Effective action and the quantum equation of motion

We carefully analyze the use of the effective action in dynamical problems, in particular the conditions under which the equation can be used as a quantum equation of motion and illustrate in detail the crucial relation between the asymptotic states involved in the definition of and the initial state of the system. Also, by considering the quantum-mechanical example of a double-well potential, where we can get exact results for the time evolution of the system, we show that an approximation to the effective potential in the quantum equation of motion that correctly describes the dynamical evolution of the system is obtained with the help of the wilsonian RG equation (already at the lowest order of the derivative expansion), while the commonly used one-loop effective potential fails to reproduce the exact results.Received: 1 April 2004, Published online: 2 July 2004     

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess δ. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ( ,) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, does not depend sensitively on the choice of the parameter γ in Skyrme interaction. Received: 5 May 2000 / Accepted: 16 January 2001     

Viscosity coefficients for nuclear fission

An expression for the energy dissipation during nuclear fission (or heavy-ion) processes has been derived in the first-order viscosity approximation. Irrotational flow and incompressibility have been assumed in order to calculate a quadratic form for the heat production, microscopically interpreted as particle-hole excitations. A modified algebraic parameterization of the nuclear shape has been found, which is more suitable than the usual ones to describe shapes close to spheroids (or spheres). Furthermore, it allows for analytical solutions of the fluid equations for one degree of freedom (and in special eases of the nuclear shapes, for all degrees).     

理想气体一维不定常流自模拟运动的基本微分方程

将一维不定常流自模拟函数推广到一般形式，结合量纲理论和流体力学基本运动方程，导出总能量为常数情况下的理想气体一维不定常流自模拟运动基本微分方程组.该理论模型表明，由流体速率u和自模拟面速率r·〖DD)]组成一个无量纲特性参数L，用L作自变量时理想气体一维不定常流自模拟运动的规律具有常微分方程的最简数学形式.该模型克服了点爆炸Taylor自模拟温度函数原点附近趋于无穷大的问题，具有重要意义. 关键词： 理想气体 自模拟运动 Taylor模型     

Effective equations for disordered one-dimensional systems

Using the method of supersymmetry, effective equations are derived for the one-particle Green's function of various one-dimensional disordered models. As an example, explicit expressions for the density of states and the localization length are derived for the two-band model of a one-dimensional semiconductor.     

Solution of Ornstein-Zernike equation for one-dimensional fluids

The application of Wiener-Hopf factorisation procedure as adopted by Baxter has been used to solve the one-dimensional Ornstein and Zernike (oz) equation for a fluid of interacting hard rods. Exact solution is obtained for the Kac potential in the van der Waals limit. We also obtain perturbative results which agree exactly with the lowest order calculations of Kac, Uhlenbeck and Hemmer.     

Cluster aspects of nuclear fission

Experimental fission data for nuclei in the mass regionA = 210 toA =258 are discussed from a unified point of view using cluster representations of nuclei. It is shown that these data can be described as resulting from a superposition of two different modes, one determined by energetically favoured cluster correlations, the other due to liquid-drop effects only. For all nuclei lighter than Fermium the above distinction coincides with that of symmetric and asymmetric fission. Contrary to that in Fermium-isotopes, both symmetric and asymmetric fission are associated with energetically favoured cluster correlations at the Fermi surface.     

Penetrability of nuclear fission barrier for muonic atoms

The nuclear fission penetrability for muonic atoms is calculated as a function of excitation energy. The results obtained for ^234,236,238U and ²⁴⁰Pu are compared with the fission of normal atoms.     

Intertwining technique for the one-dimensional stationary Dirac equation

The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac Hamiltonians, quadratic supersymmetry, closed extension of transformation operators, chains of transformations, and finally particular cases of pseudoscalar and scalar potentials. The method is widely illustrated by numerous examples.     

