1. Spontaneous Emission between ortho and para- levels of Water-Ion, H 2 O + Keiichi TANAKA K.Harada, S.Nanbu T.Oka MG06, Ohio, 2012 Herschel Space Telescope 2009 FIRST ( F ar I nfra r ed and S ubmillimeter T elescope)

2. HIFI ( H eterodyne I nstrument for the F ar I nfrared) 480~1249, 1414~1909 GHz Bands  / = 10 7 1 11 -0 00 1 10 o 1 01 o 0 00 p 1 11 p 1015 GHz 557 H2OH2O 1A11A1 O + H 3 + → OH + → H 2 O + → H 3 O + + e - → H 2 O +H 2

3. Galactic Center : Sgr B2(M) 1 10 p 1 01 p 0 00 o 1 11 o 1115 GHz 607 H2O+H2O+ 2B12B1 ortho/para = 4.8 ± 0.5 3.0/1.0 → 3.3/0.7 = 4.7 (high T) T e = 21 K T r =2.7 K H2O+H2O+ H3+H3+ ortho para 0 100 200-100 -200km/s SgrB2(M) O + H 3 + → OH + → H 2 O + → H 3 O + + e - → H 2 O +H 2 A&A 518 L111 (2010)) para → ortho Conversion (~1/3)

4. para eo,oe ortho ee,oo H2O+H2O+ FarIR-LMR 1993: Saykally 1998: Evenson K c : o/e +/- b O H1H1 H2H2 a c 2B12B1

5. T ab1 =  T ab2 T ab S a (I 1b - I 2b )  I =  1 Electron spin-Nuclear spin Magnetic Interaction of H 2 O + ortho-para conversion off-diagonal interaction O H1H1 H2H2 SaSa T ab = T ba H op = T ab (S a  I b + S b  I a )  I = I 1 – I 2 I 1b I 2b 2B12B1

6. T bb1 = T bb2 H hf = T bb S b (I 1b + I 2b ) I = (I 1 + I 2 ) Electron spin-Nuclear spin Magnetic Interaction of H 2 O + O H1H1 H2H2 diagonal SbSb I 1b I 2b  I = 0

7. EE 1/  = A ∞ 3  if 2  b = 2.37 D  ~ 1 – 60 sec 1/  = A ∞ 3  if 2  b = 2.37 D  ~ 1 – 60 sec ortho para Spontaneous Emission  ~ 1min + + - - ’’ ’’ Ortho-para Spontaneous Emission of H 2 O + o-p Emission Life Time  ’ =    2  ' =  ortho + a  para  = /  E ortho-para interaction Accidental degeneracy  E o-p Emission Life Time  ’ =    2  ' =  ortho + a  para  = /  E ortho-para interaction Accidental degeneracy  E N’ N N T r = 2.7 K

8. T ab T aa T bb 38.9 MHz obs. 0 -50 MHz -17.9 obs. 72.0 MHz calc. 12060 50 Closed shell as H 2 O C ab (J a  I b + J b  I a ) C ab ~ 10 kHz (C ab /T ab ) 2 ~ 10  7~8 Mol. Phys. 80 1485 (1993) MRD-CI/BK H2O+H2O+ O H1H1 H2H2 SbSb   Open shell : H 2 O + T ab = 72.0 MHz  E ~ 30 GHz  ~ 10  3~4  ’ ~ 1~100 year ~ Cosmic Life Time 2B12B1 ?

9. 200 400 0 600 800 cm -1 0 0 1 1 2 3 4 5 5 4 3 2 KaKa KaKa 8 08 7 35 6 42 5 51 7 26 6 33 5 42 7 17 6 24 6 15 5 33 4 40 4 31 5 24 4 22 3 31 5 15 6 06 4 13 3 22 3 13 2 2o 2 11 2 02 0 00 1 11 4 04 6 34 7 34 6 43 5 50 7 25 8 18 7 16 5 41 6 25 6 16 5 14 5 05 7 07 5 32 5 23 4 41 4 32 4 23 4 14 3 30 3 21 3 12 3 03 2 21 2 12 1 10 1 01 ortho para O H1H1 H2H2 a c b - - EE  cm -1 - -  - - + +    cm  o-p Int.  F = 0 ± ↔ ±  N = 0, ± 1  K a = ± 1 - -  E < 10cm -1 Channels  = 1.2 x 10 -3

