Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C)

Let G be a finite subgroup of SL(n,C), then the quotient C^n/G has a Gorenstein canonical singularity. Bridgeland-King-Reid proved that the G-Hilbert scheme Hilb^G(C^3) gives a crepant resolution of the quotient C^3/G for any finite subgroup G of SL(3,C). However, in dimension 4, very few crepant resolutions are known. In this paper, we will show several examples of crepant resolutions in dimension 4 and show examples in which Hilb^G(C^4) is blow-up of certain crepant resolutions for C^4/G, or Hilb^G(C^4) has singularity.

Anomalous diffusion in random dynamical systems

Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in time. What type of diffusion is exhibited by this {em random dynamical system}? We show that the resulting dynamics can generate anomalous diffusion, where in contrast to Brownian normal diffusion the mean square displacement of an ensemble of particles increases nonlinearly in time. Randomly mixing simple deterministic walks on the line we find anomalous dynamics characterised by ageing, weak ergodicity breaking, breaking of self-averaging and infinite invariant densities. This result holds for general types of noise and for perturbing nonlinear dynamics in bifurcation scenarios.

14Be(p,n)14B reaction at 69 MeV in inverse kinematics

A Gamow-Teller (GT) transition from the drip-line nucleus 14Be to 14B was studied via the (p,n) reaction in inverse kinematics using a secondary 14Be beam at 69 MeV/nucleon. The invariant mass method is employed to reconstruct the energy spectrum. A peak is observed at an excitation energy of 1.27(2) MeV in 14B, together with bumps at 2.08 and 4.06(5) MeV. The observed forward peaking of the state at 1.27 MeV and a good description for the differential cross section, obtained with a DWBA calculation provide support for the 1+ assignment to this state. By extrapolating the cross section to zero momentum transfer the GT-transition strength is deduced. The value is found to compare well with that reported in a beta-delayed neutron emission study.

Unbound excited states in 19,17C

The neutron-rich carbon isotopes 19,17C have been investigated via proton inelastic scattering on a liquid hydrogen target at 70 MeV/nucleon. The invariant mass method in inverse kinematics was employed to reconstruct the energy spectrum, in which fast neutrons and charged fragments were detected in coincidence using a neutron hodoscope and a dipole magnet system. A peak has been observed with an excitation energy of 1.46(10) MeV in 19C, while three peaks with energies of 2.20(3), 3.05(3), and 6.13(9) MeV have been observed in 17C. Deduced cross sections are compared with microscopic DWBA calculations based on p-sd shell model wave functions and modern nucleon-nucleus optical potentials. Jpi assignments are made for the four observed states as well as the ground states of both nuclei.

Mesonic and nonmesonic weak decay widths of medium-heavy lambda hypernuclei

We have measured the energy spectra of pions and protons emitted in the weak decay of 12_Lambda_C, 28_Lambda_Si, and Lambda_Fe hypernuclei produced via the (pi+, K+) reaction. The decay widths of the pi- mesonic decay (Lambda -> p + pi-) and the nonmesonic decay (Lambda + N -> N + N) were extracted. The present results demonstrate an increase of the mesonic decay width due to a distortion of the pion wave function in nuclear medium for the first time. The ratios of the neutron- to proton-induced nonmesonic decay widths, Gamma_n(Lambda + n -> n + n)/Gamma_p(Lambda + p -> n + p), were evaluated by a direct comparison of the measured proton energy spectra with the calculated ones. No theoretical calculation which has been proposed so far can simultaneously account for both the nonmesonic decay widths and the Gamma_n/Gamma_p ratios in the present data.