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     

Cluster structures in light nuclei

Clustering in light stable and unstable nuclei is discussed. After a brief review of the clustering in stable nuclei, we make a new prediction of the existence of the alpha cluster condensed states in ¹²C and ¹⁶O. Discussions of clustering in light unstable nuclei are made in the cases of Be and B isotopes up to the neutron dripline. Received: 1 May 2001 / Accepted: 4 December 2001     

Nuclear clusters and nuclear molecules

Clustering has long been known to be influential in the structure of ground and excited states of N=Z$N=Z$ nuclei. States close to the decay thresholds are of particular interest, as clustering becomes dominant. Recent studies of loosely bound light neutron-rich nuclei have focused attention on structures based on clusters and additional valence neutrons, which give rise to covalent molecular binding effects. These nuclear molecules appear only at the extremes of deformation, in the deformed shell model they are referred to as super- and hyper-deformed. The beryllium isotopes provide the first examples of such states in nuclear physics. Further nuclear molecules consisting of unequal cores and also with three centres can be considered. These arise in the isotopes of neon and carbon, respectively. Molecular states in intrinsically asymmetric configurations give rise to parity (inversion) doublets. Examples of recent experiments demonstrating the molecular structure of the rotational bands in beryllium isotopes are presented. Further experimental evidence for bands as parity doublets in nuclei with valence neutrons in molecular orbits is also analysed. Work on chain states (nuclear polymers) in the carbon isotopes is discussed. These are the first examples of hyper-deformed structures in nuclei with an axis ratio of 3:1. Future perspectives are outlined based on a threshold diagram for covalent nuclear molecules with clusters bound via neutrons in covalent molecular configurations.     

Evidence for hexadecapole vibrations in A ≈ 170 deformed nuclei; New results for 168Yb

Dominating proton structure has been identified in the K^π=3⁺ band of ¹⁶⁸Yb, contrasting with neutron structure in the corresponding band of ¹⁷²Yb. A region of low-lying K^π=3⁺ bands is now established, with N=98?104, Z=68?72. For all stable nuclei in this region, the I^πK=4⁺3 state is excited by inelastic deutron scattering.     

Structure analysis of 159Sm and properties of odd-mass neutron-rich nuclei in mass-160 region

Recent fission experiment data provide interesting structure information for neutron-rich nuclei in the mass A ∼ 160 region. We apply the projected shell model to study the strongly-deformed, neutron-rich Sm isotopes. We perform calculations for rotational bands up to spin I = 20 (29/2) for even-even (odd-neutron) Sm isotopes, and analyze the band structure of low-lying states with quasiparticle excitations. Emphasis is given to rotational bands based on one-quasiparticle (1-qp) configurations in the odd-mass ¹⁵⁹Sm. The ¹⁵⁹Sm result is discussed together with those of the even-even isotopes ^158,160Sm. New bands in ¹⁵⁹Sm based on neutron 1-qp 1/2⁻ and 5/2⁺ configurations are predicted. Electromagnetic transition probabilities are discussed.

     

New multi-phonon gamma vibrational bands in A∼110 neutron-rich nuclei

The high spin states of neutron-rich ¹⁰³Nb, ¹⁰⁷Tc and ¹⁰⁹Tc nuclei in A～110 region have been investigated by measuring prompt γ-γ-γ coincident measurements populated with the spontaneous fission of ²⁵²Cf with the Gammasphere detector array. In ¹⁰³Nb, one-phonon K = 9/2 and two-phonon K = 13/2 γ-vibrational bands have been identified. In ¹⁰⁷Tc and ¹⁰⁹Tc, one-phonon K = 11/2 and two-phonon K = 15/2 γ-vibrational bands, in which the zero-phonon bands are based on K=7/2 excited states, have also been identified. The two-phonon bands are first observed in odd-Z nuclei. The characteristics for these band structures have been discussed.     

Pushing the limits of nuclear stability

Reaching the limits of nuclear stability offers unique opportunities to understand basic nuclear properties. New shell structures close to the driplines can change the existence of neutron-rich nuclei. A new search for ¹⁶Be confirmed the previous limit for particle stable Be isotopes at A=14. Single proton knock-out reactions offer the potential for more sensitive searches of very weakly bound nuclei. In order to extend the knowledge of the neutron dripline beyond Z=8 requires new accelerator developments. The proposed new rare isotope accelerator has the potential to push the limit of the neutron dripline to at least Z=25.     

