High Resolution Laser Spectroscopy of the 18 30

High Resolution Laser Spectroscopy of the [18. 3]0 – a 3Δ 1 Transition of Tantalum Mononitride, Ta. N Colan Linton University of New Brunswick, Canada Damian L. Kokkin, Timothy C. Steimle Arizona State University, USA Funding: NSF (CSDM-A; CHE-1265885)

Ta. N and Fundamental Physics Ta. N molecule as a candidate for the search for a T, P-violating nuclear magnetic quadrupole moment L. V. Skripnikov, A. N. Petrov, N. S. Mosyagin, A. V. Titov, and V. V. Flambaum Phys. Rev. A 92, 012521 (2015) – Published 27 July 2015 It is demonstrated that the Ta. N molecule is the best candidate to search for a T, P-violating nuclear magnetic quadrupole moment (MQM)……………… We report results of coupled-cluster calculations of T, P-odd effects in Ta. N …………. . as well as of the molecule-axis hyperfine structure constant and dipole moment. Ta. N, a molecular system for probing P, T -violating hadron physics Timo Fleig, Malaya K. Nayak, and Mikhail G. Kozlov Phys. Rev. A 93, 012505 (2016) – Published 13 January 2016 All-electron configuration interaction theory in the framework of the Dirac-Coulomb Hamiltonian has been applied to the Ta. N molecule, a promising candidate in the search for physics beyond the standard model ……………………we obtain a parallel magnetic hyperfine interaction constant of − 2954 MHz for the Ta 181 nucleus, a very large molecule-frame electric dipole moment of − 4. 91 D, ……………. 2

Background Ta. N Spectroscopy: First high resolution gas-phase study R. S. Ram, J. Lievin and P. F. Bernath, J. Mol. Spectrosc. 215 , 275 (2002). High temperature emission spectroscopy. FT detection and ab initio calculations Singlet System Triplet System 3

Recent studies: (a) Pulsed laser induced fluorescence of singlet systems 1. J. L. Bouchard, T. C. Steimle, D. L. Kokkin, D. J. Sharfi, R. J. Mawhorter, J. Mol. Spectrosc. 525 (2016) 1 - 6 a) Intensity Measurements: Determined branching ratios. b) Lifetime Measurements: Determined transition dipole moments. c) Dispersed Fluorescence: Determined vibration frequencies 2. S. Mukund, S. Bhattacharyya, S. G. Nakhate, Chem. Phys. Lett. 655 -656 (2016) 51 -54. Dispersed Fluorescence: Observed v = 0 -9 in X 1Σ+, 0 – 4 in a 3Δ 1, 0 – 6 in a 3Δ 2, 0 in A 1Δ (b) CW laser induced fluorescence of singlet systems 3. T. C. Steimle, D. L. Kokkin, Y. Kim, R. J. Mawhorter, C. Linton, Chem. Phys. Lett. 664 (2016) 138 - 142 Hyperfine structure due to Ta nuclear spin (I = 7/2) in the [18. 42]0 + – X 1Σ+ (0, 0) band. Present high resolution study. Examine hyperfine structure of triplet system (a 3Δ 1 state) 4

Singlet System Triplet System Upper State? Triplet transition at 15451 cm-1 Lower state a 3Δ 1 at 2827 cm-1 . -1. . Upper state at 18278 cm Transition is [18. 28]Ω – a 3Δ 1 Quotes from Ram et al (JMS 215 , 275). “Ω values of 2 have been assigned to the excited states of these transitions, although 0+ and 0 - states are also possible. ” “First lines were not observed, so we cannot confirm these Ω values” 5

c Observation of P(1) transition shows Ω’ = 0 b a Obs Q(5) Q(4) J 0 F 3. 5 [18. 28]0 a b c 4. 5 1 Calc a 3 Δ 1 0. 50 0. 60 3. 5 2. 5 0. 70 WAVENUMBER – 15449 (cm-1) 0. 80 0. 90 1. 00 6

