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.     

Nuclear moments: An effective probe of nuclear stucture

Magnetic dipole and electric quadrupole moments are discussed in nuclei near doubly-closed shell nuclei (the T1 nuclei) and in nuclei along series of single-closed shell nuclei (plus of minus a few nucleons) (the In odd-mass and odd-odd nuclei). We discuss the “additivity” rules for nuclear moments. We also address the EO moment: the liquid drop model and the shell-model are discussed and compared to measurements of nuclear radii in the Ca, Sn and Pb region. In the latter region, the importance of intruder states across the Z=82 proton closed shell is emphasized.     

Coexisting structures in 115Sn and 116Sn

Excited states up to I ≈ 20 in ¹¹⁵Sn and ¹¹⁶Sn, populated via the (¹⁸O, αxn) reactions, have been studied using the DORIS Ge detector array in conjunction with charged particle detectors. In both nuclei, spherical as well as regular, deformed level structures were found. The spherical states are interpreted to arise from pure neutron configurations, while the deformed, intruder bands obviously involve proton 2p-2h excitations across the Z = 50 shell gap.     

Solar physics

Our current ideas about nuclear structure are reviewed with particular reference to recent developments. Exotic nuclei far from the valley of stability are now being studied, as well as high-spin states of deformed nuclei. The limitations of the shell model are reviewed, with the effects due to short-range correlations between nucleons given special attention. Nucleons in the nucleus tend to group themselves into clusters, and this too affects nuclear structure.     

Microscopic calculations for upper-fp,g<Subscript>9/2</Subscript> shell nuclei: Ge &; Se

Shell-model calculations for isotopes of Ge and Se are reported where valence nucleons beyond the N = 28 = Z core occupy levels of the normal parity upper-fp shell (f_5/2,p_3/2,p_1/2) and the unique parity g_9/2 intruder configuration. Results are given for realistic interactions of the Kuo-Brown-3 type with various model space truncations that key in on the number of nucleon pairs allowed to occupy the intruder level. Electromagnetic (E2 & M1) rates as well as decay probabilities are calculated, some of which are key in determining the structure of “waiting point” nuclei that regulate certain nucleo-astrosynthesis processes. The role of the intruder level, which is treated on an equal footing with the normal parity levels, is shown to be important for reproducing structural details. The levels of the upper-fp shell are handled within the framework of a normal ls-coupled basis as well as its pseudo-SU(3) counterpart, and respectively, the g_9/2 as a single level and as a member for the complete gds shell. The second of these two approaches, namely, the SU(3) picture, allows one to better probe the effect of deformation.     

Particle-Number Conserving Analysis for High K Multi-Quasiparticle Bands in Odd-A Deformed Nuclei 173,175Hf

Using the Particle-number Conserving (PNC) method for treating the cranked shell model, the high K multi-quasiparticle bands in odd-A deformed nuclei ^173,175Hf are analyzed, including the variation with rotational frequency of the moment of inertia, angular momentum alignment and occupation probability of each cranked Nilsson orbital. No free parameters are involved in the PNC calculation and the experimental results are reproduced well. The microscopic mechanism of the difference between the multi-quasiparticle high K bands and the yrast bands in neighboring even-even nuclei is investigated, where the blocking effects of high j intruder orbitals near the Fermi surface play a crucial role.     

稀土变形奇A核173,175Hf的多准粒子高K转动带的粒子数守恒分析

用处理推转壳模型的粒子数守恒方法分析了稀土奇A变形核^173,175Hf的3准粒子和5准粒子高K转动带,包括转动惯量、顺排角动量,以及推转Nilsson能级上的粒子填布几率随转动角频率的变化.计算中无自由参数.实验观测结果在计算中得到较好地重现.分析了多准粒子带与相邻偶偶核基态带的转动惯量变化规律不同的微观机制.在这里Fermi面邻近高j闯入态的堵塞效应起了举足轻重的作用.     

Microscopic Mechanism of Large Fluctuation in Odd-Even Differences in Moments of Inertia for Actinide Nuclei

The experimental large fluctuation in odd-even differences in moments of inertia of deformed actinide nuclei is investigated using the particle-number conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. PNC calculations show that the large odd-even difference in moments of inertia mainly comes from the interference contributions j(μν) from particles in high j intruder orbitals μ and ν quite near the Fermi surface, which have no counterpart in the BCS formalism. The effective monopole and quadrupole pairing interaction strengths are determined to fit the experimental odd-even differences in binding energies and bandhead moments of inertia. The experimental results for the variation of moments of inertia with rotational frequency ω are reproduced well by the PNC calculation. The nearly identical experimental moments of inertia between ²³⁶U(gsb) and ²³⁸U(gsb) at low frequencies ħω≤0.20 MeV are also reproduced quite well.     

