A survey of neutron and proton binding energies

Limiting values of last-nucleon binding energies are available from measured reaction energies of induced transformations satisfying the selection rule ΔA=0, ±1 (A=mass number) in about 140 cases. In 14 cases upper and lower limiting values are known separately, and these agree in each case within the limits of experimental error. Taking the other 126 values as ‘true’ (rather than limiting) values, and using information concerning total energies of β-disintegration, the number of last-nucleon binding energies which are reasonably well determined is increased to more than 600. These values are tabulated, and discussed in relation to the v. Weizsäcker mass formula. Apart from certain anomalies which are treated individually, the discussion brings out the effect of α-unit structure in light nuclei, diminishing in importance to become almost negligible beyond A=40, and yields mean values for nucleon-parity dependent terms in the range A～215. The recovery of ‘normal’ last-nucleon binding energy after completion of a closed shell is followed in detail over the range 126ˇ-Nˇ-136 (N=neutron number) and somewhat less closely over the range 82ˇ-Zˇ-92 (Z=proton number).     

On the theory of slow-particle scattering in the two-dimensional case

A solution to the problem of elastic scattering of low-energy particles on a “weak” potential U is given. An expression for the amplitude of s-wave scattering is found in this approximation, and it is shown that, for U < 0, it has a pole at the energy E ₀ of the corresponding loosely bound state. An explicit expression in terms of the potential U is obtained for the preexponential factor, which refines the known order-of-magnitude estimate for E ₀.     

Elastic Scattering of Electrons by a Cut-Off Coulomb Potential at Low Energies

Elastic scattering of electrons by cut-off Coulomb potential U_c(r) is investigated, where U_c(r) = 0, for r > r_c and U_c(r) = ?1/r + 1/r_c for r ≦ r_c. This is first considered in terms of classical, and later quantum mechanical (partial wave) methods in the low energy range 0 ≦ ? ? 1/r_c, where ? is the energy of the free electron. Scattering in this energy region displays a number of particular characteristics, such as back scattering, at certain energies. It can be concluded that some agreement does exist between the classical and quantum mechanical results.     

Thermodynamic properties of hard ellipsoid square-well fluid

The perturbation theory with non-spherical reference system is used for molecular fluid with angle-dependent square-well type potential. Simple analytic expressions are given for the thermodynamic properties such as the equation of state, excess free energy per particle, internal energy and internal heat capacity. The effects of anisotropy on the thermodynamic properties are discussed. The anisotropy effects increase with increase of density and decrease of temperature and depends on the anisotropy parameterx ₀.     

On scattering of slow particles by a “weak” 2D potential

The problem of elastic scattering of low-energy particles by a “weak” 2D potential U without an axial symmetry is considered. The expression for the scattering amplitude is found in this approximation, and it is shown that at U < 0 it has a pole at the energy E ₀ of the corresponding weakly bound state. An explicit expression in terms of the potential U is derived for the factor refining the known order-of-magnitude estimate for E ₀.     

DTO分子反应碰撞的非对称性

基于DTO分子（X¹A₁）的氢同位素效应,得到修正的Born-Oppenheimer（B-O）理论下多体展式分析势能函数.用准经典的Monte-Carlo轨迹法研究了O+DT（0,0）的分子反应动力学过程.结果表明：在碰撞能量较低时（<209.2?kJ·mol^-1）,O+DT（0,0）可以生成长寿命络合物DTO（X¹A₁）,并且该络合反应是无阈能的,这一结论与多体项展式理论计算的DTO分子势能曲线结果一致.碰撞能大于209·2?kJ·mol^-1时,逐渐出现置换产物TO和DO,随碰撞能进一步增大,分子将被完全碰散成D,T,O原子.反应O+DT（0,0）→OD+T和O+DT（0,0）→OT+D是有阈能的反应,置换产物TO和DO轨线存在非对称性. 关键词： DTO 势能函数 分子反应碰撞 轨线非对称性     

