Acta Physica Academiae Scientiarum Hungaricae, Tomus 27, pp. 351--371 (1969)
HHTEPFIPETAI2I/I~t METO,~A XAPTPH-qbOKA KAK METO,~A qACTHqHOFO CYMMHPOBAHH~I ATOMHblX
r BCKHX ,~HAFPAMM*
B. B. TOYlMALIEB
YHHBEPCHTET qHYIE, CAHTHAFO, qH.rlE**
(FI0CTyn~z0 20. II. 1969)
Ha MeTo~e XapTpH-- tDoKa [I , 2, 3] 0CHOBb~BatOTC~I n0qTH Bce np0a0An~bte B HaCTo~Imee BpeMfl aTOMHble ti MO~eKyJ~~lpHb~e pacqeTu, H rI03TOMy eF0 HHTepnpeTaIDt~t KaK MeToJxa CyMMH- p0BaHH~I orlpe~eJIeHHOFO K.rlacca aTOMHblX qbe~HMaHOBCKHX ~HaFpaMM [4] ~IB.rIJ~eTC~I oqeHb BaX'<HOH. OHa rlO3BO~/~leT r ~ y 6 ~ e rIOH~lTb CMbIC.rI rlpH6~IH)t<eHHfl, 3a~0~eHHbIX B MeTo~e XapTpH- (l)OKa, H rlpHqHHbl T0~ oco‰ 3(~qbeKTHBHOCTH 3TOrO MeT0~a, KOTOpafl np0~B~~eTCfl IIpH KOH- KpeTHbIX pacqeTax 3HeprH¡ B qaCTH0CTH, 0CHOBHbIX COCTO~IHHH JIeFKHX aTOMOB. B pe3yJ~bTaTe y~aeTC~l fio~ee 0CMblC~IeHH0 CTpOHTb Ha OCHOBe MeT0)~a XapTplt-- ( l )OKa pa3.rlHqHbte TeOpHH aJIeKTp0HH0~ K0ppe~~llLHrt.
t(p0Me TOFO TaKast HHTepnpeTaRH~ H03B0~~e~ C 60~bmOfi .rIeFK0CTblO 3(~(~eKTHBHO C0- CTaBJI~ITb CaMH ypaBHeHH~/ MeTO~a XapTpH--(DOKa B Tex H.rIH HHblX ~0C'laT0qH0 C.rl0)t<HblX KOHKpeTHblX C-rlyqa~tx, CKaH<eM C yqeToM B3aHM0~e/Ÿ KOHqbHFypaHti~. r locaeRHero Bnpo- qeM Mbl He ‰ KaCaTbC5~ B 3T0fŸ CTaTbe, H.rLrltOCTpHpy~l Bce HamH paccy~AeHHfl TO.rIbK0 Ha npocTefimnx npuMepax aT0~~UX C0CT0aH~fi C 3a~~~yTb~~H aae~TpOnHbIMn 060noq~aMB H C0CT0~IHHH C ORH0fl 0TKpbl30~ 060JI0qK0¡ KOHd)Hrypal~tlH H TepMa (hala) q SL , n p e ; m o n a r a n , qT0 DTOT TepM KOHqbHFypal2HH (nala) q eJIHHCTBeHrtblfŸ H He HOBT0pSteTCfl.
1. C0CTOIIHHfl C 3aMKHyTblMH 311eKTp0HHblMH 0‰
FaMI4~bTOHHaH MHOF03~eKTpOHHOF0 aTOMa, C0CT0~HHe KOT0p0F0 C 3aMKHy-
TblMH 9/IeKTp0HHbIMH 0‰ MbI co@paeMc~ g3yqaTb, B Hepe~~[THBHCTCKOM npg6~H>KeHHg gMeeT Bg~
H = Ho + H~~t, (1) 1 Z
no-- 2 ~7,-- 2 - - , (2) 2 ( I~ i ~N) (I~i~<N) ri
1 H ' n t = 2 " (3 )
3Recb Z - - 3apfl~ ~~pa awoMa, N - - n o ~ n o e qnc~o a~eKzpoHou B awoMe (npe~-
no~araeTcfl, qTO B 06U~eM c~yqae N J= Z, TO eCTb Bce paccMowpe~ne 0rH0C~TCfl
KaK K He¡ aTOMHblM C0CT0~IHH~IM, TaK H K C00TBeTCTByIOIIDIM C0CT0~I-
H~aM n0~0~HTe~bHbIX H 0TpmtaTeabHblX aTOMHblX HOHOB).
B Te0pHH aTOMHUX qbefiHMaHOBCKHX ~ H a r p a ~ BapbHpyeM0e xapTpH-qb0r(os- CK0e Bblpa>KeHHe R~I~I 3HeprHH I43yqaeMoFO aTOMHOF0 C0CT0~IHH~I C 3aMKHyTblMH
3JIeKTpOHHbIMH o‰163 M0)KH0 HOJIyqI4Tb c~e~yr0LttgM 06pa3oM.
* Hpoqbeccopy H. FoM6am Ha ~eHb 60 ro p0~~e~~a. ** rl0CT0~IHHbl~ aapec : M0CKOBCKH~ FOCy~(apcTBeHHbI~… YHHBepCHTeT, MaTeMaTHKO--
MexaHriqecK~~ (l)aKyJ~bTeT, M0CKBa, CCCP
Acta Physica Acad~miae Scientiarum Hungaricae 27, 1969
352 B.B. TOMMAMEB
FIpe>~~e Bcero B03bMeM HeNOT0p0e cqbepriqecNH CHMMeTpHqH0e ~0‰
I< no~m ~ ~ p a - - Z / r BHem~ee no te U(r), 0pTOHOpMHpOBaHHb~e pa~~a:ibHbte ~ym~- R~H KOTOpOro onpeRean~TC~ ri3 ypa~HeHHa
( 1 d ~ 1 d + l ( l + l ) Z 4- U(r ) )R , , ( r )=%,R ro(r), (4) 2 dr 2 r dr 2r ~ r
j ':~r~drR~t(r)R~~(r)= 1 (5)
(npeRnoJlaraeM, qT0 cnercrp ent He riMeeT cJlyqa~H0r0 Bblp0)K~eHH~t BOJ~0p0j~0rl0
jX06H0r0 aToMa, TO eCTb era peaabuo 3aBnC~T 0T l, H cKa~eM nanpriMep e2v # e ~ )
C00TBeTCTBeHH0 Mbl A0~)KHb~ BBeCTH HOBb~~ Hy~eB0~ raMnabTOHHaH ti raMnJm-
TOHriaH ~8ariMo~e~CTBria
1 ~ , /lr~ - ~ . __Z + ~, U(r~) (61 H U - - 2 " ( I ~ < i ~ N ) ( I~< i~<N) ri ( l ~ < i ~ N )
H U t ~ - H , nt = ~ " U(ri). (7) ( I ~ i ~ N )
B03t, MeM ~aaee rie|<o'ropoe HeBbipo:m,ae~moe coc'ro~Hi4e raMri~b'ro~~aH- Ho v, Ko'ropoe xapa~epri3ye 'rc~ c ne,~ymme~ co~o~ynHoc'r~m riH,aeKC0B 3anoa- HeHHb~X 3.aeKTpOHHhlX 060n0qeK nl~f o. N~a3aHHoe COCT09HHe c~eRyeT COn0CTaB- JIflTb T0~:e HeBblp0~<jleriHOMy C0CT0fIHriIO riCX0RHOF0 Hy~eB0r0 raMri~bTOHHaHa H o c TeMH >tŸ riH/~eKcaMH 3alq0JIHeHHblX 060J10qeK n l ~ f o ti rlOjI0‰ COCT0fl-
HHIO IIOJ1HOF0 raMHJlbTOHHaHa H . PaccMaTpriBaeM0e C0CTOItHHe HMeeT 9HepFrit0
E o = . ~ 2(2/1 4- 1) en,, , (8) n,l,EŸ
coorBercTBy~o~2e cocroaa~e n3.rIt3ro r a u U~hTOHUaHa 3neprmo
Eo + AE, (9)
iJpHqeM Jlo£ AE M0mH0 paccqHTaTb KaK CyMMy BK.IIa~0B OT Bcex C00TBeT- CTBytOII~HX aTOMHblX ~HarpaMM.
