Gaussian polynomial method for spin-dependent level density and new formula for spin distribution

Large-scale combinatorial calculations of level densities were performed for selected nuclei using Gaussian polynomial generating function method (GPM). Contrary to the results of previous combinatorial calculations, we find a good agreement of the combinatorial total level densities and Bethe formula. Combinatorial GPM calculations were performed also for spin-dependent level densities and comparison is made with various algebraic formulas. On the basis of our GPM calculations we propose a new phenomenological spin-dependent level density formula, which in the low-spin limit reduces to the spin-dependent formula of Bethe. The new formula (24) is for all spins factorized into the product of total level density and spin distribution function, where the spin distribution function (25) contains an additional spin correction parameter.     

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     

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     

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.     

On the competiting role of mean-field and residual interactions in flow observables

Theoretical analyses of heavy-ion reactions are performed in the framework of the semi-classical Landau-Vlasov approach. The incident energies are investigated in the range from intermediate to low energy regimes, where transverse collective motion has been experimentally evidenced. The influence of the equation of state (E.O.S.) parameters on various collective observables is studied in relation with the action of the residual interactions. From the sensitivity to both aspects, and taking into account the experimental biases limitations, our investigation indicates that E.O.S. signatures should be more expected at energies below 100 MeV per nucleon.     

Compression properties of finite nuclei in a semi-classical relativistic approach

Skyrme type potentials are known to lead — in the framework of the scaling model — to a finite-nucleus incompressibility valueK _A where the volume coefficientK _v equals roughly the negative surface coefficient K_s. This is found for Skyrme interactions with K_v between 200 and 360 MeV. In a semi-classical relativistic approach on the basis of the — model (linear as well as non-linear) using in addition local density approximations, we findK _s to depend in particular on the surface energy coefficienta _s , and not so much on the value ofK _v . For a realistic value of a_s, both the linear and the non-linear — model (with NL1 parameter set) yield a ratio ¦K _s K _v ¦ of approximately 1. We discuss implications of this finding with a particular view on recent empirical results onK _v andK _s .Dedicated to Prof. Dr. H. J. Mang on the occasion of his 60th birthday     

One-quasiparticle strength functions in medium-heavy spherical nuclei

A method to describe quantitatively the one-quasiparticle strength functions is proposed which takes approximately into account the coupling of one-quasiparticle states to many-phonon configurations. The method is used to interpret the appropriate experimental data for medium-heavy spherical nuclei. The results are compared with the calculations made in different theoretical approaches.     

Transverse energy distributions in participant number model for ultra-relativistic heavy-ion collisions

The transverse energy distribution in ultra-relativistic heavy-ion collisions has been obtained as a convolution over the number of projectile and target participants. The latter is computed using the geometrical overlap model as a function of impact parameter. The data from 10 A GeV to 200 A GeV heavy ion beams on various targets in different pseudo-rapidity domains have been successfully described.     

Evidence for a two-phonon octupole vibrational state in208Pb

Collective properties of^206,208Pb have been investigated with gamma-ray spectroscopy using nuclear and electromagnetic excitation by²⁰⁸Pb projectiles. From the measurement of particle-particle- and particle-particle- coincidences a new energy level in²⁰⁸Pb at 5.683 MeV was observed and the data suggest an interpretation as a 2-phonon octupole vibrational state with spin 4⁺ or 6⁺. For this state one finds the same dynamical deformation parameter ₃ as for the first-excited collective 3^– state. The results are compared to predictions of models which consider, in particular, the aspects of the quadrupole interaction and the interaction of the 2-particle pairing vibration with the 2-phonon octupole vibration. For the²⁰⁶Pb+²⁰⁸Pb system at 6.2 MeV/u the nuclear potential could be determined from the measured inelastic cross sections.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

High density behaviour of nuclear symmetry energy

There exists profound discrepancy in the high density behaviour of the nuclear symmetry energy obtained in realistic variational many-body (VMB) calculations and in relativistic mean-field (RMF) calculations. While the symmetry energy decreases to negative values in the former approach it increases monotonically in the latter one. The origin of this discrepancy is discussed and it is argued that VMB prediction is more reliable. It is shown that vanishing of the symmetry energy implies proton-neutron separation instability in dense matter.This work was partially supported by KBN grants 2 0204 91 01 and 2 0054 91 01.     

Approximate penetration factor and reduced width for a diffuse edge well

The so-called anticlassical approximation for solutions of the radial Schrödinger equation with rapidly varying potentialsU(r) for which ¦(kU)^–1 dU/dr¦ 1 is worked out. With the diffuseness as a small parameter and using the method of matched asymptotic expansions the regular and irregular wave functions for the Woods-Saxon potential well with Coulomb and centrifugal barrier are obtained. The penetration factor and the reduced width are also deduced and used to express the resonance width.Communicated by X. Campi     

Absorption and refraction phenomena in proton- and antiproton-nucleus scattering

The experimental data on the 180 MeV proton and 50, 180 MeV antiproton scattering by the nuclei¹²C,⁴⁰Ca and²⁰⁸Pb have been analysed on the basis of the phenomenological diffraction theory. The optical properties of the nuclei with regards to the incident protons and antiprotons are investigated. Various limiting cases of the proton- and antiproton-nucleus scattering are considered. The contribution of the Coulomb and the spin-orbit interactions to the differential cross sections of these processes has been also analysed.The authors are indebted to D.M. Skrypnik for assistance in preparing the English version of this paper.     

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     

Nuclear moments and the change in the mean square charge radius of neutron deficient thallium isotopes

The hyperfine structure, isotope and isomeric shifts in the atomic transition 6p ² P _3/2–7s ² S _1/2, =535 nm have been measured for theI=7 andI=2 states of^{190, 192, 194, 196}Tl; theI=1/2 andI=9/2 states of¹⁹¹Tl and the I=7 isomer of¹⁸⁸Tl. The thallium isotopes were prepared as fast atomic beams at the GSI on-line mass separator following fusion reactions and — in some cases — subsequent-decay. The nuclear dipole moments, electric quadrupole moments and the change in the nuclear mean square charge radius are evaluated. Theuu-isotopes show an isomeric shift which changes sign between¹⁹²Tl and¹⁹⁴Tl.Dedicated to P. Armbruster on the occasion of his 60th birthday     

Analysis of proton elastic scattering from16O and40Ca at 800 MeV within the α-particle model

Elastic scattering of proton from¹⁶O and⁴⁰Ca are analyzed within the -particle model. The results are in good agreement with the experimental data. The role displayed by the phase factor ofp- scattering amplitude is investigated.     

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     

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     

Prospects for underground accelerator research

A summer institute was convened at the Gran Sasso Laboratory (Italy), 27. June to 7. July 1994, in part to explore the advantages of an accelerator laboratory deep underground, particularly for crucial nuclear-astrophysics measurements presently limited at low energies by cosmic-ray backgrounds. Here we review specific reactions identified as needing further study in a low-background environment, and outline suitable facilities to carry out such studies.The authors would like to thank P. Aguer, C. Angulo, R.E. Azuma, R.N. Boyd, C. Broggini, E. Cecil, P. Corvisiero, C. Czerski, P. Descouvemont, H. Dzitko, U. Greife, J.W. Hammer, F. Käppeler, J. Kiener, J. Lambert, Ch. Leclerc-Willain, Th. Paradellis, W.S. Rodney, T. Shoppa, A. Shotter, E. Somorjai, F. Terrasi, H.P. Trautvetter, M. Wiescher and other colleagues for their contributions and discussions during the summer insitute, which are in part included in this report.