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Ionization Potential Depression

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Plasma Atomic Physics

Part of the book series: Springer Series on Atomic, Optical, and Plasma Physics ((SSAOPP,volume 104))

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Abstract

In a low-density environment, where atoms and ions are essentially free, atomic population kinetics of gases and plasmas has been very successful in many different scientific and technical disciplines. As density increases, the free atom model breaks down resulting in a perturbation of the atomic energy levels and a corresponding ionization potential depression IPD. The IPD is of great fundamental interest, for thermodynamic applications and also for the understanding of the various radiative properties (emission, absorption, scattering). Different IPD models are discussed including the finite temperature ion sphere FTIS model and the Atomic-Solid-Plasma ASP model. The ASP model accounts for the difference between real atomic ionization potentials in solids and free atoms taking into account the structure of the valence band and the Fermi energy. The FTIS model accounts for self-consistent screening effects of both bound and free electrons inside the ion sphere with effective radius depending on plasma density. Different regimes of ionization potential depression are considered as well as plasma polarization shifts of X-ray spectral lines. Finally, Fermi surface rising in much above solid density compressed matter is discussed leading to increased K-edge energies rather than decreased ones.

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References

  • N.W. Ashcrof, N.D. Mermin, Solid State Physics (Saunders, 1976)

    Google Scholar 

  • P. Beiersdorfer, G. Brown, A. McKelvey, R. Shepherd, D. Hoarty, C. Brown, M. Hill, L. Hobbs, S. James, J. Morton, L. WIlson, High resolution measurements of Cl15+ line shifts in hot, solid-density plasmas, Phys. Rev. A 100, 012511 (2019)

    Google Scholar 

  • T. Blenski, K. Ishikawa, Pressure ionization in the spherical ion-cell model of dense plasma and a pressure formula in the relativistic Pauli approximation. Phys. Rev. E 51, 4869 (1995)

    Article  ADS  Google Scholar 

  • S.M. Blinder, Canonical partition function for the hydrogen atom via the Coulomb propagator, Journal of Mathematical Physics 36, 1208 (1995)

    Google Scholar 

  • Z.B. Chen, Y.S. Tian, Y.M. Yin, Y.Y. Qi, G.P. Zhao, X.Z. Shen, K. Wang, Theoretical determination of level delocalizations, plasma shifts and radiative properties of fusion relevant Ni XXII in finite temperature dense plasmas using a generalized analytical b-potential, JQSRT 266 107570 (2021)

    Google Scholar 

  • O. Ciricosta, S.M. Vinko, H.-K. Chung, B.I. Cho, C.R.D. Brown, T. Burian, J. Chalupsky, K. Engelhorn, R.W. Falcone, C. Graves, V. Hajkova, A. Higginbotham, L. Juha, J. Krzywinski, H.J. Lee, M. Messerschmid, C.D. Murphy, Y. Ping, D.S. Rackstraw, A. Scherz, W. Schlotter, S. Toleikis, J.J. Turner, L. Vysin, T. Wang, B. Wu, U. Zastrau, D. Shu, R.W. Lee, P. Heimann, B. Nagler, J.S. Wark, Direct measurements of the ionization potential depression in a dense plasma. Phys. Rev. Lett. 109, 065002 (2012)

    Article  ADS  Google Scholar 

  • O. Ciricosta, S.M. Vinko, B. Barbrel, D.S. Rackstraw, T.S. Preston, T. Burian, J. Chalupsky, B.I. Cho, H.-K. Chung, G.L. Dakovski, K. Engelhorn, V. Hajkova, P. Heiman, M. Holmes, L. Juha, J. Krzywinski, R.W. Lee, S. Toleikis, J.J. Turner, U. Zastrau, J.S. Wark, Measurements of continuum lowering in solid-density plasmas created from elements and compounds. Nat. Comm. 7, 11713 (2016)

    Article  ADS  Google Scholar 

  • F.P. Condamine, E. Filippov, P. Angelo, S.A. Pikuz, O. Renner, F.B. Rosmej, High-spatial and spectral resolution spectroscopic study of Copper K-alpha open M-shell complex driven by hot electrons in dense laser produced plasmas, HEDP 32, 89 (2019)