u l-lpaBriJm C0CTaB~eHH~I aTOMHblX qberm~aHoBci<rtx ~narpar~,r n BKJIaa0B OT
HriX B cayqae U--~0 noap05H0 orIricaHbt n [41. l-lpamf~a B cJwqae U@O, KOTOpble Ha~ ce¡ riy~Hbl, npaKTnqecKn He OT~ariqatoTC~ 0T 3TriX npamta. B qaCTH0CTI4 onricbtBalOm~~ Me:~3JIercrpoHHoe B3aHMo~e~CTBne qeTBeprio~ sep- TeKC BH0CriT CBOHM BKJIa~0M pa,RrlaJlbHbll~ rirlrerpa.n
n~ t "N , r '
I ! t ! ! i - - R,, (n 1 ll, n2 lz; ng./2, n i Ir) ;
,~t; ~,-,2t,, Acta Physiea .4eademiae Scientiarum Hungarieae 27, 1969
HHTEPFIPETAL[H~ METO~A XAPTPH--d:~OI<A 353
TOYlbKO Tenepb ~~~ 3TOFO pa~(na~IbHOrO nHTerpana Mbl HMeeM c~e~y~omee BMpa- ~eHHe
Rt (nŸ l~, n; 1~; n~. 12, n~/1) =
= ~ + = r~ drx ~+~ r22drzR,qlŸ (ti) RnŸ t; (zz) Uz (rl, rz) Rn, t,(rz) R. , q (r~); dO dO
( 1 0 )
I "Ÿ r-~-+ ~- r~ < r 2,
U l ( r l ' r 2 ) = Ÿ r I
r l > r2~
(11)
B KOTOp0e BXO~,~IT pa~naab~bIe ~yHKRI414 (4), (5), a He C00TBeTCTByIomHe BO~I,0-
po~IonojIo@ble CyHKLtHH, no~yqaeMbie H3 HnX, ecaH HanO~HTb U ~ 0. I~poMe qeTBepHor0 BepTeKca, Tenepb nO~Ba~eTC~ onHcbmammH~ B3attMoJIe~CTBHe 3neKTp0HOB C BHellIHHM rIoaeM U(r) napHbI~ BepTeKC, KOT0pbI~ BHOCHT CBOHM BKYla)IoM ~HTerpaa
nŸ lŸ n 111 U(nŸ l Ÿ n 1 /1) ~lŸ , II '
npriqeM r]o~Hoe Bblpa>KetIHe An~ C00TBeTCTBym~eFo HHTerpana rIMeeT BH~
U(nŸ lŸ n i 11) : l o '~ r2 ara Rn,~ t Ÿ (Za) U(ri) RnŸ tŸ (rl) ; (12)
OrI~ITb cto~a BXO,~~T paaHaabHbie ~yHKaHH (4), (5). 05paTnM BH~MaHae, qT0 B c . a y (4), (5) rtMeeM
_;o
=~~ Taro qTO
r~ dr~ Rni tŸ (rl) U(rl) Rn Ÿ q (rl) :
{ 1 d 2 1 d Z ) r~ dr 1 RnŸ t i (ra) 2 dr~ rl dr 1 ra en111 Rnq tŸ (rl) ,
. ~ 2(21~ + 1) e., nd~Ef,
t - - . ~ 2(21~ -4- 1) U(n~ li, n~/1) = . ~ 2(2/j + 1) I(na/~)~, nxlxEfo n~l~~f o
(13) r~e
I(nl la) - - 1 2lo +~ r21drlRnŸ237 (rt) { d-~r ~ + 2 d
r I d r l
2Z
T I
l(t + 1) R,q (n). (14)
23 Acta Physica Acaderniae Scientiarum Hungaricat 27, 1969
354 B . B . TO.rlMALIEB
B xapTp~-~b0KOBCrr npHS~i4~eH~4a HaM He06x0A~tMO paccqnTaTb ~3~9 AE ~~naab~ aTO~HbtX a ~ a r p a ~ roabxo nepnoro nopa~xa, Tax KaK
En~ ~ Eo + AEx. (15)
:3TOT pacqeT 0qeHb np0CT [4], a ~ pe3ym,TaTe rabl noayqaer~ ~ ~ BX~a~on aT0~- H~x JmarpaM~ nepBoro nopn~txa 0KOHqaTe~bHble mapa~eHnn
rta[t 2 . ~ (2l~+l)(2l~+l)Ro(n~ll , nzl~; n2iz, n~la), nJ.El ., nt l~ f .