10. 3 30 (p,-) J = F 2.5 3.5 2.5 3.5 F 4 22 (o,-) 3.5 4.5 J  = 1.2 x 10 -3  = 2.7 x 10 -4 0.44 cm -1 2 cm -1 2 21 (p,+) 2.5 1.5 151 cm -1  = 0.48 s 4.4 day 53 day o-p Conversion Channel of H 2 O +

11. 3 31 + ortho para o↔p  2 ~10 -5~6 o↔p  2 ~10 -5~6 OH + +H 2 →H 2 O + +  T ns : high temp ? T ns : 21 K ~ min Radiative Cooling of H 2 O +  cm    E  =  cm   = 1.2 x 10 -3

12. 1 01 (p,+) J = F 0.5 1.5 0.5 1.5 F 1 11 (o,+) 0.5 1.5 J 16 cm -1 0.5 1.5 0.5 0 00 (o, - ) F J 0.5  = 8.1 x 10 -5  = 2.0 x 10 -5  ’  = 520 y 0.62 min  = 0.93 min  y o-p Conversion by A Coefficient between 1 01 and 0 00 21 cm -1

13. 1.5 0.5 0 00 (o, - ) F J = 0.5  ’  = 520 y  y o-p Conversion competes with the Reaction 1 01 (p,+) J = F 0.5 1.5 H 2 O + + H 2 → H 3 O + +  Life time of H 2 O + ? H 2 O + + H 2 → H 3 O + +  Life time of H 2 O + ? Diffuse Molecular Cloud n(H 2 +H) = 10~100/cm 3 T k = 100 K v H2 ~ 1.0 km/s  = 100 Ǻ 2 If life time of H 2 O H 2 : 1/cm 3  = 30.9 y Collisions Diffuse Molecular Cloud n(H 2 +H) = 10~100/cm 3 T k = 100 K v H2 ~ 1.0 km/s  = 100 Ǻ 2 If life time of H 2 O H 2 : 1/cm 3  = 30.9 y Collisions T r = 2.7 K ~ n(H 2 ) = ? /cm 3

14. SgrB2(M) FIR Source T r ~ 20K H2O+H2O+ IR IR Dust Stars Black body Rad.

15. 20 40 60 0 80 100 K T 0 5 10 15 20 O-P ratio Black Body Rad. T =20 K 4.8 1.0   10 K  h 1 01 p 1 00 o A B  E=21 cm -1   Radiative Excitation N1N1 N2N2   3  ~ n(H 2 ) = 0.1 /cm 3 ? 

16. -100 100 0 km/s 0 10 15 5 T b (K) ortho para SgrB2(M) o/p = 4.8 1.0 T < 20 K T ~100 K Strong IR Dust V 1 01 p 0 00 o 50

17. 200 0 0 0 1 1 2 2 KaKa KaKa 3 22 3 13 2 2o 2 11 2 02 0 00 1 11 4 04 4 14 3 21 3 12 3 03 2 21 2 12 1 10 cm -1 - - - + + + - + - - + 100 + ortho para Radiative Excitation Process between 1 01 and 0 00 1 01  cm   = 1.8 x 10 -4 T r ~100 K obs. H2O+H2O+ T r = 2.7 K IR  cm   cm  obs.

18. Conclusions 1) Interaction of the H 2 O + ion due to off-diagonal electron spin-nuclear spin interaction term T ab (S a  I b + S b  I a ) has been considered. 2) There are several ortho-para conversion channels below 1000 cm -1 which cause the ortho-para mixing of 10 -3 ~ 10 -4. 3) Spontaneous emission lifetimes between 1 01 (para) and 0 00 (ortho) are calculated to be 520 and 5190 year, which may be longer than the reactive lifetime of H 2 O + with H 2. 4) IR radiation correspond to T < 20 K black body will give the ortho-para ratio of 4.8 when H 2 O + lifetime is longer than the spontaneous emission lifetime,  < 2A, …...

