Nuclear three-body problem in the complex energy plane: Complex-Scaling-Slater method

The physics of open quantum systems is an interdisciplinary area of research. The nuclear "openness" manifests itself through the presence of the many-body continuum representing various decay, scattering, and reaction channels. As the radioactive nuclear beam experimentation extends the known nuclear landscape towards the particle drip lines, the coupling to the continuum space becomes exceedingly more important. Of particular interest are weakly bound and unbound nuclear states appearing around particle thresholds. Theories of such nuclei must take into account their open quantum nature. To describe open quantum systems, we introduce a Complex Scaling (CS) approach in the Slater basis. We benchmark it with the complex-energy Gamow Shell Model (GSM) by studying energies and wave functions of the bound and unbound states of the two-neutron halo nucleus 6He viewed as an $\alpha$+ n + n cluster system. In the CS approach, we use the Slater basis, which exhibits the correct asymptotic behavior at large distances. To extract particle densities from the back-rotated CS solutions, we apply the Tikhonov regularization procedure, which minimizes the ultraviolet numerical noise. While standard applications of the inverse complex transformation to the complex-rotated solution provide unstable results, the stabilization method fully reproduces the GSM benchmark. We also propose a method to determine the smoothing parameter of the Tikhonov regularization. The combined suite of CS-Slater and GSM techniques has many attractive features when applied to nuclear problems involving weakly-bound and unbound states. While both methods can describe energies, total widths, and wave functions of nuclear states, the CS-Slater method, if it can be applied, can provide an additional information about partial energy widths associated with individual thresholds.Comment: 15 pages, 16 figure

Chemotactic predator-prey dynamics

A discrete chemotactic predator-prey model is proposed in which the prey secrets a diffusing chemical which is sensed by the predator and vice versa. Two dynamical states corresponding to catching and escaping are identified and it is shown that steady hunting is unstable. For the escape process, the predator-prey distance is diffusive for short times but exhibits a transient subdiffusive behavior which scales as a power law $t^{1/3}$ with time $t$ and ultimately crosses over to diffusion again. This allows to classify the motility and dynamics of various predatory bacteria and phagocytes. In particular, there is a distinct region in the parameter space where they prove to be infallible predators.Comment: 4 pages, 4 figure

Quasi-particle continuum and resonances in the Hartree-Fock-Bogoliubov theory

The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.Comment: 12 pages,11 figures,submitted to PR

Shell corrections for finite depth potentials: Particle continuum effects

Shell corrections of finite, spherical, one-body potentials are analyzed using a smoothing procedure which properly accounts for the contribution from the particle continuum, i.e., unbound states. Since the plateau condition for the smoothed single-particle energy seldom holds, a new recipe is suggested for the definition of the shell correction. The generalized Strutinsky smoothing procedure is compared with the results of the semi-classical Wigner-Kirkwood expansion. A good agreement has been found for weakly bound nuclei in the vicinity of the proton drip line. However, some deviations remain for extremely neutron-rich systems due to the pathological behavior of the semi-classical level density around the particle threshold.Comment: 18 pages, 8 figure

Shell Corrections for Finite-Depth Deformed Potentials: Green's Function Oscillator Expansion Method

Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's function method and the generalized Strutinsky smoothing procedure. They are compared with the results of the standard prescription which are affected by the spurious contribution from the unphysical particle gas. In the new method, the shell correction approaches the exact limit provided that the dimension of the single-particle (harmonic oscillator) basis is sufficiently large. For spherical potentials, the present method is faster than the exact one in which the contribution from the particle continuum states is explicitly calculated. For deformed potentials, the Green's function method offers a practical and reliable way of calculating shell corrections for weakly bound nuclei.Comment: submitted to Phys. Rev. C, 12 pages, 7 figure

Modified two-potential approach to tunneling problems

One-body quantum tunneling to continuum is treated via the two-potential approach, dividing the tunneling potential into external and internal parts. We show that corrections to this approach can be minimized by taking the separation radius inside the interval determined by simple expressions. The resulting two-potential approach reproduces the resonance energy and its width, both for narrow and wide resonances. We also demonstrate that, without losing its accuracy, the two-potential approach can be modified to a form resembling the R-matrix theory, yet without any uncertainties of the latter related to the choice of the matching radius.Comment: 7 two-column pages, 3 figures, extra-explanation added, Phys. Rev. A, in pres

Particle-unstable nuclei in the Hartree-Fock theory

Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant states become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: 10He, 12O, 26O and 28O.Comment: 5 pages, LaTeX, submitted to Phys. Rev. Let