New analytical independent-particle model potential for atoms

A new analytical, independent-particle model potential with four shell-independent parameters is proposed, which is suitable for high, medium, and low Z atoms. The four parameters are determined for 101 atoms from Li to Lr by fitting the results of the X _a method found in the literature. The average fitting error 0.675% of the new potential for the 101 atoms is far better than 3.92% of the widely used Green’s potential. The radial Schrödinger equation with the new potential is solved by using Numerov’s numerical method for 7 typical atoms: Ne, Ca, Zn, Zr, Sn, Yb, and Th. The energy eigenvalues, radial wave functions, and atomic ground-state energy are in good agreement with the results of the X _a method. The new potential here shows greater flexibility and better accuracy compared with the Green’s potential.     

High energy collisions between heavy nuclei

Neglecting Coulomb effects we derive a very simple analytical result for nucleus-nucleus elastic scattering in an optical limit of the Glauber approximation which has the property that it does not diverge at large momentum transfers when the center-of-mass correlation function is retained and is more accurate and easier to apply than the commonly used expressions which involve numerical integrations. We then derive a corresponding analytical expression for the elastic scattering amplitude which includes the Coulomb effects arising from point charge incident and target nuclei.     

Shell model calculations for heavy deformed nuclei

The pseudo SU(3) model is shown to be a powerful scheme for describing the excitation spectra as well asB(E2) andB(M1) transition strengths in heavy deformed nuclei. It is also useful for describing double beta decay amplitudes for transitions from the ground state of an even-even nucleus to the ground and excited states of the daughter nucleus, both for the two and zero neutrino emitting modes. The existence of selection rules which strongly restricts the decays is discussed. Anti-correlations between the quadrupole deformation and the Gamow-Teller (GT⁺) strength are found in an extension of the pseudo SU(3) model which explicitly includes pairing, which is also able to describe the fragmentation of the scissors mode. The projected shell model is introduced and proposed as an alternate means for studying single and double beta decay processes. Presented by J.G. Hirsch at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work was supported in part by CONACyT (México), CONICET (Argentina), NSF and DOE (U.S.A.).     

The quantumstatistical aspects of the independent-particle model for the nucleus

We present a new justification of the independent particle model for the nucleus. It is based on a statistical theory of the short-range correlations in large Fermion systems. The statistical operator of many-body Fermion systems — if averaged over a suitable ensemble — can be written as a product of statistical operators for a one-body system. The statistical operator for the one-body system obeys a Hartree-Fock equation. Physical interpretation and conclusions are discussed.     

The relativistic Coulomb sum rule for electron scattering in the independent-particle model

The problems associated with including relativistic effects in the non-energy-weighted Coulomb sum rule for electron scattering are discussed. A new formulation of the sum rule is proposed, and this sum rule is calculated under a variety of conditions within the framework of the independent-particle model. Ambiguities due to model dependence were found to be small, and the simple factor Z, the atomic number, was found to be a good approximation to the calculated values of the sum rule. This provides a basis against which correlations or more exotic effects can be measured.     

Periodic multi-proton transfer strength in collisions between heavy nuclei

A periodic variation of the multi-proton transfer probability as a function of the nuclear charges of the residual nuclei has been observed in collisions of ²³⁸U with ¹¹⁰Pd and ¹²⁴Sn at bombarding energies close to the Coulomb barrier. After the N = 82 closed neutron shell of the light reaction partner is filled through multi-neutron transfer and an energy dissipation of about 100 MeV, transfer of pairs of protons is observed with modulated transfer strength. The proton multi-pair transfer dissipates no further energy.     

Interplay between orbital and spin motion in heavy nuclei

We investigate the role of orbital and spin motion in shaping the structure of the magnetic dipole and quadrupole spectra in spherical as well as in deformed heavy nuclei.     

On the problem of c.m. motion in the independent-particle model

The assumption that the product wave function of an independent-particle model can be approximately represented as a wave packet of states with different total momenta and definite internal motion is critically reconsidered. For the case of a simple, nonrelativistic two-body “bag-like” wave function, the lower error bound of such an approximation has been found; it turns out to be only 2% in the squared norm. However, for typical matrix elements the error may be of the order of 15%.     