HYPERFINE STRUCTURE Diagonal Terms Magnetic hyperfine energy: (Λ = 2, Σ = -1 and Ω = 1 for 3Δ 1) Quadrupole hyperfine energy: WQ = e. Qq 0. f(J, I, F, Ω) (5) Off-diagonal terms from A. Carrington, P. N. Dyer, D. H. Levy, J. Chem. Phys. 47 (1967) 1756 -1763 Data: R(1) - R(3) Q(1) – Q(10) P(1) - P(4): 251 lines State 3Δ 1 [18. 28]0 h (cm-1) e. Qq 0 (cm-1) -0. 1056(1) -0. 1224(14) -0. 1341(9) Lan Cheng Calculation -0. 127!! 7

Frosch Foley Hyperfine Parameters a For a 3Δ 1 h= 2 a – (b. F +2 c/3) Q Q Ca Parameters depend on the electron configuration calculate using known atomic parameters 8

Calculation of e. Qq 0 for a 3Δ 1 state a 3Δ 1 configuration is primarily 1σ22σ21π33σ21δ Visual inspection of orbital diagram (Ram et al. ) approximate composition of molecular orbitals 1σ ~{80% N(2 s) + 20% Ta(5 p)} 2σ and 1π ~{50% N(2 p) + 50% Ta(5 d)} 3σ ~100% Ta(6 s + 5 d) [Fleig et al. calculated 3σ primarily Ta(6 s) + ~10% Ta(5 d)}] 1δ ~ 100% Ta(5 d) Q Calculated e. Qq 0 ~ -0. 113 cm-1 Experimental = -0. 1224 cm-1 9

10

STARK EFFECT [18. 28]0 a 3Δ 1 11

STARK EFFECT a 3Δ 1 State: 1 st order Stark shift (+ small 2 nd order term included in fit) [18. 32]0 state: Ω = 0 state has only 2 nd order effect, negligible for μel < 10 D Fit gives μel = 4. 488(89) D for a 3Δ 1 State Calculations: 4. 74 D (Skripnikov et al) 4. 91(74) D (Fleig et al) B=0. 452463 cm-1; R=1. 694Å; Reduced dipole moment = μ/R = 2. 649 D/Å. Equivalent to an effective nuclear charge of 0. 55 e (Ta+0. 55 N-0. 55) 12

IDENTIFICATION OF EXCITED STATES From previous [18. 42]0+ - X 1Σ+: [18. 42]0+ assigned as calculated 13Π 0+ Dispersed Fluorescence (DF) from [18. 42]0+: Strong transitions to a 3Δ 1 and X 1Σ+ [18. 28]0: No transition to X 1Σ+ [18. 28]0 tentatively assigned as Ω = 0 -: Possibly 13Π 0 - e. Qq 0 = -0. 1341 cm-1 for [18. 28]0 - and -0. 05755 cm-1 for [18. 42]0+ If both are components of 13Π 0, why the large difference? 13

Ram et al calculated energies Ω = 0 - States: 13Π 0Ω = 0+ States: 13Π 0+ 13Σ- 21Σ+ e. Qq 0 [18. 42]0+ = -0. 058 cm-1 [18. 28]0 - = -0. 134 cm-1 13Π: e. Qq 0 (calc) = -0. 098 cm-1 13Σ-: e. Qq 0 (calc) = 0 cm-1 [18. 28]0 -: Only possibility is 13Π 0 - (consistent with e. Qq 0) [18. 42]0+: Possibly 13Π 0+ mixed with 13Σ-0+ reduces magnitude of 13Π 0+ e. Qq 0 14

Conclusions Completely resolved hyperfine structure (hfs) in a 3Δ 1 and [18. 28]0 - states Low J hfs dominated by magnetic effect in a 3Δ 1 state. Smaller quadrupole hfs in both states a 3Δ 1 dipole moment 4. 48 D is in good agreement with ab initio values Quadrupole hfs parameters indicate [18. 28]0 - is 13Π 0[18. 42]0+ is mixture of 13Π 0+ and 13Σ-0+ Need good high level ab initio calculations of hyperfine parameters and dipole moments for excited states 15