Simple formula for nuclear charge radius

A new formula for the nuclear charge radius is proposed, dependent on the mass numberA and neutron excessN-Z in the nucleus. It is simple and it reproduces all the experimentally available mean square radii and their isotopic shifts of even-even nuclei much better than other frequently used relations.This work is partly supported by the Polish Committee of Scientific Research under contract No. 203119101     

Solving the Gross-Neveu model with relativistic many-body methods

The Gross-Neveu model provides a unique opportunity to apply relativistic many-body techniques (Dirac-Hartree approximation, RPA) in a context where all calculations can be done analytically and — in the largeN limit — yield the exact results. The physical fermion as well as multifermion (baryon) and fermion-antifermion (meson) bound states are discussed in this spirit, with special emphasis on the role of the Dirac sea.Supported by the Bundesministerium für Forschung und Technologie     

Search for a transient electric field gradient in the system90Zr→148Nd with the crystal ball spectrometer

The particle- angular correlation of the 2⁺0⁺ transition in¹⁴⁸Nd, Coulomb excited by⁹⁰Zr projectiles, was investigated to search for a transient electric field gradient expected to be present during the stopping of the recoils in²⁰⁸Pb. An upper limit of V_zz <>¹⁹V/cm² was obtained for¹⁴⁸Nd recoiling with initial velocities of 0.05 c.     

Description of low-lying vibrational and two-quasiparticle states in164Dy

The calculation with the deformed Woods-Saxon potential and residual interaction allowing for a twophonon admixture of the quadrupole, octupole and hexadecapole vibrational and two-quasiparticle states in¹⁶⁴Dy have been made. The calculated excitation energies and B(E; =2, 3, 4) values are found to be in reasonable agreement with experimental data. The calculated 0⁺ states in¹⁶⁸Er do not contradict experimental data. It is shown that the wave functions of states with energies below 2.3 MeV have dominating one-phonon components.     

Microscopic calculation of pion production in nucleus-nucleus collisions around 1 GeV·A

New phonon operators are introduced for describing deformed nuclei which consist of the electric and magnetic parts. The Hamiltonian of the quasiparticle-phonon nuclear model is constructed and the basic equations for the finite rank separable isoscalar and isovector multipole and spin-multipole particle-hole and particle-particle interactions between quasiparticles are derived. It is shown that calculations of one-phonon states in the RPA encounter some difficulties due to the finite rankn _max>1 separable interaction of the electric and magnetic type. The use of complex separablen _max>1 interactions does not lead to complication of the QPNM equations for describing fragmentation of vibrational states. The matrix elements are obtained for describingE- andM- transitions between excited states of deformed nuclei. It is stated that the QPNM can serve as a basis for calculating many characteristics of excited states of deformed nuclei.     

Nucleon pair structure of realistic many body wave functions

The scalar part of the two-body density is calculated for the²⁰Ne ground band and for the yrast 2⁺ state in⁶⁸Ge as obtained by solving the Hartree-Fock-Bogoliubov problem with symmetry-projection before the variation. The nucleon pair structure of these states is analysed and the results obtained with different effective Hamiltonians are compared.Work supported by the IPNE, Bucharest, Romania under Contract No. 60-92-7, the DFG and the Internationales Büro des KfK Karlsruhe, Germany     

Level density fluctuations in the generalized interacting boson model

Level density fluctuations are calculated within the generalized interacting boson model proposed for even-even nuclei, in dependence on the truncation parameterk. For the case =2 corresponding to theSU(3) dynamical symmetry of the interacting boson model the fluctuation pattern is close to Poissonian. For cases 2, including the anharmonic vibrator model for which =, a rapid transition to the fluctuation pattern close to GOE is obtained.     

Structure of even-even beryllium isotopes studied by AMD+GCM method

The ground state properties and the properties of low-lying states of the even-even⁶Be-¹²Be beryllium isotopes are investigated using the extended version of the Antisymmetrized Molecular Dynamics Multi-Slater Determinant model. The theoretical method is found to be very useful to study ground state properties of various nuclei covering light unstable nuclei. Many experimental data can be successfully reproduced by the adopted approach. Binding energies, the energies of the 2 ₁ ⁺ states, electromagnetic transition strengths and quadrupole moments of proton and neutron distribution are calculated. This work is supported in part by Grant-in-Aid for Scientific Research (13740145) from the Ministry of Education, Science and Culture.     

Influence of the separation energy on the radius of neutron rich nuclei

The intensive studies of equilibration processes in heavy ion reactions have produced a need for information on nuclear level densities at high energies. In a recent paper, it was concluded that standard Fermi gas formulas will be incorrect by exponential factors at energies above 100 MeV. Exact calculations of the nuclear level density in bases as large as 10³⁸ have been made and are compared with Fermi gas formulas. Two possible alternative forms are considered. Both forms produce much better agreement at high energies than does the Fermi gas model. All calculations reported are for non-interacting Fermions, but the effects expected from the two-body interaction are briefly examined. These considerations have consequences not only in heavy ion physics but also in astrophysics.     

