Formation of nuclear molecules in cluster radioactivity on interpretation of the cluster radioactivity mechanism

The basis for cluster radioactivity is the property of nuclei of light isotopes of elements heavier than lead to spontaneously form clusters—nuclei of light elements—from valence nucleons, which gives rise to asymmetric nuclear molecules. The cluster formation proceeds through successive excitation-free transfer of valence nucleons to the α particle and to subsequent light nuclei. Nuclear molecule formation is accompanied by a considerable amount of released energy, which allows quantum-mechanical penetration of the cluster through the exit Coulomb barrier.     

Eine qualitative Diskussion der kollektiven potentiellen Energie im Quasispinmodell

The collective potential-energy-surface is calculated for a simple nuclear model consisting of a closed core and onej-shell. This shell can be filled up by one sort of nucleons (protons or neutrons). The residual force acting between nucleons consists of a pairing- and a quadrupol-force. In the quasi-spin-formalism, proposed by A. K.Kerman, the parameters of the collective potential energy are calculated and the collective features of even-even nuclei were discussed qualitatively.     

A STUDY OF THE NUCLEAR POTENTIAL BETWEEN TWO NUCLEI

According to the physical picture of dinucleus molecule and considering the particle-hole interaction between two nuclei, the exchange of valence nucleons and nuclear potential between two nuclei were studied.     

THE PHASE TRANSITION FROM THE "ROTATION" TO VIBRATION SPECTRA IN THE LIPKIN SU(2) MODEL

The collective monopole excitation spectra of the Lipkin SU(2) model aresolveaexactly in the truncated monopole phonon representation and also approximately in the continuous variable representation. The transition from the "rotation" to vibration spectra for lowly-lying exclted states with the increase of the particle number in the upper level and the disappearance of the monopole "deformation" with the increase of the excitation energy are exhibited. The origin of these phase transitions is explained and the shape transition of real nuclei with the number of valence nucleons i s briefly discussed.     

Understanding Quantum Phase Transitions,edited by Lincoln Carr

The concept of the superdeformed shape is first introduced classically as the most stable configuration of a rapidly rotating deformable body and is then applied to nuclei. The shape of nuclei are determined by a competition between the collective energy of the core, to which classical considerations apply quite well, and the quantal energies of the valence nucleons, which may be evaluated by the Nilsson model. The result of this competition is that slowly rotating nuclei can be either oblate or prolate but rapidly rotating nuclei can have a superdeformed prolate shape, with a 2:1 ratio of axes particularly favoured.

The evidence for superdeformation in nuclei is described under four headings. Firstly, some light nuclei are superdeformed in their ground state or in an excited state. Secondly, some nuclei pass through a well defined superdeformed shape on the way to fission. Thirdly, studies of the excitation functions of elastic and inelastic scattering of identical heavy ions provide evidence of a nuclear molecule in a superdeformed shape. Finally, recent analyses of gamma rays from nuclei formed in a very high spin state by a heavy ion collision provide conclusive evidence for superdeformation.     

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.     

Shell Effect of Superheavy Nuclei in Self-consistent Mean-Field Models

We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoreticalresults are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached.Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupysignificantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of vaJence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ,ω and ρ mesons because there is no parityviolating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.     

Shortening of the nucleon''s mean free path in heavy ion collisions

The mean free path of nucleons in heavy ion collisions is most essential for the development of nuclear collective phenomena. We discuss the effect of the nucleon Fermi motion in nuclei for shortening the mean free path. This Fermi motion together with the prior Pauli effect makes nuclei nontransparent for heavy ions in the medium energy domain.     

Three-body forces in sd-shell nuclei

The influence of three-body forces on the excitation spectra of nuclei with 3 valence nucleons in the sd-shell is investigated. Three-body forces are considered, which arise from an intermediate excitation of the interacting nucleons to the Δ(3, 3) resonance. Besides these real three-nucleon forces, effective three-body interactions are taken into account which are due to the restriction of the nuclear structure calculation to sd-shell configurations. Significant cancellations are observed between the different contributions to the effective three-nucleon force. The resulting three-body matrix elements yield only a small influence on the spectrum of the A = 19 systems. The typical size of the matrix elements, however, is large enough to expect a serious influence on the results of shell-model calculations with more than three valence nucleons.     

Search for supersymmetry in light nuclei

The supersymmetry assumption based on a system of valence interacting bosons and odd nucleons has been checked in the second half of the nuclear sd-shell. The dynamical supersymmetric hamiltonian restricted to the linear combination of chosen second-order Casimir invariants has been applied to energy levels of several nuclei organized in supermultiplets. The supersymmetry predictions for nine nuclei are in accord, to a good approximation, with experimental energy levels up to 4–7 MeV.     

Pairing in exotic and in stable nuclei

The exchange of low-lying collective vibrations between pairs of nucleons moving in time reversal states close to the Fermi energy provides a conspicuous contribution to the nuclear pairing interaction, which accounts for 30-50% of the pairing gap in the case of nuclei along the stability valley, and to essentially all of the pairing correlations of the most loosely bound nucleons in the case of halo nuclei.Received: 30 October 2002, Published online: 23 March 2004PACS: 21.30.Fe Forces in hadronic systems and effective interactions - 21.60.Jz Hartree-Fock and random-phase approximations     

Radiative strength functions for nuclei in which the number of protons is close to the magic number of Z=28

The distribution of the radiative strength in nuclei where the number of nucleons of one type is nearly magic (Z=28±1) and where there are a few valence nucleons of the other type is investigated. It is shown that the statistical approach that is based on Fermi liquid theory and which takes into account temperature and the shell structure of nuclei leads to good agreement with experimental data on radiative strength functions below the neutron binding energy in such nuclei. Only for the ⁵⁹Co and ⁶⁵Cu nuclei, which have the largest number of valence neutrons among the cobalt and copper isotopes being investigated, is the energy dependence of the radiative strength compatible with a Lorentz distribution as well.     

