Temperature dependence of quantal and thermal dampings of the hot giant dipole resonance

A systematic study of the damping of the giant dipole resonance (GDR) in ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb as a function of temperature T is performed. The double-time Green function technique is employed to determine the single-particle and GDR dampings. The single-particle energies, obtained in the Woods-Saxon potential for these nuclei, are used in the calculations. The results show that the coupling of collective vibration to the pp and hh excitations, which causes the thermal damping width, is responsible for the enlargement of the total width with increasing temperature up to T ≈ 3MeV and its saturation at higher temperatures. The quantal width, which arises from the coupling of the collective mode to the ph excitations decreases slowly with increasing temperature. The effect of single-particle damping on the GDR width is small. The results are found in an overall agreement with the experimental data for the GDR width, obtained in the inelastic α scattering and heavy-ion fusion reactions at excitation energies E^* ⩽ 450 MeV. At high excitation energies (E^* > 400 MeV) a behavior similar to the transition from zero to ordinary sounds is observed.     

Damping of high-lying single-particle modes in heavy nuclei

The recent experimental and theoretical results on the damping of high-lying single-particle modes in heavy nuclei are reviewed. In one-nucleon transfer reactions these states manifest themselves as broad “resonance”-like structures superimposed on a large continuum. The advantages and the limitations of the transfer reaction approach will be presented using the results from neutron and proton pick-up and stripping reactions. The problem raised by the subtraction of the underlying background, the assumptions made to describe the reaction process and the method used to extract the strength distributions are presented. The existing empirical systematics is summarized for nuclei ranging from ⁹⁰Zr to ²⁰⁸Pb.The theoretical approaches used to explain the damping of the high-lying single-particle modes are based on the coupling between collective and single-particle degrees of freedom. In a first step the bare single-particle mode is spread over several doorway collective states due to the interaction with surface vibrations. In a second step the doorway states spread their strengths over many other degrees of freedom. These two steps of the damping mechanism are discussed in detail within the framework of the quasiparticle-phonon nuclear model. A large-scale comparison between the measured and calculated average energies, spreading widths and spectroscopic strengths of the high-lying single-particle (hole) states in heavy nuclei is presented. The systematic features of the damping (energy, angular momentum and isotopic dependence) are discussed. Recent advances of the experimental approaches, such as the γ-decay of the high-lying states or the use of heavy-ion transfer reactions at intermediate energies, are outlined.The detailed study of the damping mechanism of high-lying single-particle modes reveals new features and leads us to a new field in nuclear structure: “the spectroscopy of inner and outer subshells”.     

Rotational bands on few-particle excitations of very high spin

An RPA formalism is developed to investigate the existence and properties of slow collective rotation around a non-symmetric axis, when there already exists a large angular momentum K along the symmetry axis built up by aligned single-particle spins. Both repeatability and E2 collectivity are required to distinguish the collective rotational-like solutions from the others, which may come lower in energy. First the formalism is applied to bands on high-K isomers in the well-deformed nucleus ¹⁷⁹Hf, where the rotational-model picture is reproduced for intermediate K-values in agreement with experiment. At high K the collectivity is suppressed even more than the diminishing vector-coupling coefficient of the rotational model would suggest, but the repeatability actually improves. The moment of inertia is predicted to remain substantially smaller than the rigid-body value, so the bands slope up steeply from the yrast line at spins where pairing effects are gone. A second application is to the initially spherical nucleus ²¹²Rn, which is believed to acquire an oblate deformation that increases steadily with K due to the oblate shape of the aligned orbitals. In this case the rotational-like excitations also exist but are still less favoured than in ¹⁷⁶Hf, even at comparable deformations. Some collective states may come closer to the average yrast trend, but they have lower repeatability because they are more like dressed single-particle excitations. The main differences between the two nuclei studied is interpreted as a general consequence of their different shell structure.     

