Status and prospects of synthesizing superheavy elements

The nuclear shell model predicts that the next doubly magic shell-closure beyond ²⁰⁸Pb is at a proton number between Z = 114 and 126 and at a neutron number N = 184. The outstanding aim of experimental investigations is the exploration of this region of spherical “Superheavy Elements”. This article describes the experiments that were performed at the GSI SHIP. They resulted in an unambiguous identification of elements 107 to 112. They were negative so far in searching for elements 113, 116 and 118 at SHIP; however, positive results were reported from experiments in Dubna on elements 114 and 116 and from experiments in Berkeley on element 118. The measured decay data are compared with theoretical predictions. Some aspects concerning the reaction mechanism and the use of radioactive beams are also presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: S.Hofmann@gsi.de     

The Z = 82 shell closure in neutron-deficient Pb isotopes

Recent mass measurements show a substantial weakening of the binding-energy difference δ_2p(Z, N) = E(Z - 2, N) - 2E(Z, N) + E(Z + 2, N) in the neutron-deficient Pb isotopes. As δ_2p is often attributed to the size of the proton magic gap, it might be speculated that reduction in δ_2p is related to a weakening of the spherical Z = 82 shell. We demonstrate that the observed trend is described quantitatively by self-consistent mean-field models in terms of deformed ground states of Hg and Po isotopes. Received: 25 October 2001 / Accepted: 28 February 2002     

Evolution of the N = 20 and N = 28 shell closures in neutron-rich nuclei

The isospin dependence of shell closure phenomena is studied for light neutron-rich nuclei within a microscopic self-consistent approach using the Gogny force. Introducing configuration mixing, ³²Mg is found to be dynamically deformed, although the N = 20 spherical shell closure persists at the mean-field level for all N = 20 isotones. In contrast, the N = 28 spherical shell closure is found to disappear for N - Z≥ 10 whereas deformed shell closures are preserved and lead to shape coexistence in ⁴⁴ S. Configuration mixing shows that the ground state of this nucleus is triaxially deformed. The first 2⁺ excitation energy E_x = 1.46 MeV and the reduced transition probability B(E2;0⁺ _gs→ 2⁺ ₁)= 420 e ² fm ⁴ obtained with our approach are in good agreement with experimental data. Received: 26 July 2000 / Accepted: 30 August 2000     

Frontiers and challenges of nuclear shell model

Two recent developments of the nuclear shell model are presented. One is a breakthrough in computational feasibility owing to the Monte Carlo Shell Model (MCSM). By the MCSM, the structure of low-lying states can be studied with realistic interactions for a wide, nearly unlimited basically, variety of nuclei. The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: otsuka@phys.s.u-tokyo.ac.jp     

Lifetime measurements in 148Gd

Lifetimes of excited states in ¹⁴⁸Gd were measured using the recoil distance method with a plunger device coupled to the EUROBALL Ge detector array. The differential decay curve method in coincidence mode allowed the unambiguous determination of lifetimes of more than 20 excited states. The obtained transition strengths are in good agreement with the shell model calculations. The effect of the Z = 64 subshell closure on the B(E2 : 2⁺ → 0⁺) reduced strengths above the N = 82 magic number is discussed.-1 Received: 14 November 2002 / Accepted: 4 February 2003 / Published online: 29 April 2003     

Quadrupole collectivity of neutron-rich neon isotopes

The Angular Momentum Projected Generator Coordinate Method, with the quadrupole moment as collective coordinate and the Gogny force (D1S) as the effective interaction, is used to describe the properties of the ground state and low-lying excited states of the even-even neon isotopes ^20-34Ne, that is, from the stability valley up to the drip line. It is found that the ground state of the N = 20 nucleus ³⁰Ne is deformed but to a lesser extent than the N = 20 isotope of the magnesium. In the calculations, the isotope ³²Ne is at the drip line in good agreement with other theoretical predictions. On the other hand, rather good agreement with experimental data for many observables is obtained. Received: 19 Novemeber 2002 / Accepted: 24 January 2003 / Published online: 8 April 2003     

Maximally aligned states in 99Ag

Excited states of ⁹⁹Ag were populated via the ⁵⁰Cr + ⁵⁸Ni (261 MeV) reaction using the NORDBALL detector array equipped with charged-particle and neutron detector systems for reaction channel separation. On the basis of the measured γγ-coincidence relations and angular distribution ratios a significantly extended level scheme has been constructed up to E _x ∼ 7.8 MeV and I = 35/2. The experimental results were described within the framework of the shell model. Candidates for states fully aligned in the πg _9/2 ^-3ν(d _5/2, g _7/2)² valence configuration space were found at 4109 and 6265 keV. Received: 18 June 2002 / Accepted: 11 October 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: sohler@atomki.hu Communicated by J. ?yst?     

