Simple applications of the pairing-plus-quadrupole-plus-octupole model

The octupole-octupole interaction has been added to the old pairing-plus-quadrupole model. Symmetries of the HF mean field are discussed. An overview is presented of the ground-state deformations for a singlej orbital and two opposite-parity,j, j – 3 orbitals. Breaking of various symmetries can be studied within this model. It is shown that the pairing and the quadrupole-quadrupole interaction stabilize the mean field against octupole deformation. For the singlej orbital, except for one particularj value, no non-axial quadrupole deformations were found. For two opposite-parityj, j –3 orbitals, non-axial octupole deformations occur in most cases. Also axial and non-axial quadrupole deformations were found to be induced by octupole deformations.Communicated by: X. Campi     

Alpha particles from the reaction12C +12C at 28.7 MeV/nucleon

A classical dynamical alpha-cluster model has been developed and applied in order to get inclusive energy spectra of alpha particles produced in the collision of¹²C +¹²C at the beam energy 28.7 MeV/A. Results of the calculations are compared with experimental data. The shapes of the experimental energy spectra and the absolute normalization at forward angles are approximately described without any free parameters. The model makes it possible to distinguish alpha particles originating from the compound system and from direct processes. The spectra at forward angles are dominated by projectile fragmentation processes. The cross section at larger angles is overestimated, which is partially due to emission of particles other than alpha particles in central collisions. The evaporation Hauser-Feshbach model predicts that alpha particles emitted from the compound nucleus constitute less than 26% of all emitted particles.     

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     

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     

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.     

Ground-state properties of neutron-deficient platinum isotopes

The hyperfine structure splitting and the isotope shift in the =266 nm transition of Pt isotopes within the mass range 183 A 198 have been determined by Resonance Ionization Mass Spectroscopy (RIMS) in combination with Pulsed-Laser Induced Desorption (PLID). The Pt isotopes were obtained at the on-line isotope separator ISOLDE-3/CERN as daugthers of the primarily produced Hg isotopes. Magnetic moments, quadrupole moments, and changes in the mean-square charge radii are deduced and compared with results of a particle-triaxial rotor model and mean field calculations. Good agreement with experimental data (including nuclear level schemes and transition probabilities) can only be obtained if triaxial shape is admitted. The calculations yield a smooth transition in the shape of odd-A Pt nuclei from a slightly deformed, nearly oblate¹⁹⁵Pt via triaxial^197-187Pt to a strongly deformed nearly prolate¹⁷⁷Pt.Dedicated to P. Armbruster on the occasion of his 60th birthday     

Low-energy pion-nucleus potential in the extended tree-level model for the pion-nucleon interaction

Starting from the extended tree-level model for theπN interaction [1] (hereafter ETLM) we demonstrated that the observed local pion-nucleus repulsion arises from the reduction of baryon masses in nucleus due to strong scalar nuclear field [2]. This is rather convincing argument in favour of nuclear relativism because such repulsion has no explanation within the traditional nonrelativistic approach to nucleus. Communicated by V.V. Anisovich     

Measurements of magnetic moments of Tc isotopes and the hyperfine field of Tc in Fe and Ni

We report measurements of nuclear magnetic resonance on oriented nuclei (NMR-ON) on⁹⁴Tc (I=7⁺,T _1/2=4.9 h),⁹⁵Tc (I =9/2⁺,T _1/2=20 h) and⁹⁶Tc (I =7⁺,T _1/2=4.3 d) in Fe and on⁹⁵Tc and⁹⁶Tc in Ni. In order to elucidate the discrepancies on the hyperfine field of TcFe in the literature, the resonances were measured with high precision as a function of the external magnetic field B_ext up to 2.0 T. In addition, TDPAC measurements were performed on⁹⁹TcFe at T=300 K and 13 K. TheT=0 K hyperfine fields of Tc in Fe and Ni were determined to be –314(3) kG and –51.8(5) kG, respectively. The g-factors of⁹³Tc,⁹⁴Tc,⁹⁵Tc,⁹⁶Tc and⁹⁹Tc(E=181 keV;I =5/2⁺) are redetermined as g(⁹³Tc)=1.405(14), g(⁹⁴Tc)=0.731(7),g(⁹⁵Tc)=1.321(13), g(⁹⁶Tc)=0.727(7), g(⁹⁹Tc)=1.390(17).We wish to thank E. Smolic and G. Seewald for experimental help. This work was funded by the German Federal Minister for Research and Technology (BMFT) under the contract number 06TM353/TP 4, by the Deutsche Forschungsgemeinschaft (DFG) under the contract numbers Ha 1282/3-1,2, and, partly, by the Kernforschungszentrum, Karlsruhe.     

