Landé interval rule (assignment!) l examples

Transcription

1 36 - Read CTD, pp AT TIME: O H = ar s ζ(,, ) s adé terva rue (assgmet!) ζ(,, ) ζ exampes ζ (oe ζfor each - term) (oe ζfor etre cofgurato) evauate matrx eemets ater determata bass ad may-e M or M M bass O off - dagoa ( = ) tracofguratoa H matrx eemets: O 3 = ee otes [page 35-9]! eg.. I6 H H6? TODAY: O. eectros vs. hoes a shortcut: e r j vs. H (hoes are a coveece spectra of soated atoms ad moecues, but they are a esseta part of the terpretve pcture for sods). Hud s 3rd rue 3. effect: adé g-factor formua va W-E Theorem (doe prevousy by projecto theorem) 4. Matrx eemets of H ater determata bass set. o dfferece betwee eectro ad hoe as far as effect s cocered. EXT TIME: e sods (CTD, pages 56-68)

2 . reatoshp betwee cofguratos wth e vs. hoes subshe / fu subshe s p d f # e for p 5 s t ecessary to cosder a 5 e? 5 e.g. αβαβ α = p P M =, M = / (± β s the uoccuped sp - orbta. It s the "hoe") 5 p P M =, M = / = ζ αβαβα O H p s = h ζ + ( ) p e 5 so expectato vaue of H O : 5e = ζ p h but for sge e (wth the same M, M as the fve e ) H O e p P M =, M = / = ζ s α =+ ζ p p h s the sg fp just a cocdece? O! TRICK: Hoe s exacty equvaet to e (for detca M M or M ) except that the sg of ts charge s reversed. * o effect o e /r j because teractg partces have charge of the same sg (ether both e or both hoe), so e /r j s aways a repusve teracto. [What happes for f 3 p? Certay dfferet from fp!] * reverse sg for H O because H O s a reatvstc eectrostatc teracto betwee e ad uceus (+ charge). Repacg e by h + ad eavg the sg o the uceus the same reverses the sg of H O!

3 36-3 p p d d 5 9 p p d d 4 8 d d d 3 7 d 4 6 etc. preted that hoes are e, ater determats descrbe sp-orbtas occuped by hoes. * a F k, G k, ζ rema postve (repusos) * a e /r j eergy eve patters are uaffected * a ζ(,,) reverse sg ook at Tkham 6-, page 87 fgure. ζ d vs. ζ(,,) for owest - term of (3d) cofgurato sg chage, too rapd evouto wth Z 3 Z eff perodcty, soeectroc seres, aufbau too IIGHT reguarato of treds EXTRAPOATIO AIGMET ABOR AVIG! hedg systematcs: Z Z + Z eff Z eff +.5 : shedg Burs Rues. G. Burs,. C. P. 4, 56 (964).

4 36-4

5 . Hud s Thrd Rue 36-5 Cosder oy -, - - term, whch Hud s st ad d rues detfy as the owest yg wth the () cofgurato Ths - term w aways be a sge ater determat for the M =, M = compoet, M,, M = = = α( - ) α dagoa eemet of H O ζ (as may α sps as possbe) ( ) =,, ζ m m ζ( ( ),, )= ζ M M Σm m s s? she ess tha / fu, < +, a sps are α =/? f a sps are α, maxme M by puttg e to each m startg at m = ad workg dowward. M terms sum get from each term sum [ ] = + ( )+ ( + )= ( ) a sps α Σm ζ(, )= ζ ζ / M = = ζ / OR WHICH IMPIE ζ!

6 36-6 he / fu =, = owest - term s + = +, a sps α, m = = + (sge for a = terms) - o fe structure he more tha / fu? + α sps + β sps M = [( + ) [ ( + )]]= + = +? for the + α sps for the + m = + m β sps, = + = M = α sps β sps ζ(, )= ζ m ( α ) ( β) m ζ ζ = [ ( + ) ] = + ζ =! # of hoes ummary for owest eergy - term: > ** ζ,, for ess tha / fu, = for / fu, < for more tha / fu ζ ** ζ(,,)=± # of e + # of h

7 36-7 Hud s thrd rue: OY FOR OWET EERGY - term, owest compoet s = for < + = = + = + > + reguar o fe structure verted Assgmets: sg of ζ() # of compoets extreme vaues (recoge va terva rue) magtude of ζ # of M compoets tug rates 3. effect may-e atoms ( + ) H =µ h B MH/Gauss Bohr mageto (Used γ prevousy) remember that H s awkward M bass set W E Theorem trck to smpfy H : cosder oy matrx eemets dagoa [There are aso oero matrx eemets of H off-dagoa.] O H ad e r are strcty dagoa. ce H has sum of vectors wth respect to j, W - E Theorem says t ca have =, ± matrx eemets. Whe we evauated matrx eemets of ad M the hard way, we saw that there were oero = ± matrx eemets. Our speca case = H << B s usefu as og as E E (Ths fas at hgh B whe ζ() s sma.)

8 36-8 for = matrx eemets, repace both ad by M M = M M M M = M M but = +. Add the equatos = ( α) = (α) [Ths trck s equvaet to, but ot as eegat as, the projecto Theorem.] H = µ ( ) + = µ α ( + ) α B B α h 4 34 {! h part part Trck to evauate α: = + = dagoa M matrx eemet of both sdes ( + )= ( + )+ ( + ) M M ** h h h M M = M M M M = M M M M M α = α M M = α + h competeess: has = seecto rue, has =, has =, s scaar wth respect to, M = Pug ths to the ** equato above ad rearrage: ( + )+ ( + ) ( + ) α= ( + )

9 H =µ BM =µ [ + ] BM 3 α from from 678 } ( α)+ α g 36-9 adé g-vaue g + = + ( + )+ ( + ) ( + ) α ( + ) de * g s tug coeffcet = = µ * equay spaced M compoets db M g * exceet dagostc for dfferet, of same r r g s arge whe ad are parae (.e. sce = +, rr parae, at costat meas smaest possbe order to have argest possbe ) rr g sma whe, are atparae e.g. = 3 : =, = 3 =, = =, = = 3, = g = 3, = : = 4 parae =3 = ( atparae) * g decreases at costat whe s repaced by. * g decreases at costat ad as decreases from + to. How to determe : * appy B-fed ad cout M compoets (costat spttgs upper ad ower - term) * measure g (Quatum Beats) * poarato depedet spttg patter: M = for poared, M = ± for x or y poared, M = + or for crcuary poared

10 36 - Compare drect evauato of matrx eemet to g determed depedety. Matrx Eemets of H ater determata bass set? e.g. f H 3 H =µ 6 M = 6 = 3αα h B ( s ) + 3αα H 3αα =µ B 3 3 = 7µ ow compare wth g equato: 3 H 6H H 6 =µ B gm 6 6 [( + ) + ( + )] B g 67 = = + 7 = =µ ( B ) = µ B agrees!

11 36 - Hoe vs. e for effect. What about a sge hoe state? Does effect reverse sg? E E f 3 f F F 7 / 7 / 7/ = 3α 3α3β β 7/ = 3α 3 ( f F7 / 7/ )=µ ( B) ( + 7) e = 4µ B 6e ( f F7 / 7/ )=µ ( B) [ 3+ ]= 4µ B 3 same as f [ ] α-sps o sg chage for for e vs. h +. WHY? same M, β-sps M