Nuclear spin conversion of hydrogen molecules trapped and polarized in solidcarbon dioxide
K. Yamakawa1), A. Ishibashi2), T. Namiyoshi2), Y. Azuma2) and I. Arakawa2)
1) : Nanoscale Gr., JAEA 2): Gakushuin Univ.

According to the total nuclear spin I, a hydrogenmolecule (H2) is classified into either the ortho (I=1) orpara (I=0) isomer. Since the total wave function of H2
must be antisymmetric under the proton permutation, theortho (para) species takes only odd (even) values of therotational quantum number J. This coupling allows us tomonitor the nuclear spin conversion (NSC) with use ofrovibrational spectroscopy. The conversion from ortho topara is strictly forbidden in the isolated state but has beenfound to proceed in condensed systems [1]. In particular,
NSC of H2 interacting with a diamagnetic insulator has
been intensively investigated recently, and its mechanism
is still open to discussion [2,3]. In the present study, wedetected weak infrared absorption by H2 trapped andpolarized in solid carbon dioxide (CO2) and measured theNSC rate of H2 to discuss the NSC mechanism [4].
Gases of H2 and CO2 were mixed in a gas handlingsystem at the molar ratio of CO2/H2=100. The gas mixture
was introduced into an ultrahigh-vacuum chamber andwas condensed on a gold plate, which was cooled down
to 5.4 K. Spectra were measured with a Fourier transform
infrared spectrometer and an external HgCdTe detector in
the reflection configuration.
Figure 1 shows the time evolution of the infraredabsorption band of H2 trapped in solid CO2. We definedt = 0 s as the moment when the condensation wascompleted. The absorption band had two components; P1
at 4149 cm-1 grew with time whereas P2 at 4138 cm-1
decayed. By using Gaussian fitting, we determined theintegrated intensities of P1 and P2 as functions of time,
which are displayed in Fig. 2. We found that both thecomponents exhibited the monoexponential timedependence and obtained the relaxation rates as follows:
k1 = (9.6 ± 0.4)  10−4 s−1 for P1 and k2 = (9.2 ± 0.4) 
10 − 4 s − 1 for P2. Since these rates coincided within theexperimental error, we ascribed the time evolution
observed in Fig. 1 to the rotational relaxation of H2 from J= 1 to J = 0 accompanied by NSC from ortho to para; inother words, we assigned P1 to para H2 and P2 to ortho H2.
The inset of Fig. 2 is a schematic diagram of thevibrational transitions corresponding to P1 and P2.
In a previous study, the electric-field-induced
conversion model was proposed to describe NSC of H2adsorbed on amorphous ice [2]. However, the small
vibrational shift of P1 from the gas-phase value of 4161
cm-1 eliminates the possibility that this model isapplicable to H2 inside solid CO2. Instead, we found thatthe measured NSC-rate agrees with the rate of 1  10−3 s−1
estimated from the three-step conversion model [3],where the Coulomb interaction causes the electron

exchange between H2 and solid CO2 in the first step, thehyperfine interaction brings about the simultaneous
singlet-triplet transitions of the electronic and nuclear
states of H2 in the second, and the spin-orbit interaction
finally realizes the electronic singlet-triplet transition
inside the solid. The way of non-destructively measuring
NSC of H2, established in the present study, can beapplied to other systems and will help to reveal the moredetailed mechanism of NSC in diamagnetic insulators.

Fig.1 Time development of the infrared absorption band of H2
trapped and polarized in solid CO2 at 5.4 K.

Fig.2 Time-dependent integrated intensities of the absorption
components of para H2 (P1, circles) and ortho H2 (P2, crosses).
The results of monoexponential fitting are represented bysolid lines. The inset schematically shows the infraredtransitions of P1 and P2. The quantum number of thestretching vibration is represented by v.

References[1] K. Yamakawa and K. Fukutani, J. Phys. Soc. Jpn. 89,051016 (2020).
[2] T. Sugimoto and K. Fukutani, Nat. Phys. 7, 307 (2011).
[3] E. Ilisca et al., R. Soc. Open Sci. 3, 160042 (2016).
[4] K. Yamakawa et al., Phys. Rev. B 102, 041401(R) (2020).