氢同位素氚水T2O(X1A1)的解析势能函数

获得T₂O(X¹A₁)解析势能函数的主要困难在于Born-Oppenheimer近似下T₂O(X¹A₁)与H₂O(X¹A₁)势能函数的不可区分性.然而,在Born-Oppenheimer近似下,分子势能函数实际上是键长、键角这些 关键词： 2O(X¹A₁)')" href="#">T₂O(X¹A₁) 同位素效应 解析势能函数     

Dark Energy with Generalized Equation of State in Bianchi Type-I Cosmological Model

Dark energy with the usually used equation of state p=γρ, where γ=const<0 is hydrodynamically unstable. To overcome this drawback we consider the cosmology of a perfect fluid with a linear equation of state of a more general form p=α(ρ−ρ ₀), where the constants α and ρ ₀ are free parameters. The anisotropic Bianchi type-I cosmological model filled with dark energy has been considered. A generalized equation of state for the dark energy component of the universe has been used. The exact solutions to the corresponding Einstein field equations and the statefinder diagnostic pair i.e. {r,s} parameters have been obtained in three interesting cases (i) when ρ _Λ>0 and A>0 (ii) when ρ _Λ>0 and A<0 and (iii) when ρ _Λ<0 and A>0 at the singularities i.e. t→0 and t→±∞.     

Singular vectors of quantum group representations for straight Lie algebra roots

We give explicit formulae for singular vectors of Verma modules over U_q(G), where G is any complex simple Lie algebra. The vectors we present correspond exhaustively to a class of positive roots of G which we call straight roots. In some special cases, we give singular vectors corresponding to arbitrary positive roots. For our vectors we use a special basis of U_q(G ^-), where G ^- is the negative roots subalgebra of G, which was introducted in our earlier work in the case q=1. This basis seems more economical than the Poincaré-Birkhoff-Witt type of basis used by Malikov, Feigin, and Fuchs for the construction of singular vectors of Verma modules in the case q=1. Furthermore, this basis turns out to be part of a general basis recently introduced for other reasons by Lusztig for U_q(^-), where ^- is a Borel subalgebra of G.A. v. Humboldt-Stiftung fellow, permanent address and after 22 September 1991: Bulgarian Academy of Sciences, Institute of Nuclear Research and Nuclear Energy, 1784 Sofia, Bulgaria.     

Quantum affine algebras and universalR-matrix with spectral parameter

Using the previously obtained universalR-matrix for the quantized nontwisted affine Lie algebras U _q (A ₁ ⁽¹⁾ ) and U _q (A ₂ ⁽¹⁾ ), we determine the explicitly spectral dependent universalR-matrix for the corresponding quantum Lie algebras U _q (A ₁) and U _q (A ₂). As applications, we reproduce the well known results in the fundamental representations and we also derive an extremely explicit formula of the spectral-dependentR-matrix for the adjoint representation of U _q (A ₂), the simplest nontrivial case when the tensor product decomposition of the representation with itself has nontrivial multiplicity.     

Analysis of A-DLTS spectra of MOS structures with thin NAOS SiO2 layers

A set of MOS structures with thin SiO₂ layers prepared by nitric acid oxidation (NAOS) method was investigated using acoustic deep level transient spectroscopy (A-DLTS) to explain the role of annealing treatment (post-oxidation annealing (POA) and post-metallization annealing (PMA)) at different conditions on the distribution of interface states. The activation energies of interface states and the corresponding capture cross-section were calculated both from Arrhenius plots constructed for individual peaks of the A-DLTS spectra and applying the method of modeling of measured acoustic spectra. The energy distribution of the interface states was determined also from the dependence of acoustoelectric response signal (ARS) on the external bias voltage (U _ac - V _G curves). By comparing the A-DLTS spectra, U _ac - V _G characteristics and some electrical measurements (G-V, I-V curves) of investigated MOS structures with no treatment with those treated with POA and/or PMA, the role of individual treatments was observed. The definite decrease of the interface states in the structures with the PMA treatment in comparison with the POA treatment was confirmed too.     

