Symmetry-conserving random phase approximation

The projected random phase approximation (PRPA) is derived from a generator coordinate ansatz. It allows the calculation of excited states in the region of phase transitions, where conventional RPA breaks down. The theory is applied for an approximate solution of the R(8) model which shows a pairing collapse at large angular momenta.     

Ikeda sum rule,self-consistency and double-beta decay in the renormalized quasiparticle random phase approximation

The effect of the inclusion of ground-state correlations into the QRPA equation of motion for the two-neutrino double-beta (ββ_2ν) decay is carefully analyzed. The resulting model, called renormalized QRPA (RQRPA), does not collapse near the physical value of the nuclear force strength in the particle-particle channel, as happens with the ordinary QRPA. Still, the ββ_2ν transition amplitude is only slightly less sensitive on this parameter in the RQRPA than that in the plain QRPA. It is argued that this fact reveals once more than the characteristic behavior of the ββ_2ν transition amplitude within the QRPA is not an artifact of the model, but a consequence of the partial restoration of the spin-isospin SU(4) symmetry. It is shown that the price paid for bypassing the collapse in the RQRPA is the violation of the Ikeda sum rule.     

Current conserving random phase approximation

The consequences of the continuity equation for the RPA are exploited, if charge and current densities are given. Simple, yet stringent conditions for the RPA amplitudes and the residual interaction are obtained. Under these conditions the RPA equations are simplified and exactly reduced to a hermitean eigenvalue problem of half the original dimensionality. Transition current matrix elements are then similar to those of an effective current recently proposed for TDA calculations.     

Extension of the renormalized quasiparticle random phase approximation

The quasiparticle random phase approximation is extended in order to restore of the Pauli principle beyond the renormalized approach by treating the so-called scattering terms in the QRPA phonon operators. It has been shown that this new framework can be described in a case of a single nuclear shell occupied by both protons and neutrons in terms of the QRPA(14,3) algebra. An application of the formalism to the double beta decay of calcium⁴⁸Ca is discussed to some extent. Presented by W.A. Kamiński at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work has been supported in part by the State Committee for Scientific Research (Poland), Contract No. 2 P03B 189 09.     

Suppression of modes in the random phase approximation

A general but simple method is proposed to eliminate the quantum fluctuations generated by selected one-body operators in the excitation spectrum of a discrete random phase approximation (RPA) Hamiltonian. This method provides an outstanding tool for the removal of the contaminating spurious effects originated from symmetry violations. It can be also applied as a mode filter for analyzing RPA response functions.     

Numerical solution of the optimized random phase approximation

An accurate, efficient and robust numerical method for the solution of the optimized random phase approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is proved rigorously. The method, hinging on the characterization of the generating functional, improves significantly on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm.     

Final results from phase II of the Mainz neutrino mass searchin tritium {\beta} decay

This paper reports on the improved Mainz experiment on tritium spectroscopy which yields a 10 times higher signal to background ratio than before. The main experimental effects and systematic uncertainties have been investigated in side experiments, and possible error sources have been eliminated. Extensive data taking took place in the years 1997 to 2001. A residual analysis of the data sets yields for the square of the electron antineutrino mass the final result of eV²/c⁴. We derive an upper limit of eV/c² at 95% confidence level for the mass itself.Received: 21 December 2004, Published online: 9 March 2005PACS: 1460.Pq, 23.40.-s, 2930.Dn, 2930.AjCh. Kraus: Present address: Department of physics, Queens university, K7L3N6 Kingston, CanadaB. Bornschein: Present address: Forschungszentrum Karlsruhe, Tritiumlabor, 76344 Eggenstein-Leopoldshafen, GermanyL. Bornschein: Present address: Universität Karlsruhe (TH), Institut für exp. Kernphysik, Postfach 6980, 76128 Karlsruhe, GermanyA. Kovalik: On leave from the Nuclear Physics Institute of the Acad. Sci. Czech Republic, 25068 Rez near PragueB. Ostrick: Present address: Helmholtz-Institut für Strahlen und Kernphysik, Universität Bonn, 53115 Bonn, Germany Corresponding author: E.W. OttenCh. Weinheimer: Present address: Institut für Kernphysik, Universität Münster, 48149 Münster, GermanyThis paper comprises principal parts of the PhD theses of Christine Kraus, Beate Bornschein and Lutz Bornschein.     

A solvable version of the collisional random phase approximation

We derive the markovian limit of the collisional Random Phase Approximation (CRPA) by resort to the linearization of the Collisional Time-Dependent-Hartree-Fock (CTDHF) equation of motion for the one-body density matrix. The CRPA spectral problem is numerically solved in the frame of a model consisting of a finite fermion system with axial symmetry interacting by means of a separable force. Calculations are performed within a range of interaction strengths, temperature and size parameters and it is shown that both the centroids and the widths of the high energy collective modes exhibit the trend of experimental data.     

