Zeinab. T. Dehghani, A. Mizoguchi, H. Kanamori Department of Physics, Tokyo Institute of Technology Millimeter-Wave Spectroscopy of S 2 Cl 2 : A Candidate Molecule for the Detection of ortho-para Transition 1

Nuclear spin of 32 S 2 is zero and 35 Cl 2 is 3/2 Effective Hamiltonian : H = H ROT + H Q + H NSR H ROT : rotational term including the centrifugal distortion H Q : nuclear quadrupole interaction H NSR : nuclear spin – rotation interaction Nuclear spin coupling scheme : I 1 =I 2 =3/2, I 1 +I 2 =I, J+I=F Basis set : |JK±,(I 1 I 2 )I,F > Wang Quantum statics for 32 S 2 35 Cl 2, when K a K c = ee, oo, → I = 0, 2 para- when K a K c = eo, oe, → I = 1, 3 ortho- Theoretical Treatments for 32 S 2 35 Cl 2 C2C2 2

“ortho-para” interaction appearing in the lowest rotational states? I,FI,F I,FI,F 1 01 J KaKc para- ortho- [1] Mizoguchi,et al., J.M.S (2008) 3 Off-diagonal terms of nuclear quadrupole interaction

Nuclear Quadrupole interaction 4 Field gradient tensor

Nuclear Quadrupole Coupling Constants of S 2 35 Cl 2 [MHz] [3] a b c a b c a b c Cl - S bond direction is helically-tilted against all three principal axes 5 [1] Mizoguchi, et al., J.M.S (2008) View from a-, b-, c-axis [3]

How “ortho-para” transition can be possible? 6 [2] Zeinab, J. Phys. Chem. A, (2013)

|Ci||Ci| E+E+ E-E- O+O+ O-O- para ortho E+E+ E-E- O+O+ O-O- Excluding the off- diagonal terms Eigen-Vectors of the hyperfine-rotational States: F=9 (150x150 matrix) 7

Eigen-Vectors of hyperfine-rotational State: F=9 (150x150 matrix) |Ci||Ci| E+E+ E-E- O+O+ O-O- E+E+ E-E- O+O+ O-O- para ortho Including the off- diagonal terms  ab,  bc,  ac 8

Relation between interacting levels Candidate States for Observing “ortho-para” Transition in S 2 Cl 2 Example of two types of mixed levels Normal transition Frequency (MHz) Intensity (a.u.) Forbidden transition Offset Freq. from the normal transition(MHz) Intensity (a.u.)

ortho-para Transitions among K-doubling States | > | > | > | > | > | > 70 GHz 1.12 MHz ortho-states para-states 81, MHz 10 81, MHz

Spectrum Pattern Predicted for the Transition |10 73 > P - |9 64 > P |10 74 > O - |9 63 > O

200K 20K 2K [cm -1 ] Rotational Term Values and Thermal Population of S 2 Cl 2 K K-doubling | >,| > 12 Accidental Neighbor | >, | > A = 0.184cm -1 B = 0.046cm -1 C = 0.041cm -1

Temperature Dependence of the Rotational Spectra T=200K 20K 2K [GHz]

Temperature Dependence of the Rotational Spectra(expanded) 200K 20K 2K [GHz] 14

15 Rapid Scanning mm-MW Pulse Jet Spectroscopy S 2 Cl 2 /(He or Ar) P = 0.5 atm InSb/He detector Pulse valve Elliptical mirror f 1 =480 f 2 =400 10” diffusion pump MW t T sweep =10ms RF Lock-in amp Source Mod. f m =100 KHz  = 0. 1 ms f sweep = 10 MHz  f = f sweep /(T sweep /  =10M/(10/0.1) = 0.1MHz 1)Pulse valve 3)MW freq. sweep 4)Molecular absorption 2)Molecules at probing region

Current Status of the ortho-para Transition Survey Experiment MHz 16 Observed Predicted

Summary Some candidates of the ortho-para transitions of S 2 Cl 2 are predicted with intensities. Experiment for survey of the ortho-para transition has begun. More precise prediction of the intensity, and more measurement is necessary. 17

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Spectrum pattern predicted for the transition 19