P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Physical Review, vol.80, issue.3B, pp.864-871, 1964.
DOI : 10.1088/0370-1328/80/5/307

W. Kohn and L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Physical Review, vol.119, issue.4A, pp.1133-1138, 1965.
DOI : 10.1103/PhysRev.119.1153

E. N. Economou, Green's Functions in Quantum Physics, Series in Solid-State Sciences, 2006.

L. P. Kadanoff and G. A. Baym, Quantum statistical mechanics: Green's function methods in equilibrium and nonequilibirum problems. Frontiers in Physics, 1962.

L. Hedin, New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem, Physical Review, vol.121, issue.3A, pp.796-823, 1965.
DOI : 10.1103/PhysRev.121.950

E. E. Salpeter and H. A. Bethe, A Relativistic Equation for Bound-State Problems, Physical Review, vol.76, issue.6, pp.1232-1242, 1951.
DOI : 10.1103/PhysRev.76.1739

P. Nozieres and D. Pines, Theory Of Quantum Liquids, Hachette UK, 1999.

E. Runge and E. K. Gross, Density-Functional Theory for Time-Dependent Systems, Physical Review Letters, vol.140, issue.12, pp.997-1000, 1984.
DOI : 10.1103/PhysRev.140.A1133

R. Van-leeuwen, N. E. Dahlen, and A. Stan, Total energies from variational functionals of the Green function and the renormalized four-point vertex, Physical Review B, vol.72, issue.19, p.195105, 2006.
DOI : 10.1103/PhysRevLett.84.1768

M. Guzzo, G. Lani, F. Sottile, P. Romaniello, M. Gatti et al., Description of Multiple Satellites, Physical Review Letters, vol.107, issue.16, p.166401, 2011.
DOI : 10.1103/PhysRevB.58.15565
URL : https://hal.archives-ouvertes.fr/hal-00659118

G. Lani, P. Romaniello, and L. Reining, Approximations for many-body Green's functions: insights from the fundamental equations, New Journal of Physics, vol.14, issue.1, p.13056, 2012.
DOI : 10.1088/1367-2630/14/1/013056
URL : http://iopscience.iop.org/article/10.1088/1367-2630/14/1/013056/pdf

J. A. Berger, P. Romaniello, F. Tandetzky, B. S. Mendoza, C. Brouder et al., Solution to the many-body problem in one point, New Journal of Physics, vol.16, issue.11, p.16113025, 2014.
DOI : 10.1088/1367-2630/16/11/113025
URL : https://hal.archives-ouvertes.fr/hal-01117310

S. Botti, F. Sottile, N. Vast, V. Olevano, L. Reining et al., Long-range contribution to the exchange-correlation kernel of time-dependent density functional theory, Physical Review B, vol.54, issue.15, p.155112, 2004.
DOI : 10.1103/PhysRevB.54.8540
URL : https://hal.archives-ouvertes.fr/hal-00077635

S. Sharma, J. K. Dewhurst, A. Sanna, and E. K. Gross, Bootstrap Approximation for the Exchange-Correlation Kernel of Time-Dependent Density-Functional Theory, Physical Review Letters, vol.107, issue.18, p.186401, 2011.
DOI : 10.1103/PhysRevB.79.233201

S. Rigamonti, S. Botti, V. Veniard, C. Draxl, L. Reining et al., Estimating Excitonic Effects in the Absorption Spectra of Solids: Problems and Insight from a Guided Iteration Scheme, Physical Review Letters, vol.114, issue.14, p.146402, 2015.
DOI : 10.1103/PhysRevB.83.035119

J. Kas, F. Vila, J. Rehr, and S. Chambers, Real-time cumulant approach for charge-transfer satellites in x-ray photoemission spectra, Physical Review B, vol.91, issue.12, p.121112, 2015.
DOI : 10.1103/PhysRevB.89.085123

S. J. Portugal, T. Y. Hubel, J. Fritz, S. Heese, D. Trobe et al., Upwash exploitation and downwash avoidance by flap phasing in ibis formation flight, Nature, vol.68, issue.7483, pp.505399-402, 2014.
DOI : 10.1088/0370-1298/68/1/111

P. A. Dirac, On the Theory of Quantum Mechanics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.112, issue.762, pp.661-677, 1926.
DOI : 10.1098/rspa.1926.0133

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Third Edition) Non-Relativistic Theor, 1977.

