LKB - Metrology of simple systems and fundamental tests

MDFGME, a general purpose Multiconfiguration Dirac-Foc program

The current version of the code is 2022.3

The main properties of the 2022.3 code version are the following:

  • Can accommodate arbitrary number of open-shells (within your computer memory and disk space) [2]
  • Perturbative [3, 4] or Self-consistent Breit interaction inclusion [3].
  • Automatic single and double excitation generation, with Brillouin theorem option [5]
  • Full JJ⇒LSJ recoupling
  • Many different nuclear models (Fermi, 3-parameters Fermi [6], Fourier-Bessel [6], Sum of Gaussian[7], Gaussian[8], Exponential[8]…)
  • Full self- consistent treatment of Uehling vacuum polarization [8]
  • First and Second order QED corrections whenever known
  • Improved nuclear recoil corrections [9, 10] based on [11]
  • Full projection operator included to eliminate negative energy continuum [12, 13]
  • Large variety of numerical methods to help convergence in difficult cases
  • Super-heavy elements [14-18]
  • Can evaluate electronic atoms with exotic particles attached (muons [19], pions [20, 21], antiproton [22], kaon [21, 23, 24], sigma [25])
  • Can do calculations for positronium and muonium

Operators that can be evaluated are the following (including Breit or vacuum polarization contribution, by evaluating wavefunction self-consistently with these contributions):

  • Landé g-factors [15, 26, 27]
  • Diagonal and non-diagonal hyperfine matrix elements (including Bohr-Weisskopf effect) [28-34]
  • parity violation [35-37]
  • Auger and photoinisation cross sections (in the frozen orbitals of the initial state) [38]
  • All multipole radiative transition rates, with non-orthogonal initial and final states, and contribution from negative energy continuum [28, 39, 40]
  • Stark matrix elements
  • Electronic excitation cross sections at the born approximation
  • Scalar product with full relaxation of two wavefunctions
  • Binary encounter Bethe model for electron-impact ionization [41, 42]
  • Shake-off probability [43, 44]
  • Magnetic part of the anomalous magnetic moment contribution to antiprotonic atoms [22, 45]
  • Two-photon transition rates for one-electron atoms, including case with resonant intermediate states [46-48]

New developments:

The 2022.3 version has many new features compared to the 2005.1 version, mostly in an experimental stage:

  • Full relaxation can now be included in the Auger and photoionization cross section
  • EDM matrix elements can be evaluated
  • Angular momentum of exotic particles and of the electronic part of the atom can be independently specified
  • For the evaluation of the Bohr-Weiskopf effect, the magnetic moment distribution of the nucleus can be specified independently of the charge distribution
  • Automatic generation of triple excitations
  • Vacuum polarization by milli-charged particles for normal and exotic atoms
  • Shift due to massive bosons interaction with the nucleus
  • The self-energy screening correction is now evaluated by two different methods, the Welton method, historically implemented in 1987-1990 [49, 50], and the model operator method [51], including super-heavy elements up to Z=170 [52].

The 2005 version, in precompiled form, is available from this web page, upon registration.


[1]       A Multiconfiguration Relativistic Dirac-Fock Program, J.P. Desclaux. Computer Physics Communications 9,31-45 (1975).

[2]       Détermination des fonctions propres des opérateurs moments angulaires L2, S2 et J2 en couplage (J.J.). Application à l’étude de certains effets relativistes, N. Bessis,  G. Bessis and J.-P. Desclaux. Journal de Physique 31,C4-231 (1970).

[3]       Effect of the complete Breit interaction on two-electron ion energy levels., O. Gorceix and P. Indelicato. Phys. Rev. A 37, 1087 (1988).

[4]       MCDF studies of two electron ions I: Electron-electron interaction, O. Gorceix,  P. Indelicato and J.P. Desclaux. J. Phys. B 20, 639-650 (1987).

[5]       Nonrelativistic limit of Dirac-Fock codes: The role of Brillouin configurations, P. Indelicato,  E. Lindroth and J.P. Desclaux. Phys. Rev. Lett. 94, 013002 (2005).

