STUDY OF THE ZEEMAN EFFECT IN THE [17. 6]7. 5-X18

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Presentation transcript:

STUDY OF THE ZEEMAN EFFECT IN THE [17. 6]7. 5-X18 STUDY OF THE ZEEMAN EFFECT IN THE [17.6]7.5-X18.5 TRANSITION OF HOLMIUM MONOXIDE (HoO) Colan Linton University of New Brunswick, Canada Hailing Wang and Timothy C. Steimle Arizona State University, USA Funding: DOE-BES and NSERC

Goals Determine magnetic g-factors of lanthanide monoxides Use results to examine configurations, coupling cases and to test theory (Ligand Field Theory = LFT) LFT model successfully predicts properties of LnO & LnX(X=F,Cl,Br). LnO ground states predominantly Ln2+[4fNσ(6s6p)]O2- Changed spelling for Lanthanide above periodic table HoO →Ho2+(4f106s)O2- → Ω = 8.5

LFT Coupling in the Ω=8.5 Ground State For f10s configuration: f10 ground state is 5I8 where Lf=6, Sf=2 and Jf=8 The s electron has l=0, s=0.5, j=0.5 Combining gives 2 states separated by exchange interaction Total atomic Angular momentum Ja=7.5 or 8.5 Sf j The ground state has Ja=8.5 Jf Ja Lf Projection on axis gives Ω=8.5 Ground State Ω

Hyperfine Structure F = 5 - 12 Lowest level J=8.5 Ho has nuclear spin I = 7/2 Each rotational level has 8 hyperfine components Ground state Ω = 8.5. Lowest level J=8.5 F = 5 - 12

R Branch 8-7 7-6

F=6-5 Perpendicular Parallel ΔM = -1 +1 22 Transitions 11 Transitions -6 +6 -5 +5 ΔM = -1 +1 22 Transitions 11 Transitions

M” = -2 +5 ΔM=+1 M” = -5 +2 ΔM=-1

Zeeman Analysis Results for R(8.5) The Zeeman shifts (first-order perturbation theory H=-mB): Results for R(8.5) State J geff Correlation Matrix Std. dev.(MHz) X18.5 8.5 10.97(2) 1.00 [17.6]7.5 9.5 9.96(3) 0.95 1.00 8.4 MHz Spelling for correlation and matrix. Don’t know what picture in middle represents. Also erased the geff= after the equation. Not sure what was meant there

Calc Obs

Calc M” = -6 +5 ΔM=-1 M” = -5 +6 ΔM=+1 Obs

P Branch

75MHz

Calc(1st order) M’ M” +4 -4 +4 -4 +3 -5 +5 -3 Obs

Including terms off diagonal in F introduces asymmetry in Zeeman shifts (Brown and Carrington p 605-606) J′=7.5 F M -4 5 +4 -4 4 +4

Zeeman Analysis Final Results X18.5 8.5 11.04(2) 1.00 State J geff Correlation Matrix Std. dev.(MHz) X18.5 8.5 11.04(2) 1.00 [17.6]7.5 9.5 10.04(2) 0.91 1.00 [17.6]7.5 7.5 9.86(2) 0.95 0.87 1.00 9.7

Calc Obs

For f10(5I8)s configuration Magnetic g-factors of ground state (Jj coupling scheme): For f10(5I8)s configuration B = 3Jf(Jf+1)+Sf(Sf+1)-Lf(Lf+1) = 3x8x9+2x3-6x7 = 180 D=3j(j+1)+s(s+1)-l(l+1) = 3x0.5x1.5+0.5x1.5-0 = 3.0 g(Lf,Sf,Jf: l,s,j: Ja,Ω) = g (6,2,8: 0,0.5,0.5: 8.5,8.5) = 11.00

Lowest f10 state, 5I8 (Lf=6,Sf=2,Jf=8) Magnetic g-factors of ground state (LS coupling scheme): Lowest f10 state, 5I8 (Lf=6,Sf=2,Jf=8) LS Ho2+(4f106s)O2- 6I8.5 ground state + s, (l=0,s=0.5,j=0.5) Hund’s Case c g(6,2.5,8.5,8.5)=11.00 Hund’s Case a g(Λ,Σ,Ω) = (Λ + 2.0023Σ) g(6,2.5,8.5)=11.01 Same result in LS or Jj scheme and same for case a and case c Experiment g = 11.04(2)

Upper State Ω=7.5 Possibly f10p configuration 4,6H, I, J States State (LS) Possibly f10p configuration 4,6H, I, J States State Case(a) Case(c) 6H7.5 10.00 4I7.5 9.00 6I7.5 9.25 6I8.5 9.71 Observed g: 9.86 at J = 7.5, 10.04 at J = 9.5

Conclusions Zeeman Effect has shown 1. The ground, X1(Ω=8.5) state of HoO originates from a single Ho2+(f10s)O2-(6I8.5) configuration as predicted by LFT. 2.The excited [17.6]7.5 state at J=9.5 appears to originate from a single 6H7.5 state whereas the J=7.5 level appears to show some configurational mixing.