奇质量核的超越平均场玻色子费米子模型描述(英文)

对近年发展起来的一个基于核密度泛函理论和粒子核心耦合方案来计算中重质量奇A核谱性质的理论方法进行了评述。该方法首先在平均场层面通过选择合适的能量密度泛函和对力结构来自洽求解偶偶核心的势能曲面、球单粒子能级和奇粒子占有率,进一步将得到的结果作为微观输入来建立相互作用玻色子费米子模型哈密顿量,其中三个与粒子核心耦合强度相关的参数需要通过拟合一些特定奇质量核低激发谱数据来最终确定。通过对轴形变奇质量Eu同位素的低激发能谱和电磁跃迁几率的系统研究来说明该模型方法的有效性。另外,还讨论了该方法在描述轴形变奇质量核形状相变以及描述丰中子奇质量Ba同位素中八极关联方面的应用。A recently developed method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is reviewed, that is based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the eveneven core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained by a self-consistent mean-field calculation with the choice of the energy density functional and pairing properties. These quantities are then used as a microscopic input to build the interacting bosonfermion Hamiltonian. Only three strength parameters for the particle-core coupling are specifically adjusted to selected data for the low-lying states of a particular odd-mass nucleus. The method is illustrated in a systematic study of low-energy excitation spectra and electromagnetic transition rates of axially-deformed odd-mass Eu isotopes. Recent applications of the method, to the calculations of the signatures of shapes phase transitions in axially-deformed odd-mass nuclei, octupole correlations in neutron-rich odd-mass Ba isotopes, are discussed.     

Description of the New Nuclide 259Db and Its α-Decay Chain in Relativistic Mean Field Theory

The new nuclide ²⁵⁹Db and its α decay chain are systematically studied in the framework of the relativistic mean field (RMF) theory with NL3 and TM1 effective interactions. The nuclide ²⁵⁹Db and its α-decay daughter nuclei are calculated in a RMF framework with and without the pairing correlation. With the pairing gaps obtained from the RCHB, the deformed RMF+BCS has been carried out for these nuclei. It has been found that the DRMF+BCS well reproduces the data and implies that the new nuclide ²⁵⁹Db and its α decay daughter nuclei are highly deformed. The α-decay energy Q_α for different channel has been given and it seems that the ground state to ground state Q_α values from DRMF+BCS reproduce the data well. Furthermore the single particle levels of the α decay chain are studied carefully and the explanation for the stability is also presented.     

Extended Theory of Finite Fermi Systems for magic and nonmagic nuclei

Consideration is given to a short review of the main features, recent results, and prospects of the Extended Theory of Finite Fermi Systems (ETFFS), which has been applied in the past 15 years to collective excitations in the neutral channel for nuclei with and without pairing. The theory is an extension of the Migdal standard TFFS to include in a consistent way the single-particle continuum and more complex 1p1h ⊗ phonon or 2qp ⊗ phonon configurations beyond the RPA or QRPA ones; i.e., the theory takes into account all three known mechanisms of giant-resonance width. To the most extent, the theory was developed and applied to nuclei without pairing. A quantitative explanation of the giant-resonance widths was obtained, with the complex configurations contributing about half of the width. In addition, a large part of the observed giant-resonance gross and fine structures can be directly traced back to the specific complex configurations, and the recent results of the (α, α′) experiments in ⁴⁰Ca and ⁵⁸Ni could be explained. Consistent use of the Green’s function method makes it possible to include and calculate some effects which were practically unstudied earlier. These are ground-state correlations induced by complex configurations and “refined” basis effects, in particular, the second (or quasiparticle-phonon) mechanism of pairing. Both of them can be studied in current experiments. In the past five years, the ETFFS has been developed and applied actively to even—even and odd-mass nuclei with pairing. Calculations of the E1 pygmy resonance in Ca and Sn isotopes have shown that this phenomenon, which is important for (n, γ) and (γ, n) reactions, cannot be explained without allowing for complex configurations. Consideration of the single-particle continuum and the practical universality of the interaction parameters allow the ETFFS to be used for calculations of unstable nuclei. The prospects and status of the necessary development of a self-consistent ETFFS for nuclei with pairing are discussed. The text was submitted by the author in English.     

Nuclear Coulomb energies and the Cottingham formula

Coulomb energy differences of a class of odd-mass mirror nuclei 3 ? A ? 41 are analyzed in a dispersion theory framework using the Cottingham formula. We establish a correspondence between the low-energy contributions and the direct, exchange,… terms of the conventional approach and also study the role of the high-energy contributions.     

