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\newlabel { eq:E_ 2x2} { { 2} { 2} { } { equation.1.2} { } }
\newlabel { eq:lambda_ EP} { { 3} { 2} { } { equation.1.3} { } }
\newlabel { eq:E_ EP} { { 4} { 2} { } { equation.1.4} { } }
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\newlabel { eq:SchrEq} { { 8} { 2} { } { equation.2.8} { } }
\newlabel { eq:SchrEq-PT} { { 9} { 2} { } { equation.2.9} { } }
\newlabel { eq:Elambda} { { 10} { 2} { } { equation.2.10} { } }
\newlabel { eq:DivExample} { { 11} { 2} { } { equation.2.11} { } }
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\newlabel { eq:CoulOp} { { 15a} { 3} { } { equation.2.15alph1} { } }
\newlabel { eq:ExcOp} { { 15b} { 3} { } { equation.2.15alph2} { } }
\newlabel { eq:HFHamiltonian} { { 16} { 3} { } { equation.2.16} { } }
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\newlabel { eq:MPHamiltonian} { { 17} { 3} { } { equation.2.17} { } }
\newlabel { eq:EMP2} { { 19} { 3} { } { equation.2.19} { } }
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\newlabel { eq:H-sph-omega} { { 24} { 7} { } { equation.4.24} { } }
\newlabel { eq:RHF_ WF} { { 25} { 7} { } { equation.4.25} { } }
\newlabel { eq:UHF_ WF} { { 26} { 7} { } { equation.4.26} { } }
\newlabel { eq:EHF} { { 28} { 7} { } { equation.4.28} { } }
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\newlabel { eq:EsbUHF} { { 33} { 8} { } { equation.4.33} { } }
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\newlabel { fig:SpheriumNrj} { { 1} { 8} { Energies of the five solutions of the HF equations (multiplied by $ R ^ 2 $ ). The dotted curves correspond to the analytic continuation of the symmetry-broken solutions} { figure.1} { } }
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\@ writefile{ lof} { \contentsline { figure} { \numberline { 3} { \ignorespaces Radius of convergence $ R _ { \text { CV } } $ for two (left) and three (right) basis functions for various partitionings.} } { 10} { figure.3} \protected @file@percent }
\newlabel { fig:RadiusPartitioning} { { 3} { 10} { Radius of convergence $ R _ { \text { CV } } $ for two (left) and three (right) basis functions for various partitionings} { figure.3} { } }
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\newlabel { eq:uhfbasis} { { 39} { 10} { } { equation.5.39} { } }
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\newlabel { fig:RadiusBasis} { { 4} { 10} { Radius of convergence $ R _ { \text { CV } } $ in the CSF basis with $ K $ basis functions for the MP (left) and WC (right) partitioning} { figure.4} { } }
\newlabel { eq:uhforbitals} { { 41a} { 10} { } { equation.5.41alph1} { } }
\newlabel { eq:MatrixElem} { { 42} { 10} { } { equation.5.42} { } }
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\@ writefile{ lof} { \contentsline { figure} { \numberline { 5} { \ignorespaces Energies $ E ( \lambda ) $ in the unrestricted basis set \textup { \hbox { \mathsurround \z @ \normalfont (\ignorespaces \ref { eq:uhfbasis} \unskip \@ @italiccorr )} } with $ R = 10 $ .} } { 11} { figure.5} \protected @file@percent }
