Abstract
We explore QED and many-body effects in super-heavy elements up to Z = 173 using the multiconfiguration Dirac–Fock method. We study the effect of going beyond the average level approximation on the determination of the ground state of element 140 and compare with the recent work of Pekka Pyykkö on the periodic table for super-heavy elements (Pyykko¨, in Phys Chem Chem Phys, 13:161, 2011). We confirm that QED corrections are of the order of 1% on ionization energies. We show that the atomic number at which the 1s shell dives into the negative energy continuum is 173 and is not affected by the approximation employed to evaluate the electron–electron interaction.
Similar content being viewed by others
References
Hofmann S, Münzenberg G (2000) Rev Mod Phys 72(3):733
Oganessian YT, Utyonkoy VK, Lobanov YV, Abdullin FS, Polyakov AN, Shirokovsky IV, Tsyganov YS, Gulbekian GG, Bogomolov SL, Mezentsev AN, Iliev S, Subbotin VG, Sukhov AM, Voinov AA, Buklanov GV, Subotic K, Zagrebaev VI, Itkis MG, Patin JB, Moody KJ, Wild JF, Stoyer MA, Stoyer NJ, Shaughnessy DA, Kenneally JM, Lougheed RW (2004) Phys Rev C 69(2):021601 (R)
Hofmann S (2009) In: The euroschool lectures on physics with exotic beams, vol III. Lecture Notes in Physics, vol 764. Springer, Berlin/Heidelberg, pp 203–252
Münzenberg G, Armbruster P, Folger H, Heßberger F, Hofmann S, Keller J, Poppensieker K, Reisdorf W, Schmidt KH, Schött HJ, Leino ME, Hingmann R (1984) Zeitschrift für Physik A Hadrons and Nuclei 317(2):235
Münzenberg G, Armbruster P, Berthes G, Folger H, Heßberger FP, Hofmann S, Poppensieker K, Reisdorf W, Quint B, Schmidt KH, Schött HJ, Sümmerer K, Zychor I, Leino ME, Gollerthan U, Hanelt E (1986) Zeitschrift für Physik A Hadrons and Nuclei 324(4):489
Münzenberg G, Armbruster P, Berthes G, Folger H, Heßberger FP, Hofmann S, Keller J, Poppensieker K, Quint AB, Reisdorf W, Schmidt KH, Schött HJ, Sümmerer K, Zychor I, Leino ME, Hingmann R, Gollerthan U, Hanelt E (1987) Zeitschrift für Physik A Hadrons and Nuclei 328(1):49
Münzenberg G, Armbruster P, Heßberger FP, Hofmann S, Poppensieker K, Reisdorf W, Schneider JHR, Schneider WFW, Schmidt KH, Sahm CC, Vermeulen D (1982) Zeitschrift für Physik A Hadrons and Nuclei 309(1):89
Münzenberg G, Reisdorf W, Hofmann S, Agarwal YK, Heßberger FP, Poppensieker K, Schneider JRH, Schneider WFW, Schmidt KH, Schött HJ, Armbruster P, Sahm CC, Vermeulen D (1984) Zeitschrift für Physik A Hadrons and Nuclei 315(2):145
Münzenberg G, Hofmann S, Heßberger FP, Folger H, Ninov V, Poppensieker K, Quint AB, Reisdorf W, Schött HJ, Sümmerer K, Ambruster P, Leino MF, Ackermann D, Gollerthqn U, Hanelt E, Morawek W, Fujita Y, Schwab T, Tüler A (1988) Zeitschrift für Physik A 330:435