D. R. Hartree, The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods, Mathematical Proceedings of the Cambridge Philosophical Society, vol.24, issue.01, pp.89-110, 1928.
DOI : 10.1017/S0305004100011919

D. R. Hartree, The Wave Mechanics of an Atom with a non-Coulomb Central Field. Part III. Term Values and Intensities in Series in Optical Spectra, Mathematical Proceedings of the Cambridge Philosophical Society, vol.24, issue.03, pp.426-437, 1928.
DOI : 10.1017/S0305004100015954

J. C. Slater, A Simplification of the Hartree-Fock Method, Physical Review, vol.57, issue.3, p.385, 1951.
DOI : 10.1007/BF01340281

D. R. Hartree, The Calculation of Atomic Structure, American Journal of Physics, vol.26, issue.2, p.113, 1947.
DOI : 10.1119/1.1996102

P. A. Dirac, Note on Exchange Phenomena in the Thomas Atom, Mathematical Proceedings of the Cambridge Philosophical Society, vol.26, issue.03, pp.376-385, 1930.
DOI : 10.1017/S0305004100016108

R. M. Martin, L. Reining, and D. M. Ceperley, Interacting Electrons, 2016.
DOI : 10.1017/CBO9781139050807

A. D. Mclean, A. Weiss, and M. Yoshimine, Configuration Interaction in the Hydrogen Molecule???The Ground State, Reviews of Modern Physics, vol.35, issue.2, pp.211-218, 1960.
DOI : 10.1139/p57-079

U. Carsten, Time-Dependent Density-Functional Theory: Concepts and Applications

T. L. Gilbert, Hohenberg-Kohn theorem for nonlocal external potentials, Physical Review B, vol.60, issue.6, pp.2111-2120, 1975.
DOI : 10.1063/1.1680827

A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Reviews of Modern Physics, vol.75, issue.200, pp.13-125, 1996.
DOI : 10.1016/0038-1098(90)90282-G

A. L. Fetter and J. D. Walecka, Quantum Theory of Many-particle Systems. Dover Books on Physics, 2003.

T. Koopmans, ??ber die Zuordnung von Wellenfunktionen und Eigenwerten zu den Einzelnen Elektronen Eines Atoms, Physica, vol.1, issue.1-6, pp.104-113, 1934.
DOI : 10.1016/S0031-8914(34)90011-2

C. C. Roothaan, New Developments in Molecular Orbital Theory, Reviews of Modern Physics, vol.46, issue.2, pp.69-89, 1951.
DOI : 10.1051/jcp/1949460497

C. C. Roothaan, Self-Consistent Field Theory for Open Shells of Electronic Systems, Reviews of Modern Physics, vol.102, issue.2, pp.179-185, 1960.
DOI : 10.1103/PhysRev.102.1303

P. S. Bagus, Self-Consistent-Field Wave Functions for Hole States of Some Ne-Like and Ar-Like Ions, Physical Review, vol.35, issue.3A, pp.619-634, 1965.
DOI : 10.1103/RevModPhys.35.465

L. Hedin and A. Johansson, Polarization corrections to core levels, Journal of Physics B: Atomic and Molecular Physics, vol.2, issue.12, p.1336, 1969.
DOI : 10.1088/0022-3700/2/12/313

L. Hedin, approximation, Journal of Physics: Condensed Matter, vol.11, issue.42, p.489, 1999.
DOI : 10.1088/0953-8984/11/42/201

L. Hedin and J. D. Lee, Sudden approximation in photoemission and beyond, Journal of Electron Spectroscopy and Related Phenomena, vol.124, issue.2-3, pp.289-315, 2002.
DOI : 10.1016/S0368-2048(02)00060-9
URL : http://arxiv.org/pdf/cond-mat/0109517

L. Hedin and S. Lundqvist, Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids, pp.1-181, 1970.
DOI : 10.1016/S0081-1947(08)60615-3

T. Fujikawa, Theoretical Studies of X-Ray Photoemission and EXAFS Based on Dyson Orbitals, Journal of the Physical Society of Japan, vol.51, issue.8, pp.2619-2627, 1982.
DOI : 10.1143/JPSJ.51.2619

B. Lundqvist, Single-particle spectrum of the degenerate electron gas, Physik Der Kondensierten Materie, vol.6, issue.3, pp.193-205, 1967.

