Autoionization Branching Ratios for Metal Halide Molecules Jeffrey J. Kay Lawrence Livermore National Laboratory Jeffrey J. Kay Lawrence Livermore National Laboratory OSU Molecular Spectroscopy Symposium Session RD (Spectroscopic Perturbations) 23 June 2011 Robert W. Field Massachusetts Institute of Technology Robert W. Field Massachusetts Institute of Technology

Cold Molecules Currently there is great interest in producing dense samples of cold molecules and ions Low velocities, long interaction times allow investigation of unexplored areas of molecular physics: Cold Chemistry Control Using External Fields Control Using External Fields Precision Spectroscopic Measurements Time Variation of m p /m e, Ammonia Time Variation of m p /m e, Ammonia New States of Matter Quantum Degeneracy

Vibrational Autoionization of MX Rydberg States Formation of MX + Ions in Selected Rovibronic States?

Producing MX + by Autoionization Most ionization methods non-state- selective Electron bombardment Nonresonant photoionization What about autoionization? Specific rovibronic MX Rydberg levels can be selected by laser and spontaneously eject an electron, leaving behind MX + ion. What is the MX + rovibrational state distribution? MX X 2S+1 Λ Ω MX Intermediate State MX Intermediate State MX Rydberg State |n, L,Λ,v,J> MX Rydberg State |n, L,Λ,v,J> MX + + e - Ionization Continua MX + + e - Ionization Continua J + =0 J + =1 J + =2 J + =3 Production of state-selected metal halide ions?

Autoionization Branching Ratios Product state distributions following autoionization difficult to calculate. MX + rovibronic state distribution depends sensitively on electron-ion electrostatic interactions, especially their dependence on R The only molecule with accurate and complete predictions of autoionization rovibronic branching ratios: H2H2 H2H2 One state 60+ decay channels!

Quantum Defect Model for CaF Recently, we developed a complete quantum defect theory (QDT) model for CaF Summarizes electron-ion interactions in terms of an R-, E-dependent quantum defect matrix, μ(R, E) 75 parameter model = Infinite # of Rydberg states Vibronic perturbations Vibrational autoionization Rotational autoionization 75 parameter model = Infinite # of Rydberg states Vibronic perturbations Vibrational autoionization Rotational autoionization

Quantum Defect Model for CaF A molecule summarized in 75 parameters All spectra. All dynamics.

Electronic Structure of CaF CaF is a prototypical MX molecule F-F- Any MX molecule can be built-up from CaF by adding core-excited states and spin-orbit effects “Sodium Atom” of diatomics: One unpaired electron outside closed shells “Sodium Atom” of diatomics: One unpaired electron outside closed shells Ca 2+ e-e-

Quantum Defect Theory Electron radial wave functions Electron radial wave functions Ion core wavefunctions Ion core wavefunctions Reaction matrix elements Reaction matrix elements Scattering Theory: Physics Embodied in Reaction Matrix 3. Form superposition of channel functions 4. Determine: At which energies do wavefunctions satisfy boundary conditions? 2. Define “channel functions” for all energies: 1. Separate H into e -, ion, interaction terms:

The Reaction Matrix Short Range: Born-Oppenheimer products Short Range: Born-Oppenheimer products Long Range: Electron-ion products Long Range: Electron-ion products Reaction Matrix is the Heart of a QDT Model “Frame Transformation” allows expression in terms of quantum defects Core Short Range Long Range

Frame Transformation At large electron-ion separation, both forms of wavefunction must be equal: By explicitly matching wavefunctions, can express LARGE number of reaction matrix elements in terms of SMALL number of quantum defects. Quantum Defect Matrix Elements (FEW) Quantum Defect Matrix Elements (FEW) Reaction Matrix Elements (MANY) Reaction Matrix Elements (MANY)

R R Rydberg States of CaF CaF + ( 1 Σ +, v=0) + e - v + =0 v + =1 Rydberg states Hund’s Case (b) Ion core 1 Σ + Hund’s Case (b) Ionization Continuum Hund’s Case (d) 1Σ+1Σ+ 1Σ+1Σ+

Autoionization Branching Ratios Rydberg State Hund’s Case (b) Rydberg State Hund’s Case (b) Continuum Hund’s Case (b) Continuum Hund’s Case (b) Eigenvector Decomposition (From MQDT Calculation) Case (b) -> Case (d) Eigenvector Decomposition (From MQDT Calculation) Case (b) -> Case (d) Quantum Defect Derivatives Quantum Defect Derivatives Branching ratios can be calculated from quantum defect derivatives

