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We measured infrared absorption spectra of crystalline II of CH4 and succeeded in detecting a prominent Q(2) peak in the ν3 vibrational region by rapid cooling after annealing as well as previously reported rovibrational and librational-vibrational peaks. The integral intensities of the R(0), R(1), and Q(2) peaks were found to show biexponential dependence on time. This clearly demonstrates the interconversion among the three nuclear-spin isomers occupying low-lying rotational levels. The two relaxation rates obtained by biexponential fitting were (0.48, 2.3), (1.1, 4.1), (2.3, 5.1), and (3.4, 15.3) in units of inverse hour (h−1) at 5.2, 6.0, 6.5, and 7.0 K, respectively.

We study the deformations of a curve $C$ on an Enriques-Fano $3$-fold $X \subset \mathbb P^n$, assuming that $C$ is contained in a smooth hyperplane section $S \subset X$, that is a smooth Enriques surface in $X$. We give a sufficient condition for $C$ to be (un)obstructed in $X$, in terms of half pencils and $(-2)$-curves on $S$. Let $\operatorname{Hilb}^{sc} X$ denote the Hilbert scheme of smooth connected curves in $X$. By using the Hilbert-flag scheme of $X$, we also compute the dimension of $\operatorname{Hilb}^{sc} X$ at $[C]$ and give a sufficient condition for $\operatorname{Hilb}^{sc} X$ to contain a generically non-reduced irreducible component of Mumford type., Comment: 18 pages, final version, to appear in Journal of Pure and Applied Algebra

We have established an apparatus for terahertz and mid-infrared spectroscopy in an ultrahigh vacuum and have measured absorption spectra of D2O clusters trapped in solid Ar. To assign terahertz absorption peaks due to the D2O dimer, trimer, and tetramer, the dependence of the spectrum on the annealing temperature and D2O dilution was analyzed. The assignment was also examined by ab initio calculations with the use of the “our own N-layered integrated molecular orbital and molecular mechanics” method, where the flexibility of surrounding Ar atoms was systematically incorporated. We identified all the intermolecular fundamentals of the dimer and those with significant intensities of the trimer and tetramer, whose structural symmetries were revealed to be broken down. After isolating the D2O clusters in solid Ar, we sublimated only Ar atoms to leave behind matrix-sublimation ice, which was found to be amorphous- or crystal-like depending on the formation conditions: the dilution and sublimation temperature. The crystallinity of matrix-sublimation ice was determined by decomposing its terahertz spectrum into the spectra of amorphous and crystalline ices. Since the crystallinity got higher by raising the dilution and sublimation temperature, the diffusion of the D2O monomer on the surface of sublimating solid Ar was found to be crucial to the crystallization of the sublimation ice.

We study the deformations of a smooth curve $C$ on a smooth projective threefold $V$, assuming the presence of a smooth surface $S$ satisfying $C \subset S \subset V$. Generalizing a result of Mukai and Nasu, we give a new sufficient condition for a first order infinitesimal deformation of $C$ in $V$ to be primarily obstructed. In particular, when $V$ is Fano and $S$ is $K3$, we give a sufficient condition for $C$ to be (un)obstructed in $V$, in terms of $(-2)$-curves and elliptic curves on $S$. Applying this result, we prove that the Hilbert scheme $\operatorname{Hilb}^{sc} V_4$ of smooth connected curves on a smooth quartic threefold $V_4$ contains infinitely many generically non-reduced irreducible components, which are variations of Mumford's example for $\operatorname{Hilb}^{sc} \mathbb P^3$., This is a postprint of an article published in Internat. J. Math. (IJM) with DOI below. This version makes a correction to Theorem 3.3 of the previous version on the arXiv, as well as to the version in IJM, in which we have made a mistake in calculations and the theorem does not hold as it stands. In this version we make a reformulation of the theorem (Theorem 3.3)