基于微观IBM对电子-核散射及核电磁性质的研究(Ⅱ) ME理论方案

从一种微观作用玻色子模型（IBM）玻色子集体态子空间映射出费米子集体态子空间,通过假定玻色子算符形式以及使物理算符在两集体态子空间中对应归一化基矢间矩阵元相等,给出了从费米子单体算符导出玻色子单体算符的一种微观理论方法（ME方法）,文中以获取玻色子结构函数亦即确定玻色子形式核跃迁电荷／电流密度算符为例对此作出了详细介绍,利用微观IBM提供的波函数可在玻色子态空间中求出核跃迁电荷／电流密度,结合电子－核散射以及核电磁跃迁的形式理论,可建立研究电子－核散射各种形状因子与微分散射截面以及核约化跃迁几率,电磁多极矩,核态g因子等物理量的理论方案,在微观sdgIBM-1下利用该方案初步计算了146Nd核21^ 态到o 1^ 态的跃迁电荷密度以及约化跃迁几率,理论结果与实验值符合较好。     

间接测量天体物理S因子的特洛伊木马方法

天体环境下的核反应速率是各种关于天体核合成理论模型所需的输入量,对于了解天体核合成过程,以及宇宙的演化很重要。但是在天体温度下,核反应是在很低的能量上发生的。由于库仑位垒的作用,反应截面非常低,直接测量很难进行。通过测量合适的三体反应截面,特洛伊木马方法提供了一种提取感兴趣的低能两体反应截面的方法;而且,采用一系列近似可得到便于计算的理论公式。本文介绍特洛伊木马方法的原理及其在天体核反应中的应用。     

The statistical theory of nuclear reactions for strongly overlapping resonances as a theory of transport phenomena

We present a unified microscopic statistical theory of preequilibrium and equilibrium processes of the compound nucleus, valid for mass numbers A ? 40, light incident projectiles (A ′4), and for excitation energies a few MeV above neutron threshold or larger. The theory is based on a two-body random matrix model for the nuclear Hamiltonian, and on the idea of a chain of statistical doorway [hallway] states, populated from the entrance channel in the direction of increasing complexity through a series of two- body collisions. Averages of fluctuating cross sections, and of other observables, are evaluated by taking ensemble averages, and by a method of calculation which is tailored to the dissipative character of the reaction processes under study. An expansion in terms of a small parametry y is introduced. This parameter is defined as a function of the mean level spacing, the spreading width, the decay width, and the rate of change with energy of these quantities, for each group of statistical doorway states of given complexity. Average cross sections, channel correlations due to direct reactions and/or isolated doorway states (isobaric analogue resonances), the probability distribution function for the elements of the scattering matrix, the correlation length of Ericson fluctuations, and the mean nuclear lifetime are evaluated to leading order in y. We have checked in special cases that the expansion in powers of y is consistent with the consraints imposed by unitarity. Average fluctuating cross sections are given in terms of transmission coefficients and a probability matrix. The latter obeys a probability balance equation, which is shown to be closely related to the Pauli master equation. In case the system equilibraates before it undergoes decay, the average fluctuation cross sections factorize, and we recover the well-known Hauser-Feshbach formula with its various modifications. Next-order correction terms to this formula are also evaluated. The connection between our results, and direct reaction theories on the one hand, and preequilibrium and equilibrium models on the other, is established. These two latter types of models emerge as special cases of the general theory, each with its own well-defined domain of validity, while direct reaction theories specify some input parameters from which channel correlations can be calculated.     

Axioms for quantum theory

The first three of these axioms describe quantum theory and classical mechanics as statistical theories from the very beginning. With these, it can be shown in which sense a more general than the conventional measure theoretic probability theory is used in quantum theory. One gets this generalization defining transition probabilities on pairs of events (not sets of pairs) as a fundamental, not derived, concept. A comparison with standard theories of stochastic processes gives a very general formulation of the non existence of quantum theories with hidden variables. The Cartesian product of probability spaces can be given a natural algebraic structure, the structure of an orthocomplemented, orthomodular, quasi-modular, not modular, not distributive lattice, which can be compared with the quantum logic (lattice of all closed subspaces of an infinite dimensional Hubert space). It is shown how our given system of axioms suggests generalized quantum theories, especially Schrödinger equations, for phase space amplitudes.     

