Two-nucleon transfer reactions in deformed nuclei using very heavy ions

Semiclassical methods found to be highly accurate for inelastic scattering are applied to the calculation of rotational population signatures in heavy-ion two-neutron transfer reactions involving highly deformed targets. Basic features to be expected for such reactions are predicted, and are shown to have straightforward semiclassical interpretations. The rotational population signatures for 2-neutron transfer are shown to be quite different from those expected for the analogous inelastic scattering case. Several calculations are shown for Xe projectiles on rare-earth targets, and it is demonstrated that such reactions can provide a unique probe of nuclear structure in high angular momentum states. The extension of the general ideas employed here to 1-nucleon transfer in deformed nuclei and to several other examples of transfer to highly collective states in deformed and vibrational nuclei using very heavy ions is briefly considered. Experimental possibilities are discussed, and it is concluded that relevant experiments in this virtually unexplored area are possible using sophisticated particle-γ spectroscopic techniques.     

Application of a Bäcklund transformation in gravity driven two phase filtration

A nonlinear boundary value/initial value problem in two-phase filtration under gravity is solved analytically via the application of two successive Bäcklund transformations.     

Observation of pure quadrupole resonance in zinc metal

We report the first observation of nuclear quadrupole resonance (NQR) in Zn metal. A resonance line, which under the assumption of axial symmetry (η=0) corresponds to the $\text{|M| =}\text{3}\text{2}\text{?}\text{5}\text{2}$ transition in the $\text{I =}\text{5}\text{2}$ ground state of ⁶⁷Zn, has been found at v = 4.086(2) MHz at 4.2K. This yields (for η=0) a quadrupole coupling constant of $\text{e}{}^2\text{qQ}\text{h}\text{= 13.620(8)}$MHz, which is the most accurate value currently available.     

Gamma and Alpha decay from the 2.1-msec isomer213mRa

The isomer^213mRa was produced by the reaction²⁰⁹Bi(¹⁰B, 6n), as well as by bombardments of¹²C on Pb isotopes,¹⁴N on Bi, and¹⁶O on natural Hg, with projectile energies in the range 60–100 MeV. The isomer decays with a halflife of 2.1 ms both via gamma internal transitions and via alpha branching to levels in²⁰⁹Rn. A level scheme is proposed in which the isomeric state is assigned as either 17/2^– or 13/2⁺ with shell-model configurations either of theh _9/2 protons coupled to ap _1/2 neutron hole, or of an uncoupledi _13/2 neutron hole. On the basis of alpha decay rate predictions from the new Fliessbach theory, the 17/2^– isomeric assignment is to be preferred.Phys. Abstracts classifications 4.200–4.375     

Subpicosecond hard x-ray streak camera using single-photon counting

We have developed and characterized a hard x-ray accumulating streak camera that achieves subpicosecond time resolution by using single-photon counting. A high repetition rate of 2 kHz was achieved by use of a readout camera with built-in image processing capabilities. The effects of sweep jitter were removed by using a UV timing reference. The use of single-photon counting allows the camera to reach a high quantum efficiency by not limiting the divergence of the photoelectrons.     

Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning

The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students’ mathematical progress.     

The Translation Invariant Massive Nelson Model: II. The Continuous Spectrum below the Two-Boson Threshold

In this paper we continue the study of the energy-momentum spectrum of a class of translation invariant, linearly coupled, and massive Hamiltonians from non-relativistic quantum field theory. The class contains the Hamiltonians of E. Nelson (J Math Phys 5:1190–1197, 1964) and H. Fröhlich (Adv Phys 3:325–362, 1954). In Møller (Ann Henri Poincaré 6:1091–1135, 2005; Rev Math Phys 18:485–517, 2006) one of us previously investigated the structure of the ground state mass shell and the bottom of the continuous energy-momentum spectrum. Here we study the continuous energy-momentum spectrum itself up to the two-boson threshold, the threshold for energetic support of two-boson scattering states. We prove that non-threshold embedded mass shells have finite multiplicity and can accumulate only at thresholds. We furthermore establish the non-existence of singular continuous energy-momentum spectrum. Our results hold true for all values of the particle-field coupling strength but only below the two-boson threshold. The proof revolves around the construction of a certain relative velocity vector field used to construct a conjugate operator in the sense of Mourre.