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Relative energy level shifts of hydrogen-like carbon bound-states in dense matter

Published online by Cambridge University Press:  22 December 2010

C.-V. Meister ,
M. Imran  and
D.H.H. Hoffmann
C.-V. Meister*
Affiliation:
Technische Universität Darmstadt, Darmstadt, Germany
M. Imran
Affiliation:
Technische Universität Darmstadt, Darmstadt, Germany
D.H.H. Hoffmann
Affiliation:
Technische Universität Darmstadt, Darmstadt, Germany
*
Address correspondence and reprint requests to: C.-V. Meister, Technische Universität Darmstadt, Schlossgartenstraße 9, Darmstadt, Germany. E-mail: c.v.meister@skmail.ikp.physik.tu-darmstadt.de
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Abstract

The aim of the present work is the further development of the thermodynamics of hydrogen-like plasmas with densities on the order of 1027–1029 m−3 at temperatures of 106−108 K. Therefore, the Jacobi-Padé approximation for the so-called relative energy level shifts is applied to a quasineutral plasma consisting of six-fold and five-fold ionized carbon atoms and electrons. The relative energy level shift of the five-fold ionized carbon is determined by the difference between Coulomb and Debye potential, and by the kinetic energy of the particles. The shift caused by the kinetic energy (KES) has to be found considering the momentum space of the particles, so that nine-fold integrals in phase space have to be calculated. Quantum-physically, former numerical calculations of KES were only performed for particle states with zero angular quantum numbers. In the present work, a detailed, to a large extent analytical analysis of the KES is given for any angular quantum number, enabling also an improved analysis of future further-developed Jacobi-Padé formulae. Relative energy shifts of the bound-states of the fivefold ionized carbon are numerically obtained as function of the Mott parameter of the plasma. Dependencies of the shifts on main quantum numbers and orbital quantum numbers are discussed.