Shell structure of cesium layer covering the C fullerene core

Strutinsky shell corrections for the cesium-coated fullerenes were investigated. The single particle levels of electrons are obtained using the spherical mean-field potential of a shifted Wood-Saxon type. The parameters of the potential are adjusted to reproduce the experimental ionization energies of the Cs(N) clusters and the magic numbers observed in their photo-ionization spectra of the C₆₀Cs(N) aggregates. Received 24 May 2002 / Received in final form 9 July 2002 Published online 15 October 2002 RID="*" ID="*"This work has been partly supported by the Polish Committee for Scientific Research under Contract No. 2P03B 115 19 and by the Program of Scientific Exchange between the IN2P3-France and the Polish Research Institution No. 99-95. RID="b" ID="b"e-mail: Krzysztof.Pomorski@umcs.lublin.pl     

Band termination in the Z = N odd-odd nuclei <Superscript>46</Superscript>V and <Superscript>50</Superscript>Mn

The configuration-dependent cranked Nilsson-Strutinsky approach has been employed to study the properties and band structures at high spin in the Z = N odd-odd nuclei ⁴⁶V and ⁵⁰Mn. The observed bands are explained and terminating states are confirmed by the calculations. The calculated and observed bands are in good agreement without normalization, especially for terminating states. Possible bands with rotation around the intermediate axis and the effect of γ-deformation on the total energy of several interesting configurations are discussed. Received: 2 April 2002 / Accepted: 27 January 2003 / Published online: 15 April 2003     

Rotational bands in 169Re

Based on the systematic investigation of the data available for nuclei with A≥ 40, a Z ^1/3-dependence for the nuclear charge radii is shown to be superior to the generally accepted A ^1/3 law. A delicate scattering of data around R _c/Z ^1/3 is inferred as owing to the isospin effect and a linear dependence of R _c/Z ^1/3 on N/Z (or (N - Z)/2) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. With the linear isospin dependence provided by the data and RCHB theory, a new isospin-dependent Z ^1/3 formula for the nuclear charge radii is proposed. Received: 23 September 2001 / Accepted: 21 January 2002     

Deformed shell model for T = 0, 1 and 2 bands in <Superscript>52</Superscript>Fe and <Superscript>72</Superscript>Kr

Deformed configuration mixing shell model based on Hartree-Fock states with extension to include isospin projection (DSMT) for two- and four-particle configurations (generated by particle-hole excitations) is applied to study the structure of the low-lying T = 0, 1 and 2 bands (or levels) in the even-even N = Z nuclei ⁵²Fe and ⁷²Kr. The pf-shell KB3 interaction for ⁵²Fe and a modified Kuos interaction for ⁷²Kr are employed in the calculations. In this first application of DSMT with four-particle T projection, low-spin (J 10) members of the T = 0, 1 and 2 bands in ⁵²Fe are compared with experiment including the known E2 transition strengths. The agreement between DSMT and experiment is reasonably good. Similarly, the low-spin members of the observed (prolate) yrast band in ⁷²Kr are also well described by DSMT.     

Molecular structure of nuclei

Cluster structures of nuclei are discussed, with emphasis on nuclear clustering in unstable nuclei. The subjects we discuss are alpha condensed states, clustering in Be and B isotopes, and clustering in ³²Mg and ³⁰Ne. The subject of alpha cluster condensation comes from the clustering nature of dilute nuclear matter. We discuss that recent heavy-ion central collision experiments give us nice evidence of the clustering in dilute nuclear matter. We then present a new prediction of the existence of the “alpha cluster condensed states” in the self-conjugate 4n nuclei around the breakup threshold energy into n alpha-particles. As for the clustering in neutron-rich Be, we discuss the comparison between the antisymmetrized molecular-dynamics results and the recent experimental data, which shows that the clustering feature manifests itself very clearly in neutron-rich Be isotopes both in the ground and excited states. Clustering in Be isotopes near neutron dripline is intimately related to the breaking of the neutron magic number N = 8. We report our recent study about the possible relationship between the clustering and the breaking of the neutron magic number N = 20 in ³²Mg and ³⁰Ne. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: horiuchi@ruby.scphys.kyoto-u.ac.jp     

High-spin states in the <Superscript>97</Superscript>Tc nucleus

High-spin states in the ⁹⁷Tc nucleus have been studied by in-beam γ-ray spectroscopy with the reaction ⁸²Se(¹⁹F,4nγ) at 68 MeV incident energy. Excited states have been observed up to about 8 MeV excitation and spin 43/2. The observed level scheme is compared with results of shell model calculations. Received: 22 November 2002 / Accepted: 23 December 2002 / Published online: 18 March 2003 RID="a" ID="a"e-mail: bucurescu@tandem.nipne.ro RID="b" ID="b"Present address: INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy. RID="b" ID="b"Present address: INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy. RID="b" ID="b"Present address: INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy. RID="c" ID="c"Present address: Università di Padova, Padova, Italy. Communicated by C. Signorini     