\newlabel { fig:UHFMiniBas} { { 5} { 11} { Energies $ E ( \lambda ) $ in the unrestricted basis set \eqref { eq:uhfbasis} with $ R = 10 $ } { figure.5} { } }
\@ writefile{ lof} { \contentsline { figure} { \numberline { 6} { \ignorespaces Energies $ E ( \lambda ) $ in the unrestricted basis set \textup { \hbox { \mathsurround \z @ \normalfont (\ignorespaces \ref { eq:uhfbasis} \unskip \@ @italiccorr )} } for $ R = 1 . 5 $ (left) and $ R = 1 . 51 $ (right).} } { 11} { figure.6} \protected @file@percent }
\newlabel { fig:UHFEP} { { 6} { 11} { Energies $ E ( \lambda ) $ in the unrestricted basis set \eqref { eq:uhfbasis} for $ R = 1 . 5 $ (left) and $ R = 1 . 51 $ (right)} { figure.6} { } }
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\newlabel { fig:UHFPT} { { 7} { 12} { Real part (left) and imaginary part (right) of $ E ( \lambda ) $ in the unrestricted basis set \eqref { eq:uhfbasis} for $ R = 1 $ } { figure.7} { } }
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\bibdata { EPAWTFTNotes,EPAWTFT}
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\bibcite { MoiseyevBook} { { 1} { 2011} { { Moiseyev} } { { } } }
\bibcite { BenderPTBook} { { 2} { 2019} { { Bender} } { { } } }
\bibcite { Burton_ 2019} { { 3} { 2019{ } } { { Burton\ \emph { et~al.} } } { { Burton, Thom,\ and\ Loos} } }
\bibcite { Bittner_ 2012} { { 4} { 2012} { { Bittner\ \emph { et~al.} } } { { Bittner, Dietz, G\" unther, Harney, Miski-Oglu, Richter,\ and\ Sch\" afer} } }
\bibcite { Chong_ 2011} { { 5} { 2011} { { Chong\ \emph { et~al.} } } { { Chong, Ge,\ and\ Stone} } }
\bibcite { Chtchelkatchev_ 2012} { { 6} { 2012} { { Chtchelkatchev\ \emph { et~al.} } } { { Chtchelkatchev, Golubov, Baturina,\ and\ Vinokur} } }
\bibcite { Doppler_ 2016} { { 7} { 2016} { { Doppler\ \emph { et~al.} } } { { Doppler, Mailybaev, B\" ohm, Kuhl, Girschik, Libisch, Milburn, Rabl, Moiseyev,\ and\ Rotter} } }
\bibcite { Guo_ 2009} { { 8} { 2009} { { Guo\ \emph { et~al.} } } { { Guo, Salamo, Duchesne, Morandotti, { Volatier-Ravat} , Aimez, Siviloglou,\ and\ Christodoulides} } }
\bibcite { Hang_ 2013} { { 9} { 2013} { { Hang\ \emph { et~al.} } } { { Hang, Huang,\ and\ Konotop} } }
\bibcite { Liertzer_ 2012} { { 10} { 2012} { { Liertzer\ \emph { et~al.} } } { { Liertzer, Ge, Cerjan, Stone, T\" ureci,\ and\ Rotter} } }
\bibcite { Longhi_ 2010} { { 11} { 2010} { { Longhi} } { { } } }
\bibcite { Peng_ 2014} { { 12} { 2014{ } } { { Peng\ \emph { et~al.} } } { { Peng, Ozdemir, Rotter, Yilmaz, Liertzer, Monifi, Bender, Nori,\ and\ Yang} } }
\bibcite { Peng_ 2014a} { { 13} { 2014{ } } { { Peng\ \emph { et~al.} } } { { Peng, \" Ozdemir, Lei, Monifi, Gianfreda, Long, Fan, Nori, Bender,\ and\ Yang} } }
\bibcite { Regensburger_ 2012} { { 14} { 2012} { { Regensburger\ \emph { et~al.} } } { { Regensburger, Bersch, Miri, Onishchukov, Christodoulides,\ and\ Peschel} } }