Autoionization Branching Ratios: CaF Branching Ratios for N = 0 ‘d’ Σ Rydberg series produces primarily N + = 0 ions Autoionization produces mostly N + = 0, 1 ‘d’ Σ Rydberg series produces primarily N + = 0 ions Autoionization produces mostly N + = 0, 1 Mostly N + = 0, 1

Autoionization Branching Ratios: CaF Branching Ratios for N = 1 Branching ratios broaden, shift to higher N + (=1, 2) Mostly N + = 0,1,2

Autoionization Branching Ratios: CaF Branching Ratios for N = 2 Branching ratios broaden, shift to higher N + at higher N Mostly N + = 1,2,3

Autoionization Branching Ratios: CaF Branching Ratios for N = 3 Branching ratios broaden, shift to higher N + at higher N Mostly N + = 2,3,4

Branching Ratios: Trends Overall trends we observe: 1. Best rotational selectivity at low N 2. Less selectivity at high N (more open channels) 3. = N 4. Propensity rule: N + = N, N ± 1 (due to ΔL = ±1 L-mixing) 1. Best rotational selectivity at low N 2. Less selectivity at high N (more open channels) 3. = N 4. Propensity rule: N + = N, N ± 1 (due to ΔL = ±1 L-mixing)

Autoionization Branching Ratios: General MX Rydberg states Hund’s Case (a) Rydberg states Hund’s Case (a) Continuum Hund’s Case (e) Continuum Hund’s Case (e) Expect similar trends for other MX molecules. (Greatest N + -selectivity at low N; Shift to high N + at high N) Methodology developed here applicable to any MX Expect similar trends for other MX molecules. (Greatest N + -selectivity at low N; Shift to high N + at high N) Methodology developed here applicable to any MX Light molecules (MgF +, TiF + ): Very similar trends Heavy molecules (BaF +, HfF + ): Coupling cases change due to spin-orbit Light molecules (MgF +, TiF + ): Very similar trends Heavy molecules (BaF +, HfF + ): Coupling cases change due to spin-orbit Rydberg states Hund’s Case (b) Rydberg states Hund’s Case (b) Continuum Hund’s Case (d) Continuum Hund’s Case (d) Low Z High Z

Acknowledgments Funding: National Science Foundation We thank Eric Cornell and the Cornell Group (JILA/Colorado) for their interest in vibrational autoionization.

eEDM Measurements: Cold Metal Halide Ions Large dipole moment enables measurements of electron electric dipole moment (eEDM) HfF + electric field ~10 10 V/cm Easily trappable using RF traps Metastable 3 Δ 1 state ideal for eEDM measurements Metal halide ions (MX + ) are candidates for ultra-high-precision spectroscopic measurements Cornell Group (JILA) eEDM Scheme HfF + : eEDM Measurements

Autoionization Branching Ratios: General MX Initial State (Hund’s Case (a)) Final States (Hund’s Case (a)) Final States (Hund’s Case (a)) Final States (Hund’s Case (e)) Final States (Hund’s Case (e)) Rydberg states Hund’s Case (a) Rydberg states Hund’s Case (a) Continuum Hund’s Case (e) Continuum Hund’s Case (e) Branching Ratios for High-Z MX + Ions

R R Rydberg States of HfF Rydberg states Hund’s Case (a) Ion core 3 Δ 1 Hund’s Case (a) Ionization Continuum Hund’s Case (e) HfF + ( 1 Σ + ) + e - v + =0 v + =1 1Σ+1Σ+ 3Δ13Δ1 v + =0 3Δ13Δ1 3Δ23Δ2 3Δ33Δ3

(To Be Added) Branching Ratios for HfF (3D Bar Chart) (Several values of J) Branching Ratios for HfF (3D Bar Chart) (Several values of J)

HfF + Ion: eEDM Measurements

Hund’s Case (b) to Hund’s Case (d) Transformation Ch. Jungen and G. Raseev, Phys. Rev. A (1998) Case (b): Good quantum numbers Case (d): Good quantum numbers

Hund’s Case (a) to Hund’s Case (e) Transformation Ch. Jungen and G. Raseev, Phys. Rev. A (1998) Case (a): Good quantum numbers Case (e): Good quantum numbers

Autoionization Branching Ratios Branching ratios are calculated directly from quantum defect matrix elements, using a simple formula: Quantum Defects (Coupling acts at short range = Case (b)) Quantum Defects (Coupling acts at short range = Case (b)) Initial State (Hund’s Case (b)) Final States (Hund’s Case (b)) Final States (Hund’s Case (b)) Final States (Hund’s Case (d)) Final States (Hund’s Case (d))