The spin-orbit field in superdeformed nuclei: a relativistic investigation

Relativistic Mean Field (RMF) theory is used to investigate the behavior of the spin orbit potential,V _ls, in nuclear states of very large deformation and high angular velocity. As a by-product we present a set of parameters for an approximation of the relativistic scalar- and vector-potentialsS andV in the Dirac equation in terms of Saxon-Woods shapes. These reproduce more or less the same single particle specta as a full selfconsistent relativistic mean field calculation.Dedicated to Prof. Dr. H.J. Mang on the occasion of his 60th birthday     

Isospin dependence of nuclear radius

Isospin dependence of proton density radius is proposed. The fit to the experimental isotopic shifts of the mean square charge radius of the even-even nuclei with 38Z78 shows that the radius is less dependent on the neutron number than is usually assumed. Uniform density distribution was assumed and the ground state deformations were taken from the microscopic calculations.This work is partly supported by the Polish Committee of Scientific Research under contract No. 203119101 and the French Ministry of Scientific Research and Education     

Approximation for shell-model level densities: Ergodicity

Using the supersymmetry method, we show that the maximum entropy approach for the calculation of nuclear shell-model partial and total level densities, developed in a previous paper, is ergodic.On leave from the Charles University, Prague, Czech Republic     

Level density fluctuations and characterization of chaos in the realistic model spectra for odd-odd nuclei

Statistical properties of the realistic energy spectra of the odd-odd nuclei¹⁰⁶Ag,¹⁹⁸Au,¹³⁴Cs,⁴⁰K and⁹⁴Rb, calculated within the Interacting Boson Fermion Fermion Model, are investigated by means of theΔ ₃ statistics and the Nearest Neighbor Spacing Distribution method. New probability distribution function, which describes well the calculated results and enables the characterization of chaos with a physically meaningfull parameter, is proposed. Level spacing fluctuations of the examined nuclei exhibit the transitional behavior between Poisson and GOE limits, revealing different degrees of chaoticity in their dynamics. Communicated by X. Campi     

Multi-strange systems in relativistic mean fields

Characteristics of multi- hypernuclei are investigated within the relativistic mean-field theory. Both linear and nonlinear models and a variety of couplings fitted to ordinary hypernuclei have been investigated. All the parametrizations used in the present work predict qualitatively similar dependence of the studied quantities (rms radii, binding energies, densities) on a number of hyperons.Deceased on May 5, 1991     

Approximation for shell-model level densities

The maximum entropy approach for the calculation of nuclear shell-model level densities developed in a previous paper is extended to the calculation of terms of higher order inN _k ^–1, whereN _K is the dimension of the shell-model subspaces of interest. We present terms of first and second order inN _k ^–1 , i.e. in the loop expansion, and the corresponding diagrams. We investigate the size of these contributions for several examples. We find that even for subspace dimensions as small as ten, the saddle-point approximation is quite reliable, the leading terms of the loop expansion are small, and the terms of next order are negligible.On leave from Department of Nuclear Physics, Charles University, S-18000 Prague 8, Czechoslovakia     

Low energy orbital magnetic dipole excitations of heavy nonspherical nuclei

To clarify the physical nature of the orbital magnetic dipole excitations discussed widely in the past few years, a semiclassical model is presented and the nuclei¹⁵⁶Gd and¹⁶⁴Dy are investigated microscopically. The semi-classical model involves a consistent treatment of vibrational and rotational degrees of freedom; the microscopic results are obtained in quasiparticle-random-phase approximation (QRPA) with a realistic effective interaction. The results disagree with the picture of scissors modes or rotational vibrations.Dedicated to Prof. Dr. H.J. Mang on the occasion of his 60th birthday     

The influence of state dependent short range correlations on the depletion of the nuclear Fermi sea

The inlfuence of state dependent short range correlations on the occupation numbers of the single particle shell model orbits of the doubly closed shell nuclei¹⁶O and⁴⁰Ca is examined. The study shows that the effect of the state dependence of the short range correlations is rather small. The total depletion of the nuclear Fermi sea changes slightly compared with the one calculated by considering state independent short range correlations.     

From microscopic to macroscopic nuclear collective dynamics

We apply smoothing procedures to response functions for isoscalar vibrations. For collective motion, we find a transition from a structured strength distribution to one corresponding to one incoherent, strongly overdamped mode. It is argued that the latter may be interpreted as macroscopic motion exhibiting, to some extent, features of the hydrodynamical model. We discuss the physical origin of this behaviour, in particular its relation to the disappearance of shell structure.Supported in part by the Deutsche Forschungsgemeinschaft