Comparison of neutron resonance spacings with microscopic theory for spherical nuclei

The nuclear level spacings determined from neutron resonance experiments for nuclei with 20 ≦ A ≦ 148 and 181 ≦ A ≦ 209 are compared with spacings calculated for spherical nuclei with a microscopic theory which includes the nuclear pairing interaction. Single particle levels of Seeger et al. and Nilsson et al. are used in the calculations. The gross features of the experimental data due to nuclear shells are reproduced with the microscopic theory. In addition, the absolute agreement between experiment and theory is reasonable (67 % of the 151 cases examined agree to within a factor of 2) in view of uncertainties in the experimental data, the theoretical single particle levels and the pairing strength. Values of the spin cutoff parameter σ²(E), calculated with a microscopic theory, are included also for several doubly even nuclei and discussed in terms of nuclear shells.     

The systematics of (n, α) reaction cross-sections at 14.5 MeV neutron energy

A comprehensive review of the experimental data for 14.5 MeV neutron induced reaction crosssections for (n, α) reaction has been made for the isotopes having Z up to 82. Two different parameter groups have been considered by the classification of nuclei into odd-mass and even-even nuclei. The empirical formulae with two parameters for the evaluation of (n, α) reaction cross-sections are discussed in the present study. The odd-even effects have been observed as the cross-sections of odd-mass nuclei are higher as compared to their neighboring even-even nuclei. The shell effects have also been established at magic nucleon numbers for these reaction cross-sections.     

Enhancement of two-proton transfer in N = 82 nuclei: A study of 1p, 2p and (2p+2n) transfer reactions induced by 16O on 140Ce, 142Nd and 144Sm near the Coulomb barrier

One-proton, two-proton, and α-particle transfer have been studied on nuclei with closed neutron shell N = 82 using ¹⁶O beams of 63 to 66.5 MeV incident energy. Transfer probabilities defined in a semiclassical model are derived for the different reaction channels. For this purpose the Q-value and angular dependence of the cross section are discussed. The two-proton transfer to the ground states shows an enhancement by a factor 20–25 compared to other nuclei, showing the effect of the proton pairing in these nuclei (they correspond to equivalent neutron configurations in ^{108, 110, 112}Sn). The total transfer probability follows a common trend for all three target nuclei as a function of energy above the Coulomb barrier for the proton and two-proton transfer, respectively, but not for the four-nucleon transfer.     

Isovector pairing and particle-number fluctuation effects on the spectroscopic factors of one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei

Expressions of the spectroscopic factors(SFs) corresponding to one-particle transfer reactions have been established using a schematic definition.These expressions have been derived by taking into account the isovector neutron-proton(np) pairing correlations and a particle-number projection in the framework of the generalized SharpBCS(SBCS) method.Recently proposed expressions of the projected wave-functions of odd-mass nuclei have been used for this purpose.The formalism has first been tested using the single-particle energies of the schematic picketfence model.It is shown that the np pairing and particle-number fluctuation effects are far from negligible and they depend on the pairing gap parameter values.Their behavior is not the same when the parent nuclei are even-even or odd.Predictions dealing with the SFs corresponding to one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei have then been established within the framework of the realistic Woods-Saxon model.It is shown that the np pairing effect as well as the particle-number projection effect are important and thus have to be included in future calculations of the SF corresponding to these kinds of reactions.     

Microscopic study of neutron-rich dysprosium isotopes

Microscopic studies in heavy nuclei are very scarce due to large valence spaces involved. This computational problem can be avoided by means of the use of symmetry-based models. Ground-state, γ and β bands, and their B(E2) transition strengths in ^160–168Dy isotopes, are studied in the framework of the pseudo-SU(3) model which includes the preserving symmetry Q · Q term and the symmetry-breaking Nilsson and pairing terms, systematically parametrized. Additionally, three rotor-like terms are considered, whose free parameters, fixed for all members of the chain, are used to fine tune the moment of inertia of rotational bands and the band head of γ and β bands. The model succesfully describes in a systematic way rotational features in these nuclei and allows to extrapolate toward the midshell nucleus ¹⁷⁰Dy. The results presented show that it is possible to study a full chain of isotopes or isotones in the region with the present model.     

Pairing and quartetting in exotic nuclei

A review is given of pair correlations in nuclei with an emphasis on the symmetry character of the superfluid solution which depends on (i) the isospin of the nucleus and (ii) the relative strength of the T=0 and T=1 pairing forces. The most general SO(8) model which accommodates neutrons and protons as well as T=0 and T=1 pairing, is solvable in three limits: only T=0 pairing, only T=1 pairing and equal strengths in the two channels. In these limits, the superfluid ground-state solution of N=Z nuclei exhibits a quartet structure. The competition between superfluidity and magicity is discussed with reference to integrable models. To cite this article: P. Van Isacker, C. R. Physique 4 (2003).     

Some problems in the generalized theory of finite Fermi systems

A realistic version of the generalization of the theory of finite Fermi systems to the case where some complex configurations involving phonons are explicitly taken into account is proposed. Secular equations describing the fragmentation of simple states in odd and even-even nuclei over complex configurations that belong to, respectively, the quasiparticle ? phonon + quasiparticle ? phonon ? phonon and the two quasiparticles ? phonon type and which are presently of greatest interest are derived on the basis of general relations for nuclei that involve pairing (nonmagic nuclei). These equations take into account effects associated with ground-state correlations due to complex configurations and with the additional quasiparticle-phonon mechanism of Cooper pairing in nuclei. The effects in question were disregarded previously, but they are of interest since they can be observed in present-day experiments.     

The effect of neutron-proton pairing correlations on the transfer of a neutron-proton pair

A theory of neutron-proton pairing interaction is developed considering bothJ=0T=1 andJ≠0T=0 correlations. The model of a singlej-shell is investigated explicitly forN=Z nuclei. Instead of solving the full HFB (Hartree Fock Bogoliubov) problem a variational method is used for determining the ground state energy and wavefunction. Our model shows that the best solutions contain either onlyT=0 or onlyT=1 correlations. A solution mixingT=0 andT=1 is energetically worse. It is estimated in PWBA (Plane Wave Born Approximation) that for ground state transitions at light nuclei in the transfer of a neutron-proton pair the cross section is enhanced up to a factor 3 by pairing correlations compared with shell model calculations.     

Conventional BCS,unconventional BCS,and non-BCS hidden dineutron phases in neutron matter

The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the nn pairing interaction is provided by a realistic bare nn potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density, where the pairing constant λ, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter, where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where λ changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei.     

Microscopic absorptive interaction for composite finite nuclei

The theoretical framework for the microscopic calculation of an effective interaction of two composite nuclei is developed by applying Feshbach's projection operator formalism. Both translational invariance and the Pauli principle are taken into account exactly. The theory is based on model wavefunctions for finite nuclei and does not require nuclear matter approximations. The model Q-space consists of channels in which one or both nuclei are excited. A 1p1h-excitation mechanism is considered in some detail and the properties of an effective absorptive interaction are studied for the α-α-system as an example.     

Complete scissors mode strength in heavy deformed odd-mass nuclei: a case study of 165Ho and 169Tm

The low-energy dipole strength distributions in ¹⁶⁵Ho and ¹⁶⁹Tm have been studied in nuclear resonance fluorescence experiments at the S-DALINAC utilizing a Euroball Cluster detector. In the energy interval between 2.5 and 4.0 MeV, where the scissors mode is expected, 35 ground state transitions could be observed in ¹⁶⁵Ho and 53 in ¹⁶⁹Tm. Assuming M1 character for all these transitions corresponds to ΣB(M1) ↑= 1.54(23), μ_N² and ΣB(M1) ↑= 2.15(63), μ_N² for ¹⁶⁵Ho and ¹⁶⁹Tm, respectively. A statistical analysis is applied to the measured spectra which is capable of reconstructing the complete strength, including contributions of transitions below the observation limit, with the ratio between M1 and E1 excitations and their total strengths taken as an average over the even-mass neighbours. This results in summed M1 transition strengths of ΣB(M1) ↑= 3.54_−0.95^+0.75, μ_N² (¹⁶⁵Ho) and ΣB(M1) ↑= 3.36_−0.57^+1.00μ_N² (¹⁶⁹Tm). The large variations of the summed dipole strength and the fragmentation in other deformed odd-mass nuclei can be reproduced by the same statistical ansatz. The total low-lying M1 strength in heavy deformed odd-mass nuclei is in agreement with the findings in the neighbouring even-mass nuclides as well as with sum-rule predictions.     

Calculations of the β-decay half-lives of neutron-deficient nuclei

In this work,β~+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation(QRPA),where neutron-neutron,proton-proton and neutron-proton(np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov(HFB) transformation.In addition to the pairing interaction,the Br¨uckner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions.Calculations are performed for even-even proton-rich isotopes ranging from Z =24 to Z =34.It is found that the np pairing interaction plays a significant role inβ-decay for some nuclei far from stability.Compared with other theoretical calculations,our calculations show good agreement with the available experimental data.Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference.     

Beta decay log ft values for transitional odd-mass nuclei

Using the wave functions yielded by the asymmetric rotor model with a decoupled odd nucléon with variable moment of inertia the absolute log ft values for some transitional odd-mass nuclei have been calculated. The dependence on the γ-deformation is important in a few cases. A great improvement is obtained in comparison with a pure spherical shell-model calculation.     

P-odd,T-even symmetries for products of the spontaneous fissioning of oriented nuclei

P-Odd, T-even asymmetries in angular distributions of products from the binary and ternary spontaneous fissioning of nuclei oriented in strong magnetic fields at ultralow temperature are described for the first time by means of the quantum theory of fission. Using the spin density matrix of a fissioning nucleus and considering the notable octupole deformations of the nucleus that appear in the vicinity of its scission point, we show that coefficients of the asymmetries in question are governed by the orientation parameters of a fissioning nucleus with Q = 1 and Q = 3. The coefficients obtained in this work are compared to the analogous coefficients in the fissioning of unoriented target nuclei by polarized neutrons and oriented target nuclei by unpolarized neutrons.