Sum-rules and Goldstone modes from extended random phase approximation theories in Fermi systems with spontaneously broken symmetries

The Self-Consistent RPA (SCRPA) approach is elaborated for cases with a continuouslybroken symmetry, this being the main focus of the present article. Correlations beyondstandard RPA are summed up correcting for the quasi-boson approximation in standard RPA.Desirable properties of standard RPA such as fulfillment of energy weighted sum rule andappearance of Goldstone (zero) modes are kept. We show theoretically and, for a modelcase, numerically that, indeed, SCRPA maintains all properties of standard RPA forpractically all situations of spontaneously broken symmetries. A simpler approximate formof SCRPA, the so-called renormalised RPA, also has these properties. The SCRPA equationsare first outlined as an eigenvalue problem, but it is also shown how an equivalent manybody Green’s function approach can be formulated.     

Influence of a continuum on cluster-decay processes

A microscopic approach to cluster decay including single-particle states in a continuum is given. The equations of motion describing cluster-like states are derived within the multistep shell-model approach. The lowest collective two-particle eigenmodes are used as building blocks for α-like states. Good agreement with low-lying states in ²¹²Po is obtained. The spectroscopic factor for the α decay between ground states is reproduced. It is shown that only by including the continuum part of the single-particle spectrum is the decay width for α-and cluster-decay processes reproduced. The α-like structure of the lowest states in ²¹²Po is analyzed, and strong high-lying resonances are predicted.     

238Pu cluster decay in the macroscopic-microscopic approach

The experimental half-life of ³²Si cluster decay from ²³⁸Pu was reproduced by using the microscopic-macroscopic approach. Several microscopic models for the inertia were tested. The best results were obtained with an effective mass given by the Gaussian overlap approximation formalism. The most probable cluster decay modes of the same parent were also predicted. A superasymmetric fission trajectory for the magic radioactivity was found by using the minimal action principle. A magic valley in the deformation energy was confirmed and its origin explained. It is due to strong shell effects of the daughter ²⁰⁶Hg . The nuclear shape parametrization takes into account five degrees of freedom associated to the elongation, necking, mass asymmetry and deformations of nascent fragments. The single particle energies and the nucleon wave functions are obtained within the superasymmetric Woods-Saxon two-center shell model.     

Elastic scattering of heavy ions and a modified liquid drop model

Zeitschrift für Physik A Hadrons and nuclei - The repulsion due to the nonlinearity of a Schrödinger equation for the elastic scattering of heavy ions is approximated by the compression...     

Systematics of proton emission

A very simple formula is presented that relates the logarithm of the half-life, corrected by the centrifugal barrier, with the Coulomb parameter in proton decay processes. The corresponding experimental data lie on two straight lines which appear as a result of a sudden change in the nuclear shape marking two regions of deformation independently of the angular momentum of the outgoing proton. This feature provides a powerful tool to assign experimentally quantum numbers in proton emitters.     

Coexistence of “ $ \alpha$ + 208Pb ” cluster structures and single-particle excitations in 212 84Po128

Excited states in ²¹²Po have been populated by a \alpha transfer using the ²⁰⁸Pb(¹⁸O,¹⁴C) reaction at 85MeV beam energy and studied with the EUROBALL IV g \gamma multi-detector array. The level scheme has been extended up to ∼ 3.2 MeV excitation energy from the triple-g \gamma coincidence data. Spin and parity values of most of the observed states have been assigned from the g \gamma angular distributions and g \gamma -g \gamma angular correlations. Several g \gamma -lines with E _γ < 1 MeV have been found to be shifted by the Doppler effect, allowing for the measurements of the associated lifetimes by the DSAM method. The values, found in the range [0.1-0.6]ps, lead to very enhanced E1 transitions. All the emitting states, which have non-natural parity values, are discussed in terms of a \alpha - ²⁰⁸Pb structure. They are in the same excitation-energy range as the states issued from shell-model configurations.     

Synthesis of Four Diastereomers of Sclerophytin F and Structural Reassignment of Several Sclerophytin Natural Products

Synthesis of the triol that has been proposed to be the marine natural product sclerophytin F has been completed along with the syntheses of three diastereomers. Comparison of the NMR spectroscopic data for all four compounds to the data reported for the natural product reveals that sclerophytin F is not the 3S diastereomer of sclerophytin A as proposed by Friedrich and Paquette. Re‐analysis of the NMR spectroscopic data for known sclerophytin natural products and synthetic analogues leads to the conclusion that sclerophytins E and F are the same compound. This finding has allowed structural reassignment of several other cladiellin natural products.     

Anisotropic α decay

A microscopic approach to the problem of anisotropic α decay in deformed nuclei is presented. Nuclear wave functions are calculated within the BCS approach, and the WKB semiclassical approximation is used for the penetration through the deformed Coulomb barrier. Results are compared with recent experimental data obtained at CERN by the ISOLDE and NICOLE collaborations. The predictions of the model for well-deformed nuclei are in very good agreement with experimental findings.     

Angular distribution in ternary cold fission

We describe the spontaneous ternary cold fission of ²⁵²Cf, accompanied by ⁴He, ¹⁰Be and ¹⁴C. The light cluster decays from the first resonant eigenstate in the Coulomb potential plus a harmonic oscillator potential. We have shown that the angular distribution of the emitted light particle is strongly connected with its deformation and the equatorial distance.