Logics for quantum mechanics

The two concepts of probability used in physics are analyzed from the formal and the material points of view. The standard theory corresponds toprob ₁ (probability of the coexistence of two properties). A general logicomathematical theory ofprob ₂ (probability of transition between states) is presented in axiomatic form. The underlying state algebra is neither Boolean nor Birkhoff-von Neumann but partial Boolean. In the Boolean subalgebras,prob ₁ theory holds. The theory presented contains the logicomathematical foundations of quantum mechanics and, as degenerate cases, the theories of stochastic games and of Markov chains.     

Detailed symmetry selection rules for reactive collisions

A simple general method for obtaining selection rules for the ro-vibronic states of reactant and product molecules connected in a reactive collision is discussed. Neglecting only the coupling with nuclear spin, rather stringent restrictions are found to occur in systems involving three and more identical nuclei. Several radical and ion molecule reactions of current interest are used to illustrate this finding. Even more restrictive selection rules are found when assuming weak coupling (‘ incomplete exchange of identical nuclei ’) in the intermediate reaction complex. These include the well-known selection rules for inelastic collisions of molecules with several identical nuclei, but less trivial examples with chemical reaction are also presented. The symmetry corrections and nuclear spin statistics in statistical theories of scattering (including the prior distributions for the information-theoretic approach) are derived. Further applications are discussed briefly.     

From stars to nuclei

We recall the basic physical principles governing the evolution of stars with some emphasis on the role played by the nuclear reactions. We argue that in general it is not possible from observations of stars to deduce constraints on the nuclear reaction rates. This is the reason why precise measurements of nuclear reaction rates are a necessity in order to make progresses in stellar physics, nucleosynthesis and chemical evolution of galaxies. There are however some stars which provides useful constraints on nuclear processes. The Wolf-Rayet stars of the WN type present at their surface CNO equilibrium patterns. There is also the particular case of the abundance of ²²Ne at the surface of WC stars. The abundance of this element is a measure of the initial CNO content. Very interestingly, recent determinations of its abundance at the surface of WC stars tend to confirm that massive stars in the solar neighborhood have initial metallicities in agreement with the Asplund et al. [1] solar abundances.     

The Fundamental Equations of Change in Statistical Ensembles and Biological Populations

A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline.     

Some problems in nuclear reaction calculations

Convergence problems arise in nuclear reaction theories when approximate wave functions are used to describe the internal motion of composite particles involved in the reaction. Implications on the results of a reaction calculation are discussed and models with unique solutions are defined. Some tentative criteria are given as to which model might have solutions similar to the ones obtained with exact channel functions. A least-squares method for linear parameter variation which does not show spurious singularities is also discussed.     

On the role of the coriolis and quasiparticle-phonon interactions in describingE1 transition probabilities in odd Eu and Tb isotopes

Study of the nuclear second moments, important inputs to pre-equilibrium reaction theories, is extended to residual interactions of finite range. The interactions are assumed to have general spin and isospin dependence. The second moments are found to be always positive definite for commonly used values of the interaction parameters. They seem to support the strong coupling limit of the pre-equilibrium reaction theory by Nishioka et al. [1], which would imply the modification of the phenomenological model used in analyzing experimental data. As an application of the second moments, it is also investigated how the nuclear level densities change with the parameter values of the residual interaction. The results show the important role of the residual interaction especially in the low energy region, which may greatly improve the agreement with experimental data at thermal neutron resonances.     

Reaction dynamics of synthesis of superheavy elements

Based on the theory of the compound nucleus reaction, a brief review is given on the special aspects of the reaction dynamics in the synthesis of the superheavy elements (SHE), where the fusion probability is the most unknown factor. A new viewpoint of the fusion reaction is proposed that it consists of two processes; the first process up to the contact of two nuclei of the incident channel and the second one of a dynamical evolution to the spherical compound nucleus from the contact configuration. The fusion probability is, thus, given as a product of a contact probability and a formation probability. Analytic studies of the latter probability are discussed in the one-dimensional model, where a simple expression is given to the so-called extra-push energy in terms of the reduced friction, the curvature parameter of the conditional saddle point and the nuclear temperature. Preliminary results of numerical analyses of the contact probability are given, using the surface friction model (SFM). Remarks are given on the present status of our knowledge and for future developments. Received: 1 May 2001 / Accepted: 4 December 2001     

Nuclear spin relaxation in paramagnetic systems (S>/=1) under fast rotation conditions