Excited states of deformable nonaxial odd nuclei

Rotationally single-particle and vibrational excitations of deformable nonaxial odd nuclei are investigated with allowance for the interaction of collective and single-particle states. The ratios of excitation energies, of reduced probabilities of E2 transitions, and of quadrupole moments for deformed nonaxial odd nuclei are calculated up to high-spin states.     

GCM analysis of the collective properties of lead isotopes with exact projection on particle numbers

We present a microscopic analysis of the collective behaviour of the lead isotopes in the vicinity of ²⁰⁸Pb. In this study, we rely on a coherent approach based on the Generator Coordinate Method (GCM) including exact projection on N and Z numbers within a collective space generated by means of the constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF + BCS calculations, we have performed a comprehensive study including monopole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify the most the conclusions drawn from the mean-field theory are the octupole and pairing vibrations. Received: 31 May 2001 / Accepted: 23 August 2001     

Microscopic analysis of octupole shape transitions in neutron-rich actinides with relativistic energy density functional

Quadrupole and octupole deformation energy surfaces, low-energy excitation spectra, and electric transition rates in eight neutron-rich isotopic chains – Ra, Th, U, Pu, Cm, Cf, Fm, and No – are systematically analyzed using a quadrupole-octupole collective Hamiltonian model, with parameters determined by constrained reflectionasymmetric and axially-symmetric relativistic mean-field calculations based on the PC-PK1 energy density functional.The theoretical results of low-lying negative-parity bands, odd-even staggering, average octupole deformations β_3,and B(E3;3_1~- →0_1~+) show evidence of a shape transition from nearly spherical to stable octupole-deformed, and finally octupole-soft equilibrium shapes in the neutron-rich actinides. A microscopic mechanism for the onset of stable octupole deformation is also discussed in terms of the evolution of single-nucleon orbitals with deformation.     

Collective excitations of the element <Emphasis Type="Italic">Z</Emphasis> = 120

The low-lying vibrational excitations of superheavy even-even nuclei around Z=120 and N=172, predicted to be spherical by the relativistic mean-field (RMF) model, are studied within a phenomenological collective approach. In the framework of the macroscopic model for giant resonances, we compute the transition densities of the isoscalar monopole, quadrupole, and octupole and isovector dipole modes for the superheavy nucleus ²⁹²120, whose ground-state density is determined from the RMF model. The results are also compared to those for²⁰⁸Pb.     

Detailed spectroscopy in the superdeformed second minimum of 240Pu

Spectroscopic studies in the superdeformed shape isomer of ²⁴⁰Pu using γ-spectroscopy, conversion electron spectroscopy and transmission resonance spectroscopy have been performed. In a high-resolution and high-efficiency γ-spectroscopy experiment the out-of-band decays of several excited superdeformed rotational sequences with K=2^? and 1^? could be identified together with evidence for a weakly populated 0^? octupole band. Surprisingly, no low-lying collective quadrupole excitations could be observed. Complementary information could be obtained in conversion electron measurements in coincidence with isomeric fission, resulting in the first identification of the lowest ß-vibrational K=0⁺ band. For all rotational bands the variation of the moment of inertia with spin could be studied. A predominant population of negative parity states in the second well could be observed, which can be explained by the selective population and depopulation of the second minimum. Complementary transmission resonance measurements have been performed, yielding new information on the fine structure of high-lying (ß-)vibrational multi-phonon states. A new method could be established to determine the excitation energy of the fission isomer ground state from measured level densities.     

Search for octupole deformation in neutron-rich Xe isotopes

A search for octupole deformation in neutron-rich Xe isotopes has been conducted through prompt gammaray spectroscopy of secondary fragments produced in the spontaneous fission of²⁴⁸Cm. The spectrometer consisted of the Eurogam 1 array and a set of 5 LEPS detectors. Level schemes were constructed for Xe isotopes with mass number ranging from 140 to 144 and excited states for^143,144Xe nuclei were observed for the first time. None of the level schemes exhibit an alternating parity quasimolecular band, a feature usually expected in nuclei in which octupole correlation effects are strong enough to produce stable octupole deformation. For several isotopes, structures observed in the level schemes are consistent with an octupole softness of the nuclei.     