Hofmann S, Ninov V, Heßberger FP, Armbruster P, Folger H, Münzenberg G, Schött HJ, Popeko AG, Yeremin AV, Andreyev AN, Saro S, Janik R, Leino M (1995) Zeitschrift für Physik A Hadrons and Nuclei 350(4):277
Hofmann S, Ninov V, Heßberger FP, Armbruster P, Folger H, Münzenberg G, Schött HJ, Popeko AG, Yeremin AV, Andreyev AN, Saro S, Janik R, Leino M (1995) Zeitschrift für Physik A Hadrons and Nuclei 350(4):281
Hofmann S, Ninov V, Heßberger FP, Armbruster P, Folger H, Münzenberg G, Schött HJ, Popeko AG, Yeremin AV, Saro S, Janik R, Leino M (1996) Zeitschrift für Physik A Hadrons and Nuclei 354(3):229
Yakushev AB, Zvara I, Oganessian YT, Belozerov AV, Dmitriev SN, Eichler B, Hubener S, Sokol EA, Turler A, Yeremin AV, Buklanov GV, Chelnokov ML, Chepigin VI, Gorshkov VA, Gulyaev AV, Lebedev VY, Malyshev ON, Popeko AG, Soverna S, Szeglowski Z, Timokhin SN, Tretyakova SP, Vasko VM, Itkis MG (2004) Nucl Phys A 734:204
Eichler R, Aksenov NV, Belozerov AV, Bozhikov GA, Chepigin VI, Dmitriev SN, Dressler R, Gaggeler HW, Gorshkov VA, Haenssler F, Itkis MG, Laube A, Lebedev VY, Malyshev ON, Oganessian YT, Petrushkin OV, Piguet D, Rasmussen P, Shishkin SV, Shutov AV, Svirikhin AI, Tereshatov EE, Vostokin GK, Wegrzecki M, Yeremin AV (2007) Nat Biotechnol 447(7140):72
Morita K, Morimoto K, Kaji D, Akiyama T, Goto Si, Haba H, Ideguchi E, Kanungo R, Katori K, Koura H, Kudo H, Ohnishi T, Ozawa A, Suda T, Sueki K, Xu H, Yamaguchi T, Yoneda A, Yoshida A, Zhao Y (2004) J Phys Soc Japan 73:2593
Oganessian YT, Yeremin AV, Popeko AG, Bogomolov SL, Buklanov GV, Chelnokov ML, Chepigin VI, Gikal BN, Gorshkov VA, Gulbekian GG, Itkis MG, Kabachenko AP, Lavrentev AY, Malyshev ON, Rohac J, Sagaidak RN, Hofmann S, Saro S, Giardina G, Morita K (1999) Nat Biotechnol 400(6741):242
Oganessian YT, Utyonkov VK, Lobanov YV, Abdullin FS, Polyakov AN, Shirokovsky IV, Tsyganov YS, Gulbekian GG, Bogomolov SL, Gikal BN, Mezentsev AN, Iliev S, Subbotin VG, Sukhov AM, Buklanov GV, Subotic K, Itkis MG, Moody KJ, Wild JF, Stoyer NJ, Stoyer MA, Lougheed RW (1999) Phys Rev Lett 83(16):3154
Oganessian YT, Utyonkov VK, Lobanov YV, Abdullin FS, Polyakov AN, Shirokovsky IV, Tsyganov YS, Gulbekian GG, Bogomolov SL, Gikal BN, Mezentsev AN, Iliev S, Subbotin VG, Sukhov AM, Ivanov OV, Buklanov GV, Subotic K, Itkis MG, Moody KJ, Wild JF, Stoyer NJ, Stoyer MA, Lougheed RW (2000) Phys Rev C 62(4):041604
Düllmann CE, Schädel M, Yakushev A, Türler A, Eberhardt K, Kratz JV, Ackermann D, Andersson LL, Block M, Brüchle W, Dvorak J, Essel HG, Ellison PA, Even J, Gates JM, Gorshkov A, Graeger R, Gregorich KE, Hartmann W, Herzberg RD, Heßberger FP, Hild D, Hübner A, Jäger E, Khuyagbaatar J, Kindler B, Krier J (2010) Phys Rev Lett 104(25):252701
Oganessian YT, Utyonkov VK, Lobanov YV, Abdullin FS, Polyakov AN, Shirokovsky IV, Tsyganov YS, Gulbekian GG, Bogomolov SL, Gikal BN, Mezentsev AN, Iliev S, Subbotin VG, Sukhov AM, Ivanov OV, Buklanov GV, Subotic K, Itkis MG, Moody KJ, Wild JF, Stoyer NJ, Stoyer MA, Lougheed RW, Laue CA, Karelin YA, Tatarinov AN (2001) Phys Rev C 63(1):011301
