Search results for " approximation"
showing 10 items of 575 documents
The Random-Phase Approximation
2007
In this chapter we extend the TDA particle-hole formalism of Chap. 9 to include correlations in the nuclear ground state. This sophisticated particle-hole formalism is called the random-phase approximation (RPA). In this description the simple Hartree-Fock particle-hole vacuum is replaced by a correlated ground state involving many-particle-many-hole excitations of the simple particle-hole vacuum. The resulting configuration mixing in excited states is more involved in the RPA than it is in the TDA. The ground-state correlations induce both particle-hole and hole-particle components in the RPA wave function.
Particle-Hole Excitations and the Tamm-Dancoff Approximation
2007
This chapter describes the configuration mixing of particle-hole excitations in doubly magic nuclei. The discussion is confined to one-particle-one-hole excitations within the simplest scheme of configuration mixing, namely the Tamm-Dancoff approximation (TDA). We show that the TDA arises from a variational principle and leads to diagonalization of the residual Hamiltonian in a basis of particle-hole excitations of the particle-hole vacuum.
Focal-shift formula in apodized nontelecentric focusing systems
2007
A single analytical formulation for evaluating the focal shift in any apodized nontelecentric focusing setup is reported. The formulation is also useful in the case of imaged paraxial beams. We show explicitly that the magnitude of the focal shift is determined by only one parameter that depends on the effective width of the pupil filter and its axial position. To illustrate our approach we examine different focusing setups.
Correlation and spin polarization in quantum dots: Local spin density functional theory revisited
2005
Using quantum dot artificial atoms as a simple toy model, we reflect on the question of whether spin density functional theory (SDFT) can accurately describe correlation effects in low-dimensional fermion systems. Different expressions for the local density approximation of the exchange-correlation energy for the two-dimensional electron gas, such as the much-used functional of Tanatar and Ceperley, and the recent suggestion by Attaccalite et al., are compared with the results of a numerical diagonalization of the many-body Hamiltonian matrix in the limit of small electron numbers. For systems with degeneracies, as shown in the present work for the example of a spin triplet with S = 1, the …
Late time approach to Hawking radiation: Terms beyond leading order
2019
Black hole evaporation is studied using wave packets for the modes. These allow for approximate frequency and time resolution. The leading order late time behavior gives the well known Hawking radiation that is independent of how the black hole formed. The focus here is on the higher order terms and the rate at which they damp at late times. Some of these terms carry information about how the black hole formed. A general argument is given which shows that the damping is significantly slower (power law) than what might be naively expected from a stationary phase approximation (exponential). This result is verified by numerical calculations in the cases of 2D and 4D black holes that form from…
Super Heavy Dark Matter Anisotropies from D-particles in the Early Universe
2004
We discuss a way of producing anisotropies in the spectrum of superheavy Dark matter, which are due to the distortion of the inflationary space time induced by the recoil of D-particles upon their scattering with ordinary string matter in the Early Universe. We calculate such distortions by world-sheet Liouville string theory (perturbative) methods. The resulting anisotropies are found to be proportional to the average recoil velocity and density of the D-particles. In our analysis we employ a regulated version of de Sitter space, allowing for graceful exit from inflation. This guarantees the asymptotic flatness of the space time, as required for a consistent interpretation, within an effec…
Numerical studies of Minimally Doubled Fermions
2013
We have performed the first numerical study of minimally doubled fermions of the Karsten-Wilczek class in the quenched approximation. This requires fixing the counterterms, which arise due to hypercubic symmetry breaking induced by the Karsten-Wilczek term. Non-perturbative renormalisation criteria are formulated after a detailed study of the parameter dependence of mesonic observables. Minimisation of the mass anisotropy of the pseudoscalar ground state fixes non-perturbative renormalisation conditions for the counterterm coefficients. These anisotropies are mapped out by probing different euclidean components of the transfer matrix through calculations of the pseudoscalar ground state mas…
Nuclear matrix elements for double beta decay in the QRPA approach: a critical review
2009
The calculation of nuclear matrix elements (NME) for double beta decay transitions (DBD) relies upon several approximations. The purpose of this note is to review some of these approximations, and their impact upon the NME. We shall present our results, which have been obtained in the framework of the proton-neutron quasiparticle random phase approximation (pnQRPA), and we shall focus on short range correlations, pairing, and symmetry effects.
Dissipation and decoherence in Brownian motion
2007
We consider the evolution of a Brownian particle described by a measurement-based master equation. We derive the solution to this equation for general initial conditions and apply it to a Gaussian initial state. We analyse the effects of the diffusive terms, present in the master equation, and describe how these modify uncertainties and coherence length. This allows us to model dissipation and decoherence in quantum Brownian motion.
β-decay measurements ofA≃ 70 − 110 r-process nuclei at the National Superconducting Cyclotron Laboratory
2011
The present paper reports on several r-process motivated β-decay experiments undertaken at the National Superconducting Cyclotron Laboratory. β-decay half-lives and β-delayed neutron-emission probabilities were measured for nuclei around the r-process A = 70–80 and A = 90 – 110 mass regions. The data are discussed on the basis of quasi-random phase approximation calculations. The emphasis is made on the impact of these data upon calculations of r-process abundances.