A theoretical study of the lowest 2 B 1, 2 A 1 and 2 B 2 electronic states in H2S+ and a comparison with corresponding states in related systems

Large scale configuration interaction calculations are employed to study the potential energy surfaces of the three lowest lying states in H₂S⁺. The calculated structural data for the X ² B ₁ and A ² A ₁ states are in very good agreement with previous evidence, but the ² B ₂ state is found to exhibit an [S---H₂]⁺ structure with large SH bond separations and a very small internuclear angle of 32°. Energies and wavefunctions are calculated for all three vibrational modes in the X ² B ₁ and A ² A ₁ excited states of H₂S⁺ and D₂S⁺ and the corresponding Franck-Condon factors for the A ² A ₁-X ² B ₁ band are determined; a maximum in absorption intensity is predicted to occur for v′₂ = 5–6 in H₂S⁺ and for v′₂ = 7–8 in D₂S⁺ for the A ² A ₁-X ² B ₁ transition, for which the calculated T ₀ energy of 18 620 cm^-1 is in excellent agreement with the experimentally determined value of 18 520 cm^-1. Extensive comparison is made with the other AH₂ systems PH₂, NH₂ and H₂O⁺ and trends with respect to geometry, vertical excitation and ionization energies as well as vibrational structure are pointed out; for this purpose the ² B ₂ potential energy curve of PH₂ has also been calculated.     

Thermodynamic perturbation theory for the (12-6-n) fluids

A perturbation method in which attractive forces are taken as perturbation of the repulsive (reference) forces is applied to calculate the thermodynamic properties of (12-6-n) fluids in terms of the properties of hard-sphere fluid. The numerical values of the thermodynamic properties (free energy per particle, compressibility and excess internal energy) for a range of temperature and density are given for (12-6-8) fluids. Further, two perturbation schemes are adopted to evaluate the total radial distribution function using the EXP version of the optimized cluster theory (OCT). The numerical results are reliable as reported at two states (T* = 1·036,ρ* = 0·65 andT* = 0·719ρ* = 0·85) for the (12-6-8) fluid and the Lennard-Jones (12-6) fluid as well.     

Accurate First-Principle Equation of State for the One-Component Plasma

Accurate “first-principle” expressions for the excess free energy F_ex and internal energy of U_ex of the classical one-component plasma (OCP) are obtained. We use the Hubbard-Schofield transformation that maps the OCP Hamiltonian onto the Ising-like Hamiltonian, with coefficients expressed in terms of equilibrium correlation functions of a reference system. We use the ideal gas as a reference system for which all the correlation functions are known. Explicit calculations are performed with the high-order terms in the Ising-like Hamiltonian omitted. For small values of the plasma parameter Γ the Debye-Huckel result for F_ex and U_ex is recovered. For Γ ? 1, these depend linearly on Γ in accordance with the Monte Carlo findings for the OCP. The MC data for the internal energy are reproduced fairly well by the expression for U_ex obtained.     

Microcanonical-ensemble computer simulation of the high-temperature expansion coefficients of the Helmholtz free energy of a square-well fluid

The microcanonical-ensemble computer simulation method (MCE) is used to evaluate the perturbation terms A_i of the Helmholtz free energy of a square-well (SW) fluid. The MCE method offers a very efficient and accurate procedure for the determination of perturbation terms of discrete-potential systems such as the SW fluid and surpass the standard NVT canonical ensemble Monte Carlo method, allowing the calculation of the first six expansion terms. Results are presented for the case of a SW potential with attractive ranges 1.1 ≤ λ ≤ 1.8. Using semi-empirical representation of the MCE values for A_i, we also discuss the accuracy in the determination of the phase diagram of this system.     

