Precise estimation of shell model energy by second order extrapolation method

A second order extrapolation method is presented for shell model calculations, where shell model energies of truncated spaces are well described as a function of energy variance by quadratic curves and exact shell model energies can be obtained by the extrapolation. This new extrapolation can give more precise energy than those of first order extrapolation method. It is also clarified that first order extrapolation gives a lower limit of shell model energy. In addition to the energy, we derive the second order extrapolation formula for expectation values of other observables.Comment: PRC in pres

Novel Extrapolation Method in the Monte Carlo Shell Model

We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model in order to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater determinants, which enables us to calculate the energy variance efficiently. The feasibility of the method is demonstrated for the full $pf$-shell calculation of $^{56}$Ni, and the applicability of the method to a system beyond current limit of exact diagonalization is shown for the $pf$+$g_{9/2}$-shell calculation of $^{64}$Ge.Comment: 4 pages, 4figure

Discovery of a 500 pc shell in the nucleus of Centaurus A

Spitzer Space Telescope mid-infrared images of the radio galaxy Centaurus A reveal a shell-like, bipolar, structure 500 pc to the north and south of the nucleus. This shell is seen in 5.8, 8.0 and 24 micron broad-band images. Such a remarkable shell has not been previously detected in a radio galaxy and is the first extragalactic nuclear shell detected at mid-infrared wavelengths. We estimate that the shell is a few million years old and has a mass of order million solar masses. A conservative estimate for the mechanical energy in the wind driven bubble is 10^53 erg. The shell could have created by a small few thousand solar mass nuclear burst of star formation. Alternatively, the bolometric luminosity of the active nucleus is sufficiently large that it could power the shell. Constraints on the shell's velocity are lacking. However, if the shell is moving at 1000 km/s then the required mechanical energy would be 100 times larger.Comment: submitted to ApJ Letter

Observation of shell structure in sodium nanowires

The quantum states of a system of particles in a finite spatial domain in general consist of a set of discrete energy eigenvalues; these are usually grouped into bunches of degenerate or close-lying levels, called shells. In fermionic systems, this gives rise to a local minimum in the total energy when all the states of a given shell are occupied. In particular, the closed-shell electronic configuration of the noble gases produces their exceptional stability. Shell effects have previously been observed for protons and neutrons in nuclei and for clusters of metal atoms. Here we report the observation of shell effects in an open system - a sodium metal nanowire connecting two bulk sodium metal electrodes, which are progressively pulled apart. We measure oscillations in the statistical distribution of conductance values, for contact cross-sections containing up to a hundred atoms or more. The period follows the law expected from shell-closure effects, similar to the abundance peaks at `magic numbers' of atoms in metal clusters.Comment: The argumentation in favour of shell structure owing to the fluctuations in the free energy of the nanowires has been strengthened. Further improvements in the presentation include the plot of the radius of the wires versus shell number in Fig.

Potential energy surfaces for cluster emitting nuclei

Potential energy surfaces are calculated by using the most advanced asymmetric two-center shell model allowing to obtain shell and pairing corrections which are added to the Yukawa-plus-exponential model deformation energy. Shell effects are of crucial importance for experimental observation of spontaneous disintegration by heavy ion emission. Results for 222Ra, 232U, 236Pu and 242Cm illustrate the main ideas and show for the first time for a cluster emitter a potential barrier obtained by using the macroscopic-microscopic method.Comment: 10 pages, 21 figures, revtex

Spin-dependent localized Hartree-Fock density-functional approach for the accurate treatment of inner-shell excitation of close-shell atoms

We present a spin-dependent localized Hartree-Fock (SLHF) density-functional approach for the treatment of the inner-shell excited-state calculation of atomic systems. In this approach, the electron spin-orbitals in an electronic configuration are obtained first by solving Kohn-Sham (KS) equation with SLHF exchange potential. Then a single-Slater-determinant energy of the electronic configuration is calculated by using these electron spin-orbitals. Finally, a multiplet energy of an inner-shell excited state is evaluated from the single-Slater-determinant energies of the electronic configurations involved in terms of Slater's diagonal sum rule. This procedure has been used to calculate the total and excitation energies of inner-shell excited states of close-shell atomic systems: Be, B^+, Ne, and Mg. The correlation effect is taken into account by incorporating the correlation potentials and energy functionals of Perdew and Wang's (PW) or Lee, Yang, and Parr's (LYP) into calculation. The calculated results with the PW and LYP energy functionals are in overall good agreement with each other and also with available experimental and other ab initio theoretical data. In addition, we present some new results for highly excited inner-shell states.Comment: 8 pages and 9 table

Dynamics of false vacuum bubbles: beyond the thin shell approximation

We numerically study the dynamics of false vacuum bubbles which are inside an almost flat background; we assumed spherical symmetry and the size of the bubble is smaller than the size of the background horizon. According to the thin shell approximation and the null energy condition, if the bubble is outside of a Schwarzschild black hole, unless we assume Farhi-Guth-Guven tunneling, expanding and inflating solutions are impossible. In this paper, we extend our method to beyond the thin shell approximation: we include the dynamics of fields and assume that the transition layer between a true vacuum and a false vacuum has non-zero thickness. If a shell has sufficiently low energy, as expected from the thin shell approximation, it collapses (Type 1). However, if the shell has sufficiently large energy, it tends to expand. Here, via the field dynamics, field values of inside of the shell slowly roll down to the true vacuum and hence the shell does not inflate (Type 2). If we add sufficient exotic matters to regularize the curvature near the shell, inflation may be possible without assuming Farhi-Guth-Guven tunneling. In this case, a wormhole is dynamically generated around the shell (Type 3). By tuning our simulation parameters, we could find transitions between Type 1 and Type 2, as well as between Type 2 and Type 3. Between Type 2 and Type 3, we could find another class of solutions (Type 4). Finally, we discuss the generation of a bubble universe and the violation of unitarity. We conclude that the existence of a certain combination of exotic matter fields violates unitarity.Comment: 40 pages, 41 figure