-- 2 (2l~+l)(2lz-4-1).~[l~lzl]2Rl(n~l~'nzl~; nxll'n~l~) ' ndxEŸ n,I t~f , l
Na[
0 -- 2 ~ (21~+l) U(nxl~;nxlx). nxlt~f ,
TaK~M o6pa3oM A~I~ no~I~0fi xapTp~-~pOKOBC~:0ii aHeprn~ Mil ~~eeM c yqeTo~ (15), (13)
EHF = . ~ 2(2/1 + 1) I(nl l~) -4- nl/i~fo
+ 2 ~ (2l~+l)(21~+l)Ro(n~l.,,~12; ,,~.I~,,,14) -- nxhEy ., n t l tE f o
- 2 (24+1) (24+1)2144q~R~(n~l ,~~ /~ ;~x l ,~ . t~ ) . (16) nd ,E f o, n , l tEf , l
EcaH BBeCTn 06~,tqHbIe o£ [2] ~za noaHoro q~c~a C0CT0am~¡ 3Jlek'TpOrtH0iŸ o6oa0q~e g(nl) = 2 ( / + 1) H R.rla npn~oro H o6~eHHoro paa~aab- max nHTerpaaos
F~(nl/1, n2/2) ~ Rl(nllo n2/2; n212q n~l~), G,(nl la, n2 12) ~ R~(n111, ni 12 ; nx 11, n212),
TO Bblpa~eHne (16) MO>~nO IlpeRCTaBI4Tb B £ IIpHBbIqHOM BI4Re
1 Er4F = . ~ q(rh l~) I(nr la) -4- . ~ o ~ q(nx l~) (q(nx la) -- 1) Fo(n t lx, nt la) +
nd~ 6.f, nt l t E " (17) + .~" q(nll~) q(nzl2) Fo(n~ Ix, n2/2) -- 2 2 -'41'I F~(nx l~, na I~) --
nll~ ( f , , nsltE ", nxl, Efo l~eO (ndt > n,4)
-- ~.~ 2 Bt1','G'(nl ll'nzl2) ' nlll E fo, n , h E ro d
(n~4 >1 n,lt)
Acta Physica ,4eademiae Scientiarum Hungaricae 27, 1969
H H T E P r l P E T A U H ~ [ METO,]~A X A P T P H - - ~ O K A 3 5 5
npttqe~ A~,~ = (21~+1)2[1~l~I] ~ npn l=/=0, (18)
B,,t,t = 2(2/1+1) (2/~.+ 1) [l x 121] ~ , (19)
r~Ie CrI~BO~ [/1 Iz l] o3HaqaeT B3~TbIi~ rio MoRy~IO C00TSeTCTSymmnti 3j - - Ko3r q~mt~enT c HyJ]eBb[Mri npoe~urmMn ~oMem'o~ [4].
r iy~bl (18), (19) nO3S0~~IOT paccqHTbIBaTb ne0fixo;m~bIe 3HaqeHri~ K09~I}HI~HeHTOB A, B ~, B qaCTH0CTH, n0JIyqHTb BamHble Ta6a~ilLU
./l lxl B h l:d
/ = 2
$ " 0
6 P 5
$$
s p
P P
/ = 0
2
0
/ = 1
0
2
/ = 2
0
0
12 5
�9 Bb[pa~eHrle (17) ~~~ EHF BMecTe C C00TBeTCTByIOIIIHMH Ta6JmtlaMrl 3HaqeHHi~ K03~){~HIIHeHTOB A, B coBnallamT c nonyqaeMblMH 06blqHHM CII0C060M B Te0pHH xapTpH-~b0KoBcKor0 npH6~m~eHHa [2]; HaCT0~mH~ Cn0C0£ no~yqeHnfl aToro IIpH6JIHXeH~~I II03BOJI~teT He rlpOBO2itiTb BbIqI4cJleHI4~ B rca:~,aoM KOHKpeTHOM cayqae, H cpa3y ~IaeT o6rIme qbopMynbI (18), (19) aJm K03~pqbmmeHTOB Al~t npH 1 ~ 0 H Blg.1.
BB0~fl MHO>KHTe.rIIJ J-IarpaHn<a H Bapbnpyn cJ~ejIytomee mapan<eHne
n~l~~f,
TO eCTb pacKpbma~ BapHavtrfOHHOe yc.aoBrfe
~FHF -- 0 , (21)
M~ no~yqaeM ~3 (16) xapTpri-qboKoscKne ypaBHeHrm S cayqae COCTO~mi~ C 3a- nonnenn~~~ ~~e~poHHSIr~n 0£
dI_~_r2 2 d l ( l+ 1) 2 Z ) + - - + Rnl(r) -- r dr r 2 r
- - 4 . ~ ( 2 / l + l ) f +~ n1[1Ef, .: 0
3-2 .~," (2/13-1)~'[11 ll']2jo +~ n:It E ~, l"
2 ~~~ R.~(r) = O,
r~ dr~ R., t~(r) Uo(r, rl) Rn~,l(rx) Rnl(r) +
r2x dr 1Rmtl(r2) Uv(r, rl) Rnl(rl) Rm,,(r ) +
(22)
23* Acta Physica Academiae Scientiarum Hungaricae 27, 1969
356 B. B, TOd-IMALIEB
rlpiiqeM, pa3yMeeTcfl,
.i+o ,o r z dr R~,(r) R~,(r) = 1. (23)
HOMH0:~a~ npaByto H aeBylO qacTb (22) Ha Rnt(r) ii iiHTerpHpya rio r OT
0 RO + ~ , C yqeTOM (23) riozyqHM ycaoniie
2 U(nl; ni) -- 4 ~ (2lx+l)Ro(ntl~,nl; nl, n~li) + nttt ~ ", (24)
+ 2 ~ ( 2 l ~ + 1 ) . ~ [l~ll']~Rr(n~lx, nl;n~l~,nl) = O. ntl~ ~ f~ l"
9TO Ba~<Hoe yc~oBne, aB~n~meec~ HenocpeJICTBeHHblM cae~ICTBrteM (21), Mbl AO~>KU~ ttHTepHpeTrlpOBaTb Ha ~HarpaMMax: Ha ~HarpaMMHOM ~3~Ke OH0 o3HaqaeT, qTO
0= - ~ , , , , + ,*-~~-.. ~ + -P-r
(HpHqeM 06e BHemHiie .IIHHHH HHKaI< He Hy>I<HO yqHTbIBaTb, 3~IeCb 0HH He JlaIOT HHKarcoro Br~~aAa).
TaKHM o6pa30M yC~0BHe (24) o3HaqaeT, qT0 cpeAH ~HarpaMM Teopiin B08- MyraeHH~, pa3BiiBaeM0~ na OCHOBe xapTpii-~b0KOBCKHX ypaBneHH~ (22), (23), MbI ~OJIM<HbI He paccMaTpHBaTb BOBCe ~IHarpaMMbI, co~ep~<amHe napHble Bep- TeKCbI ii C06CTBeHH0-3HepFeTHqeCKHe qacTii nepBoro nop~AKa, TaK Ka~ BcaeA-
CTBiie (24) BI<.rlaAbl OT BCeX yr~a3aHiib|x aHarpaMM B3aiiMHO coKpamatoTc~.
9TO xapak'repHoe CBOHCTB0 TeopHn B03My~eHH¡ Ha OCHOBe xapTpii- r ripiiS~H~eHHa no cpasHeHmo c ~pyriiM~ Te0pH~Mii B03MymeHHi~ Ha OCHOBe rip0ii3BO.rIbHOFO Hy.rleBOF0 raMH~bTOHiiaHa Ho u, r L B qaCTHOCTH, Te0pHe~
BO3MymeHiia na OCH0~e HCXOAH0r0 Hy~eBoro raMH~bTOHiiaHa Ho, ~enaeT ee 0qeHb yR06H0¡ B paSoTe. Bo~bmoe K0-qiiqeCTBO a~arpaMM, BHpTya~bHO npii- CyTCTByIO~HX B Te0pHii B03MymeHii¡ Tenepb He Hy~Ho paCCMaTpHBaTb.