Inclusive (γ, N), (γ, NN) and (γ, Nπ) reactions in nuclei at intermediate energies

Differential cross sections of nucleons excited in photonuclear reactions in medium and heavy nuclei are studied by considering all relevant reaction mechanisms leading to the excitation of protons or neutrons. We take advantage of previous microscopic studies for the absorption and scattering of photons and photoproduced pions, and implement a simulation code in order to take into account the propagation of the nucleons as well as their collisions with other nucleons in the nuclear medium, which generate secondary excited nucleons. Comparison with experimental data is done. Cross sections for nucleon emission in coincidence with one pion are also calculated, and some coincidence observables are discussed.     

A Note on the Pair Excitation Across Major Shell in Deformed Nuclei

Valence nucleons usually play a dominant role in low energy nuclear spectra. The original version of the Interacting Boson Model[1](IBM) with the assumption that all degrees of freedom arise from the valence shell reproduces well large amount of experimental data. However this assumption does not work well in some cases, for instance, in the even isotopes of Sn, Cd, and Hg, Pb rather well developed intruder bands121 lie outside the IBA model space. K. Heyde et al. attributed these low lying intruder states to the pair excitation (PE) across major shell131. In the well deformed nuclei one can hardly think of the closed shell core as being spherical and inert. The rapid change of Nilsson levels with deformation seems to indicate that there should be excitations of nucleons across major shells in the well deformed nuclei.     

Microscopic calculation of the restoring force for scissor isovector vibrations

The restoring force for scissor isovector vibrations is calculated microscopically with the wave functions of an axially symmetric Woods-Saxon potential from a density-dependent symmetry energy. The experimental energies of the low-lying magnetic dipole states in rare-earth nuclei are well reproduced. It is found that only outer particles, which contribute to the nuclear moment of inertia, take part in this collective vibration. They are about half of the total number of nucleons.     

Odd-odd nuclei as the core-particle-hole systems and chirality

Odd-odd nuclei treated as core-particle-hole systems with various collective cores and various particle-hole configurations are investigated within the Core-Particle-Hole Coupling (CPHC) model. A new symmetry, called the S-symmetry, is identified as a combination of the α-parity of the collective core and the proton-neutron symmetry of the valence proton and neutron in particle-hole configurations involving single-particle states with the same quantum numbers. It is found that the S-symmetric odd-odd nuclei show signatures which are usually considered as fingerprints of nuclear chirality, namely doublet band structure with a particular pattern of electromagnetic transitions. Reported results imply that the rigid rotor with a symmetric valence proton-neutron configuration is only a special case of the system with the novel S-symmetry. Therefore, it is an open question whether the chiral fingerprints discussed so far identify uniquely the orthogonal coupling of angular momentum in the intrinsic system.     

Why are Most Nuclei Prolate?

After seperating collective and single particle coordinates the Schrödinger equation of a system of A nucleons has a form related to the conventional unified model, but in contrast to that there are no redundant variables. Working with the transformed Schrödinger equation, using the strong coupling approximation and requiring constant nuclear volume one finds that two thirds of the nuclei should be prolate and that their largest deformations should be about 1.5 times larger than those for oblate nuclei.     

Theory of doorway states for one-nucleon transfer reactions: Model-independent study of nuclear correlation effects

Nuclear correlation effects owing to which nuclear wave functions are different from Slater determinants are studied within the theory developed in our previous study. The calculated numbers of nucleons off the nuclear Fermi surface are in reasonable agreement with the finding from the high-momentum components of the momentum distributions of nucleons in nuclei. Problems concerning the nuclear binding energy are also discussed.     

Transition fission states for heated nuclei

Induced fission reactions of fissioning compound nuclei that result from the capture of various incident particles (nucleons, γ rays, multiply charged ions) by target nuclei are investigated using the generalized nucleus model and the Wigner random matrix method. The effect produced on the fission widths of the compound nucleus by the competition between the excitation energies of its collective vibrational degrees of freedom that lead to its scission into fission fragments and its rotational and multi-quasiparticle states is analyzed. Bohr’s concept of transition fission states developed for near-barrier nuclear fission is generalized to the induced fission of nuclei with the excitation energies noticeably higher than the fission barriers. The temperature of the fissioning nucleus in the vicinity of the point of its scission into fission fragments is estimated.     

Spin-dependent potentials in the linearized collective Schrödinger equation for nuclear quadrupole vibrations

The linearized collective Schrödinger equation for nuclear quadrupole surface vibrations incorporates a new spin degree of freedom with a spin value of 3/2. We use this equation to describe the low energy spectrum of certain even-odd Ir nuclei which have a spin 3/2 in their ground state. For that purpose we explicitly introduce collective spin-dependent potentials which simulate the interaction of the valence nucleon with the core. The linearized Schrödinger equation is transformed into an effective Schrödinger equation with collective spin-dependent potentials. Already collective spin-orbit couplings of SO(3) and SO(5) type are sufficient to reproduce the lowest excited states of even-odd Ir nuclei.