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.     

Empirical proton-neutron interactions and nuclear density functional theory: global, regional, and local comparisons

Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals.     

Symmetry energies,pairing energies,and mass equations

Symmetry and pairing energies of atomic nuclei are related to the differences between the excitation energies of isobaric analog states in the same nucleus. Numerous such excitation energies are known experimentally. In addition, a comprehensive global set can be deduced from the available experimental masses by applying Coulomb energy corrections. Replacing the experimental mass data by available theoretical mass predictions as basis for this procedure to extract symmetry and pairing energies makes it possible to directly compare theoretical and experimental quantities. These comparisons reflect upon the goodness or possible shortcomings of the respective mass equation since symmetry energies are related to the curvature of the nuclear mass surface. A discussion of eleven selected mass equations or procedures for reproducing experimental masses and extrapolating into regions of unknown nuclei is presented.     

Nuclear masses set bounds on quantum chaos

It has been suggested that chaotic motion inside the nucleus may significantly limit the accuracy with which nuclear masses can be calculated. Using a power spectrum analysis we show that the inclusion of additional physical contributions in mass calculations, through many-body interactions or local information, removes the chaotic signal in the discrepancies between calculated and measured masses. Furthermore, a systematic application of global mass formulas and of a set of relationships among neighboring nuclei to more than 2000 nuclear masses allows one to set an unambiguous upper bound for the average errors in calculated masses, which turn out to be almost an order of magnitude smaller than estimated chaotic components.     

A study of the dependence of coulomb-energy shifts on the symmetry energy of density-dependent effective interactions

Using Hartree-Fock theory and standard density-dependent effective interactions, we show that by appropriately modifying their symmetry energy properties sizeable changes in the Coulomb energy shifts can be produced. These changes are the result of different degrees of isovector core polarization, while the variations coming from the neutron excess are small. Forces are presented that give satisfactory agreement with experiment for both charge radii and Coulomb displacement energies in mirror and heavy nuclei, and thus no systematic Nolen-Schiffer anomaly is found. No significant changes appear in the values of other bulk properties like total binding energies, proton densities and single-particle spectra. Properties directly related to the symmetry energy, like isotopic mass differences and electric dipole polarizabilities, are also satisfactorily reproduced.     

Extending and refining the nuclear mass surface with ISOLTRAP and MISTRAL

Through the nuclear binding energy, the atomic mass gives us important information about nuclear structure. Viewing the ensemble of mass data over the nuclear chart, we can examine the hills and valleys that form this surface and make hypotheses about the effects of certain nuclear configurations. To unveil these effects, mass measurements of very high precision (<10⁻⁶) are required. Two experiments at ISOLDE pursue this effort of nuclear cartography: the tandem Penning trap spectrometer ISOLTRAP and the radiofrequency transmission spectrometer MISTRAL. Between them, the masses of almost 150 nuclides have been measured from stable isotopes to those with half-lives as short as 30 ms. Both experiments rely on good optical properties of a low energy ion beam and are thus well suited to the ISOLDE facility. This revised version was published online in July 2006 with corrections to the Cover Date.     

Average Nuclear Binding Energies in a Lee-Wick Type Model

We find: (i) The Lee-Wick type relativistic mean-field theory with finite nucleon size effect can reproduce the binding energies for all nuclei over the nuclide table quite well. For 1654 nuclei, whose mass numbers range from 16 to 263 and charge numbers range from 8 to 106, the calculated binding energies are near to the corresponding experimental values with a systematical deviation of about 5.74%. (ii) The lowering of the calculated nuclear masses, by including Coulomb energy into the variational calculations, is very small.     

First precision mass measurements of refractory fission fragments

Atomic masses of 95-100Sr, 98-105Zr, and [corrected] 102-110Mo and have been measured with a precision of 10 keV employing a Penning trap setup at the IGISOL facility. Masses of 104,105Zr and 109,110Mo are measured for the first time. Our improved results indicate significant deviations from the previously published values deduced from beta end point measurements. The most neutron-rich studied isotopes are found to be significantly less bound (1 MeV) compared to the 2003 atomic mass evaluation. A strong correlation between nuclear deformation and the binding energy is observed in the two-neutron separation energy in all studied isotope chains.     

The state of an atomic-molecular system near the stability threshold

The state of an atomic-molecular system near its stability threshold with regard to the detachment of one of the particles is studied. The decay of the system upon a decrease in the charge of a binding particle, as well upon an increasasymmetry of masses of like-charged particles, is considered. A special variational principle that allows one to directly calculate the threshold state of the system without repeatedly calculating its energy for different values of masses and charges of particles is used. With the motion of all particles fully taken into account, the threshold states of two-electron atoms with different nuclear charges and of atomic-molecular systems corresponding to the attachment of a positron of variable mass to a neutral atom are calculated. On the basis of calculation of quantum-mechanical expectation values of the kinetic energy of particles and the potential energy of their interaction, the rearrangement of the wave function upon passage of the system through the decay threshold is examined. The threshold characteristics of a purely adiabatic system containing infinitely heavy particles are considered separately.     