Analytical independent-particle model for electron scattering by argon at low energy

The analytical independent-particle model of Berg, Purcell, and Green (BPG) is extended to describe low-energy scattering of electrons by the argon atom. The Ramsauer-Townsend minimum and the scattering length are only well reproduced when the BPG model is supplemented with a polarization potential as proposed by Sandhas.Dedicated to Prof. Werner Sandhas on the occasion of his 60th birthday     

Alpha-clustering effects in heavy nuclei

The study of cluster structures in light nuclei is extending to the heavy nuclei in these years. As for the stable N = Z nuclei, from the lighter ⁸Be, ¹²C nuclei to the heavier ²⁰Ne and even the ⁴⁰Ca and ⁴⁴Ti medium nuclei, the α cluster structures have been well studied and confirmed. In heavy nuclei, due to the dominated mean field, the existence of α cluster structure is not clear as light nuclei but some clues were found for indicating the core+α cluster structure in some nuclei, in particular, the ²⁰⁸Pb+α structure in ²¹²Po. We review some recent progress about the theoretical and experimental explorations of the α-clustering effects in heavy nuclei. We also discuss the possible α cluster structure of heavy nuclei from the view of α decay.     

Isomeric states in heavy nuclei

The one- and two-quasiparticle states in heavy nuclei are treated. The change of one-quasiparticle states in isotone chain seems to be rather smooth. Two-quasiparticle states in nuclei of alpha-decay chain of ²⁷⁰Ds are discussed.     

Cold multi-nucleon transfer between heavy nuclei and the synthesis of new elements

Experimental results of multi-nucleon transfer reactions on very heavy targets (²⁰⁸Pb,²³⁵U,²⁴⁸Cm) are analysed with respect to their properties as cold quasielastic reactions. Optimum conditions for quasi-elastic transfer are discussed for the production of very heavy elements.     

On the shell model and its application to the deformation energy of heavy nuclei

The technical realisation of the shell model with arbitrary fields is presented in detail, with special emphasis of the unusual and large deformations of the nuclear shape as they may occur in the fission process. We discuss how realistic parametrisations of the nuclear shape and the potential well can be developed and how the parameters of the average fields can be determined. We restrict ourselves to wells with a Woods-Saxon distribution in the radial coordinate. By means of Strutinsky's shell correction approach, the single particle energies deserve to calculate the potential part of a collective Hamiltonian. Its behaviour with varying deformation is discussed both qualitatively and quantitatively. Considered are the deformation types of elongation (1), necking (2), reflection (3) and axial (4) asymmetry of the nuclear shape. Evidence is given for geometrical symmetries which can be correlated to normal modes in finite nuclei. The transition from spherical to deformed nuclei is presented in detail for the radium isotopes, revealing the importance of hexadecapole deformations. Finally, we give an extensive and systematic presentation of the energies and of the deformations at the various stationary points of the deformation energy for the nuclei in the actinide region and for the hypothetical superheavy nuclei.     

Fast helium nuclei in interactions induced by very heavy nuclei

Fast helium nuclei emitted in interactions between heavy cosmic ray nuclei (12≦Z≦26) and photoemulsion nuclei at energies >1 GeV/nucleon have been studied. Comparisons with interactions where the incident particles are protons, pions or light nuclei reveal some characteristic features of nucleus-nucleus interactions. The frequency of fast target helium nuclei is much larger and the high energy tail of the energy spectrum of these helium nuclei is more pronounced in nucleus-nucleus interactions than in proton-nucleus and pion-nucleus interactions. The number of helium nuclei emitted depends on the size and disintegration of the interacting nuclei. In order to explain our experimental data several possible production mechanisms have to be considered. Some characteristics of the emission of multiply-charged projectile fragments have-also been studied.     

On the origin of the heavy nuclei

Nuclear formation processes and the conditions of their physical environment are investigated on the basis of the empirical abundance distribution of the nuclei. Three different abundance components of the heavy nuclei require very different physical conditions for their formation but appear genetically correlated. The component formed in a slow neutron capture chain indicates the pre-existence of the neutron-rich component, and of an iron abundance peak considerably smaller than found in the solar system. The neutron-rich and the proton-rich components seem to have been formed byβ-decay from progenitors which were produced at conditions of matter densityρ≈2×10¹⁰g/cm³ and of temperaturekT≈500keV, respectively.