Torleif Eric Oskar Ericson

Energy levels and wave functions of pionic atoms

Abstract Present data on strong interaction shifts and widths in pionic atoms are analyzed in terms of a non-local effective potential with five parameters. Realistic mass and charge distributions are used and strong interaction effects on the vacuum polarization are included. The dependence of predictions on parameters is discussed; properties of the wave functions are presented for different assumptions of the interaction. The effective potential predicts a change of the attractive p-wave interaction to a repulsion in the region Z ≈ 36. It also suggests important isospin effects in the gradient interaction for very heavy nuclei. The Born approximation of the real isovector part of the potential is in agreement with soft pion theory; this term, as well as the entire real potential, is also close to multiple scattering theory. The analysis suggests that the isoscalar πN amplitude is −0.01 μ −1 ⪅ a N (+) ⪅ 0. The absorptive potential is about a factor of two stronger than predicted.

On probability distributions of nuclear cross sections

The nuclear cross section probability distributions in heavy nuclei are shown to be of simple form and to yield information on the reaction mechanisms and the structure of the scattering amplitude. The form of the probability distribution obtained provides a consistency check on the results obtained from cross section correlation functions. Scattering amplitudes are considered for an inelastic process in which all initial and final spins are zero. (C.E.S.)

HADRON-NUCLEUS FORWARD DISPERSION RELATIONS.

Abstract Forward elastic scattering of pions and nucleons from complex nuclei is investigated by dispersion relations (FDR). Explicit applications cover πD , π 4 He , π 9 Be , π 12 C , π 4 He and n 12 C . Partly unpublished numerical evaluations are given. Results are expected to be typical for a wide range of nuclei. The unphysical region for π-scattering on I = 0 nuclei is unimportant. For the I = 1 2 nucleus 9 Be, an effective π-nuclear coupling constant (ƒ 2 ) eff ≈ 0.06 is determined. With simple assumptions, general sum rules are shown to give universally (ƒ 2 ) eff = ƒ 2 nucleon as well as small unphysical contributions to the isospin-independent amplitude. Important exchange contributions from exchange diagrams (poles and cuts) are shown to appear in nucleon scattering at lower energies. This is shown to be consistent with single-particle potential scattering (optical model). The phenomenological potential scattering background term in slow neutron scattering is largely due to such exchange contributions. Antiparticle cross sections are shown to give small effects in low-energy nucleon scattering. A non-relativistic approximation to the relativistic FDR is compared to FDR for potential scattering and the Born term is empirically determined for n 4 He. Good agreement is obtained by comparison with the empirical potential for differential n 4 He scattering at low energy. A self-contained elementary discussion and review of FDR is given. The relation between asymptotic wave functions and pole residues is discussed in detail. Particular attention is drawn to the importance of an exponential dependence of residues on binding and radius, and it is illustrated by simple models.

Theory of polarization shifts in exotic atoms

Abstract The level shifts caused by the electromagnetic polarizability of the nucleus (N) and the orbiting particle (H) are investigated in detail. The static E1 polarizability strongly dominates in levels with l ⩾ 4 and the shift is Δϵ = − 1 2 e 2 (α N + Z 2 α H ) 〈r −4 〉 n o l o . The polarizabilities of other multipoles are calculated with the help of sum rules. The polarization of the electron cloud is a small modification of electron screening. The quasistatic approximation for the particle iin the atomic orbit is justified by deriving a number of exact expressions for averages of excitation energies and their spread. Numerical estimates of the effects of nuclear polarizabilities are given for various exotic atoms throughout the periodic system. The polarizabilities of π−, K−, p contribute a significant fraction to the total shift indicating the possibility of obtaining experimental information on hadron polarizabilities.

Low-frequency photon scattering by nuclei

Abstract We study the low-frequency limit of elastic photon scattering by nuclei of spin zero. We calculate the energy independent cross section (Thomson scattering) and the term quadratic in the frequency (Rayleigh scattering) in two ways: within classical electrodynamics and non-relativistic quantum mechanics. Particular emphasis is put on a correct description of the c.m. motion. The origin of the various retardation and polarizability terms is discussed. They are related to polarizabilities in static external fields. We propose the existence of a diaelectric polarizability which is the electric counterpart of diamagnetism. Orders of magnitudes of the expected effects are given.

Radiative π- capture in nuclei

Abstract An effective Hamiltonian for the process π - + N ( A , Z −1) + γ is derived from pion photoproduction in the impulse approximation. Good agreement with total experimental yields is found using techniques from the theory of μ- capture in nuclei.

Fermi motion in pion deuteron scattering at high energies

Abstract The Fermi motion plays an important role in resonant multiple scattering. Its conclusion restores the agreement between experiments and Glauber theory.

Pion capture as a tool for shell model studies

The success of quasi-elastic nucleon scattering in complex nuclei as a means of studying one-hole excitntions in the shell model raises the question of two-hole excitations. Their existence is a logical consequence of a strict shell model; the deviations or simularities of energies and wave functions to the ones obtained from the one-hole excitations should provide experimental information on the range of validity and the corrections to the shellmodel picture. It is pointed out that the capture of stopped pi /sup -/ mesons should be useful for the study of two-hole excitations. (W.D.M.)

To condense or not to condense? That is the question

Abstract We investigate the dependence of the pion mass in the nuclear medium with density and the condition for s-wave pion condensation. We base our approach on multiple scattering and the consistent use of the chiral off-mass-shell properties of the πN amplitude. We find important modifications of the results based on an effective lagrangian approach. These arise from the energy dependence of the πN amplitude with the small scattering length, which lead to a different behaviour of the density dependence and a suppression of condensation. Our results also suggest that the ratio of the effective to the real pion mass goes to unity in the chiral limit.

Pion scattering by nuclei in the region of the (3, 3) resonance

Abstract The salient features of pion scattering by nuclei around E π ≈ 180 MeV are discussed within the frame of a simple model. It is found that the experimentally observed phenomena are essentially due to strong absorption and are rather insensitive to details of the scattering mechanism.