B qaCTH0CTII B0 BTOpOM nop~~r~e n paccMaTpHBaeM0~ Te0piiii BO3MyttteHiiii OCTaIOTC~I TO.rlbKO caeAymmHe RBe ~Harpa~~i
a B TpeTbeM II0pfl~Ke T0.11bK0 IIIeCTb ~HarpaMM, BepHee BCe BpeMeHHble BepCiiH 3THX LUeCTH ~HaFpaMM,
Acta Phys~ea Academiae Scientiarum Hungarieae 27, 1969
H H T E P r I P E T A U H ~ I METO,~A XAPTPH-- -~OI<A 357
1 , , [
To qT0 3T0 Taro, B 3TOM olerKo y£ paccMaTp}tBa~ B nepmax nopaA- rr petueHHe no TeopHn B03MymeHH¡ ypa~HeHH¡ (22), (23) H BUqHC~q~a B nep- BblX nop~Arr 3Heprrt~ rio qbopMyae (16). B npe~cTaB~eHtm BoAopoAon0RO£ qby~,<t~H~
( I d 2 I d /(/+l) z Em)R~ = O, (25) 2 dr 2 r dr -4- 2r 2 r
./~ ~ r 2 dr R~ R~ = ~n',n" ~r,z', (26)
Mbl ,~0YI~'<HbI pacCMOTpeTb pa3.1io~eH~e
R/1z(r) = . ~ c~.,. R~ (27) n"
np~iqeM j~y[~/ I<03qbqbI4RI4eHTOB aTor0 pa3Jio~ei4H~ rtOYlyql4M ypaBHeHI4~
+ 2 (2/1 + 1) 0 , d, ~l~ c z Ro(ni 11, n2l; n'l, nŸ ~ . n . / 1 , ~o~,/1, . ' , , , n , l , E f u n Ÿ 2 3 7
- - . ~ (211 -f- 1) .~ , [l~lk] 2 . ~ , c~Ÿ c~Ÿ176 n21; nŸ n,l) - n,13f: "o k n; , n ", n ,
l = O, - - I~nl Cn~~ n
(28)
~x' C~,,n~ C l = ~/1,, n'~/12 /12" n '
(29)
3jIecb npe~noaaraeTcn, qT0 B BemtqHHax C l n',~ I4Hj~eI<cU nlE fo. Pa3pemaa ypaBHeHI4~ (28), (29) pa3non<eHrmMrt
C~,,n = ~n',n + ~~#n + . . . . (30)
~n~ = E/1~ + ~~J~ + . . . . (31)
Acta Physica Aeademiae Scientiarum Hungarir 27, 1969
3581 B .B . TO~MAqEB
l'IOJIyqHM, B qaCTHOCTH, npn nŸ
I 0 ! �9 ~'(~) -- 1 / - - 2 ~ , (2/~ + 1) l~(n~l i, n21z, n2l, n,l,) A- "~ni,n.. En~t - - En,t n,l,Ef,
.~~" (2/1 A- 1) .~ ' [t~t2t] ~ o ' +
H np~ n ~ ~ n z
(32)
C•(•) = 0 (33) n2,n 2
1-I0~CTaB~~ pa3ao~eu~a (30), (31), (32), (33) B Bb~pa~eH~e (16). OT~eTaM npeABapnTeJIbHO, qT0
~ ( n t ) = " ; E . . , C'., .n C'., ,n =
- - En, + 2E.I r~(~) -4- . ~ En'~ C#~)n c'(O" --
Ho TaI< KaK B CHJ'Iy yCa0Br~~ 0pToH0pMI4p0BKI4
C/(l) ~l(1) ~ C/n(1) 1 C/n(l~m 0 nl,n I "~- ~nl ,n i ~ /I"
HMeeM
= - 2 ' !,,,:'(') ~~"~.,nOg-'/(2) Cln (! ~ n , . n n"
TO npH6~H>KeHHO
I ( n l ) En I -~- . ~ ( E n , l Ti:. A ClO) CJn(!]n -~ = - - ~ I~ l ] ~ n ' , r l * " " IT:
(3a)
Bo BTOp0M nopfl~Ke H0~yqHM
nd, El, nŸ
n d i E f , , n , l t ~ fo n Ÿ
4 ~ (211 A- 1) (2/2 ~ 1) . ~ [/1 ! !19 "~ r R~(n111, nŸ nl Ii, n~/2) n a l z E f , , n a l . Efo I nŸ ~. (35)
I-IOACTaB~a~ (32), (33) B (38), M~ n0~yq~M ~0BOJIbH0 rpo~o3~Koe sbIpa- >KeHae, I<0T0p0e O~HaK0 M0>KHO npeACTaBnTb B B~Ae CyMMbI BI<~a~0B 0T Tpex aTOMHbIX xapTpH-qb0KOBCKnX anarpa~t~ BTop0r0 nopa~rca s eCTeCTBeHHO BO3Hn- Katome¡ 3~eCb Te0prm Bo8Mymeanª Ha Bo~0p0~IOII0~06HbIX ~yHI~~I4flX (CM. Ta6a. I).
Ta~HM 06pa30M BrCJmAbI 0T 3THX Tpex aHarpaMM BTOpOro nopn~~a c C06- CTBeHHO-3HepreTHqeo<~MH qaCT~Ma nepBoro nop~~Ka yn<e aBTOMaTttqecK~ BKJlIOqeHbI B xapTp~-dpO~OBC~Oe npH6a~~<eH~e, H cJleAOBaTeJ]bHO, OHI~ He MOryT
II0YIBHTbC~I B TeOpHtI BO3My~eHH~ Ha xapTpI~-~OKOBCKIIX ~yHKI.(I~~x.