    Google Scholar 

  • R.D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, 1981)

    Google Scholar 

  • V. Dervieux, B. Loupias, S. Baton, L. Lecherbourg, K. Glize, C. Rousseaux, C. Reverdin, L. Gremillet, C. Blancard, V. Silvert, J.-C. Pain, C.R.D. Brown, P. Allan, M.P. Hill, D.J. Hoarty, P. Renaudin, Characterization of near-LTE, high-temperature and high-density aluminum plasmas produced by ultra-high intensity lasers. HEDP 16, 12 (2015)

    ADS  Google Scholar 

  • R.D. Desclattes, E.Jr. Kessler, P. Indelicato, L. de Billy, E. Lindroth, J. Anton, X-ray transition energies: new approach to a comprehensive evaluation. Rev. Mod. Phys. 75, 35 (2003)

    Google Scholar 

  • R.P. Drake, High-Energy-Density Physics (Springer, 2006)

    Google Scholar 

  • G. Ecker, W. Kröll, Lowering of the ionization energy for a plasma in thermodynamic equilibrium. Physics Fluids 6, 62 (1963)

    Article  ADS  Google Scholar 

  • G. Ecker, W. Weizel, Zustandssumme und effective Ionisierungsspannung eines Atoms im Inneren des Plasmas. Ann. Phys. 6, 126 (1956)

    Article  Google Scholar 

  • E. Engel, S.H. Vosko, Exact exchange-only potentials and the virial relation as microscopic criteria for generalized gradient approximations, Phys. Rev. B. 47, 13164 (1993)

    Google Scholar 

  • L.B. Fletcher, A.L. Kritcher, A. Pak, T. Ma, T. Döppner, C. Fortmann, L. Divol, O.S. Jones, O.L. Landen, H.A. Scott, J. Vorberger, D.A. Chapman, D.O. Gericke, B.A. Mattern, G.T. Seidler, G. Gregori, R.W. Falcone, S.H. Glenzer, Observations of continuum depression in warm dense matter with X-ray thomson scattering. Phys. Rev. Lett. 112, 145004 (2014)

    Article  ADS  Google Scholar 

  • T. Fujimoto, Plasma Spectroscopy (Oxford Science Publications, Oxford, 2004)

    Book  Google Scholar 

  • L. Gournay, F.B. Rosmej, Continuum Lowering of Hollow Crystals within the Atomic-Solid-Plasma Picture (in preparation, 2022)

    Google Scholar 

  • H.R. Griem, Principles of Plasma Spectroscopy (Cambridge University Press, 1997)

    Google Scholar 

  • R.D. Inglis, E. Teller, Ionic depression of series limits in one electron spectra. Astr. Phys. J. 90, 439 (1939)

    Article  ADS  Google Scholar 

  • V.V. Karasiev, 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)

    Google Scholar 

  • W. Kohn, C. Majumdar, Continuity between bound and unbound states in a fermi gas. Phys. Rev. 138, A1617 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  • H.-J. Kunze, Introduction to Plasma Spectroscopy (Springer, Berlin, 2009)

    Book  Google Scholar 

  • S.B. Hansen, E.C. Harding, P.F. Knapp, M.R. Gomez, T. Nagayama, J.E. Bailey, Changes in the electronic structure of highly compressed iron revealed by X-ray fluorescence lines and absorption edges. HEDP 24, 39 (2017)

    ADS  Google Scholar 

  • D.J. Hoarty, P. Allan, S.F. James, C.R.D. Brown, L.M.R. Hobbs, M.P. Hill, J.W.O. Harris, J. Morton, M.G. Brookes, R. Shepherd, J. Dunn, H. Chen, E. von Marley, P. Beiersdorfer, H.-K. Chung, R.W. Lee, G. Brown, J. Emig, Observation of the effect of ionization-potential depression in hot dense plasma. Phys. Rev. Lett. 110, 265003 (2013)