Generalized random phase approximation and gauge theories

Mean-field treatments of Yang-Mills theory face the problem of how to treat the Gauss law constraint. In this paper we try to face this problem by studying the excited states instead of the ground state. For this purpose we extend the operator approach to the Random Phase Approximation (RPA) well-known from nuclear physics and recently also employed in pion physics to general bosonic theories with a standard kinetic term. We focus especially on conservation laws, and how they are translated from the full to the approximated theories, demonstrate that the operator approach has the same spectrum as the RPA derived from the time-dependent variational principle, and give—for Yang-Mills theory—a discussion of the moment of inertia connected to the energy contribution of the zero modes to the RPA ground state energy. We also indicate a line of thought that might be useful to improve the results of the Random Phase Approximation.     

Calculation of double beta decay rates and the neutrino mass

Predictions for 2v and 0v double beta decay rates are given for all nuclei with A ⩾ 70, for which double beta decay is energetically allowed. These predictions are based on detailed nuclear structure studies of the beta strength distribution and replace earlier estimates basing mostly on phase space considerations. New and more stringent limits on the Majorana neutrino mass are deduced from existing double beta decay experiments. Since the collective effects arising from spin-isospin as well as quadrupole-quadrupole forces are found to lead to a strong reduction of the nuclear matrix elements for two-neutrino double beta decay, but to have only minor influence on the matrix elements M^0v for the neutrinoless decay mode, the smaller limits for m_v result mainly from the fact that the widely used scaling procedure underestimates the 0_v matrix elements. It is further discussed to what extent interference between different neutrinos affects the obtained mass limits.     

Faddeev random phase approximation applied to molecules

The Faddeev Random Phase Approximation (FRPA) is a Green’s function method which couples collective degrees of freedom to the single particle motion by resumming an infinite number of Feynman diagrams. The Faddeev technique is applied to describe the two-particle-one-hole (2p1h) and two-hole-one-particle (2h1p) Green’s function in terms of non-interacting propagators and kernels for the particle-particle (pp) and particle-hole (ph) interactions. This results in an equal treatment of the intermediary pp and ph channels. In FRPA both the pp and ph phonons are calculated on the random phase approximation (RPA) level. In this work the equations that lead to the FRPA eigenvalue problem are derived. The method is then applied to atoms, small molecules and the Hubbard model, for which the ground state energy and the ionization energies are calculated. Special attention is directed to the RPA instability in the dissociation limit of diatomic molecules and in the Hubbard model. Several solutions are proposed to overcome this problem.     

First observation of the beta decay of117Pd and the discovery of a new isotope119Pd

In this paper we wish to report the first direct observations of the beta decays of¹¹⁷Pd and of a new isotope¹¹⁹Pd. The measuredβ-half-life is 4.3±0.3 s for¹¹⁷Pd. For¹¹⁹Pd, the existence of two beta-decaying states with the same half-life but of opposite parity cannot be excluded. The measured half-life for¹¹⁹Pd is 0.92±0.13 s. The observed beta half-lifes are in good agreement with the QRPA predictions. The observed level structure of¹¹⁷Ag and¹¹⁹Ag are discussed in the frame of the level systematics of the known odd Ag isotopes closer to stability.     

Nuclear matter properties in the relativistic random phase approximation

Nuclear matter properties at zero temperature are studied in terms of the relativistic σ-ω model, including the random phase approximation (RPA) contribution. At normal density, the medium polarization adds about −35 MeV of binding energy to the mean field result. The scalar and vector effective interaction strengths are fitted to the nuclear matter saturation conditions under various approximations for the energy functional including the RPA term. The effective mass and bulk modulus are calculated with these parameters. The relative importance of different contributions to the binding energy is analyzed.     

Core polarization effects and the random phase approximation solution

A metricg _ik=η _ik+Hξ _iξ_k+2Jξ _(iPk) is investigated. WhenJ=0 this reduces to the well-known Kerr metric. Conditions on the vectorp _i are obtained under which a geodetic, shear-free null congruenceξ _i in the Minkowskian space-time (with metricη _ik) will continue to remain geodetic and shear-free in the Riemannian space-time ofg _ik. A general solution of Einstein’s equationR _ik=σξ _iξ_k is obtained whenp _iξⁱ=0 andξ _i is twist-free.     

Isovector M6 excitations in the open-shell random phase approximation

OSRPA predictions are made for the excitation energies and transition amplitudes of J^π = 6^?, T = 1 excited states in the even N = Z sd shell nuclei. The results are employed in the calculation of electron scattering form factors. New expressions are given for the double commutators appearing in the OSRPA equations, which greatly facilitate their evaluation.     

Plasma oscillations in fullerene molecules within the random phase approximation

A method is presented for calculating the density of plasma excitation modes in fullerene molecules, which makes it possible to describe more accurately the specific features of the spectra as compared to the models proposed previously. The method is based on the inclusion of the total contribution of π and σ electrons to the spectra of collective oscillations in the molecules. This allows one to consider fullerene molecules with an arbitrary symmetry and arbitrary substituents. A comparative analysis of the experimental curves obtained for resonance electron capture and the results of numerical simulations for C₆₀, C₇₀, and C₇₆ molecules has demonstrated that not only the main maxima but also the ranges of the formation of negative ions coincide.