[6]       Nuclear Charge-Density-Distribution Parameters from Elastic Electron Scattering, H. De Vries,  C.W. De Jager and C. De Vries. Atomic Data and Nuclear Data Tables 36, 495-536 (1987).

[7]       Model-independent nuclear charge densities from elastic electron scattering, I. Sick. Nucl. Phys. A 218, 509-541 (1974).

[8]       Nonperturbative evaluation of some QED contributions to the muonic hydrogen n=2 Lamb shift and hyperfine structure, P. Indelicato. Phys. Rev. A 87, 022501 (2013).

[9]       Relativistic calculations of 1s 2 2s2p level splitting in Be-like Kr, J.M. Sampaio,  F. Parente,  C. Nazé,  M. Godefroid,  P. Indelicato and J.P. Marques. Physica Scripta 2013, 014015 (2013).

[10]     Mass- and field-shift isotope parameters for the $2s\ensuremath{-}2p$ resonance doublet of lithiumlike ions, J. Li,  C. Nazé,  M. Godefroid,  S. Fritzsche,  G. Gaigalas,  P. Indelicato and P. Jönsson. Phys. Rev. A 86, 022518 (2012).

[11]     QED theory of the nuclear recoil effect in atoms, V.M. Shabaev. Phys. Rev. A 57, 59-67 (1998).

[12]     Projection operators in the Multiconfiguration Dirac-Fock Method, P. Indelicato and J.P. Desclaux. Physica Scripta T46, 110-114 (1993).

[13]     Projection operators in Multiconfiguration Dirac-Fock calculations. Application to the ground state of heliumlike ions., P. Indelicato. Phys. Rev. A 51, 1132-1145 (1995).

[14]     Effects of the Breit interaction on the 1s binding energy of  super heavy elements., P. Indelicato. J. Phys. B 19,1719 (1986).

[15]     QED and relativistic corrections in superheavy elements, P. Indelicato,  J.P. Santos,  S. Boucard and J.-P. Desclaux. Eur. Phys. J D 45, 155-170 (2007).

[16]     Are MCDF calculations 101% correct in the superheavy elements range?, P. Indelicato,  J. Bieroń and P. Jönsson. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 129, 495-505 (2011).

[17]     Relativistic calculations of atomic parameters in Ununoctium, J.M. Sampaio,  M. Guerra,  T.I. Madeira,  F. Parente,  P. Indelicato,  J.P. Santos and J.P. Marques. J. Phys. Conf. Ser. 635, 092095 (2015).

[18]     Dirac-Fock calculations of $K\text{-}$, $L\text{-}$, and $M$-shell fluorescence and Coster-Kronig yields for Ne, Ar, Kr, Xe, Rn, and Uuo, J.M. Sampaio,  T.I. Madeira,  M. Guerra,  F. Parente,  J.P. Santos,  P. Indelicato and J.P. Marques. Phys. Rev. A 91, 052507 (2015).

[19]     Low-energy X-ray standards from hydrogenlike pionic atoms, D.F. Anagnostopoulos,  D. Gotta,  P. Indelicato and L.M. Simons. Phys. Rev. Lett. 91, 240801 (2003).

[20]     Measurement of the charged pion mass using X-ray spectroscopy of exotic atoms, M. Trassinelli, D.F. Anagnostopoulos, G. Borchert, A. Dax, J.P. Egger, D. Gotta, M. Hennebach, P. Indelicato, Y.W. Liu, B. Manil, N. Nelms, L.M. Simons and A. Wells. Physics Letters B 759, 583 (2016).

[21]     Relativistic calculations of pionic and kaonic atoms’ hyperfine structure M. Trassinelli and P. Indelicato. Phys. Rev. A 76, 012510-7 (2007).

[22]     X-ray transitions from antiprotonic noble gases, D. Gotta,  K. Rashid,  B. Fricke,  P. Indelicato and L.M. Simons. Eur. Phys. J D 47, 11-26 (2008).