J. J. Rehr and R. C. Albers, Theoretical approaches to x-ray absorption fine structure, Reviews of Modern Physics, vol.21, issue.209, pp.621-654, 2000.
DOI : 10.1103/PhysRevA.21.1561

W. Bardyszewski and L. Hedin, A New Approach to the Theory of Photoemission from Solids, Physica Scripta, vol.32, issue.4, p.439, 1985.
DOI : 10.1088/0031-8949/32/4/033

J. J. Rehr, Lars Hedin and the quest for a theory of excited states, Physica Scripta, vol.115, issue.T115, p.19, 2005.
DOI : 10.1088/0031-8949/2005/T115/001

F. Sottile, Response functions of semiconductors and insulators: from the bethe-salpeter equation to time-dependent density functional theory, 2003.
URL : https://hal.archives-ouvertes.fr/tel-00007531

G. Strinati, Application of the Green???s functions method to the study of the optical properties of semiconductors, La Rivista del Nuovo Cimento, vol.49, issue.12, 1988.
DOI : 10.1143/PTP.49.37

M. Gell-mann and F. Low, Bound States in Quantum Field Theory, Physical Review, vol.82, issue.2, pp.350-354, 1951.
DOI : 10.1103/PhysRev.82.840

F. J. Dyson, Matrix in Quantum Electrodynamics, Physical Review, vol.12, issue.11, pp.1736-1755, 1949.
DOI : 10.1103/PhysRev.74.1070

J. Schwinger, On the Green's functions of quantized fields. I, Proceedings of the National Academy of Sciences, pp.452-455, 1951.
DOI : 10.1073/pnas.37.7.452

G. Baym and L. P. Kadanoff, Conservation Laws and Correlation Functions, Physical Review, vol.34, issue.2, pp.287-299, 1961.
DOI : 10.1098/rspa.1957.0017

D. Pines and D. Bohm, Individual Particle Aspects of the Interactions, Physical Review, vol.24, issue.2, pp.338-353, 1952.
DOI : 10.1002/andp.19484370302

F. Aryasetiawan and O. Gunnarsson, method, Reports on Progress in Physics, vol.61, issue.3, p.237, 1998.
DOI : 10.1088/0034-4885/61/3/002

N. M. Hugenholtz, Perturbation theory of large quantum systems, Physica, vol.23, issue.1-5, pp.481-532, 1957.
DOI : 10.1016/S0031-8914(57)92950-6

W. Nelson, P. Bokes, P. Rinke, and R. W. Godby, Self-interaction in Green???s-function theory of the hydrogen atom, Physical Review A, vol.75, issue.3, p.32505, 2007.
DOI : 10.1103/PhysRevA.56.5191.2

P. Romaniello, S. Guyot, and L. Reining, The self-energy beyond GW: Local and nonlocal vertex corrections, The Journal of Chemical Physics, vol.4, issue.15, p.131154111, 2009.
DOI : 10.1103/PhysRevLett.96.226402
URL : https://hal.archives-ouvertes.fr/hal-00990134

F. Aryasetiawan, R. Sakuma, and K. Karlsson, approximation with self-screening correction, Physical Review B, vol.85, issue.3, p.35106, 2012.
DOI : 10.1088/0953-8984/9/4/002
URL : http://arxiv.org/pdf/1110.6765

G. D. Mahan, Many-Particle Physics. Physics of Solids and Liquids, 2000.

J. S. Zhou, J. J. Kas, L. Sponza, I. Reshetnyak, M. Guzzo et al., Dynamical effects in electron spectroscopy, The Journal of Chemical Physics, vol.1, issue.18, p.109, 2015.
DOI : 10.1103/PhysRevLett.80.2389

J. J. Fernandez, calculations in an exactly solvable model system at different dilution regimes: The problem of the self-interaction in the correlation part, Physical Review A, vol.79, issue.5, p.52513, 2009.
DOI : 10.1103/PhysRevLett.93.249701

L. G. Molinari, Hedin???s equations and enumeration of Feynman diagrams, Physical Review B, vol.71, issue.11, p.113102, 2005.
DOI : 10.1063/1.2916419