.4eta Phffsica Academiae Sr Hungaricae 27, 1969
IdHTEPFIPETAIIH~ METO~A XAPTPH--~OI<A 359
2. C0CT0~IHHfl C 0TgpblTblMH 3JlegTpOHHblMH 060~10qgaMH
OrpaHnqgmca 3AeCb paccmoTpeHHem BblpO~)IeHH0rO COCTO~tHHa aToma c 3alIO~IHeHHbIMH 3~eKTp0HHblmH 060~10qKaMH nl ~fo 14 0TKpbIT0~ 060r241 hala; Bce 0CTa~bHble rIyCTble 3~eKTpOHHble O60~IOqKH ~T0rO COCT0aHHa nl~g o. Borne TORO, 5yAem paccMaTprIBaTb 3AeCb T0~IbKO npocTefimnfi c~yqa~i HenoBTopalonle- roca TepMa S L KOHqbHrypaumt la q, rAe q - - qHc~o ~~IeKTp0H0~ B OTKpbITOH 0£
OnaTb Mbl paccMaTpnsaem T0qH0e COCT0aHHe raMn~bToHnaHa Ha U ti COOT- neTcTsym~ee emy, MO HeH3BeCTH0e Hato COCTOaHtte, nO~HOrO ram~~]bTOHttaHa H. TaK qT0 paccMaTpnBaeMoe C0CT0aHHe 14MeeT 3Heprnm
Ea = ~ 2(2/~ + 1) e.,,. + q2(2/~ + 1) e..,. ; (36) n,lx 6f,
COOTBeTCTByIOIIIee eMy C0CT0aHHe IIO.IIHOFO FaMH.lIbTOHHaHa HMeeT 3HepFI4IO
E o + A E , (37)
Cor~iacHo o£ Te0p~IH [4] Be~IHqI4Hy A E Hy)KHO npeACTaBHTb B BI~Ae CyMMbI
A E = AEo + A E ' , (38)
npHqem EA o - - 9TO Be~Hq~Ha ~.rlfl HeBblp0>KReHH0r0 C0CT0~tHHa 0CTOBa nll 1 E fa, B NOT0p0m OTKpbITa~l 0£ hala HyCTa~; •Ta BeYIHqHHa ~aeTca CyMMO~ BKJIa- ~0B 0T C00TBeTCTBylOIIIHX aT0mHbIX qbe~HMaHOBCKHX ~marpaMM 6e3 BHemHHX aHnn~, cm. w 1.
CorzacHo o6me¡ Te0pHH [4], qT06bI BblqnCnHTb BeJlnqHHy AE', Hy~HO peLUaTb ceKy~~pHbIe ypaBHeHH~ C MaTpHile¡ M rio riHRev~cy x nOBT0paemOCTH TepMa SL paccMaTpHBaeM0~ KoHqbHrypaI~HH la. Taro KaK MbI paccmaTpHBaem cnyqa~ HenOBTOp~iolileroca Tepma SL, T0, cne~IoBaTe~b~4o, HaM He Hy)KH0 pe- UlaTb HHKaKBx ceKy~~pHb~X ypaBHeHnfi, a HyM~H0 Hp0CTO BblqHc.IIHTb COOTBeT- CTBylomHfi ~HarOHa~IbHbI~ MaTpHqHbl~ 3~lemeHT MaTpHIlbI M, 146o B paccMaT- pnBaemom cayqae yrr ce~ynapHbie y0aBHeHna CBO~HTCa K C00THOIIIeHHIO
AE" : M((na la) q S L , (n a la) q SL; A E ' ) . (39)
~Haroaa:mHbI~ 3aeMenT (39) MaTpI4IXbl M aaeTc~ CyMm0~ m(na~0B COOTBeT- CTByIOIIIHX aTOmHbIX ~ n a r p a ~ c ~Bym~, qeTbIpbMfl H T. ~l. BHeHIHHMH 331eKTp0H-
HblMH 5IHHH~IMPl; Hy~4<HO paccmaTpHBaTb TOJIbKO ~marpaMMbl c qHCn0M 9~eKTpOH-
Acta Physica Aeademiae Scientiarum Hungaricae 27, 1969
360 B.B. TOYIMAMEB
HblX ~II4HI4~ MeHbIIH4M HJHI paBHb~M y~B0eHHOMy qHc~y 9JIeK'Tp0HOB B 0TKpbITOH 060~10qKe 2q.
l-lpa~~na C0CTaB~IeltI491 BK~Ia~0B 0T Tal<I4X ~narpaMM c B~emHnM~ ~mmaM~ npa U=--0 n0~Ip0£ pa3o£ B [4], ~ aaecb HeT Heo6x0/DIM0CTI4 I4X IIOBTO- p~lTb. E~I4HCTBeHH0, qT0 Ba)KH0, qTO B paccMaTpnBaeMoM c~yqae U ~ 0 Mu •MeeM B Teopmt KpoMe qeTBepHOr0, TaK~e H napHble BepTeKCbI, CM. w 1.
~[]~HaFpaMMbI qbaKTHqecKH C0CTaB~I~IOTC~I T0.IIbKO J~.lI~/ TOF0 cYiyqafl, KoF~a qHC.rl0 BHettlHrlX 3.rleKTpOHHblX .rlVlHI4~ B TOqHOCTH paSMO yAB0eHHOMy qrlC.rly 9.rleKTp0HOB B OTKpbIT0~ 060JlOqKe [4]. ECylI4 0H0 MeHbIIIe ero, TO HaAO IIOJlb30- BaTbCgl qb0pMy.rI0~ pe~yKt~rtH, ~<oTopaa B cayqae paccMaTprmaeMoro C0CT0~IHH~I (nala)qSL IlpI, IHHMaeT BH~ ,/~.llfl cyMMbl Bcex A n a r p a ~ c 2p CBO‰ KOHI2aMI~
PazyMeeTca
Mp((na lo)q SL; (n a l.)q SL; AE') =
= . ~ g(l~ SL , lP ~S'L'; Ig f lS'L' , l~a SL) • ~~s'l"
• Mp((n a la) p ~S'L'; (n a la) p flS'L'; AE ' ) . (40)
q M = ~.~ M p . (41)
p=l
l-IpH COCTas~eHrm m,lpa~eHr~a X~~ xapTpg-qboKoBcKo~ aHeprHn .EHF HaM 3jleCb He0‰ pacCMOTpeTb TOJIbKO j~rlarparr nepBoro nop~~,Ka; B aTOM n0p~nKe HMe~OTCZ ; I H a r p a ~ b l T0m, KO C asyM~ H qeTb~pbMa BHetUHHMH a m ~ p O . H b I ~ m aHHnSMa. TaK qT0 qbarcrHqecKH HaM Hy~Hbt se~nq~HbI g na (40) T0abr~0 nprl p = 1 H p = 2.
IAcnoas3yfl o5mee ycJmsne HOpMnp0sK~ BeJmqnH g, ~0mH0 cpa3y 0npeRe- JIHTb HX RJI~I cJ Iyqa~ p = 1. ~]~r COFJIaCH0 3TOMy yCJ~OBHIO
~" g(l q SL, lP ~S'L'; lP c~S'L', lq SL) = q! :~s'L' p t (q - - p)!