Oganessian YT, Utyonkov VK, Lobanov YV, Abdullin FS, Polyakov AN, Shirokovsky IV, Tsyganov YS, Gulbekian GG, Bogomolov SL, Gikal BN, Mezentsev AN, Iliev S, Subbotin VG, Sukhov AM, Voinov AA, Buklanov GV, Subotic K, Zagrebaev VI, Itkis MG, Patin JB, Moody KJ, Wild JF, Stoyer MA, Stoyer NJ, Shaughnessy DA, Kenneally JM, Lougheed RW (2004) Phys Rev C (Nucl Phys) 69(5):054607
Oganessian YT, Utyonkov VK, Yu VL, Abdullin VL, Polyakov AN, Sagaidak RN, Shirokovsky IV, Yu ST, Voinov AA, Gulbekian GG, Bogomolov SL, Gikal BN, Mezentsev AN, Iliev S, Subbotin VG, Sukhov AM, Subotic K, Zagrebaev VI, Vostokin GK, Itkis MG, Moody KJ, Patin JB, Shaughnessy DA, Stoyer MA, Stoyer NJ, Wilk PA, Kenneally JM, Landrum JH, Wild JF, Lougheed RW (2006) Phys Rev C (Nucl Phys) 74(4):044602
Oganessian YT, Abdullin FS, Bailey PD, Benker DE, Bennett ME, Dmitriev SN, Ezold JG, Hamilton JH, Henderson RA, Itkis MG, Lobanov YV, Mezentsev AN, Moody KJ, Nelson SL, Polyakov AN, Porter CE, Ramayya AV, Riley FD, Roberto JB, Ryabinin MA, Rykaczewski KP, Sagaidak RN, Shaughnessy DA, Shirokovsky IV, Stoyer MA, Subbotin VG, Sudowe R (2010) Phys Rev Lett 104(14):142502
Oganessian YT, Utyonkov VK, Lobanov YV, Abdullin FS, Polyakov AN, Shirokovsky IV, Tsyganov YS, Gulbekian GG, Bogomolov SL, Gikal BN, Mezentsev AN, Iliev S, Subbotin VG, Sukhov AM, Voinov AA, Buklanov GV, Subotic K, Zagrebaev VI, Itkis MG, Patin JB, Moody KJ, Wild JF, Stoyer MA, Stoyer NJ, Shaughnessy DA, Kenneally JM, Lougheed RW (2004) Nucl Phys A 734:109
Schädel M (2007) Eur Phys J D 45(1):67
Werner FG, Wheeler JA (1958) Phys Rev 109(1):126
Pyykkö P (2011) Phys Chem Chem Phys 13:161
Indelicato P, Desclaux J (2005) Mcdfgme, a multiconfiguration dirac fock and general matrix elements program (release 2005). http://dirac.spectro.jussieu.fr/mcdf
Fricke B, Greiner W, Waber JT (1971) Theor Chem Acc: Theory Comput Model (Theoretica Chimica Acta) 21(3):235
Nefedov VI, Yarzhemcky VG, Trzhaskovskaya MB (2004) Russ J Inorg Chem 49(12):1871
Nefedov VI, Trzhaskovskaya MB, Yarzhemskii VG (2006) Doklady Phys Chem 408(2):149
Indelicato P, Desclaux JP (2010) The mcdfgme multiconfiguration dirac-fock program. V2010
Grant IP (1970) Adv Phys 19(82):747
Desclaux JP (1975) Comput Phys Commun 9:31
Desclaux JP (1993) Small systems. In: Clementi E (eds) Methods and techniques in computational chemistry, METTEC, vol A. STEF, Cagliary, p 253
Desclaux JP, Dolbeault J, Esteban MJ, Indelicato P, Séré E (2003) In: Le Bris C, De Franceschi M (eds) Computational chemistry, handbook of numerical analysis, vol X. Elsevier, Amsterdam, p 1032
Grant IP (2007) Relativistic quantum theory of atoms and molecules: theory and computation. Springer, New York
