The droplet model energy of axially asymmetric nuclei

The shape dependent factors of the droplet model energy are evaluated for the special case of an ellipsoid and expressed in terms of four incomplete elliptic integrals. Generalization to other axially asymmetric shapes is considered.     

The anomalies of the droplet model

The droplet model predictions for nuclear density distributions are systematically compared with the results of a self-consistent model with Strutinsky smoothing. The discrepancies between the two predictions for stable nuclei are as large as the discrepancies between the old liquid drop model and the self-consistent one: although the droplet model reproduces quite well the trends of the variations of nuclear radii and neutron skins, it is not able to predict correctly their values. A preliminary discussion is given as to which hypothesis of the droplet model should be modified to generalise it, and two possible variants are suggested.     

A spin dependent droplet model for high energy pion-nucleon elastic scattering

The Chou-Yang droplet model of hadron-hadron diffractive scattering is reinterpreted in a way that allows the spin structure of the amplitudes to be incorporated. The model is developed in the particular case of pion-nucleon elastic collisions, in which theA ⁽⁺⁾ andA′⁽⁺⁾ amplitudes are related respectively to theF ₂ andF ₁ Dirac form factors of the nucleon. A version of the model, which does not conserves-channel helicities, is first considered and its predictions compared with the high energy π±p elastic data, including polarization. Finally an interpretation of asymptotic helicity conservation is provided in terms of the model.     

Intermittency in the Fisher's droplet model

Intermittent behaviour of fragment multiplicity distributions in the nuclear liquid-gas phase transition is studied in terms of the droplet model of Fisher. The anomalous fractal dimensions are compared with data on heavy ion reactions and classical molecular dynamics simulations. A signature of the transition in the anomalous fractal dimensions is shown.We thank Profs. S. Ayik, M. Di Toro and V. Kondratyev for discussions. One of us (T.K.) acknowledges the support of INFN-LNS.     

The deuteron binding energy

The ¹H(n, γ)²H γ-ray energy has been measured relative to ⁴⁸V and ¹⁴⁴Ce γ-rays, which are both based on the gold standard for γ-ray energies. The ensuing deuteron binding energy, $\text{B(}{}^2\text{H}\text{= 2224575 ± 9}\text{eV}$, confirms (with higher accuracy) the value from one of two conflicting recent precision measurements. This value has been used to recalculate the energies of γ-rays from thermal-neutron capture in ²H, ¹²C, ¹³C and ¹⁴N, which serve as mass-based γ-ray energy standards.     

Mechanism of energy dissipation in a droplet cluster

It has been shown that thermocapillary processes on the surface of the drops in a drop cluster that appears above a locally heated liquid ensure additional energy transfer. Thus, the drop cluster is a typical dissipative structure. The energy dissipated by an individual drop of the cluster has been estimated.     

闪锌矿GaN量子点中类氢杂质态的束缚能

在有效质量近似下,用变分法研究了闪锌矿GaN/AlxGa1-xN单量子点中的类氢杂质态。结果表明量子点中的杂质位置和量子点结构参数（量子点高度H、半径R及Al含量x）对施主束缚能有很大的影响。当杂质位于量子点中心时,施主束缚能 有最大值。此外,施主束缚能 随着量子点高度H（半径 ）的增大而减小,随着量子点中Al含量x的增大而增大。     

A theorem for dissociation energy and binding energy of biexcitons in the isotropic model of a semiconductor

A theorem is proved for the dissociation energy W and the binding energy E_b of biexcitons in the isotropic model of a semiconductor. The theorem determines the upper limits of the values W and E_b for the given mass ratio $\text{m}{}^1{}_{\mathrm{e}}\text{m}{}^1{}_{\mathrm{h}}$.     

New approach to nuclear binding energy in integrated nuclear model

In this paper, the integrated nuclear model is introduced and a binding energy formula based on this model is presented. The binding energies of most nuclides in this model are compared with available experimental values and also with values from the liquid drop model (LDM).     

The binding energy of electrons in supercritical atoms

In a supercritical atom, the most tightly bound electrons do not occupy bound-state eigenfunctions of the Dirac Hamiltonian. We discuss the binding energy of supercritical atoms in the light of this fact. We derive an expression for the binding energy which relates the supercritical and the undercritical cases in a smooth fashion.     

