Vertex operator algebras of rank 2 - the Mathur-Mukhi-Sen theorem revisited

Let $V$ be a strongly regular vertex operator algebra and let $\frak{ch}_V$ be the space spanned by the characters of the irreducible $V$-modules.\ It is known that $\frak{ch}_V$ is the space of solutions of a so-called \emph{modular linear differential equation (MLDE)}.\ In this paper we obtain a near-classification of those $V$ for which the corresponding MLDE is irreducible and monic of order $2$.\ As a consequence we derive the complete classification when $V$ has exactly two simple modules.\ It turns out that $V$ is either one of four affine Kac-Moody algebras of level $1$, or the Yang-Lee Virasoro model of central charge ${-}22/5$.\ Our proof establishes new connections between the characters of $V$ and Gauss hypergeometric series, and puts the finishing touches to work of Mathur, Mukhi and Sen who first considered this problem forty years ago

Test of the Conserved Vector Current Hypothesis by beta-ray Angular Distribution Measurement in the Mass-8 System

The beta-ray angular correlations for the spin alignments of 8Li and 8B have been observed in order to test the conserved vector current (CVC) hypothesis. The alignment correlation terms were combined with the known beta-alpha-angular correlation terms to determine all the matrix elements contributing to the correlation terms. The weak magnetism term, 7.5\pm0.2, deduced from the beta-ray correlation terms was consistent with the CVC prediction 7.3\pm0.2, deduced from the analog-gamma-decay measurement based on the CVC hypothesis. However, there was no consistent CVC prediction for the second-forbidden term associated with the weak vector current. The experimental value for the second-forbidden term was 1.0 \pm 0.3, while the CVC prediction was 0.1 \pm 0.4 or 2.1 \pm 0.5.Comment: 31 pages, 12 figures, Accepted for publication in Phys. Rev.

Ground-state electric quadrupole moment of 31Al

Ground-state electric quadrupole moment of 31Al (I =5/2+, T_1/2 = 644(25) ms) has been measured by means of the beta-NMR spectroscopy using a spin-polarized 31Al beam produced in the projectile fragmentation reaction. The obtained Q moment, |Q_exp(31Al)| = 112(32)emb, are in agreement with conventional shell model calculations within the sd valence space. Previous result on the magnetic moment also supports the validity of the sd model in this isotope, and thus it is concluded that 31Al is located outside of the island of inversion.Comment: 5 page