Grant IP (2010) J Phys B: At Mol Opt Phys 43(7):074033
Gorceix O, Indelicato P (1988) Phys Rev A 37:1087
Lindroth E, Mårtensson-Pendrill AM (1989) Phys Rev A 39(8):3794
Indelicato P (1986) J Phys B: At Mol Opt Phys 19:1719
Indelicato P, Santos JP, Boucard S, Desclaux JP (2007) Eur Phys J D 45(1):155
Angeli I (2004) At Data Nucl Data Table 87(2):185
Dyall KG, Grant IP, Johnson CT, Parpia FA, Plummer EP (1989) Comp Phys Commun 55:425
Cheng KT, Johnson WR (1976) Phys Rev A 14(6):1943
Soff G, Schlüter P, Müller B, Greiner W (1982) Phys Rev Lett 48(21):1465
Neghabian AR (1983) Phys Rev A 27(5):2311
Mohr PJ (1982) Phys Rev A 26(5):2338
Mohr PJ, Kim YK (1992) Phys Rev A 45(5):2727
Indelicato P, Mohr PJ (1998) Phys Rev A 58(1):165
Indelicato P, Mohr PJ (1998) Hyperfine Interact 114(1–4):147
LeBigot É O, Indelicato P, Mohr PJ (2001) Phys Rev A 64(5):052508 (14)
Cheng KT, Johnson WR, Sapirstein J (1991) Phys Rev Lett 66(23):2960
Blundell SA (1992) Phys Rev A 46(7):3762
Blundell SA (1993) Phys Rev A 47(3):1790
Cheng KT, Chen MH, Sapirstein J (2000) Phys Rev A 62(3):054501
Indelicato P, Mohr PJ (2001) Phys Rev A 63(4):052507
Chen MH, Cheng KT, Beiersdorfer P, Sapirstein J (2003) Phys Rev A 68(2):022507
Sapirstein J, Cheng KT (2006) Phys Rev A 73(1):012503
Pyykkö P, Tokman M, Labzowsky LN (1998) Phys Rev A 57(2):R689
Labzowsky L, Goidenko I, Tokman M, Pyykkö P (1999) Phys Rev A 59(4):2707
Thierfelder C, Schwerdtfeger P (2010) Phys Rev A 82(6):062503
Goidenko I, Tupitsyn I, Plunien G (2007) Eur Phys J D 45(1):171
Goidenko IA (2009) Eur Phys J D 55(1):35
Indelicato P, Boucard S, Lindroth E (1998) Eur Phys J D 3(1):29
Deslattes RD, Kessler EG Jr, Indelicato P, de Billy L, Lindroth E, Anton J (2003) Rev Mod Phys 75(1):35
Gaston N, Schwerdtfeger P, Nazarewicz W (2002) Phys Rev A 66(6):062505
Andersson LL, Rudolph D, Golubev P, Herzberg RD, Hoischen R, Merchán E, Ackermann D, Düllmann CE, Eberhardt K, Even J, Gerl J, Heßberger FP, Jäger E, Khuyagbaatar J, Kojouharov I, Kratz JV, Krier J, Kurz N, Prokopowicz W, Schädel M, Schaffner H, Schausten B, Schimpf E, Semchenkov A, Türler A, Wollersheim HJ, Yakushev A, Thörle-Pospiech P, Hartmann W, Hübner A, Lommel B, Kindler B, Steiner J (2010) Nucl Instr Meth Phys Res A: Accelerators, Spectrometers, Detectors and Associated Equipment 622(1):164
Thierfelder C, Schwerdtfeger P, Heßberger F, Hofmann S (2008) Eur Phys J A-Hadrons and Nuclei 36(2):227
Düllmann CE, Schädel M, Yakushev A, Türler A, Eberhardt K, Kratz JV, Ackermann D, Andersson LL, Block M, Brüchle W, Dvorak J, Essel HG, Ellison PA, Even J, Gates JM, Gorshkov A, Graeger R, Gregorich KE, Hartmann W, Herzberg RD, Heßberger FP, Hild D, Hübner A, Jäger E, Khuyagbaatar J, Kindler B, Krier J (2010) Phys Rev Lett 104(25):252701