L. G. Molinari and N. Manini, Enumeration of many-body skeleton diagrams, The European Physical Journal B, vol.16, issue.3, pp.331-336, 2006.
DOI : 10.1140/epjb/e2006-00223-9
URL : http://arxiv.org/pdf/cond-mat/0512342

R. Del-sole, L. Reining, and R. W. Godby, ?? approximation for electron self-energies in semiconductors and insulators, Physical Review B, vol.243, issue.12, pp.8024-8028, 1994.
DOI : 10.1098/rspa.1958.0003

G. Onida, L. Reining, and A. Rubio, Electronic excitations: density-functional versus many-body Green???s-function approaches, Reviews of Modern Physics, vol.41, issue.118, pp.601-659, 2002.
DOI : 10.1002/pssb.19700410103
URL : https://digital.csic.es/bitstream/10261/98472/1/Electronic%20excitations.pdf

L. J. Sham and M. Schlüter, Density-Functional Theory of the Energy Gap, Physical Review Letters, vol.14, issue.20, pp.1888-1891, 1983.
DOI : 10.1103/PhysRevA.14.36

L. J. Sham, Exchange and correlation in density-functional theory, Physical Review B, vol.51, issue.2, pp.3876-3882, 1985.
DOI : 10.1103/PhysRevLett.51.1884

Y. Pavlyukh and W. H-´-'ubner, Analytic solution of Hedin???s equations in zero dimensions, Journal of Mathematical Physics, vol.5, issue.5, p.52109, 2007.
DOI : 10.1016/S0010-4655(00)00042-4

W. Tarantino, P. Romaniello, J. A. Berger, and L. Reining, Self-consistent Dyson equation and self-energy functionals: An analysis and illustration on the example of the Hubbard atom, Physical Review B, vol.96, issue.4, p.45124, 2017.
DOI : 10.1088/0953-8984/13/43/304
URL : https://hal.archives-ouvertes.fr/hal-01583906

A. Stan, P. Romaniello, S. Rigamonti, L. Reining, and J. A. Berger, Unphysical and physical solutions in many-body theories: from weak to strong correlation, New Journal of Physics, vol.17, issue.9, p.93045, 2015.
DOI : 10.1088/1367-2630/17/9/093045
URL : https://hal.archives-ouvertes.fr/hal-01222216

R. T. Sharp and G. K. Horton, A Variational Approach to the Unipotential Many-Electron Problem, Physical Review, vol.141, issue.2, pp.317-317, 1953.
DOI : 10.1098/rspa.1933.0118

J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Physical Review B, vol.1, issue.10, pp.5048-5079, 1981.
DOI : 10.1103/PhysRevB.1.1044

A. Görling, Orbital- and state-dependent functionals in density-functional theory, The Journal of Chemical Physics, vol.69, issue.6, p.62203, 2005.
DOI : 10.1016/S0009-2614(03)00908-4

Y. H. Kim and A. Görling, Exact Kohn-Sham exchange kernel for insulators and its long-wavelength behavior, Physical Review B, vol.82, issue.3, p.35114, 2002.
DOI : 10.1103/PhysRevLett.82.4416
URL : http://arxiv.org/pdf/cond-mat/0205579

F. Bruneval, F. Sottile, V. Olevano, and L. Reining, Beyond time-dependent exact exchange: The need for long-range correlation, The Journal of Chemical Physics, vol.17, issue.14, p.144113, 2006.
DOI : 10.1063/1.1460869
URL : https://hal.archives-ouvertes.fr/hal-00358798

M. E. Casida, Generalization of the optimized-effective-potential model to include electron correlation: A variational derivation of the Sham-Schl??ter equation for the exact exchange-correlation potential, Physical Review A, vol.50, issue.3, pp.2005-2013, 1995.
DOI : 10.1103/PhysRevA.50.4707

N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Reviews of Modern Physics, vol.84, issue.4, pp.1419-1475, 2012.
DOI : 10.1002/cphc.200500133
URL : http://arxiv.org/pdf/1112.5411

P. Nozières and C. T. De-dominicis, Singularities in the X-Ray Absorption and Emission of Metals. III. One-Body Theory Exact Solution, Physical Review, vol.121, issue.3, pp.1097-1107, 1969.
DOI : 10.1103/PhysRev.121.1090

D. C. Langreth, Singularities in the X-Ray Spectra of Metals, Physical Review B, vol.28, issue.2, pp.471-477, 1970.
DOI : 10.1103/PhysRev.84.108

B. I. Lundqvist, Characteristic structure in core electron spectra of metals due to the electronplasmon coupling, Phys kondens Materie, vol.9, pp.236-248, 1969.

