Influence of an enlargement of the model space on number projected quasiparticle calculations

Results of number projected quasiparticle calculations for Sn isotopes in large and in small model spaces are compared when the force strengths and single-particle energies are determined consistently within each model space. When extending the model space, one observes that the model parameters extracted from the odd nuclei become more satisfactory. For even nuclei the collective states are not lowered in energy although electromagnetic transition rates increase considerably. Spectroscopic factors for one-nucleon transfer reactions change noticeably only for shells close to the Fermi level. Two-nucleon transfer cross-sections are strongly increased for ground state to ground state transitions only. We criticize a usual approximation formula for theL=0 two-nucleon transfer cross-section.     

Influence of an enlargement of the model space on number projected quasiparticle calculations

Results of number projected quasiparticle calculations for Sn isotopes in large and in small model spaces are compared when the force strengths and single-particle energies are determined consistently within each model space. When extending the model space, one observes that the model parameters extracted from the odd nuclei become more satisfactory. For even nuclei the collective states are not lowered in energy although electromagnetic transition rates increase considerably. Spectroscopic factors for one-nucleon transfer reactions change noticeably only for shells close to the Fermi level. Two-nucleon transfer cross-sections are strongly increased for ground state to ground state transitions only. We criticize a usual approximation formula for theL=0 two-nucleon transfer cross-section.     

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.     

Self-consistent calculations within the quasiparticle time blocking approximation with exact account taken of the single-particle continuum

A self-consistent version of the model based on the method of Green’s functions which takes into account conventional phonons of the random phase approximation, complex configurations like 2 quasiparticles?phonon ones, and exact single-particle continuum is used to describe many discrete natural-parity states and giant resonances in the ¹²³Sn and ²⁰⁸Pb nuclei. The quasiparticle-phonon interaction is shown to be important not only for low-lying and high-lying collective states but also for low-lying noncollective states.     

Role of the nuclear surface in a unified description of the damping of single-particle states and giant resonances

The damping widths of single-particle states and of giant resonances are estimated in spherical nuclei, based on the excitation of surface modes.A Skyrme III interaction with an effective mass consistent with that resulting from infinite nuclear matter calculations with “realistic” forces $\text{(m}{}^1\text{/m = 0.76)}$, was utilized. The single-particle basis needed to construct the unperturbed nuclear response function for each multipolarity was obtained, treating this force in the Hartree-Fock approximation. Diagonalizing a schematic interaction in this basis, the surface modes were calculated. They are used to dress the single-particle and single-hole states and to renormalize the vertex interaction, taking into account the proper energy dependence of the couplings.The essential new feature of the present calculation as compared to the calculations reported in ref.¹) is that the energy dependence of the real and imaginary part of the self-energy is taken into account. This is done utilizing a strength function model.About 70 % of the damping widths arise from the coupling to specific intermediate states containing one low-lying collective surface vibration. The rest, from the coupling to many nonspecific states.Qualitative agreement is found with the experimental data for spherical nuclei throughout the mass table for both the single-particle states and the giant resonances. The model seems however to predict widths which are smaller than those experimentally observed.     

Effect of nuclear-reaction mechanisms on the population of excited nuclear states and isomeric ratios

Experimental data on the cross sections for channels of fusion and transfer reactions induced by beams of radioactive halo nuclei and clustered and stable loosely bound nuclei were analyzed, and the results of this analysis were summarized. The interplay of the excitation of single-particle states in reaction-product nuclei and direct reaction channels was established for transfer reactions. Respective experiments were performed in stable (⁶Li) and radioactive (⁶Не) beams of the DRIBs accelerator complex at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, and in deuteron and ³Не beams of the U-120M cyclotron at the Nuclear Physics Institute, Academy Sciences of Czech Republic (?e? and Prague, Czech Republic). Data on subbarrier and near-barrier fusion reactions involving clustered and loosely bound light nuclei (⁶Li and ³He) can be described quite reliably within simple evaporation models with allowance for different reaction Q-values and couple channels. In reactions involving halo nuclei, their structure manifests itself most strongly in the region of energies below the Coulomb barrier. Neutron transfer occurs with a high probability in the interactions of all loosely bound nuclei with light and heavy stable nuclei at positive Q-values. The cross sections for such reactions and the respective isomeric ratios differ drastically for nucleon stripping and nucleon pickup mechanisms. This is due to the difference in the population probabilities for excited single-particle states.     

On pionic degrees of freedom in atomic nuclei

The possibility of explicit pionic degrees of freedom in atomic nuclei and their association with pionic reactions involving fragment emission is discussed. Although no present direct evidence for such degrees of freedom is available they could be searched for in doorway states — other than the anticipated N¹ doorway — in the excitation function in the pion-induced partial reaction cross sections. Such a search is underway. A framework is discussed in terms of which such new pion doorways might be described.     

