On the validity of the narrow band approximation

The accuracy of the narrow band approximation is estimated. It is shown that, in order to assess the accuracy of the approximation, not only the form of the source function but also the form of the integrand is required. The accuracy is improved when the integrand is symmetric.     

Study of the validity of the Gaussian approximation for the nuclear spectral distributions in a solvable model

It is shown in a two-level model using either a pairing or monopole-monopole interaction that the predominance of the one-body part of the Hamiltonian over the two-body one is responsible for the occurence of Gaussian distributions.     

On the validity of the capillarity approximation in the rate theory of homogeneous nucleation

An Einstein model is used to calculate the internal vibrational free energy of approximately spherical fcc crystallites as a function of crystallite size at T/θ = 1. It is found that the free energy per surface atom does not become convergent until a size of about 3 × 10⁷ atoms is reached. The excess free energy at convergence is used to define the macroscopic surface tension for use in the capillarity approximation. The internal free energy of microcrystallites containing of the order of 100 atoms is fortuitously well described by the capillarity approximation. A good estimate of the total free energy of the microcrystallite (nucleus) is obtained from the capillarity approximation only by adding the contributions from free translation and rotation and the replacement partition function.     

On the validity of the variational approximation in discrete nonlinear Schrödinger equations

The variational approximation is a well known tool to approximate localized states in nonlinear systems. In the context of a discrete nonlinear Schrödinger equation with a small coupling constant, we prove error estimates for the variational approximations of site-symmetric, bond-symmetric, and twisted discrete solitons. This is shown for various trial configurations, which become increasingly more accurate as more parameters are taken. It is also shown that the variational approximation yields the correct spectral stability result and controls the oscillatory dynamics of stable discrete solitons for long but finite time intervals.     

On the validity of the inclusion of geometrical shadowing functions in the multiple-scatter Kirchhoff approximation

The validity of the geometrical shadowing functions for use in calculations of the light distribution scattered from a rough surface is investigated. By the use of the multiple-scatter Kirchhoff approximation, single- and double-scattered contributions are calculated with and without the incident, intrasurface and scatter-shadowing functions. Explicit conditions are given for the validity of the geometrical shadowing functions.     

Perspectives in nuclear physics

We discuss some of the many important questions in modern subatomic physics that have been addressed over the past two decades at Mainz. These achievements range from precision studies of nucleon form factors, to nucleon spectroscopy, novel probes of nucleon structure such as virtual Compton scattering and fundamental tests of quantum chromodynamics. In the future one may expect to see this effort expanded to precision tests of physics beyond the Standard Model.     

The behavior of quasi-particle levels with allowance for neutron-proton correlations within the HFB cranking approximation

The cranking model taking into account the residual neutron-proton correlations with Gaussian interaction in the Hartree-Fock-Bogolyubov approximation has been formulated. The behavior of quasi-particle levels as a function of the rotation frequency of even-even and odd-odd nuclei with A = 158 has been investigated within this approach.     

Impurity nuclear physics

Using a germanium-detector array for hypernuclear γ spectroscopy (Hyperball), we measured B(E2) of the ⁷ _ΛLi hypernucleus and observed a significant shrinkage of the ⁶Li core induced by a Λ-particle. In this way, nuclear properties can be drastically changed by introducing a Λ-particle, which can be investigated by high-resolution hypernuclear γ spectroscopy. In the future neutron-rich hypernuclei will also be studied, where interesting modifications of nuclear structure by a Λ-particle are expected. Received: 1 May 2001 / Accepted: 4 December 2001     

The validity of the Thomas Fermi approximation

The Thomas Fermi method is applied to calculate energies of nuclei with density dependent effective forces. The Thomas Fermi equations have both continuous and discontinuous solutions. From the continuous solutions the terms of the semiempirical mass formula are determined. The neutron-proton density distributions are given for the 50–240 mass range.     

Strangeness nuclear physics

An overview of strangeness nuclear physics is given, focussing on spin dependent effects in Λ hypernuclei, on the ΛN → NN weak interaction in Λ hypernuclei, on the density dependence of the Σ nuclear potential and on double strangeness physics. A special emphasis is placed on the recent proposal to study experimentally Ξ⁻ atoms.     

Algebraic approaches in nuclear physics

I critically discuss the various algebraic approaches in nuclear physics, looking for limitations and successes. Special emphasis is placed on open problems and active research areas. Presented at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Quantum chaos in nuclear physics

A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.     

Renormalization in few-body nuclear physics

Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac-delta and/or its derivatives). They express the renormalization group invariance of quantum mechanics. The present approach for the renormalization scheme relies on a subtracted T-matrix equation.     

Parity nonconservation in nuclear physics

We present an overview of the parity-nonconservation effects in nuclear physics. In the processes of polarized neutron scattering by nuclei, apart from the ordinary dynamical enhancement, we also consider the additional resonant enhancement in the entrance channel due to the proximity of the compound-nucleus p-wave resonance. We discuss the problem of extracting information on the electroweak interaction of nucleons from nuclear data.