L. Hedin, B. I. Lundqvist, and S. Lundqvist, New structure in the single-particle spectrum of an electron gas, Solid State Communications, vol.5, issue.4, pp.237-239, 1967.
DOI : 10.1016/0038-1098(67)90264-5

L. Hedin, Effects of Recoil on Shake-Up Spectra in Metals, Physica Scripta, vol.21, issue.3-4, p.477, 1980.
DOI : 10.1088/0031-8949/21/3-4/039

F. Aryasetiawan, L. Hedin, and K. Karlsson, Cumulant Expansion, Physical Review Letters, vol.40, issue.11, pp.2268-2271, 1996.
DOI : 10.1103/PhysRevLett.40.568

G. Stefanucci and R. Van-leeuwen, Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction, 2013.
DOI : 10.1017/CBO9781139023979

G. D. Mahan, Excitons in Metals: Infinite Hole Mass, Physical Review, vol.18, issue.3, pp.612-617, 1967.
DOI : 10.1103/PhysRevLett.18.1049

M. Combescot and P. Nozières, Infrared catastrophy and excitons in the X-ray spectra of metals, Journal de Physique, vol.18, issue.C, p.32, 1971.
DOI : 10.1051/jphys:019710032011-12091300
URL : https://hal.archives-ouvertes.fr/jpa-00207191

W. Hänsch and W. Ekardt, Structure of the L ii iii -absorption-edge singularity of na metal

D. C. Langreth, Born-Oppenheimer Principle in Reverse: Electrons, Photons, and Plasmons in Solids???Singularities in Their Spectra, Physical Review Letters, vol.178, issue.20, pp.1229-1233, 1971.
DOI : 10.1103/PhysRev.178.1340

J. J. Chang and D. C. Langreth, Deep-Hole Excitations in Solids. I. Fast-Electron-Plasmon Effects, Physical Review B, vol.38, issue.9, pp.3512-3522, 1972.
DOI : 10.1002/pssb.19700380144

S. Doniach and M. Sunjic, Many-electron singularity in X-ray photoemission and X-ray line spectra from metals, Journal of Physics C: Solid State Physics, vol.3, issue.2, p.285, 1970.
DOI : 10.1088/0022-3719/3/2/010
URL : http://iopscience.iop.org/article/10.1088/0022-3719/3/2/010/pdf

S. M. Bose, P. Kiehm, and P. Longe, Excitation energy dependence of the photoemission spectra of metals, Physical Review B, vol.183, issue.2, pp.712-723, 1981.
DOI : 10.1103/PhysRev.183.687

C. O. Almbladh and U. Barth, The spherical-solid model: An application to x-ray edges in Li, Na, and Al, Physical Review B, vol.84, issue.8, pp.3307-3319, 1976.
DOI : 10.1103/PhysRev.84.495

R. Kubo, Generalized Cumulant Expansion Method, Journal of the Physical Society of Japan, vol.17, issue.7, pp.1100-1120, 1962.
DOI : 10.1143/JPSJ.17.1100

E. Müller-hartmann, T. V. Ramakrishnan, and G. Toulouse, Localized Dynamic Perturbations in Metals, Physical Review B, vol.40, issue.4, pp.1102-1119, 1971.
DOI : 10.1103/PhysRev.40.502

G. D. Mahan, Collective excitations in x-ray spectra of metals, Physical Review B, vol.12, issue.12, pp.4814-4824, 1975.
DOI : 10.1007/978-1-4684-7293-6

G. D. Mahan, Core-hole Green's function: Dispersion theory, Physical Review B, vol.45, issue.8, pp.5021-5031, 1982.
DOI : 10.1016/0375-9601(73)90449-0

A. Barth and L. S. Cederbaum, Many-body theory of core-valence excitations, Physical Review A, vol.22, issue.3, pp.1038-1061, 1981.
DOI : 10.1103/PhysRevA.22.206