Collective and single-particle states at high excitation energy

Damping of high-lying single-particle states was investigated by the study of decay by proton emission from high-lying states in ⁹¹Nb, populated by the ⁹⁰Zr(α, t) reaction at E_α=180 MeV. In addition to decay to the ground state of ⁹⁰Zr, semi-direct decay was observed to the low-lying (2⁺/5^? and 3^?) phonon states, confirming the conclusion from other experiments that phonon states play an important role in the damping process of the single-particle states. Furthermore, the population and decay of isobaric analogue states of ⁹¹Zr, which are located at an excitation energy of about 10–12 MeV in ⁹¹Nb, has been studied in the same reaction.     

Effect of the Structure of Light Loosely Bound Nuclei on the Mechanisms of Nuclear Reactions

The results of experiments devoted to studying fusion and transfer reactions in beams of loosely bound (³He) and cluster (⁶Li, ⁷Li) nuclei, as well as nuclei that have a halo structure (⁶He and ⁸He), with nuclei of light and heavy elements are generalized. Special features in the behavior of cross sections for the formation of evaporation residues and transfer-reaction products at energies near the barrier are revealed. The behavior of cross sections for nucleon- and cluster-transfer reactions leads to different populations of single-particle and collective states in target-like nuclei. The effect of various channels of nuclear reactions involving light nuclei on the population of the ^195mHg and ^197mHg(13/2⁺), ^198mTl and ^196mTl(7⁺), and ^196mAu and ^198mAu(12⁻) pairs of isomeric states is considered. The values of the isomeric ratios (σ_m/σ_g) for reaction products originating from fusion reactions followed by particle evaporation and from nucleon-and cluster-transfer reactions are explained.

     

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.     

Investigation of the neutron shell structure of the even-even isotopes <Superscript>40–56</Superscript>Ca within the dispersive optical model

Within the method of matching experimental data obtained in the neutron-stripping and neutron-pickup reactions on ^{40,42,44,46,48}Ca isotopes, the single-particle energies and probabilities that neutron states are filled are obtained for the even-even calcium isotopes. These data are analyzed within the dispersive optical model, and good agreement between the calculated and experimental values of the energies of states is obtained. The dispersive optical potential is extrapolated to the region of the unstable ^50,52,54,56Ca nuclei. The calculated single-particle energies of bound states in these isotopes are compared with the results of the calculations within the multiparticle shell model, the latter predicting a new magic number N = 34 for Z = 20 nuclei.     

The FBCS model and the inverse gap equations applied to the tin isotopes

The FBCS model for odd nuclei and the inverse gap equations are applied to a whole sequence of tin isotopes,viz.^111–125Sn. From spectroscopic data on the odd isotopes, the single-particle energies and interaction strengths are obtained. With these parameters the lowest states of the even isotopes are calculated by a number-projected two-quasiparticle diagonalization and by the usual BCS one. This is done with two Gaussian interactions and the SDI. In the case of the Gaussian forces the experimental energies are well reproduced by the number-projected treatment. Effective charges for Eλ transitions, which are required to reproduce the experimental transition rates, are rather constant for the whole series of isotopes, in case of the number-projected treatment. In addition a number of spectroscopic factors for one-nucleon transfer reactions are calculated and good agreement with experiments is observed.     

Shell-model description of the noncompound component of nucleon-induced reactions on light and medium-mass nuclei at incident-nucleon energies of up to 12 MeV

The coupled-channel method as implemented within the intermediate-coupling scheme of the shell model is used to describe the noncompound component of nucleon-nucleus reactions. The proposed model is aimed at taking into account the effect of collective doorway states (giant resonances) on the properties of nucleon-induced reactions on light and medium-mass nuclei at incident-nucleon energies of up to 12 MeV.     

Investigation of special features of the neutron and proton shell structure of the isotopes 90,92,94,96Zr

The neutron and proton single-particle energies and the occupation probabilities for the valence states of the even-even isotopes ^90,92,94,96Zr are determined by matching data on nucleon-stripping and nucleon-pickup reactions on the same nucleus. The data obtained in this way suggest the magicity of the number N = 56 for Z = 40. The single-particle energies of all bound neutron and proton states in the ^90,92,94,96Zr nuclei are described within the experimental errors on the basis of the dispersive optical model.     

核子与核力决定的核形状(英文)

