Zeeman Spectroscopy of CaH Jinhai Chen, J. Gengler &T. C. Steimle, The 60 th International Symposium on Molecular Spectroscopy

Interpretation: gaining magnetic moment from A 2  state Observation: X 2  g s =2.0023; g l = ) Matrix isolated Electron spin resonance Knight& Weltner, J. Chem. Phys. 54, 3875 (1971) 3) Magnetic trapping analysis Friedrich et al J. Chem. Phys. 110, 2376 (1999) Observation: R 1 (0.5) (0,0)B 2  X 2  line from 0-26kG Observation: “anomalous” Zeeman splitting in (0,0)B 2  X 2  Interpretation: interaction with J=1.5,A 2   (v=1)  level

J=1.5,A 2  3/2 (v=1) N=1,J=1.5 B 2  + (v=0) Doyle’s group model (JCP 110, 2376 (1999) N=0,J=0.5 X 2  + (v=0) R 1 (0.5) =0.40 Too large; Unrealistic !! H Zee = m  B with m L = -  B g L L, m S = -  B g S S

Goal of present study Model and interpret the Zeeman splitting in all transitions of the (0,0)B 2  X 2  and (0,0) A 2  -X 2  bands g l = H Zee(Eff) = -  B B z (g L L+g S S) +g l [S x B x +S y B y ] +g l ’[e -2i  S + B + +e -2i  S - B - ]

High-resolution spectrometer Electromagnet Optical Zeeman Spectroscopy

Electromagnet for Zeeman spectroscopy (0G-2.5kG) Mirror

Zeeman effect: S R 21 (0.5) (0,0) A 2  3/2 - X 2  + with g l & g l ’ without g l & g l ’ (v=0)A 2  3/2 (v=0)X 2 

Zeeman effect:R 1 (0.5) (0,0) A 2  1/2 - X 2  + with g l & g l ’ without g l & g l ’ (v=0)A 2  1/2 (v=0)X 2  A B C D

Low-resolution LIF B 2  + (v=0)/A 2  r (v=1) X 2  + (v=0) (viewed through a 640 nm bandpass filter) Next slide * * * *=measured

R 1 (0.5) LIF B 2  + (v=0)/A 2  r (v=1) X 2  + (v=0) Feature used by Doyle et al for magnetic field measurements (640 nm bandpass filter)

Zeeman effect:R 1 (0.5) (0,0) B 2  - X 2  + with interaction without interaction A B CD

This splitting used to measure field in mag. trap

Modeling the field free A 2  r (v=1)/B 2  + (v=0) -X 2  + band Generate “supermatrix” representation – Use effective hamiltonian for  v=0 interactions: B 2  + terms (4x4) : H eff ( 2  + ) = BN 2 - DN 4 +  NS + b F IS + c(I z S z -IS) A 2  (v=0) terms (8x8 matrix): H eff ( 2  ) =T v + AL z S z + ½A D [N 2 L z S z + L z S z N 2 ] + BN 2 -D(N 2 ) 2 + ½(p+2q)(e -2i J + S + + e +2i J - S - ) -½q(e -2i + e 2i ) - use explicit terms for  v= 1 interactions: {(-1) q (A+2B)T q (L)T q (S)-2BT q (J)T q (L)} - Interaction parameters: M 1 = - M 2 =

Modeling the A 2  /B 2  + Field free interaction 12x12 Matrix

Determined “field free” parameters from A 2  r (v=1)/B 2  + (v=0) X 2  + band analysis M 2 constrained to =0 Note :  -doubling in A 2  (v=1) approximately =A 2  (v=0) & approximately =  of B 2  + (v=0) Standard deviation of the fit: cm-1.

Two adjustable parameters: g l and

Two adjustable parameters: g l and g l ’

-0.09 a b gl’gl’ glgl (v=0)A 2  Exp (4) Corr. coef (1) Model a) g l ’ = p/2B b) g l = -  /2B (lower limit) glgl (v=0)B 2   Exp. 0.22(4) Corr. coef (1) Model 0.09 a 0.16 b a) g l = -  /2B b) = x Results

Why we prefer this model over Dolye’s 1.Realistic value for 2. Works for all transitions (not just R 1 (0.5)) 3. Many internal consistencies are met: i) g l (B 2  + ) ~ -g l ’(A 2  ) ii) ~ /A etc. iii) Curl relationships give approx. correct results

Conclusions drawn from the CaH Zeeman studies 1)The Zeeman effect in the A 2  (v=1)/B 2  (v=0)- X 2  (v=0) band system can be modeled with two (one?) adjustable parameters for fields as high as those in the magnetic confinement experiments (approx. 25,000 G!) 2)Sorting out the field-free A 2  (v=1)/B 2  (v=0) interaction was crucial to the anlaysis of even the low-field Zeeman spectra.

Funding provided by NSF

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