrusse, and F. B. Rosmej, “Generalized atomic processes for interaction of intense femtosecond XUV- and X-ray radiation with solids,” Europhys. Lett. 108, 53001 (2014).10.1209/0295-5075/108/53001
|
[29] |
E. Galtier, F. B. Rosmej, T. Dzelzainis, D. Riley, F. Y. Khattak et al., “Decay of cystalline order and equilibration during the solid-to-plasma transition induced by 20-fs microfocused 92-eV free-electron-laser pulses,” Phys. Rev. Lett. 106, 164801 (2011).10.1103/physrevlett.106.164801
|
[30] |
X. Li, F. B. Rosmej, V. S. Lisitsa, and V. A. Astapenko, “An analytical plasma screening potential based on the self-consistent-field ion-sphere model,” Phys. Plasmas 26, 033301 (2019).10.1063/1.5055689
|
[31] |
X. Li and F. B. Rosmej, “Analytical approach to level delocalization and line shifts in finite temperature dense plasmas,” Phys. Lett. A 384(25), 126478 (2020).10.1016/j.physleta.2020.126478
|
[32] |
S. M. Vinko, O. Ciricosta, B. I. Cho, K. Engelhorn, H.-K. Chung et al., “Creation and diagnosis of a solid-density plasma with an x-ray free-electron laser,” Nature 482, 59 (2012).10.1038/nature10746
|
[33] |
S. M. Vinko, O. Ciricosta, T. R. Preston, D. S. Rackstraw, C. R. D. Brown et al., “Investigation of femtosecond collisional ionization rates in a solid-density aluminium plasma,” Nat. Commun. 6, 6397 (2015).10.1038/ncomms7397
|
[34] |
O. Ciricosta, S. M. Vinko, B. Barbrel, D. S. Rackstraw, T. R. Preston et al., “Measurements of continuum lowering in solid-density plasmas created from elements and compounds,” Nat. Commun. 7, 11713 (2016).10.1038/ncomms11713
|
[35] |
O. Ciricosta, S. M. Vinko, H.-K. Chung, B.-I. Cho, C. R. D. Brown et al., “Direct measurements of the ionization potential depression in a dense plasma,” Phys. Rev. Lett. 109, 065002 (2012).10.1103/physrevlett.109.065002
|
[36] |
F. B. Rosmej, “Ionization potential depression in an atomic-solid-plasma picture,” J. Phys. B: At., Mol. Opt. Phys. 51, 09LT01 (2018).10.1088/1361-6455/aab80f
|
[37] |
S. M. Vinko, O. Ciricosta, and J. S. Wark, “Density functional theory calculations of continuum lowering in strongly coupled plasmas,” Nat. Commun. 5, 3533 (2014).10.1038/ncomms4533
|
[38] |
S.-K. Son, R. Thiele, Z. Jurek, B. Ziaja, and R. Santra, “Quantum-mechanical calculation of ionization-potential lowering in dense plasmas,” Phys. Rev. X 4, 031004 (2014).10.1103/physrevx.4.031004
|
[39] |
F. Zhou, Y. Qu, J. Gao, Y. Ma, Y. Wu, and J. Wang, “Atomic-state-dependent screening model for hot and warm dense plasmas,” Commun. Phys. 4, 148 (2021).10.1038/s42005-021-00652-x
|
[40] |
B. J. B. Crowley, “Continuum lowering—A new perspective,” High Energy Density Phys. 13, 84 (2014).10.1016/j.hedp.2014.04.003
|
[41] |
B. Deschaud, O. Peyrusse, and F. B. Rosmej, “Simulation of XFEL induced fluorescence spectra of hollow ions and studies of dense plasma effects,” Phys. Plasmas 27, 063303 (2020).10.1063/5.0011193
|
[42] |
C. A. Iglesias, “Comment on ‘Free-free opacity in warm aluminum,’” High Energy Density Phys. 7, 38 (2011).10.1016/j.hedp.2010.08.003
|
[43] |
C. A. Iglesias and P. A. Sterne, “Fluctuations and the ionization potential in dense plasmas,” High Energy Density Phys. 9, 103 (2013).10.1016/j.hedp.2012.11.007
|
[44] |
C. A. Iglesias, “A plea for a reexamination of ionization potential depression measurements,” High Energy Density Phys. 12, 5 (2014).10.1016/j.hedp.2014.04.002
|
[45] |
V. V. Karasiev and S. X. Hu, “Unraveling the intrinsic atomic physics behind x-ray absorption line shifts in warm dense silicon plasmas,” Phys. Rev. E 103, 033202 (2021).10.1103/physreve.103.033202
|
[46] |
P. Beiersdorfer, G. V. Brown, A. McKelvey, R. Shepherd, D. J. Hoarty et al., “High resolution measurements of Cl15+ line shifts in hot, solid-density plasmas,” Phys. Rev. A 100, 012511 (2019).10.1103/physreva.100.012511
|
[47] |
S. B. Hansen, E. C. Harding, P. F. Knapp, M. R. Gomez, T. Nagayama et al., “Changes in the electronic structure of highly compressed iron revealed by x-ray fluorescence lines and absorption edges,” High Energy Density Phys. 24, 39 (2017).10.1016/j.hedp.2017.07.002
|
[48] |
E. Engel and S. H. Vosko, “Exact exchange-only potentials and the virial relation as microscopic criteria for generalized gradient approximations,” Phys. Rev. B 47, 13164 (1993).10.1103/physrevb.47.13164
|
[49] |
O. Renner, D. Salzman, P. Sondhauss, A. Djaoui, E. Krousky et al., “Experimental evidence for plasma shifts in Lyman series of aluminium,” J. Phys. B:At., Mol. Opt. Phys. 31, 1379 (1998).10.1088/0953-4075/31/6/022
|
[50] |
J. J. Bekx, S.-K. Son, B. Ziaja, and R. Santra, “Electronic-structure calculations for nonisothermal warm dense matter,” Phys. Rev. Res. 2, 033061 (2020).10.1103/physrevresearch.2.033061
