J. Hüfner

Rows on rows — A theory for collisions between heavy ions at high energy

Abstract The double differential cross section d σ/ d Ω d E is computed for protons and pions from collisions between nuclei at high energies (250 to 2100 MeV/nucleon). We derive the following within Glauber theory: At high energies the interaction between two nuclei reduces to a series of collisions between rows of target nucleons and rows of projectile nucleons. The scattering “rows on rows” can be obtained from a one-dimensional cascade calculation. We perform it in a simple approximation, using experimental nucleon-nucleon cross sections as the only input. The introduction of the Δ-degree of freedom leads to a satisfactory description of the proton and pion data at 2.1 GeV/nucleon. At 250 MeV/nucleon our agreement with experiment compares favourably with the one achieved in other approaches. A scaling law may be the reason why many simple approaches come already close to experiment. We discuss the question of thermalization.

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.

The distribution of grey particles in very high-energy hadron-nucleus collisions ☆

Abstract On its passage through the nucleus a very high-energy hadron strikes several target nucleons. These recoil nucleons initiate an intranuclear cascade. “Grey particles”, mostly protons with energy between 40 and 400 MeV result from the cascade. We can describe the mean number and distribution of grey particles by truncating the intranuclear cascade after the second generation. The number N g of grey particles is very simply related to the number ν of initial hadron-nucleon collisions: 〈ν〉 N g 〈ν〉 = a( N g 〈N g 〉) 1 2 , where a is a numerical constant close to 1.

Treatment of the continuum-continuum interaction in the shell-model approach to nuclear reactions

Abstract In the shell-model approach to nuclear reactions, the treatment of the continuum-continuum interaction due to the residual nucleon-nucleon potential causes a serious numerical problem. A method, based upon work by Wienberg is proposed to modify the continuum-continuum interaction operator in such a way that it may be treated in perturbation theory. This is achieved by subtracting from this operator an operator of finite rank. A prescription for the construction of the latter is given, and an approximation scheme to this prescription is introduced. Numerical examples show that the method converges rapidly. The relation of the method to the Fano treatment and several other approaches is discussed. The S -matrix is decomposed into two parts, the first of which is the compound nuclear contribution, the second of which resembles the familiar DWBA amplitude.

Nucleons after pion absorption

Abstract We calculate energy spectra and angular distributions of single and correlated spectra after the absorption of stopped pions in nuclei. We assume: The pion is abosrbed by a pair of nucleons; these primary nucleons may leave the nucleus directly or only after one or more collisions with other nucleons. We propose a multiple scattering expansion for the intranuclear cascade after pion absorption. Various experimental data are successfully described in shape and absolute magnitude. The ratio R np = R ( π − np → nn)/ R ( π − pp → np) is determined from the experimental proton spectra: R np = 13 ± 6.

Correlated nucleons in inclusive backward proton-nucleus collision at intermediate energies

Abstract We investigate the mechanism for inclusive proton-nucleus collision with the transfer of large momentum but little energy. We argue that the incident proton is back-scattered by correlated nucleons (“cluster”). The microscopic calculation based on this picture reproduces quantitatively important regions of the experimental cross section without free parameters. The momentum distribution is computed for the recoiling nucleons which are emitted forward in coincidence with the back-scattered proton. This prediction may be checked experimentally to support or rule out our model and to distinguish between other approaches and ours.

DWBA in the shell-model approach to nuclear reactions

Abstract The scattering matrix S is decomposed into two parts, the compound nucleus part and the direct interaction part S (DC). The compound nucleus part S (CN) has uncorrelated partial width amplitudes, so that its energy average has vanishing non-diagonal matrix elements. The direct interaction part is defined as the difference S  S (CN). The decomposition is carried our, in the shell-model approach to nuclear reactions, by a suitable decomposition of the residual interaction, which bears close analogy to the separation proposed recently by Austern and Ratcliff in the frame of a simple model. Under proper statistical assumptions, it is shown that the energy average of S (DI) can often be calculated in first-order perturbation theory and is then given by the familiar DWBA term, if the channels are weakly coupled. The conditions for convergence of the Born series are investigated. The wave functions entering into the DWBA expressions are defined by optical-model potentials. The potentials are derived, and some of their properties are discussed. It is shown that they are equal to the conventionally defined, phenomenological optical-model potentials inasmuch as they reproduce the energy average of the elastic scattering phase shifts. The modifications of the DWBA due to a giant or microgiant resonance or to strong coupling between some channels are given. The analysis of experimental data is discussed for the case when both compound and direct processes contribute to the cross section. The connection between the present work and the approaches used by other authors is exhibited and discussed.

Momentum distributions after fragmentation in nucleus-nucleus collisions at high energy

Abstract We analyse the results of the experiment 4 He + target → 3 He + X at 1 GeV/nucl . We concentrate on the “spectator peak”, where the velocity of the final fragment 3 He is equal to or larger than the projectile velocity. The shape and absolute value of the cross section can be understood quantitatively. Several effects contribute to the cross section in the transverse, direction. But the 3 He fragments emitted at 0° reflect pure spectator physics: the momentum distribution of the observed 3 He is related in a simple way to the momentum distribution in 4 He. Using the experimental fragmentation cross section at 0° we deduce the shape of the momentum space wave function for the relative neutron- 3 He motion inside 4 He.

Premiere observation de la production de π0 dans la reaction d+d→α+π0 interdite par la conservation de la symetrie de charge et mesure de la reaction d+d→α+γ

Abstract The reaction d+d→α+π0 which is in clear violation of charge symmetry conservation, has been observed for the first time at a laboratory energy of 1.10 GeV in an experiment carried out at the Saturne synchroton at Saclay. The number of π0s detected corresponds to a differential cross section d σ d Ω ∗ (π 0 ) = 0.97 ± 0.20 ± 0.15 pb/sr at a centre-of-mass angle of θc.m. = 107°, where the first error bar refers to the statistical uncertainty and the second to the systematic. The reaction d+d→α+γ was measured simultaneously with the π0 production, leading to a differential cross section of d σ d Ω ∗ (γ) = 0.82±0.18±0.10 pb/sr at the slightly larger angle of θc.m. = 110°. The available predictions of theoretical models of charge symmetry breaking, based upon η/π mixing, fall an order of magnitude below our measurement. However, these predictions for the η/π mixing level might be boosted by the η threshold (1.121 GeV) proximity, where this experiment is performed.

Multiple scattering in random colour fields

Abstract Multiple scattering of a meson inside a nucleus is viewed in colour space. Nucleons are represented by random colour fields which couple to the colour degrees of freedom of the meson. An exact expression can be derived for the survival probability after n collisions. There is a strong analogy to spin precession in an outside magnetic field.