(42)
H OTCm~a B cYtyqae p = 1 cpa3y noayqaeM
g(l q SL, lo) =: q. (43)
~ ~ a p = 2 Be.rlHqHHbl g cne~tyeT CHelXHa~bHO paccqHTblBaTb, HCl'10~b3y~ HX Bbxpa~eHua qepe3 COOTBeTCTBytOmrte reuea~ornqecKHe K03qbqbI4l~rteHTbI. MbI FIpHB0~,HM 3~,eCb Ta~YlHIXbI 3HaqeHH~ COOTBeTCTBylOIKI, IX BeYlHqHH g B Ba~KHbIX
qacTHblX c~yqaflx
Acta Physiea .4cademiae Scientiarum Hungaricae 27, 1969
PIHTEPFIPETAI~HH METO~A XAPTPI4--~Ob(A 361
pa/p~
~S
2p
~D
g(p3 SL, pZ S' L')
'S 3p ~D
- ~ ~ a o
~ 3 5 -g- -2- -6-
- - - - - - 3 - - 3 o ! 2 T
nop~AKa, t~u no~yqtiM A~~ nopan~a B cnyqae ~/-----p.
o, r~la i~
naL~ n~la nal a
(n~~o)~ S' L'
flete ~a[a
g(p4 SL , p2 S ' L ' )
p4/p~ l S
~S
~p - T
~D i ~
3
4
ID
5 3 5 3 8 3
(gp~ SL ; pe S' L')
p~/p~ 1S ap 1D
3
OCTaBngg BKJIaA~I aTONHNX dpe~HMaHOBCKHX ~Harpa~u~, TOJIbK0 nepBoro BeJltiql414b! AE'HFAJlfl BKJIaAOB A t i a r p a ~ nepBoro
2 , ~ (2/~ + 1) Ro(n , l~, n a lo; no lo, n, I~), nd, EIa
- - ,~, (2/1-[-1)X'[lalxl]2R,(nll l , na la ;n t l l , nola), nll, Ef, l
(__ 1)L' (~8",1/2,1/2 2 Rl(na la, na la; na la, na la) X l
X [l a lo/]2 (2la + 1) y.t., /
- - u ( n a la; n,, la) ,
r~La nata ! ii
ti OKoHqaTe~bH0 A~~ no~Ho~ xapTpti-qb0KOBCK0fi 3HeprHti paccMaTptiBaeMoro C0CT0~tHti~l (hala) q S L
E H e = ~ 2 ( 2 / t + l ) I(n~l~)4- n, l lEh
+ 2 ~ (2/1+ 1) (2/2 + X) Ro(nll. n~Z~;~~12, n l l l ) - - nlli (fa, nll, ~ f ,
- .2" (2J1 + 1) (% + 1) ~ , [l~ & tl ~ R,(nl I . ,,~ l~; ,,~ 11, "~.l~) + n,l, E. *, n,l, Ef* l
-4-f [2(2/a 4- 1) I (na lo ) + !
Acta Physica .4cademiae Scientiarum Hungarieae 27, 1969
362 B.B. TO2]MAL1EB
-f- 4 ~ ' (2/a A- 1) (2/1 -4- 1) Ro(nt 11, na la; na la, n111) -- nj, ~fo
2 ~'' (2la + 1) (2ll + 1) .~[lal l l ]2Rl(nala. nlll;nala, n~l~)l+ n,, Efo l J
-4- .~ .~'g(Iq SL. PaS'L ') ( - 1)L" t,.,.L'J X l S ' L '
X (2/a -1- 1)2 [l a la/]2 Rl(n a la, na la; na la, na la), (44)
r~e f=q /2 (2 la+l ) , H 3Ta BennqnHaxapaKTepH3yeT CTeneHb 3ano~neHn~ 3nek'Tp0- HaMH paccMaTpnBaeMo~ OTl<pbIT0¡ 060.rI0qKI, I.
B Ba~HOM cnyqae la ---- 1 ~~~ C0CT0~HH~ (nop)r PyTaH [3], HCnOab3yg npotle~ypy ycpe~tHeHr~~ 3Heprm~ no nceM COCTO~~H~M ~anHoro TepMa SL, FIO3IyqHJI BbIpa~eHHe
E . F = 2 ..~~" Hk + ~ (2I~, -- Kk,) + k kl
+ f { 2 ~ m H m §
~- f . ~ (2airo, -- bKm~)l . (45) mn I
3~eCb I, IH~eKCbI k, 10THOCHTC~I K 3aII031HeHHbIM o6on0qKaM; HH~eKCbI m, n - - k ocTa:mrmiM o6onoq~aM. 2~aaee k ~ (nllxml), 1 ~--- (n,~12m2) H T. ~.
Hk ~ I (n l / i ) ,
I~~ ~ Ro(ni/1, -~/2; -~/~, ~~/,),
K~~ ~- .,Ÿ [ l~ l~ l]2 R~(n~ l~, n~ 12; n~ 11, n~/2) l
H T../~. Bbipa~eHr~e PyTaHa (45) FIOJIHOCTbtO COBna~aeT c HatuHM (44) npI~ la = 1, npHqe~t Mb~ no~yqaeM o£ ~]SHr~~e Bbipa>~eHn~ ~I~~ KO3qb~HIII, IeHTOB a, b PyTaHa
b - - 36 S,~L; g(pq SE; p2 S'L') (-- 1)L' {: :~ ,} , (46) q~
36 ~,g(pq SL;p ~ S'L') (-- 1)L' {~ ~O} (47) 6 a - - b = ~1 ~ ~_ S'L'
[-lo 3THM ~0pMy~taM JIeFK0 COCTaBHTb Ta‰ 3HaqeHH~ K03~~HIIHeHTOB et, b,
HOJ'IHOCTbIO coBr~a~aIo~ym c np~BeaeHHOfi PyTaHOM [3].
p2 3/) p4 p5
1S ap ] iD 2D 1S 3p 1D 2p
0
--3
• 4 2 o
3
4S ~p
2 1
2 0
4
5
4
3 15 4 16
9 o -ff-
Acta Phy sica Academiae Scientiarum Hungaricae 27, 1969
69 24 80 25
27 24 -@- 2--g
IdHTEPFIPETAI.~PIYI METO.~A XAPTPPI---OOI-(A 363
Bbipa~eHHe (44) M0)KH0 TaKme cpaBHnTb C npHBoabIMnM XapTpn [2], KOTOpbd~ HcrIOYIb3OBaSl npoRe~ypy ycpejl~eHHa caMocor~acoBaHuoro noaa no pa3aaqHbIM HanpaBneHnaM B npocTpaHCTBe. DTO BbIpa)KeHt~e HMeeT caeAyro~rffŸ
BH~ 1
EnF = . ~ q(n 1 l~) I(n~ 11) .2~ nx/x~~f. -~- q(n111) (q(/'gl 11) -- 1) Fo(nt lx, ni/1) -4- ngl EA
+ . ~ q(nxll)q(nzl,,)Fo(n~ll, n212) - ~.~ .a~Al~tFt(nlll, n~l~)-- ndt E h, n,l, Ef, n~la (f, 1~0
(nd, > nal,)
- - . ~ ~ , B,~t2, G~(nl la, nz lz) + nd~ (f,,, n,l.E eo 1
(ntlj. ~ nsl2)
-b q(na la) I(na la) + q(na la) . ~ q(n111) Fo(na la ;nxll) + nd~ (f,
1 n + 2 q( a la) (q(na lo)-- 1) IZo(na la; no la) --
q(na la) ~ ~ " Bl,,h, Gl(n a la; nj 11) -- 2(2/a+1) n,t, ~I,
- - . ~ A,,,z F~(na 1,~; na la). (48) l
CpaBHH~a~t (48) C (44), rloayqaeM flBHbIe sbIpa~eH~~t ~aa K03OdpHRI4eHTOB XapTpa
Bt.kt ~ 2(2/a + 1) (2/1 -b 1) [lalll]2, (49)
I \ L ' Jlalal ] A~.,--=-- . ,~g(/q SL; q a S'L) ( -- 11 t,~*.L'f • S'L"
• (21 a + 1)~ [lz la l]Z. (50)
Ho 9THM ~bop~y~aM MOCHO COCTaBHTb Ta‰ 3HaqeHrI~ 9THX ~O3~3t~HRrleHTO/3, IIOJ1HOCTbIO conrta~arotune co 3HaqeHH~mI~ H3 Ta6aHI L nprIBO~~MblX B [2].