Yrast excitations in A = 126–131 Te nuclei from deep inelastic 130Te+64Ni reactions

Thick target γγ coincidence measurements for the system ¹³⁰Te + 275 MeV ⁶⁴Ni have been performed using the GASP Ge detector array at Legnaro. For the isotopic assignments of previously unknown γ-ray cascades, prompt γγ coincidences observed between Te and Ni partner products were of vital importance. The results yield much new information about excited states of moderate spins in A = 126–131 tellurium nuclei, especially about yrast excitations of the little studied odd-A isotopes ¹²⁷Te, ¹²⁹Te, and ¹³¹Te. Level systematics of tellurium nuclei are presented, and both single-particle and collective aspects of the level spectra are discussed.     

Nuclear structure studies at Saha Institute of Nuclear Pysics using gamma detector arrays

In-beam gamma-ray spectroscopy, carried out at the Saha Institute of Nuclear Physics in the recent past, using heavy-ion projectiles from the pelletron accelerator centres in the country and multi-detector arrays have yielded significant data on the structure of a large number of nuclei spanning different mass regions. The experiments included the study of two-fold γγ-coincidence events for establishing decay schemes, directional correlation of oriented nuclei (DCO) for help in spin assignments and Doppler shift attenuation for lifetime information. The studies have led to the observation of rotational sequences of states in nuclei near closed shell in the mass A=110 region, vibrational spectra in nuclei with A ∼ 60, interplay between single-particle and collective modes of excitation in the doubly-odd bromine isotopes, decoupled bands with large quadrupole deformation in ⁷⁷Br, shape transition with rotational frequency within a band in ¹³⁵Pm and octupole collectivity in ¹⁵³Eu. Particle-rotor-model and cranked-shell-model calculations have been carried out to provide an understanding of the underlying nuclear structure.     

M1 resonances in unstable magic nuclei

Within a microscopic approach which takes into account RPA configurations, the single-particle continuum and more complex 1p 1 h?phonon configurations isoscalar and isovector M1 excitations for the unstable nuclei^56,78Ni and^100,132Sn are calculated. For comparison, the experimentally known Ml excitations in⁴⁰Ca and²⁰⁸Pb have also been calculated. In the latter nuclei good agreement in the centroid energy, the total transition strength and the resonance width is obtained. With the same parameters we predict the magnetic excitations for the unstable nuclei. The strength is sufficiently concentrated to be measurable in radioactive beam experiments. New features are found for the very neutron rich nucleus⁷⁸Ni and the neutron deficient nucleus¹⁰⁰Sn.     

Self-consistent theory of finite Fermi systems and Skyrme–Hartree–Fock method

Recent results obtained on the basis of the self-consistent theory of finite Fermi systems by employing the energy density functional proposed by Fayans and his coauthors are surveyed. These results are compared with the predictions of Skyrme–Hartree–Fock theory involving several popular versions of the Skyrme energy density functional. Spherical nuclei are predominantly considered. The charge radii of even and odd nuclei and features of low-lying 2⁺ excitations in semimagic nuclei are discussed briefly. The single-particle energies ofmagic nuclei are examined inmore detail with allowance for corrections to mean-field theory that are induced by particle coupling to low-lying collective surface excitations (phonons). The importance of taking into account, in this problem, nonpole (tadpole) diagrams, which are usually disregarded, is emphasized. The spectroscopic factors of magic and semimagic nuclei are also considered. In this problem, only the surface term stemming from the energy dependence induced in the mass operator by the exchange of surface phonons is usually taken into account. The volume contribution associated with the energy dependence initially present in the mass operator within the self-consistent theory of finite Fermi systems because of the exchange of high-lying particle–hole excitations is also included in the spectroscopic factor. The results of the first studies that employed the Fayans energy density functional for deformed nuclei are also presented.

