Optical Zeeman Spectroscopy of the (0,0) bands of the B 3 -X 3 and A 3 -X 3 Transitions of Titanium Monoxide, TiO Wilton L. Virgo, Prof. Timothy C. Steimle and Prof. John M. Brown Ap. J. 628, 2005 July 20
Jan 13, 2016
Optical Zeeman Spectroscopy of the (0,0) bands of the B3-X3 and A3-X3 Transitions of Titanium Monoxide, TiO
Wilton L. Virgo, Prof. Timothy C. Steimle and Prof. John M. Brown
Ap. J. 628, 2005 July 20
Zeeman Spectroscopy of TiO: Dual Purpose
• Magnetic “g” factors are useful in unraveling the nature of electronic states of metal containing molecules.– Analyze electronic state composition and
provide evidence for mixing between states.
• Optical Zeeman effect of TiO is used to probe ambient stellar magnetic fields. – Experimentally determine magnetic tuning
rates of molecular energy levels.
TiO Stokes V Spectrum of SunspotS.V. Berdyugina et. al. A&A 364, L101 2000
3000G
Calc. Stokes V Profile of (0,0) R3(10) line with magnetic field strengths .5-3.5kG
TiO (0,0) R3 band head in a sunspot
Dashed: ObservedSolid: Calculated
Origin of the Stokes V Spectrum
Profiles calculated for low-J lines of Q branch in ’(B3-X3)
Zeeman Effect in Diatomic Molecules:Berdyugina’s Astrophysical Model
mL = -BgLL, mS = -BgSS
Magnetic dipole moment operator is a sum of terms directly proportional to angular momentum operators:
In principle, Zeeman effect can be predicted a priori from field freeeigenvalues and eigenvectors given the g-values:
J JJ MnΛ S nΛ S J M m B
J ( / ( 1)B L SBM g g J J
1. Only diagonal terms in J included2. Predicts linear field dependence3. gS, gL fixed to 2.002 and 1.04. and are rigorously good
Berdyugina et. al. A&A 412, 513 (2003), A&A 385, 701 (2002).
Modeling the Zeeman Effect in TiO:Sophisticated Effective Hamiltonian Approach
1. Spin-orbit and rotational mixing significant in metal species2. Evident in large -doubling in B3 state of TiO
2 2
( .) g L g S
g μ S B S B g S B S B
L B z S B z
i il B x x y y l B
eff
e e
ZeeH
Key difference from astrophysical model:Accounts for both linear and non-linear field dependence byincluding off diagonal in J matrix elements
Eff. Hamiltonian absorbs effects of other states into the g parametersMakes allowance for all possible admixtures of electronic statesAdjustable g parameter values glean insight into the perturbations
Laser Ablation and Molecular Beam Production
Free JetExpansion
High-Resolution Spectrometer
Electromagnet
Optical Zeeman Spectroscopy
Electromagnet for Zeeman Spectroscopy (56G-1.2kG)
Electronic Transitions of TiOW
avenum
ber (c
m) x
10
-1-3
X3
B3
A3
E312.0
0.0
14.0
16.0
(D3
-band= 101ns
band= 4900 ns
C3
18.0
20.0
Zeeman Spectra: R11(1) (A32-X31)
Zeeman Spectra: Q11b(1) (0,0) ’(B30 - X31) Feature
‘Stick’ Spectra of Q11b(J) ’(B 30 - X31) Branch
A) Berdyugina model with only diagonal (in J) matrix elements and fixed g-factorsB) Steimle model w/off diagonal J=+/-1 matrix elements and determined g-factors
Results: Zeeman Fitting Parameters
State Fit A Fit BgL gL gl
A3 0.994(2) 0.994(2)B3 1.037(8) 1.035(8) -0.02(4)a
Std. dev. 18.9MHz 18.9MHza Consistent w/value predicted by Curl’s relationship:gl = -/2B = -.02
Conclusion #1: Chemistry
• gL values indicate that C3 is reasonable candidate for state that interacts strongly with both A3 and B3.
• C~A and C~B satisfy rules for S.O. mixing– C3 state differs by one spin-orbital from A3
and B3 states• A3,B3: 82341141
• C3: 823411101
– C3 state differs from A3 and B3 states by one unit of orbital angular momentum.
Conclusion #2: Astrophysics
• Significant -doubling in B30 state requires inclusion of J=+/-1 matrix elements.
• Strong off-diagonal J interaction will impose a non-linear response to magnetic field in the low-J lines. Fitted g-factors necessary to reproduce experimental observations. Unexpected by current astrophysical model.
Thank YouFunding provided by NSF Experimental Physical Chemistry