Perturbation theory for the effective interaction in nuclei

Starting from a decomposition of the Hamiltonian H(x) of the nuclear many-body problem in the form H(x) = H₀ + xV, where H₀ is a shell-model Hamiltonian, V the residual interaction, and x a strength parameter, we introduce a general effective interaction W(x) describing the interaction of nucleons within a shell, and the associated effective operators $\text{A}\text{?}\text{(x)}$. We display some properties of these operators. From a particular choice of W(x) we obtain the expressions introduced earlier by several authors. The convergence of the expansions for W(x) and $\text{A}\text{?}\text{(x)}$ in powers of x is investigated. It is shown that W(x) and $\text{A}\text{?}\text{(x)}$ are holomorphic in a domain of the complex x-plane including the point x = 0. With the help of a generalization of the von Neumann-Wigner noncrossing rule, we exhibit the nature of the common singularity of W(x) and $\text{A}\text{?}\text{(x)}$ which is closest to the origin and thus defines the radius r₀ of convergence of the expansions of W and $\text{A}\text{?}$. It is shown that r₀ is unaffected by the cancellation of unlinked diagrams. A criterion of consistency is established, which shows that most of the practical calculations of W lead to results which are inconsistent with the definition of W.     

Nonperturbative approximation schemes for the effective interaction in nuclei

Several methods are investigated to deal with the singularities of the effective interaction which cause the perturbation series to diverge. Some of these methods, which are found to be quite useful, are based upon a semiphenomenological treatment of the “intruder” states. One method, based upon the use of Padé approximants, seems to be free of such semiphenomenological input data and appears to yield a particular effective interaction which has as eigenvalues those levels of the system for which the corresponding eigenfunctions have maximum overlap with the model space. The methods are investigated with the help of simple examples. Those methods which are found to be useful are applied to the 0⁺ and 2⁺ levels of ¹⁸O.     

Interference between multi-step transitions in exotic atoms

We discuss the interference effects due to coherent transitions involving more than one photon in exotic atoms. It is found that the populations are not influenced by this interference. In the case of muonic atoms there is an influence on the polarizations under specific conditions.     

The influence of finite line widths on parity mixing in muonic atoms

The parity mixing due to parity-violating neutral currents in muonic atoms is discussed in the case where the line widths of two mixing states are comparable with or larger than their energy difference. It is shown that the line widths give rise to a considerable reduction of the parity mixing effects.     

Properties of Padé approximants to the effective interaction

Some properties of Padé approximants to effective interactions in nuclei are investigated. The behaviour of higher order approximants is discussed in model calculations. In the case of [2, l]-approximants a criterion is derived for the occurrence of spurious poles which are not related to level crossings.     

Association of Molybdenum Ionic Species with Alumina Surface

The adsorption isotherms at 25, 45, and 65 degrees C of molybdenum solutions of concentration ranges between 10(-3) and 3x10(-2) M(Mo) (pH 4-5) on different alumina samples are investigated. The analysis is conducted using a modified Frumkin isotherm which takes a more realistic account of the lateral interaction between adsorbed species and considers that the adsorption takes place on the most basic OH groups on the surface of alumina. The results are discussed in view of the difference in solutions speciation, and the changes in the pH of the remaining supernatant solutions. The solution temperature, PZC of the used aluminas, the configuration of the basic OH groups on their surface, and the pore structure have been shown to intervene effectively. Copyright 2000 Academic Press.     

A comparison between various expressions for effective interactions and operators in nuclei

Different choices of effective interactions and operators are related to each other and to definitions given in the literature. Perturbation expansions are given, and the degree of complexity in evaluating terms of a given order is exhibited. The application of Padé approximants to different choices of effective interactions and to effective operators is investigated numerically.     

Femtosecond quadrature-squeezed light generation in CdSe at 1.55 mum

We generated pulsed quadrature-squeezed light by cross-phase modulation in single-crystal hexagonal CdSe at wavelengths of 1.4 to 1.55mum . We measured 0.4-dB squeezing (0.7 dB is inferred at the crystal) with 100-fs laser pulses. The wavelength and the intensity dependence, as well as variations in the local oscillator configuration, are examined. At higher intensities squeezing is shown to deteriorate owing to competing nonlinear processes.