The neutron binding energy in the neutron-rich nucleus93Sr

The neutron binding energy in⁹³Sr has been determined to (5230±6) keV from energy correspondences between levels defined by γ-ray transitions and β-delayed neutron emission.     

The binding energy of an adsorbed atom

Summary We discuss the effect of substrate vibrations on the binding of an adsorbed atom. At zero temperature, we compute the binding energyD ₀-E, whereD ₀ is the surface well depth (classical binding energy) andE is the quantum correction. For several simple models, we find thatE is surprisingly model independent. We compareD ₀-E with the binding energies to a rigid substrate,D ₀-E _rs, and to a vibrationally averaged substrate,D ₀-E _va. We prove thatE _va≥E≥E _rs and that similar relations hold at finite temperature for the free energy of binding. We find that in most casesE _rs is better thanE _va as an approximation toE. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

A model of laminar flames in droplet suspensions

A mathematical model of steady laminar flame propagation through a suspension of liquid droplets was proposed, and numerical calculations within the framework of this model were performed. The model is constructed based on one-dimensional differential equations of the theory of laminar flames in homogeneous gaseous mixtures in conjunction with the theory of droplet burning in uniform monodisperse suspensions. The chemical process was described using a multistage kinetic scheme. A comparison of model predictions with the available experimental data demonstrated satisfactory agreement.     

The free energy of the spin-boson model

Forn spins 1/2 coupled linearly to a boson field in a volumeV _n, the existence of the specific free energy is proved in the limitn ,V _n withn/V _n=const. The interaction is essentially of the mean field type, in as much as it is proportional to 1/V _n; the coupling constants are allowed to be spin dependent. A variational expression is obtained for the limiting specific free energy, and a critical temperature is identified above which the system behaves as if there were no coupling at all.     

Absence of diffusion in the Anderson tight binding model for large disorder or low energy

We prove that the Green's function of the Anderson tight binding Hamiltonian decays exponentially fast at long distances on ? ^v , with probability 1. We must assume that either the disorder is large or the energy is sufficiently low. Our proof is based on perturbation theory about an infinite sequence of block Hamiltonians and is related to KAM methods.     

Nuclear radii: A critique of the droplet model

Equivalent sharp radii of a number of nuclei are calculated with the droplet model, using parameters that have been determined by the Hartree-Fock (HF) method with a given force (Gogny). They are found to be systematically smaller than the sharp radii given by direct HF calculations on the nucleus in question with the same force. This is shown to be a result of nuclear matter being squeezed by the surface tension much more in the droplet model than in the HF method. Inclusion of higher-order terms in the droplet model's expansion in powers of $\text{A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$ in no way helps to remove the anomaly, and in fact serious questions concerning the convergence of this expansion arise.     

A kinetic model for droplet growth in the transition regime

A variant of the moment expansion method, used in an earlier paper to describe the flow of a gas toward an absorbing sphere, is applied to a more realistic model of a droplet condensing from a supersaturated vapor. In the simplest version a spherical droplet absorbs all incoming vapor molecules, but spontaneously emits molecules with a Maxwellian distribution at the droplet temperature and with the corresponding saturated vapor density. From a solution of the stationary linearized Boltzmann equation with these boundary conditions we obtain expressions for the heat and mass currents toward the sphere as a function of the supersaturation and the temperature difference between the droplet and the vapor at infinity. For small droplet radii the known free flow limit is obtained in a natural way. From the calculated expressions for the heat and mass current we derive evolution equations for the radius and temperature of the droplet. The temperature evolves more rapidly and can thus be eliminated adiabatically; the resulting growth curve for the radius shows a sharp transition from a kinetically controlled regime for small radii to a regime dominated by heat conduction for large radii. The effect of incomplete absorption at the surface is also studied. The actual calculations are carried out for Maxwell molecules, with parameters corresponding to argon at 0.65T _c and 100% supersaturation.     

The influence of the lattice polarization on the biexciton binding energy

The ground state of the biexciton in the lattice polarization field using both Haken and recently derived effective Hamiltonians is studied. The variational wave function possessing the full symmetry of the complex and allowing the analytical evaluation of the energy matrix elements is proposed. The biexciton binding energy is calculated as a function of electron-phonon coupling constant and of phonon energy in the case of equal electron and hole masses.