Semiempirical pseudopotential surfaces for chemical reactions: The (AB)+ X - dialkali halide systems

A generalization of the Roach-Child semiempirical pseudopotential calculation for K + NaCl to several analogous dialkali halide systems has been used to elucidate the chemical interactions governing the reaction dynamics. The Li + LiF ground-state potential surface, which exhibits a ～ 20 kcal/mole basin for isosceles Li₂F, is qualitatively similar to one obtained in a recent configurational interaction calculation. It is shown that regions of the Na₂Cl ground-state surface corresponding to Na₂ ⁺ interacting with Cl^- can be described in terms of an ion-pair Rittner potential model similar to that employed for the alkali halides. Chemical trends in the triangular complex well depths satisfactorily account for the experimentally observed transition between the collision complex mechanism (Rb + KCl) and the osculating complex model (Li + KBr) for the alkali-alkali halide exchange reactions at thermal energies. For collinear configurations with the alkalis on opposite ends, avoided intersections between the lowest two potential surfaces are characterized in terms of diabatic surfaces computed from truncated basis sets. Crossings of these surfaces account for the vibrational-electronic energy transfer between alkali atoms and vibrationally excited alkali halides. The ionic X ^- + A ₂ ⁺ potential surfaces are used to predict the product electronic excitation and partitioning of exoergicity in reactions of halogen atoms with alkali dimer molecules.     

A Statistical Mechanics Approach for a Rigidity Problem

We focus the problem of establishing when a statistical mechanics system is determined by its free energy. A lattice system, modelled by a directed and weighted graph (whose vertices are the spins and its adjacency matrix M will be given by the system transition rules), is considered. For a matrix A(q), depending on the system interactions, with entries which are in the ring Z[a ^q :a∈R ⁺] and such that A(0) equals the integral matrix M, the system free energy β _A (q) will be defined as the spectral radius of A(q). This kind of free energy will be related with that normally introduced in Statistical Mechanics as proportional to the logarithm of the partition function. Then we analyze under what conditions the following statement could be valid: if two systems have respectively matrices A,B and β _A = β _B then the matrices are equivalent in some sense. Issues of this nature receive the name of rigidity problems. Our scheme, for finite interactions, closely follows that developed, within a dynamical context, by Pollicott and Weiss but now emphasizing their statistical mechanics aspects and including a classification for Gibbs states associated to matrices A(q). Since this procedure is not applicable for infinite range interactions, we discuss a way to obtain also some rigidity results for long range potentials.     

The Discrete Spectrum in the Gaps of the Continuous One for Non-Signdefinite Perturbations with a Large Coupling Constant

Given two selfadjoint operators A and V=V ₊ -V _-, we study the motion of the eigenvalues of the operator A(t)=A-tV as t increases. Let α>0 and let λ be a regular point for A. We consider the quantities N ₊(λ,α), N _-(λ,α), N ₀(λ,α) defined as the number of the eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right or change the direction of their motion exactly at point λ, respectively, as t increases from 0 to α>0. An abstract theorem on the asymptotics for these quantities is presented. Applications to Schr?dinger operators and its generalizations are given. Received: 9 April 1997 / Accepted: 26 August 1997     

Production of charged pions, kaons and antikaons in relativistic C + C and C + Au collisions

Production cross-sections of charged pions, kaons and antikaons have been measured in C+C and C+Au collisions at beam energies of 1.0 and 1.8 AGeV for different polar emission angles. The kaon and antikaon energy spectra can be described by Boltzmann distributions whereas the pion spectra exhibit an additional enhancement at low energies. The pion multiplicity per participating nucleon M(π⁺)/<A _part> is a factor of about 3 smaller in C+Au than in C+C collisions at 1.0 AGeV whereas it differs only little for the C and the Au target at a beam energy of 1.8 AGeV. The K⁺ multiplicities per participating nucleon M(K⁺)/ <A _part> are independent of the target size at 1 AGeV and at 1.8 AGeV. The K^- multiplicity per participating nucleon M(K^-)/ <A _part> is reduced by a factor of about 2 in C+Au as compared to C+C collisions at 1.8 AGeV. This effect might be caused by the absorption of antikaons in the heavy target nucleus. Transport model calculations underestimate the K^-/K⁺ ratio for C+C collisions at 1.8 AGeV by a factor of about 4 if in-medium modifications of K-mesons are neglected. Received: 10 December 1999 / Accepted: 14 November 2000