    Article  ADS  Google Scholar 

  • S.X. Hu, Continuum lowering and fermi-surface rising in strongly coupled and degenerate plasmas. Phys. Rev. Lett. 119, 065001 (2017)

    Article  ADS  Google Scholar 

  • D.G. Hummer, D. Mihalas, The equation of state for stellar envelopes: an occupation probability formalism for the truncation of internal partition functions. Astr. J. 331, 794 (1988)

    Article  Google Scholar 

  • Hyperphysics: http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/fermi.html (2021)

  • C.A. Iglesias, Comment on “Free-free opacity in warm aluminum”. HEDP 7, 38 (2011)

    Google Scholar 

  • C.A. Iglesias, A plea for a reexamination of ionization potential depression measurements. HEDP 12, 5 (2014)

    ADS  Google Scholar 

  • C.A. Iglesias, On spectral line shifts from analytic fits to the ion-sphere model potential, HEDP 30, 41 (2019)

    Google Scholar 

  • C.A. Iglesias, P.A. Sterne, Fluctuations and the ionization potential in dense plasmas. HEDP 9, 103 (2013)

    Google Scholar 

  • X. Li, F.B. Rosmej, Quantum number dependent energy level shifts of ions in dense plasmas: a generalized analytical approach. Europhys. Lett. 99, 33001 (2012)

    Article  ADS  Google Scholar 

  • X. Li, F. B. Rosmej, Analytical approach to level delocalization and line shifts in finite temperature dense plasmas, Phys. Lett A 384, 126478 (2020)

    Google Scholar 

  • X. Li, F.B. Rosmej, V.A. Astapenko, V.S. Lisitsa, An analytical plasma screening potential based on the self-consistent-field ion-sphere model. Phys. Plasmas 26, 03301 (2019)

    Google Scholar 

  • X. Li, F.B. Rosmej, V.A. Astapenko, V.S. Lisitsa, Generalized free-bound approach for ions embedded in dense plasmas (in preparation, 2019)

    Google Scholar 

  • X. Li, Z. Xu, F.B. Rosmej, Exchange energy shifts in dense plasma conditions. J. Phys. B: At. Mol. Opt. Phys. 39, 3373 (2006)

    Google Scholar 

  • V.S. Lisitsa, Atoms in Plasmas (Springer, 1994)

    Google Scholar 

  • K. Ma, Y. Chu, Z.B. Chen, Analytical Calculation of Cl15+ Ion Immersed in Dense Plasmas, Few-Body Systems 61, 42 (2020)

    Google Scholar 

  • G. Massacrier, J. Dubeau, A theoretical approach to n-electron ionic structure under dense plasma conditions: I. blue and red shift. J. Phys. B: At. Mol. Opt. Phys. 23, 24595 (1990)

    Google Scholar 

  • D. Mihalas, Stellar Atmospheres (W. H. Freeman and Company, San Francisco, 1978)

    Google Scholar 

  • D. Mihalas, B. Weibel-Mihalas, Foundations of Radiation Hydrodynamic (Dover Publications, 1999)

    Google Scholar 

  • R.M. More, Atomic Physics in Inertial Confinement Fusion, LLNL technical report, no. ucrl-84991 (unpublished, 1981)

    Google Scholar 

  • H. Nguyen, M. Koenig, D. Benredjem, M. Caby, G. Coulaud, Atomic structure and polarization line shift in dense and hot plasmas. Phys. Rev. A 33, 1279 (1986)

    Article  ADS  Google Scholar 

  • NIST-data base: https://physics.nist.gov/PhysRefData/XrayTrans/Html/search.html (2021)

  • S.G. Rautian, A.M. Shalagin, Kinetic Problems of Non-Linear Spectroscopy (North-Holland, Amsterdam, 1991)

    Google Scholar 

  • O. Renner, F.B. Rosmej, Challenges of X-ray spectroscopy in investigations of matter under extreme conditions. Matter Radiat. Extrem. Rev. 4, 024201 (2019)

