On SIC-POVMs in Prime Dimensions

The generalized Pauli group and its normalizer, the Clifford group, have a rich mathematical structure which is relevant to the problem of constructing symmetric informationally complete POVMs (SIC-POVMs). To date, almost every known SIC-POVM fiducial vector is an eigenstate of a "canonical" unitary in the Clifford group. I show that every canonical unitary in prime dimensions p > 3 lies in the same conjugacy class of the Clifford group and give a class representative for all such dimensions. It follows that if even one such SIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them are (for a given such dimension). I also conjecture that in all dimensions d, the number of conjugacy classes is bounded above by 3 and depends only on d mod 9, and I support this claim with computer computations in all dimensions < 48.Comment: 6 pages, no figures. v3 Refs added, improved discussion of previous work. Ref to a proof of the main conjecture also adde

Modular Invariance and Uniqueness of Conformal Characters

We show that the conformal characters of various rational models of W-algebras can be already uniquely determined if one merely knows the central charge and the conformal dimensions. As a side result we develop several tools for studying representations of SL(2,Z) on spaces of modular functions. These methods, applied here only to certain rational conformal field theories, may be useful for the analysis of many others.Comment: 21 pages (AMS TeX), BONN-TH-94-16, MPI-94-6

A pp-adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices

Suppose that $M$ is an even lattice with dual $M^{*}$ and level $N$. Then the group $Mp_{2}(\mathbb{Z})$, which is the unique non-trivial double cover of $SL_{2}(\mathbb{Z})$, admits a representation $\rho_{M}$, called the Weil representation, on the space $\mathbb{C}[M^{*}/M]$. The main aim of this paper is to show how the formulae for the $\rho_{M}$-action of a general element of $Mp_{2}(\mathbb{Z})$ can be obtained by a direct evaluation which does not depend on ``external objects'' such as theta functions. We decompose the Weil representation $\rho_{M}$ into $p$-parts, in which each $p$-part can be seen as subspace of the Schwartz functions on the $p$-adic vector space $M_{\mathbb{Q}_{p}}$. Then we consider the Weil representation of $Mp_{2}(\mathbb{Q}_{p})$ on the space of Schwartz functions on $M_{\mathbb{Q}_{p}}$, and see that restricting to $Mp_{2}(\mathbb{Z})$ just gives the $p$-part of $\rho_{M}$ again. The operators attained by the Weil representation are not always those appearing in the formulae from 1964, but are rather their multiples by certain roots of unity. For this, one has to find which pair of elements, lying over a matrix in $SL_{2}(\mathbb{Q}_{p})$, belong to the metaplectic double cover. Some other properties are also investigated.Comment: 29 pages, shortened a lo

Three beta-decaying states in 128In and 130In resolved for the first time using Penning-trap techniques

Isomeric states in 128In and 130In have been studied with the JYFLTRAP Penning trap at the IGISOL facility. By employing state-of-the-art ion manipulation techniques, three different beta-decaying states in 128In and 130In have been separated and their masses measured. JYFLTRAP was also used to select the ions of interest for identification at a post-trap decay spectroscopy station. A new beta-decaying high-spin isomer feeding the 15− isomer in 128Sn has been discovered in 128In at 1797.6(20) keV. Shell-model calculations employing a CD-Bonn potential re-normalized with the perturbative G-matrix approach suggest this new isomer to be a 16+ spin-trap isomer. In 130In, the lowest-lying (10−) isomeric state at 58.6(82) keV was resolved for the first time using the phase-imaging ion cyclotron resonance technique. The energy difference between the 10− and 1− states in 130In, stemming from parallel/antiparallel coupling of (π0g9/2−1)⊗(ν0h11/2−1), has been found to be around 200 keV lower than predicted by the shell model. Precise information on the energies of the excited states determined in this work is crucial for producing new improved effective interactions for the nuclear shell model description of nuclei near 132Sn

Measurement of the heaviest beta-delayed 2-neutron emitter : Sb-136

The beta-delayed neutron emission probability, P-n, of very exotic nuclei is crucial for the understanding of nuclear structure properties of many isotopes and astrophysical processes such as the rapid neutron capture process (r-process). In addition beta-delayed neutrons are important in a nuclear power reactor operated in a prompt sub-critical, delayed critical condition, as they contribute to the decay heat inducing fission reactions after a shut down. The study of neutron-rich isotopes and the measurement of beta-delayed one-neutron emitters (beta 1n) is possible thanks to the Rare Isotope Beam (RIB) facilities, where radioactive beams allow the production of exotic nuclei of interest, which can be studied and analyzed using specific detection systems. This contribution reports two recent measurements of beta-delayed neutron emitters which allowed the determination of half-lives and the neutron branching ratio of isotopes in the mass region above A = 200 and N > 126, and a second experiment which confirmed Sb-136 as the heaviest double neutron emitter (beta 2n) measured so far.The beta-delayed neutron emission probability, P-n, of very exotic nuclei is crucial for the understanding of nuclear structure properties of many isotopes and astrophysical processes such as the rapid neutron capture process (r-process). In addition beta-delayed neutrons are important in a nuclear power reactor operated in a prompt sub-critical, delayed critical condition, as they contribute to the decay heat inducing fission reactions after a shut down. The study of neutron-rich isotopes and the measurement of beta-delayed one-neutron emitters (beta 1n) is possible thanks to the Rare Isotope Beam (RIB) facilities, where radioactive beams allow the production of exotic nuclei of interest, which can be studied and analyzed using specific detection systems. This contribution reports two recent measurements of beta-delayed neutron emitters which allowed the determination of half-lives and the neutron branching ratio of isotopes in the mass region above A = 200 and N > 126, and a second experiment which confirmed Sb-136 as the heaviest double neutron emitter (beta 2n) measured so far.The beta-delayed neutron emission probability, P-n, of very exotic nuclei is crucial for the understanding of nuclear structure properties of many isotopes and astrophysical processes such as the rapid neutron capture process (r-process). In addition beta-delayed neutrons are important in a nuclear power reactor operated in a prompt sub-critical, delayed critical condition, as they contribute to the decay heat inducing fission reactions after a shut down. The study of neutron-rich isotopes and the measurement of beta-delayed one-neutron emitters (beta 1n) is possible thanks to the Rare Isotope Beam (RIB) facilities, where radioactive beams allow the production of exotic nuclei of interest, which can be studied and analyzed using specific detection systems. This contribution reports two recent measurements of beta-delayed neutron emitters which allowed the determination of half-lives and the neutron branching ratio of isotopes in the mass region above A = 200 and N > 126, and a second experiment which confirmed Sb-136 as the heaviest double neutron emitter (beta 2n) measured so far.Peer reviewe