Binding energy for inhomogeneous nuclear matter

For a spatial finite nuclear density distribution a binding energy formula is developed. A modified Thomas-Fermi method which deduces the mixed density by taking into account an anisotropic local momentum space occupation is used. This method presents the binding energy as a functional of the proton and neutron density distributions. It was possible within this framework to derive in a consistent way the energy correction terms due to density inhomogeneities. The structure of these energy correction terms is shown and an estimate is given for the adjustable parameters of this model to fit the experimental nuclear masses.     

原子核质量中的奇偶性

原子核质量的描述和预言是原子核结构理论中的基础问题之一。相邻原子核质量存在奇偶性,这些奇偶性对于构造局域质量关系和研究核子对力相互作用有参考意义。本文回顾了我们在近年来注意到的相邻原子核质量之间的奇偶性方面研究的主要结果,包括最后一个质子与中子相互作用[标记为δV1p-1n]的奇偶性及其起源、δV1p-1n奇偶性导致的Garvey-Kelson质量关系的奇偶性、单核子分离能与原子核的质子和中子数奇偶相关性等。     

手征σ模型中σ介子的质量与核物质结合能曲线关系的研究

文中研究了手征σ模型下σ介子的质量m_σ与核物质结合能曲线的关系,主要的目的是研究在单圈图近似下所谓的“快子极点”问题,即σ或π介子质量的平方变为负数,这将导致能量密度为虚数.把m_σ看成自由参数并通过拟合核物质的饱和性质而确定,结果表明,在单圈图真空起伏近似下,并选重整化点在质量壳上,当m_σ=307.5MeV而且核密度小于4.43倍正常饱和密度时,“快子极点”没有出现,因此首先得到了核物质结合能曲线以及计算了不可压缩系数K(≌175.7MeV).     

On the masses of elementary particles

We make an attempt to describe the spectrum of masses of elementary particles, as it comes out empirically in six distinct scales. We argue for some rather well defined mass scales, like the electron mass; we elaborate on the assumption that there is a minimum mass associated to any electric charge. Another natural mass scale is Λ = Λ _QCD coming arbitrarily at quantizing a classically conformal SU(3) _c theory. Indeed, some scales of masses will cover also masses of composite particles or mass differences. We extend some plausible arguments for other scales, as binding or self-energy effects of the microscopic forces, plus some speculative uses, here and there, of gravitation. We also consider briefly exotics like supersymmetry and extra dimensions in relation to the mass scale problem, including some mathematical arguments (e.g. triality), which might throw light on the three-generation problem. We also address briefly the issues of dark matter and dark energy.     

Quartet effects in the nuclear masses and excitations

The assumptions of the quartet model are given and it is shown that they are consistent with the fine structure of the nuclear mass curves throughout the table. It is also shown by an analysis of the nuclear masses that the quarteting effect accounts for 2/3 of the neutron binding energies. The consequences of the quartet picture for the existence of low-lying many particle-many hole states in medium and heavy nuclei are discussed.     

High-precision masses of 29-33Mg and the N = 20 shell “closure”

High-precision mass measurements have been performed on the exotic magnesium isotopes ^29-33Mg using the MISTRAL radiofrequency spectrometer, especially suited for very short-lived nuclides. This method, combined with the powerful tool of resonant laser ionization at ISOLDE, has provided a significant reduction of uncertainty for the masses of the most exotic Mg isotopes: a relative error of 7×10^-7 was achieved for the weakly produced ³³Mg that has a half-life of only 90ms. Moreover, the mass of ³³Mg is found to change by over 250keV. Verifying and minimizing binding energy uncertainties in this region of the nuclear chart is important for understanding the lack of binding energy that is normally associated with magic numbers.     

Finite nuclei to nuclear matter: a leptodermous approach

The liquid drop model (LDM) expansions of energy and incompressibility of finite nuclei are studied in an analytical model using Skyrme-like effective interactions to examine, whether such expansions provide an unambiguous way to go from finite nuclei to nuclear matter, and thereby can yield the saturation properties of the latter, from nuclear masses. We show that the energy expansion is not unique in the sense that, its coefficients do not necessarily correspond to the ground state of nuclear matter and hence, the mass formulas based on it are not equipped to yield saturation properties. The defect is attributed to its use of liquid drop without any reference to particles as its basis, which is classical in nature. It does not possess an essential property of an interacting many-fermion system namely, the single particle property, in particular the Fermi state. It is shown that, the defect is repaired in the infinite nuclear matter model by the use of generalized Hugenholtz–Van Hove theorem of many-body theory. So this model uses infinite nuclear matter with well defined quantum mechanical attributes for its basis. The resulting expansion has the coefficients which are at the ground state of nuclear matter. Thus a well defined path from finite nuclei to nuclear matter is found out. Then using this model, the saturation density 0.1620 fm⁻³ and binding energy per nucleon of nuclear matter 16.108 MeV are determined from the masses of all known nuclei. The corresponding radius constant r₀ equal to 1.138 fm thus determined, agrees quite well with that obtained from electron scattering data, leading to the resolution of the so-called ‘r₀-paradox’. Finally a well defined and stable value of 288±20 MeV for the incompressibility of nuclear matter K_∞ is extracted from the same set of masses and a nuclear equation of state is thus obtained.