f / l
1S
All
0 2
--1 2 5 1 --1 5 1 --1
25
f / t
All
3p
1D
Atl
0 2
4S --3 3 5
2p --3 0
2D --3 6 25
p5/l ~ 2
~p 3 -T-
Al1
p41~ o 2
1s - 6 o
3p - 6 3 5 9 1D --6 25
4eta Physica Academiae Scientiarum Hungaricae 27, 1969
364 B. B. TOSIMALIEB
{ la laO } (__ 1)L' t~l~ l~,L" 14 qT0 OTMeTI4M, qT0 BB14Ry Toro, qT0 la la L' = 214 +---------i- '
1 [l~ ~~ o ] - - -
2la + 1 , MbI H M e e M
At . 0 - - q(q - - 1) (51) 2
Ho~yqHM Tenepb xapTpH-qbor<o~cK~e ypaBHeH~~. B~OR~ mHO>KI~Te~IVi YlarpaH.a H Bapbtlpy~ Bb~pa.eHne
. . . . . . r 2 dr R,~~~(r) R,,~,(r) - - FHF EHF X ' 2(2/1 + 1) eml ~ n~l~ E fe
lo ~~ -- 2(21 a + 1)fen~ u r e dr Rn.t.(r ) Rn.,~(r) - -
- - 4 f ~~,-~'~fi,~ (2/~ + 1) (2/1 + 1) e.~t~ ' ~~t~fo ~" &dr Rn~~~(r)R~,,~(r) - -
f +~ r 2 dr Rn~t~(r ) Rml~(r ) - - 4 f . ~ (2/~ + 1) (2/1 -r 1) en~,., .~,~ nd~~y~ 0
(52)
TO eCTb pacKpbIBa~ B ~IBHOM BI/I~e Bap14aRriOHHbIe yCaOBI4fl
~F,F - o , ~F~F . = 0 , (53) ~R.t,~(r ) 6R~.z.(r)
n0~yqHM xapTpH-~0KOBCKHe ypaBHeHnfl B c~yqae C0CT0~HHfi C 0~HOH 0TKp~T0fi 3aeKTp0HH0~ 060~0qK0¡ (nalo)qSL C Hen0BT0p~mmHMCZ TepMoM
+ + Rnz(r) - - r dr r 2 r
-- 4 . ~ (2/1 + 1) r~ dr 1Rnlt~(rl) Uo(r, rl) Rnlll(rl) RI~ l (r) .3f- nd, ~$Q
-4- 2 _~~" (2l~ + 1) .~~ [/1 ll'] 2 r~ dr~ R~~~,(r~) Uf(r , rx) R,~(r~) Rm~l(r ) -}- n~l~ ~ f ~ l"
+f[ -4 (21~ + 1) r~ d~~ R~o~o(r~) Uo (r, r~) R~o~o(~~) R~~(r) +
+ 2(I a + 1) ~," [l a li'] e r~ dr Rno,~ (r) Uf(r , rl) Rra(rl) R.~l.(r ) + l,
+ 2enzR~z (r) + f4(2/a + 1) enl, ~~,o R~.t~(r ) = 0, (54)
Acta Physica .4cademiae Scientiarurrt Hungarieae 27, 1969
I/IHTEPFIPETALIIAft METO}XA XAPTPI4--q:,OI-(A 365
( d ~ 2 d l(l + 1) 2z ] f ~ + - - r dr r ~ + -r-J Rnd~(r) --
~ o~
- - 4 f . ~ (211+1) r~drlRnj,(r~)U~(r, rx) Rn,l,(rl)R.d.(r)- nd, ~ fo
+ 2f ~ (211+l).~[lllal '] 2 r~dr~Rn:t,(r~)U((r, rx)R.d.(r~)Rn,t,(r)= n t l x ~ Ÿ I"
- - ( 2 l a + l ) 2.~~g(I~ 1)c'llal~l" I [lalal']2 r S'L" "-- " [I~I~L'J
X (55)
+O ~176
X r2~ dr 1 Rnd,(ri) U,,(r, rl) Rnd~(rl) Rnd,(r) +
+ 2fe. . ,R. .~.(r) + 4 f ~" (2/1+1) e..,~,.,~,R.l,~(r) = O, n,t, ~$o
npriqeM riMeeM e....,/d. ~ 8n ,n , , l a l ~ pa3yMeeTc~, 3~y Ba)KHyIO Be.llriqHHy Mbl He i0XeM rip0CTO rI0.rt0~l, ITb paBH0~ Hym0 Ÿ
3. HHTepnpeTauHa ypaBHeHHfl XapTpH-Oo~a ~taa 0TKpb~T0iŸ 0fi0JlOqKH (nala)qSL Ha aTOMHblX ~e~HMaHOBCKHX ~riarpaMMax
l-I0cTyrlriM Terlepb TaK )Ke, Kai< B KOHLIe w I B C.rlyqae 3aMKHyTblX 3~eKTp0H- HbXX o£ B03bMeM xapTpri-qb0~(0BcKHe ypaBHeHri~ (54), (55), npe¡ B HHX B npe~cTaBJIeHrie B0~0p0~0rI0~06HblX OpyHKt~rt¡ (25), (26), (27) ri pa3petIIHM HOYlyqHBILIriecS:I ypaBHeHH~ rio TeopI~ri B03MylI~eHH.q. 3aTeM rlO~CTaBriM 3TH IIpH- £ pemeHrin B Bbxpa~eHrie ~t~~ aHeprrm (44) H riOnblTaeMc~ nHTepnpeTH- p0'3aTb B03HriKatOIIlrie TaM pa3JIHqHbIe BKJIa,Rbl B xapTpri-qb0KoBcI~yIO 3HeprH~o da aTOMHbIX ~e~HMaHOBCKHX ~riarpaMMax. Tar( MbI yCTaHOBHM, C KaKoro po~a RHarpaMMaMri CBFI3aHO npu£ XapTpr i - -~oKa B c~yqae OTKpbITbIX
o6oJloqeK. He ‰ 3ReCb BbIFIriCbIBaTb riCXO~Hble TOqHble ypaBHeHri~ ~~~ C, IIOtlHO-
CTb~ aHanornqHb~e (28), (29), a cpa3y npnBe~eM ypasHeHri~ nepsoro npri6~u- >KeHH~I
c~,n = ~n, , + c'(l!n,, + . . . , (56)
e,~l = E,~t + ecr,ll ) + - . - , (57)
e"): �9 + . (58) Etlala, tlxl 1 ~ i lala, l lxt t �9 �9 �9
A c t a P h y s i c a Acadera iae S c i e n t i a r u m H u n g a r i c a e 27 , 1969
366 B.B. TOTIMAqEB
H~ee~ ana qbyHKtltI~ 3aMKHyTbIX o£
(End �9 -/(1) - - E , ~ t ) %,. +
-q- 2 .~" (2ll+l)RO(nll~,n~l; nl, n~ll) -- n~lt ~f,
-- 2 (21x~' l) .~[l~Ik]2R~(n~lt ' nzl; n~l~,nl) § n,l~ ~f , k
+ f {2(2l~-k 1)R~ l~, n~ l; ni, n a l~) - -