|
[51] |
R. D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkely, 1981).
|
[52] |
R. D. Deslattes, E. G. Kessler, Jr., P. Indelicato, L. de Billy, E. Lindroth et al., “X-ray transition energies: New approach to a comprehensive evaluation,” Rev. Mod. Phys. 75, 35 (2003).10.1103/revmodphys.75.35
|
[53] | |
[54] |
S. X. Hu, D. T. Bishel, D. A. Chin, P. M. Nilson, V. V. Karasiev et al., “Probing atomic physics at ultrahigh pressure using laser-driven implosions,” Nat. Commun. 13, 6780 (2022).10.1038/s41467-022-34618-6
|
[55] |
B. F. Kraus, L. Gao, K. W. Hill, M. Bitter, P. C. Efthimion et al., “Streaked sub-ps-resolution x-ray line shapes and implications for solid-density plasma dynamics (invited),” Rev. Sci. Instrum. 93, 103527 (2022).10.1063/5.0101853
|
[56] |
D. Bailie, S. White, R. Irwin, C. Hyland, R. Warwick et al., “K-edge structure in shock-compressed chlorinated parylene,” Atoms 11, 135 (2023).10.3390/atoms11100135
|
[57] |
F. B. Rosmej and R. W. Lee, “Hollow ion emission driven by pulsed intense x-ray fields,” Europhys. Lett. 77, 24001 (2007).10.1209/0295-5075/77/24001
|
[58] |
F. B. Rosmej, R. Dachicourt, B. Deschaud, D. Khaghani, M. Dozières et al., “Exotic x-ray emission from dense plasmas,” J. Phys. B: At., Mol. Opt. Phys. 48, 224005 (2015).10.1088/0953-4075/48/22/224005
|
[59] | |
[60] |
A. H. Gabriel, “Dielectronic satellite spectra for highly-charged helium-like ion lines,” Mon. Not. R. Astron. Soc. 160, 99 (1972).10.1093/mnras/160.1.99
|
[61] |
S. Sahoo, G. F. Gribakin, G. Shabbir Naz, J. Kohanoff, and D. Riley, “Compton scatter profiles for warm dense matter,” Phys. Rev. E 77, 046402 (2008).10.1103/physreve.77.046402
|
[62] |
W. R. Johnson, J. Nilsen, and K. T. Cheng, “Thomson scattering in the average-atom approximation,” Phys. Rev. E 86, 036410 (2012).10.1103/physreve.86.036410
|
[63] |
J.-C. Pain, “Multi-configuration calculation of ionization potential depression,” Plasma 5, 384 (2022).10.3390/plasma5040029
|
[64] |
T.-G. Lee, M. Busquet, M. Klapisch, J. W. bates, A. J. Schmitt et al., “Radiative and atomic properties of C and CH plasmas in the warm-dense-matter regime,” Phys. Rev. E 98, 043203 (2018).10.1103/physreve.98.043203
|
[65] |
G. Faussurier and C. Blancard, “Density effects on electronic configurations in dense plasmas,” Phys. Rev. E 97, 023206 (2018).10.1103/physreve.97.023206
|
[66] |
T. Döppner, M. Bethkenhagen, D. Kraus, P. Neumayer, D. A. Chapman et al., “Observing the onset of pressure-driven K-shell delocalization,” Nature 618, 270 (2023).10.1038/s41586-023-05996-8
|
[67] |
M. Bethkenhagen, B. B. L. Wite, M. Schörner, G. Röpke, T. Döppner et al., “Carbon ionization at gigabar pressures: An ab initio perspective on astrophysical high-density plasmas,” Phys. Rev. Res. 2, 023260 (2020).10.1103/PhysRevResearch.2.023260
|
[68] |
T. Yan, L. G. Jiao, A. Liu, Y. C. Wang, H. E. Montgomery et al., “Bound state energies and critical bound region in the semiclassical dense hydrogen plasmas,” Phys. Plasmas 31, 042110 (2024).10.1063/5.0185339
|
[69] |
I. P. Grant, Relativistic Quantum Theory of Atoms and Molecules: Theory of Computations (Springer Science and Buisiness Media, LLC, New York, 2007).
|
[70] |
P. Jönsson, M. Godefoid, G. Gaifalas, J. Ekman, J. Frumer et al., “An introduction to relativistic theory as implemented in GRASP,” Atoms 11, 7 (2023).10.3390/atoms11010007
|