Reorientation-effect measurement of the first 2+ state in 12C : Confirmation of oblate deformation

A Coulomb-excitation reorientation-effect measurement using the TIGRESS γ−ray spectrometer at the TRIUMF/ISAC II facility has permitted the determination of the 〈21 +‖E2ˆ‖21 +〉 diagonal matrix element in 12C from particle−γ coincidence data and state-of-the-art no-core shell model calculations of the nuclear polarizability. The nuclear polarizability for the ground and first-excited (21 +) states in 12C have been calculated using chiral NN N4LO500 and NN+3NF350 interactions, which show convergence and agreement with photo-absorption cross-section data. Predictions show a change in the nuclear polarizability with a substantial increase between the ground state and first excited 21 + state at 4.439 MeV. The polarizability of the 21 + state is introduced into the current and previous Coulomb-excitation reorientation-effect analyses of 12C. Spectroscopic quadrupole moments of QS(21 +)=+0.053(44) eb and QS(21 +)=+0.08(3) eb are determined, respectively, yielding a weighted average of QS(21 +)=+0.071(25) eb, in agreement with recent ab initio calculations. The present measurement confirms that the 21 + state of 12C is oblate and emphasizes the important role played by the nuclear polarizability in Coulomb-excitation studies of light nuclei

Spatio-featural scale-space

Linear scale-space theory is the fundamental building block for many approaches to image processing like pyramids or scale-selection. However, linear smoothing does not preserve image structures very well and thus non-linear techniques are mostly applied for image enhancement. A different perspective is given in the framework of channel-smoothing, where the feature domain is not considered as a linear space, but it is decomposed into local basis functions. One major drawback is the larger memory requirement for this type of representation, which is avoided if the channel representation is subsampled in the spatial domain. This general type of feature representation is called channel-coded feature map (CCFM) in the literature and a special case using linear channels is the SIFT descriptor. For computing CCFMs the spatial resolution and the feature resolution need to be selected. In this paper, we focus on the spatio-featural scale-space from a scale-selection perspective. We propose a coupled scheme for selecting the spatial and the featural scales. The scheme is based on an analysis of lower bounds for the product of uncertainties, which is summarized in a theorem about a spatio-featural uncertainty relation. As a practical application of the derived theory, we reconstruct images from CCFMs with resolutions according to our theory. The results are very similar to the results of non-linear evolution schemes, but our algorithm has the fundamental advantage of being non-iterative. Any level of smoothing can be achieved with about the same computational effort.DIPLEC