Preequilibrium emission in (p,x n) reactions on palladium isotopes

Energy spectra of neutrons from the^{104, 105, 106, 108, 110}pd(p, xn) reactions atE _p=26.1 MeV have been measured using the time-of-flight technique with good overall energy resolution (< 250=" kev).=" the=" hard=" part=" of=" angle-integrated=" spectra=" corresponding=" to=" low=" residual=" excitations=">U6MeV) exhibits pronounced structure varying from isotope to isotope. The observed structure can be reasonably well described by preequilibrium-model calculations with two-quasiparticle state densities for proton-particle neutron-hole configurations based on Nilsson-model single-particle levels instead of equidistant ones. The influence of nuclear deformation and pairing on preequilibrium particle emission is explored.Supported in part by the exchange program of the Universities of Hamburg and Zagreb, Internationales Büro — KFA Jülich, and by the BMFT (Contract 06 HH 142)     

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     

Nuclear structure study of the neutron deficient cadmium isotopes100, 101, 102Cd

The neutron-deficient nuclei^100,101Cd were identified for the first time in — beam following the reactions⁵⁸Ni +^46,48Ti and⁵⁸Ni +⁵⁰Cr at 230 MeV and 245 MeV bombarding energy of the⁵⁸Ni beams. The-decay of the isotopes^100,101,102Cd was studied inp, pp,n, nn, andn prompt and delayed coincidence spectra. Isomers were found with spin and half life {ie1-01}=8⁺, T_1/2=52(5) ns in¹⁰⁰Cd, {ie1-02}=(19/2⁺), T_1/2=4.6(4) ns in¹⁰¹Cd and {ie1-03}=8⁺, T_1/2=56(4) ns in¹⁰²Cd. In a PAD experiment theg-factor of the {ie1-04}=8⁺ isomer in¹⁰⁰Cd was measured to be g=1.24(6). Using the reaction³⁶Ar +⁷⁰Ge at 135 MeV energy of the³⁶Ar beam, theg-factor and the quadrupole moment of the {ie1-05}=8⁺ isomer in¹⁰²Cd were measured to be g=1.29(3) and Q=87(10) fm², respectively. The spectroscopic results are discussed within a shell model approach using a¹⁰⁰Sn core, which accounts well for the electromagnetic properties of the proton aligned isomers. The structure of the spherical neutron states, dominated by the close lying vd_5/2, g_7/2 orbitals, and the gradually developing quadrupole collectivity are reproduced by the shell model calculations.The authors gratefully acknowledge fruitful discussions with K. Heyde and are indebted to him for communicating unpublished theoretical results. The help of N.A.F.M. Poppelier and A.G.M. van Hees in running the RITSSCHIL code is very much appreciated.     

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.     

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     

Supersymmetry in74Se,75Se,73As,and74As nuclei

New experimental data, obtained on⁷³As and⁷⁴As, were used to test the predictions of the U(6/12)U (6/12) supersymmetry scheme in its vibrational limit. The level spectra of ₃₄ ⁷⁴ Se₄₀, ₃₄ ⁷⁵ Se₄₁, ₃₃ ⁷³ AS₄₀ and ₃₃ ⁷⁴ As₄₁ supermultiplet nuclei have been calculated using a simple closed energy formula. 44 states in four different nuclei have been reasonably described using only 7 fitted parameters. The existence of supersymmetry was supported also by one-nucleon transfer reaction data, electromagnetic properties, and by a comparison between the supersymmetry and interacting boson-fermion-fermion model wave functions.     

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     

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.     

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     

Extended operator expansion method for neutrinoless double beta decay

Reliable calculations of nuclear matrix elements are a prerequisite for the determination of the effective neutrino mass and other particle physics parameters from neutrinoless double beta decay. Here, the operator expansion method is improved by including Coulomb, tensor and central interactions simultaneously. Furthermore, the formalism of the OEM is extended to those matrix elements necessary to extract the right-handed parameters and from 0 decay. OEM includes the dependence of the nuclear matrix elements on the intermediate states implicitly and can therefore be understood as a step beyond the closure approximation. Numerical studies are carried out for the isotope⁷⁶Ge combining the OEM expressions with ground-state wave functions calculated within a proton-neutron quasiparticle Random Phase Approximation (pn-QRPA) model. The influence and relative importance of central, tensor and Coulomb interactions is investigated. Within the OEM, contributions from the Coulomb force are found to be negligible in 0 decay, while the tensor force leads to a moderate change of the results, of the order of (10–30)%, giving a better agreement between sets of calculations which employ different NN-interactions. Generally, results of the OEM+QRPA calculation are similar to previous calculations of 0 decay matrix elements, indicating that 0 decay is not sensitive to model approximations and might therefore be more accurately calculated than the strongly suppressed 2 decay matrix elements.