Microscopic structures of parity doublets in the151Pm,153Eu and155Eu nuclei

Microscopic structures of the proposed parity doublet bands in the odd-proton Z=61¹⁵¹Pm and Z=63^{153, 155}Eu nuclei are examined using the quasiparticle phonon nuclear model Hamiltonian including the residual pairing and multipole-multipole interactions. Octupole correlations between intrinsic nonrotational states are studied to check the suggested assignments of parity doublet partners in these nuclei. We conclude significant octupole correlations between a pair ofK ^π = 1/2^± doublets in each of these nuclei, with somewhat weaker correlations betweenK ^π = 3/2^± bands in both the Eu isotopes. No octupole connection between the lowestK ^π = 5/2^± bands is found; however, significant octupole collectivity, built on the low-lying 5/2^? bands, is predicted in the higher-lying 5/2⁺ bands which contain the 5/2⁺ [402] fragmented strength.     

Study of neutron-rich Mo isotopes by the projected shell model approach

The projected shell model (PSM) calculations have been performed for the neutron-rich even–even ^102?110Mo and odd—even ^103?109Mo isotopes. The present calculation reproduces the available experimental data on the yrast bands. In case of even–even nuclei, the structure of yrast bands is analysed and electromagnetic quantities are compared with the available experimental data. The g-factors have been predicted for high spin states. For the odd-neutron nuclei, the structures of yrast positive- and negative-parity bands are analysed and found to be in reasonable agreement with the experiments for ^103?107Mo. The disagreement of the calculated and observed plots for energy staggering quantity clearly establishes the occurrence of sizable triaxiality in ^103,105Mo and also predicts a decrease in the quantum of triaxiality with increasing neutron number and angular momentum for odd mass neutron-rich Mo isotopes.     

Exotic cluster structure in light neutron-rich nuclei

The cluster structure of C isotopes is investigated using a microscopic α+α+α+n+n… model based on the molecular orbit (MO) model. The stability of the linear chain of 3α with respect to the breathing mode and the bending mode for various neutron configurations is investigated. The combination of the valence neutrons in the π- and σ-orbits is promising to stabilize for these modes, and the excited states of ¹⁶C with the (3/2 _π ^- )²(1/2 _σ ^- )² configuration for the four valence neutrons are one of the most promising candidates for such structure. Furthermore, the equilateral-triangular shape of 3α surrounded by valence neutrons is suggested for ¹⁴C. The 3^-, 4^-, and 5^- members of this rotational band appear around the ¹⁰Be+α threshold, and these calculated states correspond to the experimentally observed 3^- state (9.80 MeV) and 4^- state (11.67 MeV). A positive-parity rotational band (0⁺, 2⁺, 4⁺) also arises around this threshold energy, and these results suggest that the picture of inversion doublet structure works also in neutron-rich nuclei.     

Spectroscopy of nuclei far from stability at GANIL: Recent experiments

The structure of neutron-rich light nuclei around N = 20, 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: 1 May 2001 / Accepted: 4 December 2001     

Collective and two-quasiparticle states in 158Gd observed through study of radiative neutron capture in 157Gd

The level structure of ¹⁵⁸Gd has been studied using the prompt γ-rays and conversion electrons emitted following neutron capture in ¹⁵⁷Gd. The γ-ray energy and intensity measurements were made using both Ge(Li) detectors and a curved-crystal spectrometer. Conversion-electron energy and intensity measurements were made using two separate magnetic spectrometers: one to measure the primary electron spectrum and the other to measure the lower energy secondary electron spectrum. Some γ-γ coincidence measurements were also made among the secondary γ-rays. From these data, a neutron separation energy of 7937.1 ± 0.5 keV has been determined for ¹⁵⁸Gd. A level scheme containing 59 excited states with energies < 2.25 MeV, for which de-excitation modes have been identified, is proposed for ¹⁵⁸Gd. Many of these states have been grouped into rotational bands. A total of thirteen excited rotational bands with band-head energies below 2.0 MeV are contained in the level scheme. Features of the proposed level scheme include: the K^π = 0^?, 1^? and 2^? octupole-vibrational bands with band-head energies of 1263, 977 and 1793 keV, respectively; the γ-vibrational band at 1187 keV; three excited K^π = 0⁺ bands with band-head energies of 1196, 1452 and 1743 keV; several two-quasiparticle bands with band-head energies in keV (and K^π assignments) of 1380 (4⁺), 1636 (4^?), 1847 (1⁺), 1856 (1^?), 1920 (4⁺) and 1930 (1⁺). An analysis of (d, p) reaction data is presented which permits definite two-quasiparticle configuration assignments to be made to most of these latter bands. Evidence is presented which suggests strong mixing of some two-neutron and two-proton bands. A phenomenological four-band mixing analysis is made of the energy and E2 transition-probability data for the ground-state band and the three lowest-lying excited collective positive-parity bands. Good agreement with experiment is obtained. A Coriolis-mixing analysis of the octupole bands has been carried out and good agreement with the data on level energies and E1 transition probabilities to the ground-state band has been achieved. Values of Z, the ratio of the E1 transition matrix element with ΔK = 1 to that with ΔK = 0, involving the octupole bands and the first four 0⁺ bands are derived. For three of these 0⁺ bands, absolute values of these matrix elements are deduced. An interesting alternation in the sign of Z is observed for these four 0⁺ bands.     