Mohr PJ (1974) Ann Phys 88(1):52
Indelicato P, Gorceix O, Desclaux JP (1987) J Phys B: At Mol Phys 20:651
Indelicato P, Desclaux JP (1990) Phys Rev A 42(9):5139
Boucard S, Indelicato P (2000) Eur Phys J D 8(1):59
Greiner, W (eds) (1983) Quantum electrodynamics of strong fields. Plenum Press, New York
Greiner W, Müller B, Rafelski J (1985) Quantum electrodynamics of strong fields. Springer-Verlag, Berlin
Borschevsky A, Eliav E, Vilkas MJ, Ishikawa Y, Kaldor U (2007) Phys Rev A 75(4):042514
Eliav E, Kaldor U, Ishikawa Y (1995) Phys Rev A 52(1):291
Borschevsky A, Eliav E, Vilkas MJ, Ishikawa Y, Kaldor U (2007) Eur Phys J D 45(1):115
Eliav E, Kaldor U, Ishikawa Y (1995) Phys Rev Lett 74(7):1079
Eliav E, Kaldor U, Schwerdtfeger P, Hess BA, Ishikawa Y (1994) Phys Rev Lett 73(24):3203
Eliav E, Kaldor U, Ishikawa Y (1995) Phys Rev A 52(4):2765
Eliav E, Kaldor U, Ishikawa Y, Seth M, Pyykkö P (1996) Phys Rev A 53(6):3926
Landau A, Eliav E, Ishikawa Y, Kaldor U (2001) J Chem Phys 114(7):2977
Borschevsky A, Pershina V, Eliav E, Kaldor U (2009) Chem Phys Lett 480(1–3):49
Eliav E, Kaldor U, Ishikawa Y (1998) Mol Phys 94(1):181
Eliav E, Kaldor U, Ishikawa Y, Pyykkö P (1996) Phys Rev Lett 77(27):5350–5352
Goidenko I, Labzowsky L, Eliav E, Kaldor U, Pyykkö P (2003) Phys Rev A 67(2):020102
Eliav E, Landau A, Ishikawa Y, Kaldor U (2002) J Phys B: At Mol Opt Phys 35(7):1693
Dinh TH, Dzuba VA, Flambaum VV (2008) Phys Rev A 78(6):062502
Backe H, Dretzke A, Fritzsche S, Haire R, Kunz P, Lauth W, Sewtz M, Trautmann N (2005) Hyperfine Interact 162(1–4):3
Liu Y, Hutton R, Zou Y (2007) Phys Rev A 76(6):062503
Gaigalas G, Gaidamauskas E, Rudzikas Z, Magnani N, Caciuffo R (2010) Phys Rev A 81(2):022508
Acknowledgments
PI acknowledges partial support by the Helmholtz Alliance HA216/EMMI for this research. Laboratoire Kastler Brossel is “Unité Mixte de Recherche n° 8552” of École Normale Supérieure, CNRS and Université Pierre et Marie Curie. PI wishes to thank Jean-Paul Desclaux with whom the mcdfgme 2010 version is being developed, and Valeria Pershina for interesting discussions and for bringing to his attention Refs. [30, 31]. All authors wish to thank Pekka Pyykkö for many years of fruitful collaboration. We should mention that both the subject and the title of the present paper were inspired by an entangled influence of Pekka.
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor Pekka Pyykkö on the occasion of his 70th birthday and published as part of the Pyykkö Festschrift Issue.
Rights and permissions
About this article
Cite this article
Indelicato, P., Bieroń, J. & Jönsson, P. Are MCDF calculations 101% correct in the super-heavy elements range?. Theor Chem Acc 129, 495–505 (2011). https://doi.org/10.1007/s00214-010-0887-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00214-010-0887-3