[23]     X-ray energies of circular transitions and electron screening in kaonic atoms, J.P. Santos,  F. Parente,  S. Boucard,  P. Indelicato and J.P. Desclaux. Phys. Rev. A 71, 032501-8 (2005).

[24]     Energy Levels of Hydrogenlike Kaonic Atoms, J.P. Santos,  F. Parente,  S. Boucard and P. Indelicato. Hyp. Int. 146, 325-329 (2003).

[25]     X-ray energies of circular transitions in sigmonic atoms, J.P. Santos,  F. Parente,  S. Boucard and P. Indelicato. Nucl. Instrum. Methods B 235, 206-209 (2005).

[26]     The gJ factor in the ground state of Ca+, G. Tommaseo,  T. Pfeil,  G. Revalde,  G. Werth,  P. Indelicato and J.P. Desclaux. Eur. Phys. J D 25, 113-121 (2003).

[27]     Correlation and relativistic effects on Landé gj factors of atomic ions, P. Indelicato,  A.M. Mårtensson-Pendrill,  W. Quint and J.P. Desclaux. Hyp. Int. 146-147, 127-131 (2003).

[28]     Effect of the hyperfine structure on the 2 3P1 and the 2 3P0 lifetime in heliumlike ions, P. Indelicato,  F. Parente and R. Marrus. Phys. Rev. A 40, 3505-3514 (1989).

[29]     M1, M2 and hyperfine-induced decay rates in Mg-like ions of Co, Ni and Cu measured at a heavy-ion storage ring, E. Träbert,  M. Grieser,  J. Hoffmann,  C. Krantz,  S. Reinhardt,  R. Repnow,  A. Wolf and P. Indelicato. New Journal of Physics 13, 023017 (2011).

[30]     Hyperfine quenching of the 4s4p 3P0 level in Zn-like ions, J.P. Marques,  F. Parente and P. Indelicato. Eur. Phys. J D 41, 457-465 (2007).

[31]     Relativistic Many-Body and QED effects on the hyperfine structure of lithium-like ions, S. Boucard and P. Indelicato. Eur. Phys. J D 8, 59-73 (2000).

[32]     Hyperfine Quenching of the 3s23p63d4 J=4 level in titaniumlike ions, F. Parente,  J.P. Marques and P. Indelicato. EPL 26, 437-442 (1994).

[33]     Hyperfine quenching of the 1s2 2s2 2p6 3s3p 3P0 level in magnesium-like ions, J.P. Marques,  F. Parente and P. Indelicato. Atomic Data and Nuclear Data Tables 55, 157-170 (1993).

[34]     Hyperfine Quenching of the 1s2 2s2p3P0  Level in Berylliumlike Ions, J.P. Marques,  F. Parente and P. Indelicato. Phys. Rev. A 47, 929-935 (1993).

[35]     Prospects for an atomic parity-violation experiment in U90+, A. Schäfer,  G. Soff,  P. Indelicato,  B. Müller and W. Greiner. Phys. Rev. A 40, 7362-7365 (1989).

[36]     Stark quenching for the 1s22s2p 3P0 level in beryllium-like ions and parity-violating effects, M. Maul,  A. Schäfer and P. Indelicato. J. Phys. B 31, 2725-2734 (1998).

[37]     Prospects for Parity-nonconservation Experiments with Highly Charged Heavy Ions, M. Maul,  A. Schäfer,  W. Greiner and P. Indelicato. Phys. Rev. A 53, 3915-3925 (1996).

[38]     Estimation of the ratio of double and single Auger transition rates for the L shell of Kr, Nb and Gd, J.P. Marques,  F. Parente,  P. Indelicato and J.P. Desclaux. J. Phys. B 31, 2897-2901 (1998).

[39]     Electric Dipole, Quadrupole and Magnetic Dipole Transition Probabilities of Na-Like ions, D.H. Baik,  Y.G. Ohr,  K.S. Kim,  J.M. Lee,  P. Indelicato and Y.-K. Kim. Atomic Data and Nuclear Data Tables 47, 177-203 (1991).