The decay scheme of 228Fr and K = 0 BANDS in 228Ra

The γ-rays following the β^?-decay of ²²⁸Fr have been studied by means of γ-ray singles including multi-spectrum analysis and γ-γ coincidence measurements using Ge(Li) spectrometers. Most of the observed γ-transitions could be placed in the level scheme of ²²⁸Ra. The accuracy the energy of the first-excited state in ²²⁸Ra has been improved and 35 new excited levels have been established, 11 of them grouped into the ground-state band, the low-lying K^π = 0^? band with the head at 474.14 keV and two excited K^π = 0⁺ bands with heads at 721.17 and 1041.9 keV. Candidates for two close-lying K^π = 2⁺ bands have also been found. It is concluded that the ground state octupole deformation, if any, is less pronounced in ²²⁸Ra than in lighter radium isotopes.     

Two-center molecular states in9B,9Be,10Be,and10B

The molecular states in the mass 9 and 10 nuclei, which consist of two α-particles plus one or two valence nucleons (protons or neutrons) are discussed. Arguments for the existence of two-center dimers as excited states in¹⁰Be and corresponding resonances (p+⁹Be) in¹⁰B are given. The latter states are observed as anomalous (non statistical) population in the final state interactions in thep+⁹Be channel in various heavy ion collisions. With the establishment of two-center states (dimers) based on the αα-potential and a localized binding via two nucleons in¹⁰Be, the existence of more extended structures (multimers) by adding (α2n) structures to¹⁰Be* is postulated. Generally clustering intoα-particles and nucleons in terms of molecular states is expected to occur at excitation energies close to the threshold for these substructures in analogy to the clustering rules of Ikeda forα-particle nuclei. Consequences to clustering properties of neutron rich nuclei are discussed.     

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     

γ-Spectroscopy of light neutron-rich nuclei after secondary reactions at relativistic energies

After the fragmentation reaction of ⁵⁰Ti on ⁹Be at 330 MeV/u, more than 30 neutron-rich isotopes from B to Ca were selected by the fragment separator FRS at GSI. Peripheral collisions with a secondary Pb target at relativistic energies were used to study the excited states of these isotopes. De-excitation γ-rays were detected with the Darmstadt-Heidelberg Crystal Ball spectrometer. The first results demonstrate the feasibility of in-beam γ-spectroscopy at relativistic energies.     

Structure of neutron-rich Be and C isotopes

The structure of neutron-rich beryllium isotopes has been investigated using different heavy-ion-induced transfer reactions. In neutron transfer reactions, the population of final states shows a strong sensitivity to the chosen core nucleus, i.e., the target nuclei ⁹Be or ¹⁰Be, respectively. Molecular rotational bands up to high excitation energies are observed with ⁹Be as the core due to its pronounced 2α-cluster structure, whereas only a few states at low excitation energies are populated with ¹⁰Be as the core. For ¹¹Be, a detailed investigation has been performed for the three states at 3.41, 3.89, and 3.96 MeV, which resulted in the most probable spin-parity assignments 3/2⁺, 5/2^?, and 3/2^?, respectively. Furthermore, we have studied particle-hole states of ¹⁶C using the ¹³C(¹²C, ⁹C)¹⁶C reaction and found 14 previously unknown states. Using the ¹²C(¹²C, ⁹C)¹⁵C reaction, five new states were observed for ¹⁵C.     

