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

The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.

Quadrupole Moments of Neutron-Deficient 20,21^{20, 21}Na

The electric-quadrupole coupling constant of the ground states of the proton drip line nucleus $^{20}$Na($I^{\pi}$ = 2$^{+}$, $T_{1/2}$ = 447.9 ms) and the neutron-deficient nucleus $^{21}$Na($I^{\pi}$ = 3/2$^{+}$, $T_{1/2}$ = 22.49 s) in a hexagonal ZnO single crystal were precisely measured to be $|eqQ/h| = 690 \pm 12$ kHz and 939 $\pm$ 14 kHz, respectively, using the multi-frequency $\beta$-ray detecting nuclear magnetic resonance technique under presence of an electric-quadrupole interaction. A electric-quadrupole coupling constant of $^{27}$Na in the ZnO crystal was also measured to be $|eqQ/h| = 48.4 \pm 3.8$ kHz. The electric-quadrupole moments were extracted as $|Q(^{20}$Na)$|$ = 10.3 $\pm$ 0.8 $e$ fm$^2$ and $|Q(^{21}$Na)$|$ = 14.0 $\pm$ 1.1 $e$ fm$^2$, using the electric-coupling constant of $^{27}$Na and the known quadrupole moment of this nucleus as references. The present results are well explained by shell-model calculations in the full $sd$-shell model space.Comment: Accepted for publication in Physics Letters