Keywords

Carbon plasmaHydrogen-like plasmasMott transitionPlasma theoryRelative energy level shiftsWarm dense matter
Type
Research Article
Information
Laser and Particle Beams , Volume 29 , Issue 1 , March 2011 , pp. 17 - 27
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Abramowitz, M. & Stegun, I.A. (eds) (1970). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover Publications.Google Scholar
Beule, D., Ebeling, W., Förster, A., Juranek, H., Nagel, S., Redmer, R. & Röpke, G. (1999a). Equation of state for hydrogen below 10000 K: From the fluid to the plasma. Phys. Rev. B. 59, 14177–14181.CrossRefGoogle Scholar
Beule, D., Ebeling, W., Förster, A., Juranek, H., Redmer, R. & Röpke, G. (1999b). Hydrogen equation of state and plasma phase transition. Contr. Plasma Phys. 39, 21–24.CrossRefGoogle Scholar
Ebeling, W., Blaschke, D., Redmer, R., Reinholz, H. & Röpke, G. (2009). The influence of Pauli blocking effects on the properties of dense hydrogen. J. Phys. A, Math. Theor. 42, 214033.CrossRefGoogle Scholar
Ebeling, W., Blaschke, D., Redmer, R., Reinholz, H. & Röpke, G. (2010). The influence of Pauli blocking effects on the Mott transition in dense hydrogen. In Metal to Nonmetal Transitions, eds. Redmer, R., Holst, B., Hensel, F.Berlin-Heidelberg: Springer.Google Scholar
Ebeling, W., Förster, A., Fortov, V.E., Gryaznov, V.K. & Polishchuk, A.Y. (1991). Thermophysical Properties of Hot Dense Plasmas. Stuttgart-Leipzig: Teubner Verlag.Google Scholar
Ebeling, W., Hache, H., Juranek, H., Redmer, R. & Röpke, G. (2005). Pressure ionization and transitions in dense hydrogen. Contr. Plasma Phys. 45, 160–167.CrossRefGoogle Scholar
Ebeling, W. & Kilimann, K. (1989). Ionization energy and level shifts of multiply charged ions in nonideal plasmas. J. Phys. Sci. 44a, 519–523.Google Scholar
Ebeling, W., Kraeft, W.D. & Kremp, D. (1976). Theory of bound states and ionization equilibrium in plasmas and solids, series Ergebnisse der Plasmaphysik und der Gaselektronik, Band 5. Berlin: Akademie-Verlag.Google Scholar
Ebeling, W. & Leike, J. (1991). Kinetics of ionization-recombination processes in nonideal hydrogen plasmas. Phys. A 170, 682–688.CrossRefGoogle Scholar
Ebeling, W., Leike, J. & Leonhardt, U. (1991a). Bound states and ionization kinetics in dense plasmas. Proc. 8th Am. Phys. Soc. Conf., Atomic Processes in Plasmas. Portland, Maine, 25–29.Google Scholar
Ebeling, W., Meister, C.-V., Sändig, R. & Kraeft, W.-D. (1979). Pressure ionization in nonideal alkali plasmas. Annal. der Phys. 36, 321–332.CrossRefGoogle Scholar
Ebeling, W., Redmer, R., Reinholz, H. & Röpke, G. (2008). Thermodynamics and phase transitions in dense hydrogen - the role of bound state energy shifts. Contrib. Plasma Phys. 48, 670–685.CrossRefGoogle Scholar
Endres, M. (2010) Einfluss der Kernfusion auf das nichtideale Sonnenplasma, Bachelor thesis, Darmstadt: Technische Universität.Google Scholar
Fisher, D.V., Henis, Z., Eliezer, S. & Meyer-Ter-Vehn, J. (2006a). Core holes, charge disorder, and transition from metallic to plasma properties in ultrashort pulse irradiation of metals. Laser Part. Beams 24, 81–94.CrossRefGoogle Scholar
Fisher, D.V., Henis, Z., Eliezer, S. & Meyer-Ter-Vehn, J. (2006b). Core holes, charge disorder, and transition from metallic to plasma properties in ultrashort pulse irradiation of metals. Laser Part. Beams 24, 332.CrossRefGoogle Scholar
Förster, A., Beule, D., Conrads, H. & Ebeling, W. (1998). Highly ionised carbon in capillary discharge plasma. Contr. Plasma Phys. 38, 655–660.CrossRefGoogle Scholar
Fortmann, C., Bornath, T., Redmer, R., Reinholz, H., Röpke, G., Schwarz, V. & Thiele, R. (2009). X-ray Thomson scattering cross-section in strongly correlated plasmas. Laser Part. Beams 27, 311–319.CrossRefGoogle Scholar
Günter, S., Hitzschke, L. & Röpke, G. (1991). Hydrogen spectral lines with the inclusion of dense plasma effects. Phys. Rev. A 44, 6834–6844.CrossRefGoogle ScholarPubMed
Gradshteyn, I.S. & Ryzhik, I.M. (1994). Table of integrals, series, and products. London: Academic Press.Google Scholar
Hitzschke, L. & Röpke, G. (1988). Relationship between kinetic theory and Greens function approach with respect to electron shift and the broadening of spectral lines. Phys. Rev. A 37, 4991–4994.CrossRefGoogle ScholarPubMed
Hoffmann, D.H.H., Blazevic, A., Ni, P., Rosmej, O., Roth, M., Tahir, N.A., Tauschwitz, A., Udrea, S., Varentsov, D., Weyrich, K. & Maron, Y. (2005). Present and future perspectives for high energy density physics with intense heavy ion and laser beams. Laser Part. Beams 23, 47–53.CrossRefGoogle Scholar
Hoffmann, D.H.H., Tahir, N.A., Udrea, S., Rosmej, O., Meister, C.-V., Varentsov, D., Roth, M., Schaumann, G., Frank, A., Blazevic, A., Ling, J., Hug, A., Menzel, J., Hessling, Th., Harres, K., Günther, M., El-Moussati, S., Schumacher, D. & Imran, M. (2010). High energy density physics with heavy ion beams and related interaction phenomena. Contr. Plasma Phys. 50, 17–25.CrossRefGoogle Scholar