The neutron drip line in the region of <Emphasis Type="Italic">N</Emphasis>=20 and <Emphasis Type="Italic">N</Emphasis>=28 closures

Experimental studies of neutron drip line nuclei are introduced. The neutron drip line in the oxygen-magnesium region has been explored by the projectile fragmentation of a ⁴⁸Ca beam. New neutron-rich isotopes, ³⁴Ne and ³⁷Na, have been observed together with some evidence for the particle instability of ³³Ne and ³⁶Na. Recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells, and together with the measurements of instability of doubly magic nuclide ²⁸O, they provide information on changes in neutron shell closures of very neutron-rich isotopes from carbon up to calcium. The conclusion about a rearrangement in neutron shell closures is given. The spectroscopic measurements can reveal details of the underlying microscopic structures; in-beam γ-ray spectroscopy is an effective tool to check for shell closures. The results on the γ-ray energies of the first 2⁺ level in even-even nuclei for the range N=12–32 are discussed. The strength of N=20 and N=28 shells is variable in the region from carbon up to magnesium.     

Level structure of 184W from the 183W(n, γ) reaction

The level structure of ¹⁸⁴W has been studied from the prompt γ-rays emitted following the capture of both thermal and 2 keV neutrons by ¹⁸³W. Energies and intensities were measured for both the primary and the secondary (low-energy) prompt γ-rays. From these data, a level scheme is proposed for ¹⁸⁴W in which all the I^π = 0⁺, 1⁺ and 2⁺ states below ≈ 2.0 MeV are observed. Where possible, rotational-band assignments have been made to these and other levels. Additional evidence is presented which confirms the 1130 keV state as being the band head of a K^π = 2^? octupole vibrational band. Admixed K^π = 0⁺ and 2⁺ bands are established at 1322 and 1386 keV, respectively, with the I^π = 2⁺ states (at 1431 and 1386 keV) having a mutual admixture of ≈ 12%. In the energy region above 1.5 MeV, the following bands and band-head energies are identified: K^π = 1⁺, 1613 keV; K^π = 0⁺, 1614 keV; K^π = 1⁺, 1713 keV; K^π = 2⁺, 1877 keV. The neutron binding energy in ¹⁸⁴W has been determined to be 7411.1±0.6 keV. The band structure of the 1613 keV (1⁺) and 1614 keV (0⁺) bands is observed to be strongly distorted, the observed $\text{A (}\text{h}\text{?}{}^2\text{/2}\text{I}\text{)}$ values being ≈ 3.6 keV and ≈ 32 keV, respectively. This strong distortion is shown to be explainable in terms of Coriolis coupling of reasonable strength between the two bands. A similar explanation is shown to account for the somewhat less anomalous A-values (22.8 keV and 14.0 keV, respectively) of the 2⁺ band at 1386 keV and the 3⁺ band at 1425 keV. The results of a phenomenological fiveband-mixing analysis involving the K^π = 0⁺ and 2⁺ bands below ≈ 1.5 MeV are presented and discussed. These calculations indicate, among other things, that the direct E2 matrix element connecting the 1322 keV, K^π = 0⁺ band and the ground-state band is quite small, possibly zero. They also indicate that a nonzero E2 matrix element exists between this excited K^π = 0⁺ band and the γ-vibrational band and that the magnitude of this element is comparable with that between the γ-vibrational and ground-state bands. Arguments favoring and apparently refuting the interpretation of the 1322 keV, 0⁺ band as a “two-phonon γ-vibration” are presented.     

The beta-decay scheme of <Superscript>232</Superscript>Fr and the K = 0 ground-state band in <Superscript>232</Superscript>Ra

The beta-decay of ²³²Fr to excited states in ²³²Ra has been studied using gamma-gamma coincidence detection combined with the isotope separator on-line technique at the ISOLDE PSB facility at CERN. Earlier findings are confirmed and three new gamma lines are reported. In addition to the beta-decay characteristics of ²³²Fr, the K = 0 ground-state band in ²³²Ra is identified. A yield survey of neutron-rich Fr isotopes, important also for the EURISOL project, is incorporated.Received: 20 April 2004, Revised: 12 May 2004, Published online: 13 July 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 23.20.-g Electromagnetic transitions - 28.60. + s Isotope separation and enrichment - 29.25.Rm Sources of radioactive nuclei