    Google Scholar 

  • O. Renner, T. Missalla, P. Sondhauss, E. Krousky, E. Förster, C. Chenais-Popovics, O. Rancu, High-luminosity, high-resolution, X-ray spectroscopy of laser-produced plasma by vertical-geometry Johann spectrometer. Rev. Sci. Instrum. 68, 2393 (1997a)

    Google Scholar 

  • O. Renner, P. Sondhauss, D. Salzmann, A. Djaoui, M. Koenig, E. Förster, Measurement of the polarization shifts in hot and dense aluminum plasma. JQSRT 58, 851 (1997b)

    Article  ADS  Google Scholar 

  • O. Renner, D. Salzmann, P. Sondauss, A. Djaoui, E. Krousky, E. Förster, Experimental evidence for plasma shifts in Lyman series of aluminum. J. Phys. B At. Mol. Opt. Phys. 31, 1379 (1998)

    Article  ADS  Google Scholar 

  • O. Renner, F.B. Rosmej, E. Krouský, P. Sondhauss, M.P. Kalachnikov, P.V. Nickles, I. Uschmann, E. Förster, Overcritical density plasma diagnosis inside the laser-produced craters. Appl. Phys. Lett. 79, 177 (2001)

    Article  ADS  Google Scholar 

  • F.B. Rosmej, Hot electron X-ray diagnostics. J. Phys. B. Lett.: At. Mol. Opt. Phys. 30, L819 (1997)

    Google Scholar 

  • F.B. Rosmej, A new type of analytical model for complex radiation emission of hollow ions in fusion and laser produced plasmas. Europhys. Lett. 55, 472 (2001)

    Article  ADS  Google Scholar 

  • F.B. Rosmej, An alternative method to determine atomic radiation. Europhys. Lett. 76, 1081 (2006)

    Article  ADS  Google Scholar 

  • F.B. Rosmej, Exotic states of high density matter driven by intense XUV/X-ray Free Electron Lasers, in Free Electron Laser, InTech 2012, ed. by S. Varró, ISBN 978-953-51-0279-3 (2012), p. 187–212. Free download: http://www.intechopen.com/books/free-electron-lasers/exotic-states-of-high-density-matter-driven-by-intense-xuv-x-ray-free-electron-lasers

  • F.B. Rosmej, Ionization potential depression in an atomic-solid-plasma picture. Letter J. Phys. B. 51(9), LT01 (2018)

    Google Scholar 

  • F.B. Rosmej, K. Bennadji, V.S. Lisitsa, Dense plasmas effects on exchange energy shifts in highly charged ions: an alternative approach for arbitrary perturbation potentials. Phys. Rev. A 84, 032512 (2011)

    Article  ADS  Google Scholar 

  • F.B. Rosmej, U.N. Funk, M. Geißel, D.H.H. Hoffmann, A. Tauschwitz, A.Ya. Faenov, T.A. Pikuz, I.Yu. Skobelev, F. Flora, S. Bollanti, P.Di. Lazzaro, T. Letardi, A. Grilli, L. Palladino, A. Reale, A. Scafati, L. Reale, T. Auguste, P. D’Oliveira, S. Hulin, P. Monot, A. Maksimchuk, S.A. Pikuz, D. Umstadter, M. Nantel, R. Bock, M. Dornik, M. Stetter, S. Stöwe, V. Yakushev, M. Kulisch, N. Shilkin, X-ray radiation from ions with K-shell vacancies. JQSRT 65, 477 (2000)

    Google Scholar 

  • A. Saemann, K. Eidmann, I.E. Golovkin, R.C. Mancini, E. Andersson, E. Förster, K. Witte, Isochoric heating of solid aluminum by ultrashort laser pulses focused on a tampered target. Phys. Rev. Lett. 82, 4843 (1999)

    Article  ADS  Google Scholar 

  • D. Salzman, Atomic Physics in Hot Plasmas (Oxford University Press, 1998)

    Google Scholar 

  • I. Shimamura, T. Fujimoto, State densities and ionization equilibrium of atoms in dense plasmas. Phys. Rev. A 42, 2346 (1990)