     

Proton-neutron interactions in nuclei withA∼90

An extension of the cluster-(quadrupole-octupole) phonon model is proposed for nuclei withA～90 to describe simultaneously positive- and negative-parity states, in which quadrupole as well as octupole vibrations of the⁸⁸Sr core are allowed. The cluster states include particle and particle-hole core excitations. The residual interaction is a delta-function force with spin-spin exchange plus a quadrupole-quadrupole force. The model is applied to⁸⁷Sr,⁸⁹Sr,⁸⁸Y, and⁹⁰Y nuclei. For each case, energy levels, spectroscopic factors, and electromagnetic properties are calculated and compared with experiment.     

Description of low-lying vibrationalK π≠0+ states of deformed nuclei in the quasiparticle-phonon nuclear model

The QPNM equations are derived taking account of p-h and p-p interactions. The calculated quadrupole, octupole and hexadecapole vibrational states in¹⁶⁸Er,¹⁷²Yb and¹⁷⁸Hf are found to be in reasonable agreement with experimental data. It is shown that distribution of theEλ strength in some deformed nuclei differs from the standard one. There are cases when for a givenK ^π theEλ strength is concentrated not on the first but on higher-lying states. The assertion made earlier about the absence of collective two-phonon states in deformed nuclei is confirmed.     

Isotopic dependence of the shape of Se nuclei in the collective-model representation

The energy structure of low-lying excited states in the nuclei of even selenium isotopes is considered on the basis of a soft-nucleus model. The nuclei are treated as nonaxial rotors, longitudinal and transverse vibrations of their surface being taken into account in the quadrupole-deformation approximation featuring an admixture of an octupole deformation. The parameters of a phenomenological collective model for the ^{72,74,76,78,80,82}Se nuclei are found both in the case of β vibrations (longitudinal vibrations) and in the presence of additional γ vibrations (transverse vibrations) of the nuclear surface.     

A test of the DWIA at 135 MeV using the 207Pb(p,p′) reaction

Data for the excitation of the strongly collective octupole doublet in ²⁰⁷Pb at E_X = 2.64 MeV is used to test the distorted wave impulse approximation (DWIA) at a proton bombarding energy of 135 MeV. A complex, effective local interaction derived from the nucleon-nucleon phase shifts is used together with the wave functions of Ring and Speth for the low-lying octupole state in ²⁰⁸Pb. The DWIA (including central and spin-orbit terms) is found to be in reasonable agreement with both the magnitude and shape of the observed cross section.     

Differences between dynamical theories of giant resonances

It is the objective of dynamical theories of collective excitations to describe the influence of particle-vibration coupling on the excitation energies of giant resonances. This yields dynamical corrections to the energies calculated in the random-phase approximation (RPA). The existing dynamical theories can be characterized by the effective particle-hole gap which they prescribe for RPA-type calculations of collective excitations. We investigate three dynamical theories in the framework of a schematic model for the nucleon self-energy. In the case of the giant dipole resonance in ²⁰⁸Pb, the microscopic dynamical model prescribes an effective p-h gap which is smaller than the experimental value; in contradistinction, the effective p-h gap is larger than the experimental value in the case of the isoscalar octupole surface vibration. These dynamical corrections are opposite to the corrections predicted by two other models which have been proposed. The origin of these differences is discussed.     

Dipole excitations in 122Te, 126Te and 130Te

Excited states of the nuclei ¹²²Te, ¹²⁶Te and ¹³⁰Te were populated via the (γ, γ') reaction at endpoint energies of the bremsstrahlung between 4.5 and 5.5 MeV. Gamma rays were detected with a EUROBALL-CLUSTER detector and a single detector. In all nuclei several dipole transitions were identified at energies around 3 MeV. The lowest corresponding J = 1 states are interpreted as two-phonon excitations. Quasiparticle-phonon-model calculations predict one 1^? state arising from the coupling of the first quadrupole and the first octupole phonon and one 1⁺ state arising from the coupling of the first and the isovector second quadrupole phonon at about 3 MeV. The calculated transition strengths are compatible with experimental ones.