PACS. 25.90. -Other topics in nuclear reactions and scattering: specific reactions.Abstract. -Some aspects of the clan picture for particle production in nuclear and in highenergy processes are examined. In particular, it is shown that the requirement of having logarithmic distribution for the number of particles within a clan in order to generate a negative binomial should not be taken strictly. Large departures are allowed without distorting too much the negative binomial. The question of the undetected particles is also studied. It is shown that, under reasonable circumstances, the latter do not affect the negative binomial character of the multiplicity distribution.

Résumé. 2014

General and average properties of nuclei; properties of nuclear energy levels.Abstract. -We show explicitly that the ground-state density of a system of noninteracting fermions in a hmonic-oscillator potential well can be given in terms of the wave functions of the single-particle states around the Fermi level.

(ricevuto il 17 Dicembre 1982) PACS. 21.10.-General and average properties of nuclei; properties of nuclear energy levels.Summary. -The ground-state density of a system of noninteraeting fermions in a harmonic-oscillator potential well can be given in terms of the wave functions of a few single-particle states around the Fermi level.We are going to demonstrate that the derivative of the density of a system of fermions occupying the lowest levels in a three-dimensional harmonic-oscillator well can be written in terms of a few radial wave functions. If N major oscillator shells are occupied, the derivative implies only the last occupied shell and the first nonoceupied one.In the one-dimensional case, the relation is very simple. If _F is the quantum number of the last occupied shell (Fermi level), and if the qi's are the normalized wave functions, one has In this relation, ~ is the density and a o is the harmonic-oscillator length~o being the oscillator frequency. The proof of relation (1) is given in ref.(1) and is based on recurrence relations fulfilled by the harmonic-oscillator wave functions. The method cannot be extended to the three-dimensional case easily. We therefore prefer to start Q) J. CUGNON and O.