Albrecht Lindner

ABSORPTION CROSS SECTIONS AND TRANSMISSION COEFFICIENTS FOR PROTONS AND NEUTRONS ACCORDING TO THE OPTICAL MODEL

Tl-values and absorption cross sections for protons and neutrons are calculated with optical potentials, which have been fitted to experimental scattering data. Values are given forZ=10, 20, 30, 50, 70, 90, and energies between 0.1 und 25 MeV. For protons we used the local optical potential ofPerey and for neutrons the nonlocal optical potential ofPerey andBuck. The results are compared with those of other optical potentials. In addition it is shown, that the spin-orbit-interaction leads toTl j-values which sometimes differ appreciably depending whetherj equalsl+1/2 orl−1/2.

Two-particle emission in nuclear reactions

Abstract The cross sections for the emission of two particles are calculated with the statistical theory of nuclear reactions using reasonable values for the cross sections for the formation of a compound nucleus and for the level density. The emission of γ-rays is taken into account as a process competing with the evaporation of particles. It is found that the agreement between the calculated and observed cross sections is satisfactory in the examples studied (Cr50, 52, Fe54, 56, Ni58, 60 bombarded with neutrons up to 16 MeV). The competition of γ-emission is only important near the threshold of the considered reaction, where the level density formula fails to give a reliable result. Some systematics of the dependence of the cross sections on nucleon numbers are discussed.

Zur statistischen Theorie der Kernreaktionen

ZusammenfassungBerechnet man (n, α)- und (n, p)-Wirkungsquerschnitte für 14,5 MeV-Neutronen nach der statistischen Theorie, so hängen die Ergebnisse empfindlich von den benutzten Hilfsgrößen ab. Wir haben die Wirkungsquerschnitte für die Bildung eines Zwischenkernes nach dem optischen Modell berechnet und in der Termdichte-formel Paareffekte und die Schalenstruktur berücksichtigt. Außerdem benutzten wir neuereQ-Werte. Damit konnten die vonPaul undClarke gefundenen starken Abweichungen zwischen experimentellen und theoretischen Werten deutlich verringert werden.

Elastic deuteron-nucleus scattering as a discretized three-body problem

Abstract We describe the elastic deuteron scattering by using nucleon optical potentials and the Hulthen potential for the np interaction and including approximately the break-up states of the deuteron. In order to avoid the numerical difficulties when using a continuous basis for H np we propose a discretization which is uniquely determined by this sub-Hamiltonian. The resulting coupled system of differential equations is solved numerically and takes into account the important coupling to states with different angular momentum. Results are given for 58 Ni and 40 Ca at 21.6 MeV in order to compare with experiments and other calculations.

Triple correlation functions for describing three-body reactions and polarization experiments

Abstract The triple correlation functions P O n 1 n 2 (Ω 0 , Ω 1 , Ω 2 ) form a rotational invariant basis for all experiments depending on three directions. Their usefulness for the description of three-body reactions and polarization experiments is demonstrated. In the latter case the sum n0 + n1 + n2 may be odd, pertaining to the well-known right-left asymmetries. Numerical methods are given to calculate these functions and the relevant expansion coefficients. The directions are tabulated which are best suited for experiments.

Shell model formulation of reactions with two nucleons in the continuum

Abstract The shell model is extended to the case of two nucleons in the continuum, including deuteron scattering, break-up and stripping reactions. For the various transition amplitudes we derive uncoupled Lippmann-Schwinger equations with completely connected kernels, usable for numerical calculations.

Nuclear reactions with polarized particles of arbitrary spin

Abstract Cross sections and polarization of reaction products are given for two-particle reactions in terms of S -matrix elements. The beam and target may be polarized.

Langevin equation for the parametric oscillator: a model for ion confinement in a radio frequency trap

We have calculated 〈x2〉 and 〈v2〉 for an ion in a rf trap being cooled by a stochastic force. The results agree with earlier work (using a Fokker-Planck equation) as long as there is white noise. However, there is an appreciable reduction for both quantities, if non-Markovian processes are included.

ANGULAR CORRELATIONS IN THREE-BODY REACTIONS.

Abstract The differential cross section dσ/dω1dω2dE for reactions of the type a + A → B + b1 + b2 is given in terms of Biedenharns triple correlation functions and the elements of the transition matrix, which may be given in the channel spin representation or in the j-representation. The particles involved may have arbitrary spin.

The uncertainty relation between particle number and phase

Abstract With the usual definitions of the uncertainty, especially Δ Φ = (〈Φ 2 〉 − 〈Φ〉 2 ) 1 2 , we give the uncertainty relation for the Pegg-Barnett operators N, Φ pertaining to bosons in the same single particle state. For rather sharp phases we confirm the relation Δ N Δ Φ ≥ 1 2 of other authors. When increasing ΔΦ, however, the periodicity (mod 2π) shows up in the form ΔΦ ⩽ ΔΦ max  π 3 and the particle number may be sharp already at ΔΦmax: In nearly half of the range of ΔΦ the uncertainty ΔN may be smaller than given by the former relation.