\bibcite { Ruter_ 2010} { { 15} { 2010} { { R\" uter\ \emph { et~al.} } } { { R\" uter, Makris, { El-Ganainy} , Christodoulides, Segev,\ and\ Kip} } }
\bibcite { Schindler_ 2011} { { 16} { 2011} { { Schindler\ \emph { et~al.} } } { { Schindler, Li, Zheng, Ellis,\ and\ Kottos} } }
\bibcite { Szameit_ 2011} { { 17} { 2011} { { Szameit\ \emph { et~al.} } } { { Szameit, Rechtsman, { Bahat-Treidel} ,\ and\ Segev} } }
\bibcite { Zhao_ 2010} { { 18} { 2010} { { Zhao\ \emph { et~al.} } } { { Zhao, Schaden,\ and\ Wu} } }
\bibcite { Zheng_ 2013} { { 19} { 2013} { { Zheng\ \emph { et~al.} } } { { Zheng, Hao,\ and\ Long} } }
\bibcite { Choi_ 2018} { { 20} { 2018} { { Choi\ \emph { et~al.} } } { { Choi, Hahn, Yoon,\ and\ Song} } }
\bibcite { El-Ganainy_ 2018} { { 21} { 2018} { { El-Ganainy\ \emph { et~al.} } } { { El-Ganainy, Makris, Khajavikhan, Musslimani, Rotter,\ and\ Christodoulides} } }
\bibcite { Heiss_ 1990} { { 22} { 1990} { { Heiss\ and\ Sannino} } { { } } }
\bibcite { Heiss_ 1999} { { 23} { 1999} { { D.} } { { } } }
\bibcite { Heiss_ 2012} { { 24} { 2012} { { Heiss} } { { } } }
\bibcite { Heiss_ 2016} { { 25} { 2016} { { Heiss} } { { } } }
\bibcite { Yarkony_ 1996} { { 26} { 1996} { { Yarkony} } { { } } }
\bibcite { Benda_ 2018} { { 27} { 2018} { { Benda\ and\ Jagau} } { { } } }
\bibcite { Berry_ 1984} { { 28} { 1984} { { Berry} } { { } } }
\bibcite { BenderBook} { { 29} { 1978} { { Bender\ and\ Orszag} } { { } } }
\bibcite { Olsen_ 1996} { { 30} { } { { Olsen\ \emph { et~al.} } } { { Olsen, Christiansen, Koch,\ and\ J{ \o } rgensen} } }
\bibcite { Olsen_ 2000} { { 31} { } { { Olsen\ \emph { et~al.} } } { { Olsen, J{ \o } rgensen, Helgaker,\ and\ Christiansen} } }
\bibcite { Olsen_ 2019} { { 32} { 2019} { { Olsen\ and\ J{ \o } rgensen} } { { } } }
\bibcite { SzaboBook} { { 33} { 1989} { { Szabo\ and\ Ostlund} } { { } } }
\bibcite { Goodson_ 2012} { { 34} { 2012} { { Goodson} } { { } } }
\bibcite { Moller_ 1934} { { 35} { 1934} { { M{ \o } ller\ and\ Plesset} } { { } } }
\bibcite { Gill_ 1986} { { 36} { 1986} { { Gill\ and\ Radom} } { { } } }
\bibcite { Gill_ 1988} { { 37} { 1988} { { Gill\ \emph { et~al.} } } { { Gill, Pople, Radom,\ and\ Nobes} } }
\bibcite { Handy_ 1985} { { 38} { 1985} { { Handy\ \emph { et~al.} } } { { Handy, Knowles,\ and\ Somasundram} } }
\bibcite { Lepetit_ 1988} { { 39} { 1988} { { Lepetit\ \emph { et~al.} } } { { Lepetit, P{ \' e} lissier,\ and\ Malrieu} } }
\bibcite { JensenBook} { { 40} { 2017} { { Jensen} } { { } } }
\bibcite { Seidl_ 2018} { { 41} { 2018} { { Seidl\ \emph { et~al.} } } { { Seidl, Giarrusso, Vuckovic, Fabiano,\ and\ Gori-Giorgi} } }
\bibcite { Cremer_ 1996} { { 42} { 1996} { { Cremer\ and\ He} } { { } } }
\bibcite { Christiansen_ 1996} { { 43} { 1996} { { Christiansen\ \emph { et~al.} } } { { Christiansen, Olsen, J{ \o } rgensen, Koch,\ and\ Malmqvist} } }
\bibcite { Sergeev_ 2005} { { 44} { 2005} { { Sergeev\ \emph { et~al.} } } { { Sergeev, Goodson, Wheeler,\ and\ Allen} } }