Nuclear vibrations and rotations of like nucleons in the same shell in even-even nuclei

The vibrational and rotational motions in even nuclei are considered. A microscopic study of these motions leads to a relation between the vibrational motion in spherical nuclei and the rotational motion in deformed nuclei. Nuclei with like nucleons in the same shell are considered. The quadrupole two-body interactions are used in the large singlej-shell of even nuclei. The energies and transition operators of nuclei in the nuclear rotational region are calculated using this microscopic method. Quadrupole moments are also calculated. These calculations are compared with the rotational model of the aligned coupling scheme. The present calculations are in good agreement with previous calculations.     

A PSDPF interaction to describe the 1 ?ω intruder states in sd shell nuclei

In the level schemes of sd shell nuclei, there is generally at relatively low excitation energies, coexistence of normal 0 ?ω positive parity states and of intruder 1 ?ω negative parity states. The aim of the present work is to describe these intruder states in the full p-sd-pf model space with a ⁴He core allowing one nucleon jump between the major shells. To construct our PSDPF interaction, we first modified the p-sd and sd-pf cross-monopole terms and then applied a fitting procedure to adjust all PSDPF parameters by comparing an extended set of experimental and calculated excitation energies. Results obtained with the new interaction have been finally compared with experimental data for nuclei throughout the sd shell.     

A shell-model description of 0+ intruder states in even-even nuclei

Starting from the nuclear shell structure in medium-heavy and heavy nuclei, the excitation energy for low-lying 0⁺ intruder states is studied. Taking as a simplified model two particle-two hole (2p-2h) excitations across closed shells, the effects of the pairing and the proton-neutron (monopole and quadrupole component) residual interaction on the unperturbed energies are calculated. Application to major closed-shell (fZ = 50, Z = 82) and to subshell (Z = 40, Z = 64) regions is performed. We especially concentrate on 0⁺ intruder states in the even-even Pb nuclei.     

Density-dependent Brueckner-Hartree-Fock approach in deformed nuclei

Recently a method has been developed which includes into the Brueckner-Hartree-Fock (BHF) approach in a finite nucleus those terms which produce the density dependence of the effective interaction between nucleons. This method is extended to the deformed open shell nuclei ¹²C and ²⁰Ne. The results indicate that it is possible to describe these nuclei starting from a bare realistic nucleon-nucleon interaction (Reid soft-core potential). Binding energies, quadrupole moments, root mean square radii are improved compared to the usual BHF approach with the same force or the HF approach with a phenomenological effective force.     

哪些核适合被液滴模型描述:基于不确定度分解方法的统计研究（英文）

一个模型适合描述哪些物理量? 这个问题可以通过模型的物理来源来回答。比如,液滴模型适合描述重核和远离满壳核。这是因为液滴近似更适用于核子数多的核以及液滴模型不包含壳效应。这样的回答是定性的并需要清楚模型的物理来源。是否可能仅通过模型的数学形式和实验数据就能给出半定量的解答? 利用最近提出的不确定度分解方法尝试对液滴模型适合描述哪些核这一问题进行半定量的回答。并且不需已知液滴模型的物理来源,仅需其数学形式以及实验数据。通过不确定度分解方法,液滴模型与实验数据间的残差可以分解为系统不确定度和统计不确定度。两者分别代表了模型的缺陷和模型不精确的参数带来的不确定度。基于这一分解,核素图上的原子核可以按其对应的残差被半定量地划分为系统不确定度主导、统计不确定度主导、以及中间区域。液滴模型适合描述的核就是统计不确定度主导残差的核而不是像通常认为的是残差最小的核。从核素图上看,统计不确定度主导残差的核正是重核以及远离满壳核,与液滴模型物理来源一致,但得到这一结果的过程是半定量的且仅需液滴模型的数学形式以及实验数据。如果对由统计不确定度主导残差的核重新拟合液滴模型的参数,模型可以很好地描述这些核（标准差小于0.7 MeV）。Which data are well described by a theoretical model? Such questions can be answered through the physical origin of the model. For example, the liquid drop model (LDM) well describes the heavy and far from shell nuclei. Because the liquid-drop assumption is more suitable for nuclei with more nucleons and LDM does not include the shell effect. Such answer is qualitative and needs a clear view on the physical origin of the model. Is it possible to give an semi-quantitatively answer only from the mathematical form of the model and the observed data. In the present work, the recently suggested uncertainty decomposition method (UDM) is used to answer which nuclei are well described by LDM. The residues between LDM and the observed data can be decomposed through UDM to systematic and statistical uncertainties, which represent the uncertainty of the deficiency of the model and the indeterminate parameters, respectively. Based on UDM, the chart of nuclides are semi-quantitatively divided into three parts, areas dominated by the systematic and statistical uncertainties, and the cross area. Contrary to the common sense, the well described nuclei by LDM are not the nuclei with small residues, but actually the nuclei of which the residues are dominated by the statistical uncertainty. These nuclei are indeed the heavy and far from shell nuclei, which agrees with the physical consideration of LDM. But only the mathematical form of the model and the experimental data are needed during the use of UDM. The nuclides dominated by the statistical uncertainty can be well described by LDM (standard deviation less than 0.7 MeV) with parameters fitting to these nuclei.     