A new theoretical model for nuclear spin relaxation in paramagnetic systems in solution has been developed. Fast rotational motion is included in the model, both as a source of modulation of the static zero-field splitting, which provides a mechanism for electron spin relaxation, and as an origin of the stochastic variation of the electron spin-nuclear spin dipole-dipole interaction leading to nuclear spin relaxation. At the limit of low magnetic field, the model is essentially identical to the earlier formulations from our laboratory, but new closed-form expressions are given for the inner- and outer-sphere relaxation at the high-field limit. Numerical comparisons with a general theory are reported for the inner-sphere case. In addition, some nuclear magnetic relaxation dispersion (NMRD) profiles from the literature are considered for systems where experiments have been done with both low-molecular weight paramagnetic complexes and their adducts with proteins. Previously developed theories are used to interpret data for the slowly rotating protein adducts, and good fits of the fast-rotating counterparts are obtained by further adjustment of one or two additional parameters.     

Muon-pair creation by two x-ray laser photons in the field of an atomic nucleus

The generation of muon-antimuon pairs is calculated in the collision of an ultrarelativistic bare ion with an intense x-ray laser beam. The reaction proceeds nonlinearly via absorption of two laser photons. By systematic study throughout the nuclear chart, we show that the interplay between the nuclear charge and size, along with the possibility of nuclear excitation leads to saturation of the total production rates for high-Z ions, in contrast to the usual Z2 scaling for pointlike projectiles. The process is experimentally accessible by combining present-day ion accelerators with near-future laser sources and in principle allows for the measurement of nuclear form factors.     

Relativistic nonperturbative above-threshold phenomena in strong laser fields

Relativistic features of various nonperturbative above-threshold phenomena in strong laser fields are discussed and compared. This includes above-threshold ionization of multiply charged ions as well as pair production in an ultrastrong laser wave, superimposed with either a nuclear Coulomb field or another counterpropagating laser wave. For the probability of above-threshold pair production, a new scaling relation is given. Particular attention is paid to similarities among these processes, regarding the energy and angular spectra of the particles as well as the total reaction rates.     

Inelastic scattering of electrons andE2 transition in6Li

A simple nucleon-nucleon correlation function has been included in the independent-particle shell-model (IPSM) wave functions of⁶Li. The reduced transition probability and the nuclear form factor of⁶Li as obtained from the inelastic scattering of electrons have been calculated using the correlated as well as the uncorrelated wave functions of the ground and the first excited states. The correlated transition probability and the form factor are considerably improved over the uncorrelated ones. The correlated form factor is more consistent with the experimental data than the uncorrelated one.     

Theoretical analysis of the formation of η mesic nuclei in γ + A → N + ηA′ reactions

A model that describes the formation of η mesic nuclei in the γ+A → N+ηA′ reactions is formulated on the basis of the quasifree meson photoproduction on nuclei and the concept of a meson-nucleus optical potential. The amplitude of this reaction involving more than four nucleons is obtained in the general form within the nuclear shell model featuring intermediate coupling. The dependences of the cross sections for these reactions on the excitation levels of η mesic nuclei, on the discrete excitation levels of the nucleonic cores of these nuclei, on the type of emitted nucleon, and on the final-state interaction are analyzed for the incident-photon energies from the reaction threshold to 1 GeV.     

低能核反应理论的研究与应用

介绍有关低能核反应理论的研究与应用工作．The work for research and application of low energy nuclear reaction theories is introduced.     

Solid state effects on tunneling probability for d+d nuclear fusion at room temperature

Abstract

The tunneling probability for d+d nuclear fusion reaction is calculated, incorporating the screening on the Coulomb potential and effective electron mass in solids. The possibility of cold (room temperature) nuclear fusion is discussed.     

Wave function renormalization constants and one-particle form factors in Dl(1) Toda field theories

We apply the method of angular quantization to the calculation of the wave function renormalization constants in D₁⁽¹⁾ affine Toda quantum field theories. A general formula for the wave function renormalization constants in ADE Toda field theories is proposed. We also calculate all one-particle form factors and some of the two-particle form factors of an exponential field.     

THE GENERAL FORM OF THE DIVERGENT PART OF 1PI VERTEX GENERATING FUNCTIONAL IN QUANTUM GAUGE THEORIES

rn this paper, the Slavnov equations are solved presence of Niggs fields, where the gauge group is a general compact semi-simple Lie group. A general form of the dins gent paxt of 1PI vertex generating functional is ottained, which provides a fairly general theoretical basis to the proof of renormalizability of quantum gauge theories.