\bibcite { Sergeev_ 2006} { { 45} { 2006} { { Sergeev\ and\ Goodson} } { { } } }
\bibcite { Stillinger_ 2000} { { 46} { 2000} { { Stillinger} } { { } } }
\bibcite { Baker_ 1971} { { 47} { 1971} { { { Baker} } } { { } } }
\bibcite { Goodson_ 2004} { { 48} { 2004} { { Goodson\ and\ Sergeev} } { { } } }
\bibcite { Heiss_ 1988} { { 49} { 1988} { { Heiss} } { { } } }
\bibcite { Heiss_ 2002} { { 50} { 2002} { { Heiss\ and\ M{ \" u} ller} } { { } } }
\bibcite { Cejnar_ 2005} { { 51} { 2005} { { Cejnar\ \emph { et~al.} } } { { Cejnar, Heinze,\ and\ Dobe{ \v s} } } }
\bibcite { Cejnar_ 2007} { { 52} { 2007} { { Cejnar\ \emph { et~al.} } } { { Cejnar, Heinze,\ and\ Macek} } }
\bibcite { Cejnar_ 2009} { { 53} { 2009} { { Cejnar\ and\ Jolie} } { { } } }
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\@ writefile{ toc} { \contentsline { section} { \numberline { } References} { 13} { section*.22} \protected @file@percent }
\bibcite { Borisov_ 2015} { { 54} { 2015} { { Borisov\ \emph { et~al.} } } { { Borisov, Ru{ \v z} i{ \v c} ka,\ and\ Znojil} } }
\bibcite { Sindelka_ 2017} { { 55} { 2017} { { { \v S} indelka\ \emph { et~al.} } } { { { \v S} indelka, Santos,\ and\ Moiseyev} } }
\bibcite { Sachdev_ 2011} { { 56} { 2011} { { Sachdev} } { { } } }
\bibcite { Cejnar_ 2015} { { 57} { 2015} { { Cejnar\ \emph { et~al.} } } { { Cejnar, Str{ \' a} nsk{ \' y} ,\ and\ Kloc} } }
\bibcite { Cejnar_ 2016} { { 58} { 2016} { { Cejnar\ and\ Str{ \' a} nsk{ \' y} } } { { } } }
\bibcite { Caprio_ 2008} { { 59} { 2008} { { Caprio\ \emph { et~al.} } } { { Caprio, Cejnar,\ and\ Iachello} } }
\bibcite { Macek_ 2019} { { 60} { 2019} { { Macek\ \emph { et~al.} } } { { Macek, Str{ \' a} nsk{ \' y} , Leviatan,\ and\ Cejnar} } }
\bibcite { Stransky_ 2018} { { 61} { 2018} { { Str{ \' a} nsk{ \' y} \ \emph { et~al.} } } { { Str{ \' a} nsk{ \' y} , Dvo{ \v r} { \' a} k,\ and\ Cejnar} } }
\bibcite { Lipkin_ 1965} { { 62} { 1965} { { Lipkin\ \emph { et~al.} } } { { Lipkin, Meshkov,\ and\ Glick} } }
\bibcite { Ushveridze_ 1994} { { 63} { 1994} { { Ushveridze} } { { } } }
\bibcite { Thompson_ 2005} { { 64} { 2005} { { Thompson\ and\ Alavi} } { { } } }
\bibcite { Seidl_ 2007} { { 65} { 2007} { { Seidl} } { { } } }
\bibcite { Loos_ 2009b} { { 66} { 2009{ } } { { Loos\ and\ Gill} } { { } } }
\bibcite { Loos_ 2009} { { 67} { 2009{ } } { { Loos\ and\ Gill} } { { } } }
\bibcite { Wigner_ 1934} { { 68} { 1934} { { Wigner} } { { } } }
\bibcite { Coulson_ 1949} { { 69} { } { { Coulson\ and\ Fischer} } { { } } }
\bibcite { AngularBook} { { 70} { 1996} { { Edmonds} } { { } } }
\bibcite { GiulianiBook} { { 71} { 2005} { { Giuliani\ and\ Vignale} } { { } } }
\bibcite { Hiscock_ 2014} { { 72} { 2014} { { Hiscock\ and\ Thom} } { { } } }
\bibcite { Burton_ 2019a} { { 73} { 2019{ } } { { Burton\ \emph { et~al.} } } { { Burton, Thom,\ and\ Loos} } }
\bibcite { SlaterBook} { { 74} { 1960} { { Slater} } { { } } }
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