[40]     Correlation and Negative Continuum effects for the relativistic M1 transition in two-electron ions using the multiconfiguration Dirac-Fock method, P. Indelicato. Phys. Rev. Lett. 77, 3323-3326 (1996).

[41]     Binary-encounter-dipole model for electron-impact ionization, Y.-K. Kim and M.E. Rudd. Phys. Rev. A 50,3954-3967 (1994).

[42]     Extension of the binary-encounter-dipole model to relativistic incident electrons, Y.-K. Kim,  J.P. Santos and F. Parente. Phys. Rev. A 62, 052710 (2000).

[43]     Structure of $K{\ensuremath{\alpha}}_{1,2}$- and $K{\ensuremath{\beta}}_{1,3}$-emission x-ray spectra for Se, Y, and Zr, Y. Ito, T. Tochio, M. Yamashita, S. Fukushima, A.M. Vlaicu, J.P. Marques, J.M. Sampaio, M. Guerra, J.P. Santos, Ł. Syrocki, K. Słabkowska, E. Wȩder, M. Polasik, J. Rzadkiewicz, P. Indelicato, Y. Ménesguen, M.C. Lépy and F. Parente. Phys. Rev. A 102, 052820 (2020).

[44]     $K{\ensuremath{\alpha}}_{1,2}$ x-ray linewidths, asymmetry indices, and $[KM]$ shake probabilities in elements Ca to Ge and comparison with theory for Ca, Ti, and Ge, Y. Ito, T. Tochio, H. Ohashi, M. Yamashita, S. Fukushima, M. Polasik, K. Słabkowska, Ł. Syrocki, E. Szymańska, J. Rzadkiewicz, P. Indelicato, J.P. Marques, M.C. Martins, J.P. Santos and F. Parente. Phys. Rev. A 94, 042506 (2016).

[45]     Balmer a transitions in antiprotonic hydrogen and deuterium, D. Gotta, D.F. Anagnostopoulos, M. Augsburger, G. Borchert, C. Castelli, D. Chatellard, J.P. Egger, P. El-Khoury, H. Gorke, P. Hauser, P. Indelicato, K. Kirch, S. Lenz, T. Siems and L.M. Simons. Nucl. Phys. A 660, 283-321 (1999).

[46]     Resonance effects on the two-photon emission from hydrogenic ions, P. Amaro,  J.P. Santos,  F. Parente,  A. Surzhykov and P. Indelicato. Phys. Rev. A 79, 062504 (14) (2009).

[47]     Spontaneous relativistic two-photon decay rate mathematical expression in heliumlike systems, J.P. Santos,  P. Patté,  F. Parente and P. Indelicato. Eur. Phys. J D 13, 27-31 (2001).

[48]     Application of B-splines finite basis sets to relativistic two-photon decay rates of 2s level in hydrogenic ions, J.P. Santos,  F. Parente and P. Indelicato. Eur. Phys. J D 3, 43-52 (1998).

[49]     Multiconfiguration Dirac-Fock calculations of transition energies with QED corrections in three-electron ions, P. Indelicato and J.P. Desclaux. Phys. Rev. A 42, 5139-5149 (1990).

[50]     MCDF studies of two electron ions II: Radiative corrections and comparison with experiment., P. Indelicato,  O. Gorceix and J.P. Desclaux. J. Phys. B 20, 651 (1987).

[51]     Model operator approach to the Lamb shift calculations in relativistic many-electron atoms, V.M. Shabaev,  I.I. Tupitsyn and V.A. Yerokhin. Phys. Rev. A 88, 012513 (2013).

[52]     Model-QED operator for superheavy elements, A.V. Malyshev,  D.A. Glazov,  V.M. Shabaev,  I.I. Tupitsyn,  V.A. Yerokhin and V.A. Zaytsev. Phys. Rev. A 106, 012806 (2022).

Page updated April 11th, 2023