Nike Dattani Oxford University Xuan Li Lawrence Berkeley National Lab

2 Σ states: For each v and each N, there are two J: v  vibration N  nuclear rotation ( B v ) J  nuclear rotation + electron spin ( γ v )

2 Σ states: For each v and each N, there are two J: 1927 Hund 1929 Van Vleck 1930 Mulliken J = N - ½ J = N + ½

3 Σ states: For each v and each N, there are three J. v  vibration N  nuclear rotation ( B v ) J  nuclear rotation + electron spin ( γ v )  electron spin + electron spin ( λ v )

3 Σ states: For each v and each N, there are three J. J = N +1 J = N J = N Kramers 1937 Schlapp

2 Σ state 3 Σ state 1927 Hund, 1929 Van Vleck1937 Schlapp

2 Σ state 3 Σ state 1927 Hund, 1929 Van Vleck1937 Schlapp Each v and each N has two J ( 1 energy gap ) Each v and each N has three J ( 2 energy gaps )

2 Σ state 3 Σ state 1927 Hund, 1929 Van Vleck1937 Schlapp Each v and each N has two J ( 1 energy gap ) Each v and each N has three J ( 2 energy gaps )

2 Σ state 3 Σ state 1927 Hund, 1929 Van Vleck1937 Schlapp Each v and each N has two J ( 1 energy gap ) Each v and each N has three J ( 2 energy gaps )

2 Σ state 3 Σ state 1927 Hund, 1929 Van Vleck1937 Schlapp Each v and each N has two J ( 1 energy gap ) Each v and each N has three J ( 2 energy gaps )

2 Σ state 3 Σ state 1927 Hund, 1929 Van Vleck1937 Schlapp Each v and each N has two J ( 1 energy gap ) Each v and each N has three J ( 2 energy gaps )

For v = 20-26, N = 1, all three J energies are seen to (+/ cm -1, +/- 600 kHz) ie. λ v and γ v can easily be determined We want to know their uncertainties. We have an excellent MLR potential ie. we have the parameters and their uncertainties, for the potential

Given the parameters of an MLR potential and their uncertainties, we can find the uncertainties of properties that come from the potential. For B v : w.r.t. each parameter of the potential uncertainty of each parameter of the potential Correlation matrix

Given the parameters of the potential and their uncertainties, we can find the uncertainties of properties that come from the potential. For B v : R. J. Le Roy (1998) JMS 191, 223

Jeremy Hutson (1981) solved a similar DE, but with POTFIT now has Tellinguisen’s implementation in CDJOEL, thanks to Bob Le Roy !

We now have ΔB v. We also have uncertainty in ΔE 1 and ΔE 2 from experiment. Δλ v, Δγ v ?

 

Derivatives calculated analytically Uncertainties in λ v and γ v calculated analytically

No spin-spin or spin-rotation coupling. Three Zeeman levels.

Spin-spin and spin-rotation coupling back. Now four levels !

Problem 1: How do we calculate uncertainty in B v given an analytic potential ? Solution: POTFIT now readily does it (uses Hutson’s 1981 perturbation theory) Problem 2: How do we propagate the uncertainty in B v to get unc. in λ v and γ v ? Solution: Analytic formulas now available Problem 3: What about Zeeman interaction ? Solution: Unknown at the moment