- (2t~ + 1) ~ [~~ ~k]~ ~~ (~. ~o, ~~ t; ~. to, ~t)} - - k
e (~) (~ 21 1~ 6(1) " (~n n (~ - - ( a 'q - : nl,nal . . . . l,l~ 0
(59)
a.aa r OTKpblTO~ 060nOqKa
f (En,t, w x ~t,(1) -4- - - .iE~tl~ t'n2,thl
4- 2 f . ~ (211+l)R~ nala, n~ll) -- k~l~ ~f~
-- f .~~" [l, la k] ~ R~ (n~ l~, n2 la; n~ l~, n a la)q- n,lt~ o
-4- (2 ta+ 1 ) . ~ . ~ g(Iq SL; I~S'L')(--1) c" { la la k I X s ' L ' la la L'I
• [la la k] ~ R~ (n~ la, nz l~; na la, n~ l~) --
- - (2/~+1) en~t,,n,t ~ 6n,tt 6t.,t, = 0 - - f e(.1)t. ~,~,,.. 2 f . ~ , (i) .
n,l,E~%
(60)
I<poMe Toro, ti3 yCnOBn~ HOpMrip0BK~I nMeeM
el(l) + C/(1) = 0 n p t t nxlEfo, n21Efo (61) /22tn 1 F/I tF/2
t./.(1) ...1_ .la(l) = 0 r l p r l ni la ~ lo, cia(X) : O . (62) t'/ll ,/'/a
B pe3ynbTaTe BblqI4CneH14~ MbI nonyqaeM cneRytomH~ pe3y.rlbTaT. ~)HeprH~ nepBoro nop~~Ka ~H, BKntoqaeT B ce6a BKnaRb! OT Bcex COOTBeTCTByIOmHX ~ H a r p a ~ nepBoro nopz~rca, n rI03T0/~y ee He naao paccMaTprmaTb. 3HeprHn BToporo n0pfl~I<a ~HF,~(2) HaIIp0THB, He BKnioqaeT B ce~~I BI<na~bl Bcex ~narpaMM BT0p0Fo nopa~rca.
l-lpe~~e acero, cy~eCTByeT 6onbmoe K0nI.IqeCTBO ~HarpaMM, co~ep~amHx CO~~TBeHH0-3HepFeTHqecKI4e qaCTH nepBOF0 n0pflz, Ka, BKna~bI KoTopbIX non-
w(2) 3TH ~narpaMMbi H305pa~eHbl Hn~e, KpoMe oqeBH~- HOCTbIO B K n I O q e H b I B ~ H F o
HbIX B a K y y M H b I X ~narpaMM, OTn~qa~ou4nxcfl OT npnBe~eHHbIX B T a ‰ I a n ~
Acta Physiea Academiae Sr Hungaricae 27, 1969
IdHTEPFIPETAIAHyl METO}lA XAPTPId--(POI~A 367
Ta6amla I
BKJ~a~Ib[ BaKyyMHb~X XapTp~--~OKOBCKHX RHarpaMM BT0p0Fo nop~~Ka
2A) r r
r
--8 2 TM (2/2+1) , ~ 1 n~l~~f o n~l,~g, EnŸ
X
X [ ~ (21x+1)R~ nŸ nfl:, n~l,)) ~ "nxlx ~/,
8 . ~ (2/~+1) . ~ 1 X 1~. ~.
X (2/1+1) R O (n 1 t~, nŸ 12; /12 l~, n~ lt) • nal, ~f,
2 o )< ( ~ (21lq-1) ~ [ l ~ L , l ] l~l(nlll , nŸ ntl~ ~f, l
--2 . ~ (2lz+l) , ~ 1 n,l,~f, nil~~g, EnŸ
)<
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Acta Physica Academiae Scientiarum Hungaricae 27, 1969
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Acta Physica Academiae Scientiarum Hungaricae 27, 1969
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24 Acta Physica Academiae Scientiarum Hungaricae 27, 1969
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Acta Physica Academiae Scientiarum Hungarir 27, 1969
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L[HTHPOBAHHA~ MHTEPATYPA
I. II. FoM6am, IIpo6~eMa MHOFHX qaCTHI~ B KBaHTOB0ª MexaHH•e, HM, MocKna, 1952. 2. D. R. I-IARTREE, The Calculation of Atomie Stuetures, John Wiley, N. Y.--London, 1957. $. C. C. J. ROOTHXAN, Rey. Mod. Phys., 32, 178, 1860. 4. V. V. TOLMACHEV, Adv. Phys. Chem., ed. I. R. Prigogine, v. 14, 1969.
INTERPRETATION OF THE HARTREE- -FO CK METHOD AS THE METHOD OF PARTIAL SUMMATION OF ATOMIC FEYNMAN DIAGRAMS
V. V. TOLMACHEV
S u m m a r y
The Hartree--Fock method is now the basis for almost all numerical calculations of characteristics of atomie and molecular states. So its interpretation as the method of partial summation of some class of atomie Feynman diagrams is very important. This interpretation permit sus to understand deeply the sense ofapproximation inherent in the Hartree--Foek method and also the reasonsof its peeuliareffeetiveness which werealize for example in ealculations of ground states of light atoms. As a result we will be able to construet on the basis of the Hartree- Foek method the different theories of eleetronic corre]ations more thoughtfully.
24* A eta Ph)sica Academiae Scientiarum Hungaricae 97. 1969
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