    Article  ADS  Google Scholar 

  • A.K. Shing, D. Dawra, M. Dimri, A.K.S. Jha, R.K. Pandey, M. Mohan, Plasma screening effects on the atomic structure of He-like ions embedded in strongly coupled plasma, Phys. Lett. A 384, 126369 (2020)

    Google Scholar 

  • M. Smid, O. Renner, A. Colaitis, V.T. Tikhonchuk, T. Schlegel, F.B. Rosmej, Characterization of suprathermal electrons inside laser accelerated solid density matter via axially-resolved Kα-emission, Nature Comm. 10, 4212 (2019)

    Google Scholar 

  • I.I. Sobelman, L.A. Vainshtein, E.A. Yukov, Excitation of Atoms and Broadening of Spectral Lines (Springer, 1995)

    Google Scholar 

  • S.-K. Son, R. Thiele, Z. Jurek, B. Ziaja, R. Santra, Quantum-mechanical calculation of ionization-potential lowering in dense plasmas. Phys. Rev. X 4, 031004 (2014)

    Google Scholar 

  • J. Stewart, K. Pyatt, Lowering of ionization potentials in plasmas. Astrophys. J. 144, 1203 (1996)

    Article  ADS  Google Scholar 

  • C.R. Stillman, P.M. Nilson, S.T. Ivancic, I.E. Golovkin, C. Mileham, I.A. Begishev, D.H. Froula, Picosecond time-resolved measurements of dense plasma line shifts. PRE 95, 063204 (2017)

    Article  ADS  Google Scholar 

  • A. Thompson, I. Lindau, D. Attwood, Y. Liu, E. Gulliksn, P. Pianetta, M. Howells, A. Robinson, K.-J. Kim, J. Scofield, J. Kirz, J. Underwood, J. Kortright, G. Williams, H. Winick, X-ray Data Booklet, Center for X-ray Optics and Advanced Light Source, LBNL/PUB-490 Rev. 3 (2009)

    Google Scholar 

  • A. Unsöld, Physik der Sternatmosphären (Springer, 1955)

    Google Scholar 

  • S.M. Vinko, O. Ciricosta, J.S. Wark, Density functional theory calculations of continuum lowering in strongly coupled plasmas. Nature Comm. 5, 3533 (2014)

    Article  ADS  Google Scholar 

  • S.M. Vinko, G. Gregori, B. Nagler, T.J. Whitcher, J.S. Wark, U. Zastrau and E. Förster, S. Mazevet, J. Andreasson, S. Bajt, R.R. Fäustlin, S. Toleikis, and T. Tschentscher, J. Chalupsky, J. Cihelka, V. Hajkova, L. Juha, H. Chapman, T. Dzelzainis, D.Riley, E. Galtier, F.B. Rosmej, P. A. Heimann, M. Jurek, J. Krzywinski, R.W. Lee, A.J. Nelson, R. Sobierajski, Electronic structure of an XUV photo-generated solid-density aluminum plasma. Physical Review Letters 104, 225001 (2010)

    Google Scholar 

  • Ya.B. Zeldovich, Yu.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynmaic Phenomena (Dover Publications, 2002)

    Google Scholar 

  • G.B. Zimmermann, R.M. Moore, Pressure ionization in laser fusion target simulation. JQSRT 23, 417 (1980)

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Science and Engineering, Sorbonne University, Paris, France

    Frank B. Rosmej

  2. Moscow Institute of Physics and Technology, Moscow, Russia

    Valery A. Astapenko

  3. National Research Center “Kurchatov Institute”, Moscow, Russia

    Valery S. Lisitsa

Authors
  1. Frank B. Rosmej
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  2. Valery A. Astapenko
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  3. Valery S. Lisitsa
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Correspondence to Frank B. Rosmej .

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Rosmej, F.B., Astapenko, V.A., Lisitsa, V.S. (2021). Ionization Potential Depression. In: Plasma Atomic Physics. Springer Series on Atomic, Optical, and Plasma Physics, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-030-05968-2_8

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