讨论了最近提出的作为量子多体系统重要潜在机制之一的量子自组织,原子核无疑是最好的实例。由于原子核内核子的单粒子和集体运动共存,它们的相互制约决定了核结构。集体模式因其驱动力,如使椭球形变的四极力及其阻力达到平衡形成,而单粒子能量就是产生阻力的一种根源。当存在较大单粒子能隙时,相关的集体运动更易受到阻碍。因此,一般认为,单粒子运动和集体运动是相互对抗的"天敌"。然而,由于核力的多样和复杂性,单极相互作用使单粒子能量改变也能减小其对集体运动的阻碍而加强集体模式,该现象将通过Zr同位素实例加以说明。这就导致了量子自组织的产生:单粒子能量由两种量子液体（质子和中子）和控制阻力的单极相互作用自组织。于是,不同于朗道费米液体理论的结论,原子核不一定像填装了自由核子的刚性瓶。Ⅱ型壳演化即是包含跨准幻壳能隙激发的直观实例。在重核中,量子自组织因其轨道和核子数更多而更为重要。We discuss the quantum self-organization introduced recently as one of the major underlying mechanisms of the quantum many-body systems. Atomic nuclei are actually a good example, because two types of the motion of nucleons, single-particle states and collective modes, interplay in determining their structure. The collective mode appears as a consequence of the balance between the effect of the mode-driving force (e.g., quadrupole force for the ellipsoidal deformation) and the resistance power against it. The single-particle energies are one of the sources to bring about such resistance power:a coherent collective motion is more hindered by larger spacings between relevant single particle states. Thus, the single-particle state and the collective mode are "enemies" against each other in the usual understanding. However, the nuclear forces are rich and complicated enough so as to enhance relevant collective mode by reducing the resistance power by changing single-particle energies for each eigenstate through monopole interactions. This will be demonstrated with the concrete example taken from Zr isotopes. In this way, the quantum self-organization occurs:single-particle energies can be self-organized by (i) two quantum liquids, e.g., protons and neutrons, (ii) monopole interaction (to control resistance). Thus, atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naïve Fermi liquid picture a la Landau. Type Ⅱ shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger.     

States of intermediate charge symmetry as low-lying, 0 collective excitations of medium weight nuclei

A method for calculating the states of the charge-independent pairing hamiltonian that have intermediate charge symmetry is presented. The states are shown to be collective 0⁺ excitations with energies that fall well within the gap in the single-particle spectrum.     

Shell model calculations of two to four identical-“particle” systems near 208Pb

The structure of the nuclei ^204–206Pb, ^210–212Pb, ²¹⁰Po, ²¹¹At, and ²¹²Rn is studied in terms of conventional nuclear shell models. An inert ²⁰⁸Pb core is assumed, and active particles (holes) are distuibuted in the low-lying single-particle (hole) orbits. Experimental single-particle energies are used for the one-body part of the effective residual interaction. Realistic interaction matrix elements developed for this mass region by Kuo and Herling are used for the matrix elements of the two-body part of the residual interactions. As much as possible, other effective one-body operators for electromagnetic observables are derived from experimental data on the single-particle (hole) nuclei ²⁰⁷Pb, ²⁰⁹Pb, and ²⁰⁹Bi. Observables treated are ground state binding energies, excitation energies, strengths for one- and two-particle transfers, and E2 and M1 observables. Generally, excellent agreement is found. The configuration mixing calculations do not remove anomalies in the magnetic moments of excited states in ²⁰⁶Pb and ²¹²Rn. Many states in these nuclei are predicted by the models which have not been observed as yet. It is found that a truncation scheme for doubly even nuclei treated here in which only seniority-0 and seniority-2 states are allowed is potentially very useful.     

Nuclear structure at finite temperature: A review

Information on nuclear structure at finite temperature is obtained from the physics of the level density, of the rotational damping, and of the giant dipole resonance thermally excited on a compound nucleus at very large excitation energy (and angular momentum). The current understanding in terms of mean-field theories and beyond is reviewed. The coupling to doorway states and the coupling to many-particle-many-hole states in the random-matrix-theory limit are discussed. Emph asis will be on the close relation between the single-particle damping and the damping of collective vibrations. The coherence between the particle and the hole strongly suppresses the vibrational damping, in particular, the temperature dependence.     

Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

A method is presented to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei. In such nuclei, always there is a collective low-lying 2⁺ phonon, and a strong mixture of single-particle and particle–phonon states often occurs. As in magic nuclei the so-called g _L ² approximation, where g _L is the vertex of the L-phonon creation, can be used for finding the PC correction δΣ^PC(ε) to the initial mass operator Σ₀. In addition to the usual pole diagram, the phonon “tadpole” diagram is also taken into account. In semi-magic nuclei, the perturbation theory in δΣ^PC(ε) with respect to Σ₀ is often invalid for finding the PC-corrected single-particle energies. Instead, the Dyson equation with the mass operator Σ(ε) = Σ₀ + δΣ^PC(ε) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.     

Oblique-basis shell-model calculations

A one-dimensional harmonic oscillator in a box is used to introduce the oblique-basis concept. The method is extended to the nuclear shell model by combining traditional spherical shell model states, which yield a diagonal representation of the usual single-particle interaction, with SU(3) shell model collective configurations that track deformation. An application to ²⁴Mg, using the realistic two-body interaction of Wildenthal, is used to explore the validity of this mixed-mode shell-model scheme. The theory is also applied to lower pf-shell nuclei, ^44–48Ti and ⁴⁸Cr, using the Kuo-Brown-3 interaction. These nuclei show strong SU(3) symmetry breaking due mainly to the single-particle spin-orbit splitting. Nevertheless, the results also show that yrast band B(E2) values are insensitive to fragmentation of SU(3) symmetry. Specifically, the quadrupole collectivity as measured by B(E2) strengths remains high even though the SU(3) symmetry is rather badly broken. The results suggest that an oblique-basis mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics.