The Gamow shell model with realistic interactions: a theoretical framework for ab initio nuclear structure at drip-lines

Ab initio approaches are among the most advanced models to solve the nuclear many-body problem. In particular, the no-core–shell model and many-body perturbation theory have been recently extended to the Gamow shell model framework, where the harmonic oscillator basis is replaced by a basis bearing bound, resonance and scattering states, i.e. the Berggren basis. As continuum coupling is included at basis level and as configuration mixing takes care of inter-nucleon correlations, halo and resonance nuclei can be properly described with the Gamow shell model. The development of the no-core Gamow shell model and the introduction of the $\hat{\bar{Q}}$-box method in the Gamow shell model, as well as their first ab initio applications, will be reviewed in this paper. Peculiarities compared to models using harmonic oscillator bases will be shortly described. The current power and limitations of ab initio Gamow shell model will also be discussed, as well as its potential for future applications.     

Nucleon-pair approximation to the nuclear shell model

Atomic nuclei are complex systems of nucleons–protons and neutrons. Nucleons interact with each other via an attractive and short-range force. This feature of the interaction leads to a pattern of dominantly monopole and quadrupole correlations between like particles (i.e., proton–proton and neutron–neutron correlations) in low-lying states of atomic nuclei. As a consequence, among dozens or even hundreds of possible types of nucleon pairs, very few nucleon pairs such as proton and neutron pairs with spin zero, two (in some cases spin four), and occasionally isoscalar spin-aligned proton–neutron pairs, play important roles in low-energy nuclear structure. The nucleon-pair approximation therefore provides us with an efficient truncation scheme of the full shell model configurations which are otherwise too large to handle for medium and heavy nuclei in foreseeable future. Furthermore, the nucleon-pair approximation leads to simple pictures in physics, as the dimension of nucleon-pair subspace is always small. The present paper aims at a sound review of its history, formulation, validity, applications, as well as its link to previous approaches, with the focus on the new developments in the last two decades. The applicability of the nucleon-pair approximation and numerical calculations of low-lying states for realistic atomic nuclei are demonstrated with examples. Applications of pair approximations to other problems are also discussed.     

The structure of neutron-rich calcium isotopes studied by the shell model with realistic effective interactions

We study the structure of neutron-rich calcium isotopes in the shell model with realistic interactions. The CD-Bonn and Kuo-Brown (KB) interactions are used. As these interactions do not include the three-body force, their direct use leads to poor results. We tested whether the adjustment of the single particle energies (SPEs) would be sufficient to include the three-body correlations empirically. It turns out that the CD-Bonn interaction, after the adjustment of SPEs, gives good agreement with the experimental data for the energies and spectroscopy. For the KB interaction, both the SPEs and monopole terms require adjustments. Thus, the monopole problem is less serious for modern realistic interactions which include perturbations up to the third order. We also tested the effect of the non-central force on the shell structure. It is found that the effect of the tensor force in the CD-Bonn interaction is weaker than in the KB interaction.     

Projected shell model study of neutron-deficient 122Ce

The observed excited states of ¹²²Ce nucleus have been studied in the framework of projected shell model (PSM). The yrast band has been studied up to spin 26ħ. The first band crossing has been predicted above a rotational frequency of 0.4 MeV/ħ that corresponds to first backbending. The calculation reproduces the experimentally observed ground state band up to spin 14 ħ. The electromagnetic quantities, transition quadrupole moments and g-factors are predicted and there is a need to measure these quantities experimentally.     

Frontiers and challenges of nuclear shell model

Two recent developments of the nuclear shell model are presented. One is a breakthrough in computational feasibility owing to the Monte Carlo Shell Model (MCSM). By the MCSM, the structure of low-lying states can be studied with realistic interactions for a wide, nearly unlimited basically, variety of nuclei. The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: otsuka@phys.s.u-tokyo.ac.jp     

Influence of binding energies of electrons on nuclear mass predictions

Nuclear mass contains a wealth of nuclear structure information, and has been widely employed to extract the nuclear effective interactions. The known nuclear mass is usually extracted from the experimental atomic mass by subtracting the masses of electrons and adding the binding energy of electrons in the atom. However,the binding energies of electrons are sometimes neglected in extracting the known nuclear masses. The influence of binding energies of electrons on nuclear mass predictions are carefully investigated in this work. If the binding energies of electrons are directly subtracted from the theoretical mass predictions, the rms deviations of nuclear mass predictions with respect to the known data are increased by about 200 ke V for nuclei with Z, N 8. Furthermore, by using the Coulomb energies between protons to absorb the binding energies of electrons, their influence on the rms deviations is significantly reduced to only about 10 ke V for nuclei with Z, N 8. However, the binding energies of electrons are still important for the heavy nuclei, about 150 ke V for nuclei around Z = 100 and up to about 500 ke V for nuclei around Z = 120. Therefore, it is necessary to consider the binding energies of electrons to reliably predict the masses of heavy nuclei at an accuracy of hundreds of ke V.     

Frontiers and challenges of the nuclear shell model

Two recent developments of the nuclear shell model are presented. One is a breakthrough in computational feasibility owing to the Monte Carlo Shell Model (MCSM). By the MCSM, the structure of low-lying states can be studied with realistic interactions for a wide, nearly unlimited basically, variety of nuclei. The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed. Received: 1 May 2001 / Accepted: 4 December 2001     

Nuclear compressibility and its effect on nuclear binding energies from the study of muonic atoms

The variation of nuclear parameter with mass number elicits information about nuclear compressibility. Analysis of muonic x-ray transitions provides an elegant method to investigate the behaviour of the nuclear parameterr ₀. It is observed from the behaviour ofr ₀ that nuclei in the regionA⩽70 are highly compressible while those in the regionA∼210 are almost incompressible. The behaviour ofr ₀ is incorporated into the semi-empirical mass formula through the Coulomb energy term. From the modified mass formula thus obtained binding energies of about 440 spherical nuclei have been calculated. The results suggest that nuclear compressibility imposes certain relationship between excess binding energies (E _exp−E _cal) and neutron. proton number. The present study also points out that shell effects exhibited by nuclear binding energies cannot be accounted for by simply varying the coefficients of the mass formula: on the other hand extra terms are necessary to explain them.     

Recursive calculation of matrix elements for the generalized seniority shell model

A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of one-body and two-body operators and basis state overlaps.     

The nuclear symmetry energy from relativistic Brueckner-Hartree-Fock model

The microscopic mechanisms of the symmetry energy in nuclear matter are investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF) model with a high-precision realistic nuclear potential, pvCDBonn A. The kinetic energy and potential contributions to symmetry energy are decomposed. They are explicitly expressed by the nucleon self-energies, which are obtained through projecting the G-matrices from the RBHF model into the terms of Lorentz covariants. The nuclear medium effects on the nucleon self-energy and nucleon-nucleon interaction in symmetry energy are discussed by comparing the results from the RBHF model and those from Hartree-Fock and relativistic Hartree-Fock models. It is found that the nucleon self-energy including the nuclear medium effect on the single-nucleon wave function provides a largely positive contribution to the symmetry energy, while the nuclear medium effect on the nucleon-nucleon interaction, i.e., the effective G-matrices provides a negative contribution. The tensor force plays an essential role in the symmetry energy around the density. The scalar and vector covariant amplitudes of nucleon-nucleon interaction dominate the potential component of the symmetry energy. Furthermore, the isoscalar and isovector terms in the optical potential are extracted from the RBHF model. The isoscalar part is consistent with the results from the analysis of global optical potential, while the isovector one has obvious differences at higher incident energy due to the relativistic effect.     

Investigation of non-adiabatic effects for the ro-vibrational spectrum of H3+: the use of a single potential energy surface with geometry-dependent nuclear masses

ABSTRACT

The influence of non-adiabatic effects on the ro-vibrational bound states of H⁺ ₃ has been investigated using geometry-dependent reduced masses and only one single potential energy surface. The used potentials (BO electronic energy, adiabatic corrections and relativistic contributions) are based on explicitly correlated wavefunctions. For the first time, several different fully geometry-dependent reduced mass surfaces in three dimensions have been incorporated for the vibrational and rotational contributions.     

Evaluation of nuclear shell correction energies for realistic level schemes by temperature smearing method

Calculations of shell correction energies by the temperature smearing method for realistic single particle level schemes of finite depth potentials are described and discussed. It is found that the method provides unique values of the shell correction energies for the various shapes relevant in the fission of actinide nuclei including those shapes where breakdown of the usual Gaussian energy smearing procedure was observed.     

Zur Kondensationsenergie des Nukleons im Kern und ihre Abhängigkeit vom Kernradius

Die Kondensationsenergie des Nukleons b_v hängt vom Krümmungsradius des Kerns ab. Sie nimmt mit der Gröβe des Kerns zu und erreicht für die unendlich ausgedehnte Kernmaterie einen Wert von 28,71 MeV. Der b_v-Mittelwert für 35 betrachtete Kerne beträgl dagegen 17,03 ± 1,50 MeV. Der Radiusparameter des Kerns r₀ ist ebenso krümmungsabhängig. Sein Wert sinkt aber mit der Kerngröβe

Es werden mathematische Zusammenhänge zwischen der Kondensationsenergie und der molaren Oberflächenenergie der Kerne und zwischen den Proportionalitätskoeffizienten der beiden ersten Glieder der Bethe-Weizsäckerschen Gleichung hergeleitet.     

Shell Model Description of Neutron-Deficient Sn Isotopes

The shell model calculations in the sdgh major shell for the neutron-deficient ^106,107,108,109Sn isotopes have been carried out by using CD-Bonn and Nijmegenl two-body effective nucleon-nucleon interactions. The singleshell states and the corresponding matrix elements needed for describing Sn isotopes are reconstructed to calculate the coefficient of fractional parantage by reducing the calculation requirements. This reconstruction allows us to do the shell model calculations of the neutron deficient Sn isotopes in very reasonable time. The results are compared to the recent high-resolution experimental data and found to be in good agreement with experiments.     

Systematic study of odd-mass 151-161Pm and 154,156Pm isotopes using projected shell model

Inspired by the availability of recent experimental as well as theoretical data on the energy levels of odd-mass ^151-161Pm and odd-odd ^154,156Pm, we applied the theoretical framework of the projected shell model to further understand the nuclear structure of these nuclei. The calculations closely reproduced the experimental data reported for the yrast bands of these isotopes by assuming an axial (prolate) deformation of ~0.3. Other properties along the yrast line, such as transition energies and transition probabilities, have also been discussed. Band diagrams are plotted to understand their intrinsic multi-quasiparticle structure, which turn out to be dominated by 1-quasiparticle bands for the odd-mass Pm isotopes and 2-quasiparticle bands for the doubly-odd Pm isotopes under study. The present study not only confirms the recently reported experimental/theoretical data, but also extends the already available information on the energy levels and adds new information regarding the reduced transition probabilities.     

Evolution of nuclear charge radii in copper and indium isotopes

Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton (np) correlations, is here applied for the first time to the study of odd-Z copper and indium isotopes. Theoretical results obtained by the relativistic mean field (RMF) model with NL3, PK1 and NL3^* parameter sets are compared with experimental data. Our results show that both OES and the abrupt changes across begin{document}$ N = 50 $end{document} and 82 shell closures are clearly reproduced in nuclear charge radii. The inverted parabolic-like behaviors of rms charge radii can also be described remarkably well between two neutron magic numbers, namely begin{document}$ N = 28 $end{document} to 50 for copper isotopes and begin{document}$ N = 50 $end{document} to 82 for indium isotopes. This implies that the np-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-Z isotopic chains. Also, our conclusions have almost no dependence on the effective forces.     

WLW 原子核质量模型在r过程研究中的应用

本工作利用最近提出的WLW宏观-微观原子核质量模型, 在经典 r过程框架下 很好地描述了太阳系r过程核素丰度分布. 与常用的FRDM质量模型相比, 新计算更好地再现了A≈ 135和A≈ 180质量区的太阳系r过程核素丰度, 尤其 避免了其他相似计算中A=135 附近出现的 与观测不符的丰度峰问题. 分析表明, 这种差异可能暗示WLW更为合理地处理了壳结构和对称能.     

改进的核密度模型与强子-核Drell-Yan过程中的核效应

提出了改进的核密度模型，用唯象的方法找到了束缚核子内价夸克和海夸克的核效应的参数公式，其中利用了核密度与原子核的平均结合能之间的联系. 利用该模型所得到的束缚核子内部分子分布函数，对强子与核的Drell-Yan过程的核效应给出了满意的解释, 深化了对原子核内夸克分布受核效应影响的认识. 关键词： 核密度模型 核效应 强子-核Drell-Yan过程