U. Harbola and S. Mukamel, Many-body Green???s function approach to attosecond nonlinear x-ray spectroscopy, Physical Review B, vol.109, issue.23, p.235129, 2009.
DOI : 10.1063/1.1703727
URL : http://arxiv.org/pdf/0906.0551

T. Hansen and T. Pullerits, Nonlinear response theory on the Keldysh contour, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.45, issue.15, p.154014, 2012.
DOI : 10.1088/0953-4075/45/15/154014

V. M. Silkin, P. Lazi´clazi´c, D. , N. , H. Petek et al., Ultrafast electronic response of Ag(111) and Cu(111) surfaces: From early excitonic transients to saturated image potential, Physical Review B, vol.323, issue.15, p.155405, 2015.
DOI : 10.1103/PhysRevB.3.2452

B. Gumhalter, Stages of hot electron dynamics in multiexcitation processes at surfaces: General properties and benchmark examples, Progress in Surface Science, vol.87, issue.5-8, pp.5-8163, 2012.
DOI : 10.1016/j.progsurf.2012.05.004

B. Gumhalter, Ultrafast dynamics and decoherence of quasiparticles in surface bands: Development of the formalism, Physical Review B, vol.30, issue.288, p.165406, 2005.
DOI : 10.1103/PhysRevLett.94.033901

B. Gumhalter, V. Kova?, F. Caruso, H. Lambert, and F. Giustino, On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands, Physical Review B, vol.6, issue.3, p.2016
DOI : 10.1103/PhysRevB.43.1993

A. Arnau, Nonlinear screening of highly charged ions in metals, Physica Scripta, vol.73, issue.T73, p.303, 1997.
DOI : 10.1088/0031-8949/1997/T73/099

V. I. Grebennikov, Y. A. Babanov, and O. B. Sokolov, Extra-atomic relaxation and X-ray spectra of narrow-band metals. I. Formalism, Physica Status Solidi (b), vol.31, issue.2, pp.423-432, 1977.
DOI : 10.1016/S0081-1947(08)60424-5

V. I. Grebennikov, Y. A. Babanov, and O. B. Sokolov, Extra-atomic relaxation and X-ray spectra of narrow-band metals. II. Results, Physica Status Solidi (b), vol.3, issue.1, pp.73-82, 1977.
DOI : 10.1002/pssb.2220800108

T. Privalov, F. , and H. Ågren, Role of relaxation and time-dependent formation of x-ray spectra, Physical Review B, vol.112, issue.16, p.165115, 2001.
DOI : 10.1063/1.481134

T. Privalov, F. , and H. Ågren, X-ray Raman scattering from molecules and solids in the framework of the Mahan-Nozi??res-De Dominicis model, Physical Review B, vol.62, issue.111, p.165116, 2001.
DOI : 10.1103/PhysRevB.62.13996

B. Brena, Y. Luo, M. Nyberg, S. Carniato, K. Nilson et al., Equivalent core-hole time-dependent density functional theory calculations of carbon 1s shake-up states of phthalocyanine, Physical Review B, vol.90, issue.19, 2004.
DOI : 10.1016/0368-2048(90)85063-F

B. Brena, S. Carniato, and Y. Luo, Functional and basis set dependence of K-edge shake-up spectra of molecules, The Journal of Chemical Physics, vol.23, issue.18, p.184316, 2005.
DOI : 10.1016/0301-0104(84)80019-1

J. Kas, J. Rehr, and . Curtis, Particle-hole cumulant approach for inelastic losses in x-ray spectra, Physical Review B, vol.8, issue.3, p.2016
DOI : 10.1103/PhysRevB.50.10462
URL : http://arxiv.org/pdf/1604.06829

A. J. Morris, M. Stankovski, K. T. Delaney, P. Rinke, P. García-gonzález et al., Vertex corrections in localized and extended systems, Physical Review B, vol.8, issue.15, p.155106, 2007.
DOI : 10.1103/PhysRevB.73.205334

J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy, Physical Review Letters, vol.50, issue.23, pp.1691-1694, 1982.
DOI : 10.1063/1.1671628

C. Almbladh and U. Barth, Exact results for the charge and spin densities, exchange-correlation potentials, and density-functional eigenvalues, Physical Review B, vol.29, issue.6, pp.3231-3244, 1985.
DOI : 10.1103/PhysRevA.29.2322