Kilimann, K. & Ebeling, W. (1990). Energy-gap and line shifts for H-like ions in dense plasmas. J. Phys. Sci. 45, 613–617.Google Scholar
Kilimann, K., Kraeft, W.-D. & Kremp, D. (1977). Lifetime and level shifts of bound-states in plasmas. Phys. Lett A 61, 393–395.CrossRefGoogle Scholar
Knudson, M.D., Desjarlais, M.P. & Dolan, D.H. (2008). Shock-wave exploration of the high-pressure phases of carbon. Sci. 322, 1822–1825.CrossRefGoogle ScholarPubMed
Kraeft, W.D., Kremp, D., Ebeling, W. & Röpke, G. (1986). Quantum statistics of charged particle systems. New York: Plenum Press.CrossRefGoogle Scholar
Kraeft, W.D., Kremp, D., Kilimann, K. & De Witt, H.E. (1990). Two-body problem in a many-particle system. Phys. Rev. A 42.CrossRefGoogle Scholar
Kremp, D., Schlanges, M. & Kraeft, W.D. (2005). Quantum statistics of nonideal plasmas. Berlin: Springer.Google Scholar
Kuehl, T., Ursescu, D., Bagnoud, V., Javorkova, D., Rosmej, O., Cassou, K., Kazamias, S., Klisnick, A., Ros, D., Nickles, P., Zielbauer, B., Dunn, J., Neumayer, P., Pert, G. & The Phelix Team. (2007). Optimization of the non-normal incidence, transient pumped plasma X-ray laser for laser spectroscopy and plasma diagnostics at the facility for antiproton and ion research (FAIR). Laser Part. Beams 25 (1), 93–97.CrossRefGoogle Scholar
Meister, C.-V. (1982). On the theory of conductivity and thermodynamics of nonideal plasmas, PhD, University Rostock.Google Scholar
Meister, C.-V., Endres, M. & Hoffmann, D.H.H. (2010). Static screening effects and influence of nuclear fusion on the pressure of the plasma mixture in the solar interior, in preparation for Astronomical Notes.Google Scholar
Meister, C.-V., Staude, J. & Pregla, A.V. (1999). An attempt to estimate nonideal effects on the electron partial pressure in the solar interior up to density order 5/2. Astronomische Nachrichten, 320, 43–52.3.0.CO;2-P>CrossRefGoogle Scholar
Nardi, E., Fisher, D.V., Roth, M., Blazevic, A., & Hoffmann, D.H.H. (2006). Charge state of Zn projectile ions in partially ionized plasma: Simulations. Laser and Particle Beams, 24, 131–41.CrossRefGoogle Scholar
Nardi, E., Maron, Y. & Hoffmann, D.H.H. (2007). Plasma diagnostics by means of the scattering of electrons and proton beams. Laser and Particle Beams 25, 489–495.CrossRefGoogle Scholar
Nardi, E., Maron, Y. & Hoffmann, D.H.H. (2009). Dynamic screening and charge state of fast ions in plasma and solids. Laser and Particle Beams 27, 355–61.CrossRefGoogle Scholar
Ni, P.A., Kulish, M.I., Mintsev, V., Nikolaev, D.N., Ternovoi, V.Y., Hoffmann, D.H.H., Udrea, S., Hug, A., Tahir, N.A. & Varentsov, D. (2008). Temperature measurement of warm-dense-matter generated by intense heavy-ion beams. Laser and Particle Beams 26, 583–589.CrossRefGoogle Scholar
Rogers, F.J., Graboske, H.C. Jr. & Harwood, D.J. (1970). Bound eigenstates of static screened coulomb potential. Physical Review A 1, 1577–1583.CrossRefGoogle Scholar
Röpke, G., Kilimann, K., Kremp, D. & Kraeft, W.-D. (1978). 2-particle energy shifts in low-density non-ideal plasmas. Phys. Lett. A 68, 329–332.CrossRefGoogle Scholar
Röpke, G., Kilimann, K., Kremp, D., Kraeft, W.D. & Zimmermann, R. (1978). The influence of dynamical effects on the two-particle states (excitons) in the electron-hole plasma. Phys. Stat. Solidi b 88, K59–K63.Google Scholar
Schaumann, G., Schollmeier, M.S., Rodriguez-Prieto, G., Blazevic, A., Brambrink, E., Geissel, M., Korostiy, S., Pirzadeh, P., Roth, M., Rosmej, F.B., Faenov, A. Ya., Pikuz, T.A., Tsigutkin, K., Maron, Y., Tahir, N.A. & Hoffmann, D.H.H. (2005). High energy heavy ion jets emerging from laser plasma generated by long pulse laser beams from the NHELIX laser system at GSI Laser and Part. Beams 23, 503–512.Google Scholar
Tahir, N.A., Schmidt, R., Brugger, M., Shutov, A., Lomonosov, I.V., Piriz, A.R. & Hoffmann, D.H.H. (2009a). Simulations of full impact of the Large Hadron Collider beam with a solid graphite target, Laser and Part. Beams 27, 475–483.Google Scholar
Tahir, N.A., Matveichev, A., Kim, V., Ostrik, A., Shutov, A., Sultanov, V., Lomonosov, I.V., Piriz, A.R. & Hoffmann, D.H.H. (2009b). Three-dimensional simulations of a solid graphite target for high intensity fast extracted uranium beams for the Super-FRS, Laser and Part. Beams 27, 9–17.Google Scholar
Tahir, N.A., Weick, H., Shutov, A., Kim, V., Matvechev, A.V., Ostrik, A., Sultanov, V., Lomonosov, I.V., Piriz, A.R., Lopez Cela, J.J. & Hoffmann, D.H.H. (2008b) Simulations of a solid graphite target for high intensity fast extracted uranium beams for the Super-FRS, Laser and Part. Beams 26, 411–423.Google Scholar
Tahir, N.A., Kim, V.V., Matvechev, A.V., Ostrik, A., Shutov, A., Lomonosov, I.V., Piriz, A.R., Lopez Cela, J.J. & Hoffmann, D.H.H. (2008a). High energy density and beam induced stress related issues in solid graphite Super-FRS fast extraction targets, Laser and Part. Beams 26, 273–286.Google Scholar
Zimmermann, R., Kilimann, K., Kraeft, W.-D., Kremp, D. & Röpke, G. (1978). Dynamical screening and self-energy of excitons in the electron-hole plasma. Phys. Stat. Solidi b 90, 175–187.CrossRefGoogle Scholar