Isomorphic shell model for closed-shell nuclei

The classical part of the isomorphic model for closed-shell nuclei is presented based on two physical assumptions, namely (a) the nucleons of a closed shell nucleus, considered at their most probable positions, are in an instantaneous dynamic equilibrium on spherical shells, and (b) the dimensions of the shells are determined by their close packing given that a neutron and a proton are represented by hard spheres of definite sizes. The first assumption leads to the instantaneous angular structure, and the second to the instantaneous radial structure of closed-shell nuclei. Applications of the model coming from this classical part alone and presented here are structural justification of all magic numbers, neutron (proton) and charge rms radii, nuclear densities of closed-shell nuclei, and Coulomb, kinetic, and binding energies. All the predictions are in good agreement with experimental data. A characteristic novelty of the isomphic model is that assumption (a) is related to the independent particle model, and assumption (b) to the liquid-drop model. The isomorphic model may provide a link between these two basic nuclear physics models since it incorporates features of both.     

Electric monopole transitions from low energy excitations in nuclei

Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ϱ²(E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also pay attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between ϱ²(E0) and isotopic shifts.     

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.     

Measurement of the spin and magnetic moment of 31Mg: evidence for a strongly deformed intruder ground state

Unambiguous values of the spin and magnetic moment of 31Mg are obtained by combining the results of a hyperfine-structure measurement and a beta-NMR measurement, both performed with an optically polarized ion beam. With a measured nuclear g factor and spin I=1/2, the magnetic moment mu(31Mg)=-0.88355(15)mu(N) is deduced. A revised level scheme of 31Mg (Z=12, N=19) with ground state spin/parity I(pi)=1/2(+) is presented, revealing the coexistence of 1p-1h and 2p-2h intruder states below 500 keV. Advanced shell-model calculations and the Nilsson model suggest that the I(pi)=1/2(+) ground state is a strongly prolate deformed intruder state. This result plays a key role for the understanding of nuclear structure changes due to the disappearance of the N=20 shell gap in neutron-rich nuclei.     

Particle-Number Conserving Calculation for Low-Lying Excited High-K Multi-Quasiparticle Bands in 172,174Hf

Using the particle-number conserving method for treating the cranked shell model,the microscopic mechanism of the variation of the kinematic moments of inertia with rotational frequency ω for the rare-earth deformed nuclei ^172,174Hf is investigated. The observed J⁽¹⁾ and angular momentum alignment are reproduced satisfactorily in the PNC calculation,in which no free parameters are involved. The PNC analysis shows that the difference between the variations of J⁽¹⁾ with ω for the high K multi-quasiparticle bands and for ground state band is mainly due to the Pauli blocking effect of high j intruder orbitals near the Fermi surface.     

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.     

Single Particle Schr dinger Fluid and Moments of Inertia of Deformed Nuclei

We have applied the theory of the single-particle Schrodinger fluid to the nuclear collective motion of axially deformed nuclei. A counter example of an arbitrary number of independent nucleons in the anisotropic harmonic oscillator potential at the equilibrium deformation has been also given. Moreover, the ground states of the doubly even nuclei in the s-d shell ²⁰Ne,²⁴Mg,²⁸Si,³²S and ³⁶Ar are constructed by filling the single particle states corresponding to the possible values of the number of quanta of excitations n_x,n_y, and n_z. Accordingly, the cranking-model, the rigid-body model and the equilibrium-model moments of inertia of these nuclei are calculated as functions of the oscillator parameters ω_x,ω_yand ω_z which are given in terms of the non deformed value ω00 , depending on the mass number A, the number of neutrons N, the number of protons Z, and the deformation parameter β. The calculated values of the cranking-model moments of inertia of these nuclei are in good agreement with the corresponding experimental values and show that the considered axially deformed nuclei may have oblate as well as prolate shapes and that the nucleus ²⁴Mg is the only one which is highly deformed. The rigid body model and the equilibrium model moments of inertia of the two nuclei ²⁰Ne and ²⁴Mg are also in good agreement with the corresponding experimental values.