19. 4.8 H 2 O + ortho/para 1.0 -60 0 60 km/s -100 para ortho 10 12 10 13 IR: T=100K km/s SgrB2(M) column densities and o/p-ratios

22. -200 0 100 km/s -100 0 10 20 T b (K) SgrB2(M) H 2 O + (o) 1 11 -0 00 60 Calc. 1.1160 1.1150 1.1155 THz para ortho

23. Molecular symmetry : C 2v (M), G 4 (E, E*, (12), (12)*) Inversion E* : E*  t  ±  t  Parity : ± Permutation (12) : (12)  t = ±  t, + Boson (D) - Fermion (H)  t =  e  v  r  ns (12)  e  v  r = ±  e  v  r a,s ; ± (12)  ns = ±  ns a,s ; ± ortho, para is the symmetry only for  ns Molecular symmetry : C 2v (M), G 4 (E, E*, (12), (12)*) Inversion E* : E*  t  ±  t  Parity : ± Permutation (12) : (12)  t = ±  t, + Boson (D) - Fermion (H)  t =  e  v  r  ns (12)  e  v  r = ±  e  v  r a,s ; ± (12)  ns = ±  ns a,s ; ± ortho, para is the symmetry only for  ns C 2v (M) CC X1X1 X2X2 H(D). Reserved Broken !

24. 200 400 0 600 800 cm -1 0 0 1 1 2 3 4 5 5 4 3 2 KaKa KaKa 8 08 7 35 6 42 5 51 7 26 6 33 5 42 7 17 6 24 6 15 5 33 4 40 4 31 5 24 4 22 3 31 5 15 6 06 4 13 3 22 3 13 2 2o 2 11 2 02 0 00 1 11 4 04 6 34 7 34 6 43 5 50 7 25 8 18 7 16 5 41 6 25 6 16 5 14 5 05 7 07 5 32 5 23 4 41 4 32 4 23 4 14 3 30 3 21 3 12 3 03 2 21 2 12 1 10 1 01 ortho para O H1H1 H2H2 a c b - - EE  cm -1 - -  - - + +    cm  o-p Int.  F = 0 ± ↔ ±  N = 0, ± 1  K a = ± 1 - -  E < 10cm -1 Channels  = 1.2 x 10 -3

25. 3 30 (p,-) J = F 2.5 3.5 2.5 3.5 F 4 22 (o,-) 3.5 4.5 J  = 1.2 x 10 -3  = 2.7 x 10 -4 0.44 cm -1 2 cm -1 2 21 (p,+) 2.5 1.5 151 cm -1  = 0.48 s 4.4 day 53 day o-p Conversion Channel of H 2 O +

26. 3 30 (p,-) J = F 2.5 3.5 2.5 3.5 F 4 22 (o,-) 3.5 4.5 J  = 1.2 x 10 -3  = 2.7 x 10 -4 2 cm -1 4 23 (p,+) 4.5 3.5 210 GHz o-p interaction of H 2 O +  E = 20 kHz A Spectroscopic Determination of T ab A Spectroscopic Determination of T ab 6 kHz

27. H3+H3+ H H H Ortho I = 3/2 Para I = 1/2

28. Ortho Para H3+H3+ (3,3) (1,1) J 1 2 3 K 1 23 0 Radiative Relaxation Process of H 3 + Oka, Epp, APJ (2004) Ortho Para Ortho  ＋ HH H  K = + 3 Centrifugal Distortion (2,2) T n.s. » T rot 500 K H 3 + Galactic Center R(3,3) R(1,1)

29. Ortho Para H3+H3+ (3,3) (1,1) J 1 2 3 K 1 23 0 Radiative Relaxation Process of H 3 + Oka, Epp, APJ (2004) Ortho Para Ortho  ＋ HH H  K = + 3 Centrifugal Distortion (2,2) T n.s. » T rot 500 K

30. 0 00 1 01 2 02 3 03 0 00 1 01 2 02 3 03 ortho 0+0+ 00 H 2 CCD        2 11 2 12 1 10 1 11 para     2 11 2 12 1 10 1 11       T = 0.8 K ortho-para Relaxation: Radiative 0+0+ 00 T n.s. ～ T rot  days  days T rot ~ 3K