Probing shell structure in neutron-rich nuclei with in-beam γ-spectroscopy

The structure of neutron-rich light nuclei around N = 20 and 28 has been investigated at GANIL by means of in-beam gamma-spectroscopy using fragmentation reactions of ³⁶S and ⁴⁸Ca beams on a Be target. Gamma-decay of relatively high-lying excited states have been measured for the first time in nuclei around ³²Mg and ⁴⁴S. Level schemes are proposed and discussed for a large number of these neutron-rich nuclei around N = 20 and N = 28. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: azaiez@ipno.in2p3.fr     

High-spin structure of the neutron-rich odd-odd 106, 108 45Rh and 110, 112 47Ag isotopes

The ^{106, 108}Rh and ^{110, 112}Ag nuclei have been produced as fission fragments following the fusion reaction ²⁸Si + ¹⁷⁶Yb at 145 MeV bombarding energy and studied with the Eurogam2 array. The yrast high-spin states of these four odd-odd nuclei, which are observed for the first time, consist of rotational bands in which the odd proton occupies the πg _9/2 subshell and the odd neutron the νh _11/2 subshell. Their behaviour as a function of spin values does not vary with the number of neutrons: as observed in the odd-N neighbouring nuclei, the motion of the odd neutron remains decoupled from the motion of the core, from N = 61 to N = 65. Moreover, the staggering observed in the yrast bands of odd-odd isotopes is strongly reduced as compared to the large values displayed by the rotational bands built on the πg _9/2 subshell in the odd-A Rh and Ag isotopes. The results of particle-rotor calculations indicate that this reduction is related to a change of the core deformation. Received: 1 June 2001 / Accepted: 23 July 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: porquet@csnsm.in2p3.fr RID="b" ID="b"Present address: CSNSM IN2P3-CNRS and Université Paris-Sud 91405 Orsay, France. RID="c" ID="c"Present address: NAC, Faure, ZA 7131, South Africa. RID="d" ID="d"Present address: Department of Nuclear Physics, ANU, Canberra ACT 0200, Australia. Communicated by D. Schwalm     

High-spin states in <Superscript>36</Superscript>Ar and their underlying shell model configurations

Eight high-spin states in ³⁶Ar below 10MeV excitation energy, among them a prospective J ^π = 8^- state at 9408keV and the J? 8 levels of the recently discovered superdeformed rotational band, have been observed by n-γ coincidence measurements with the ³³S(α, nγ) reaction at E _α = 14.4 and 13.4MeV. High-spin assignments of, respectively, J ^π = 6⁺ and 5^- were obtained for the E _p = 1209 and 1462keV (E _x = 9682 and 9927keV) resonances of the ³⁵Cl (p,γ) reaction by a measurement of γ-ray angular distributions. The spectrum of the high-spin and of the E _x? 7.4MeV levels is decomposed according to the underlying shell model configurations with n = 0, 1, 2, 4 particles excited from the N = 2 into the N = 3 major shell. The role of four-particle excitations, all connected with large prolate distortions, is elucidated for the entire A = 36-40 mass region. Received: 21 December 2001 / Accepted: 25 March 2002     

Properties unique in nuclei far from β stability line

Nucleons with very small binding energies present in nuclei far from the β stability line produce a unique shell structure, which leads to the disappearance of traditional magic numbers or to the creation of new magic numbers and new deformation regions. We study the shell structure in terms of the variation of two important ingredients, the kinetic energy and the spin-orbit splitting, as a function of the orbital angular momentum ℓ, when binding energies of neutrons decrease towards zero. It is also shown that for low-lying threshold strength, a negative sign is possible for the polarization charge coming from the coupling of one-particle to isoscalar shape oscillations. Received: 1 May 2001 / Accepted: 4 December 2001     

Proton-neutron structure of collective excitations in 94Mo

Due to the recent development of radioactive beam production, various direct reaction studies in reversed kinematics have been made to investigate the behavior of the N = 20 shell closure in the neutron-rich region. Coulomb excitation, proton inelastic scattering, and fragmentation of unstable nuclei have been studied with γ-ray detection. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: motobaya@rikkyo.ne.jp     

Shape coexistence and the N = 20 shell closure far from stability by inelastic scattering

Following mass measurements in the region N = 20 and N = 28, we have studied inelastic nuclear scattering for the nuclei ³⁴Si, ³³Al and ³²Mg. No evidence for a low-lying shape isomeric 0⁺ state was found in ³⁴Si, and an upper limit for the population cross-section could be established, rendering its existence very unlikely. A new transition was found in ³³Al, that is a good candidate for a 2p-2h state and therefore a determination of the 2p-2h gap at N = 20. Inelastic nuclear scattering strongly excites 3^- states, as seen in ³⁴Si. A strong transition was found in ³²Mg that should correspond to the first 3^- in this nucleus, lying very low as compared to theory and systematics in this region. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: mittig@ganil.fr