Search for heavy neutron clusters in nuclear fission

An experiment on search for heavy neutron clusters in fission of ²³⁵U nuclei has been carried out on a nuclear reactor. The method of searching for neutron clusters is based on irradiation of tellurium dioxide and lead oxide targets in reactor channels near the active zone and far from it. The method of γ-spectrometric analysis of irradiated targets was used to search for nuclei whose occurrence in the targets cannot be explained by other nuclear reactions, except for the reactions of original target nuclei with neutron clusters. The reactions of tellurium and lead nuclear fission by neutron clusters (nuclei) and direct capture of neutron clusters have been revealed.     

相对转动运动学方程的级数解

为解决相对转动体非线性运动微分方程的计算难题，构造了一种级数解耦方法，把微分方程转化为代数方程求解，得到了相对转动体运动方程的级数解.据此可以计算工程应用中稳态相对转动体的真实转速波动.同时该法可实现测控标定仪器的转动体匀速旋转时的不均匀性测量误差分离，也为大型复杂重型旋转轴系在线实时扭振监测提供了高效算法. 关键词： 相对转动 运动学方程 速度波动 级数解     

Separation of Coulomb fission from nuclear fission at medium energies

The cross sections for fission induced by one neutron transfer and by the electromagnetic field in the reaction 24.3 MeV/u ²³⁸U + ¹⁹⁷Au are calculated and compared to the experimental data. It turns up that the two calculated cross sections differ by five orders of magnitude at a distance of closest approach of 25 fm. It is shown that in the experiment in which one is able to select the events corresponding to a large distance of closest approach, a separation of Coulomb fission from nuclear fission events can be efficiently obtained.     

Interference effects in nuclear fission

Various interference effects governing the character of angular distributions of binary and ternary nuclear fission products and P-odd, P-even, and T-odd asymmetries in these angular distributions have been studied within the quantum theory of spontaneous and low-energy induced nuclear fission.     

Eigenvalues of the one-dimensional Smoluchowski equation

The eigenvalues and eigenfunctions of the Smoluchowski equation are investigated for the case of potentials withN deep wells. The small parameter =kT/V, which measures the ratio of the thermal energy to a typical well depth, is used in connection with the method of matched asymptotic expansion to obtained asymptotic approximations to all the eigenvalues and eigenfunctions. It is found that the eigensolutions fall into two classes, namely (i) the top-of-the-well and (ii) the bottom-of-the-well eigensolutions. The eigenvalues for both classes of solutions are integer multiples of the squqres of the frequencies at the top or bottom of the various wells. The eigenfunctions are, in general, localized to the top or bottom of the corresponding well. The very small eigenvalues require special consideration because the asymptotic analysis is incapable of distinguishing them from the zero eigenvalue with multiplicityN. Another approximation reveals that, in addition to the true zero eigenvalue, there areN-1 eigenvalues of order exp(–). The case of other possible multiple eigenvalues is also examined.     

Energy partition in nuclear fission

A scission point model (two spheroid model TSM) including semi-empirical, temperature-dependent shell correction energies for deformed fragments at scission is presented. It has been used to describe the mass-asymmetry-dependent partition of the total energy release on both fragments from spontaneous and induced fission. Characteristic trends of experimental fragment energy and neutron multiplicity data as function of incidence energy in the Th — Cf region of fissioning nuclei are well reproduced. Based on model applications, information on the energy dissipated during the descent from second saddle of fission barrier to scission point have been deduced.     

Angular correlations in nuclear fission

Interference effects in the angular distributions of products originating from binary and ternary nuclear fission induced by slow neutrons are reviewed.     

Quantum description of quaternary nuclear fission

The quantum theory of binary and ternary fission is generalized to the case of recently observed quaternary nuclear fission. Formulas for the amplitudes of partial fission widths and angular and energy distributions of quaternary fission products are derived with allowance for strong channel coupling. The nonevaporation mechanism for formation of light particles is used to explain the experimentally observed decrease in the probability for emission of light particles (α, α), (α, t), and (t, t) as compared with the product of emission probabilities for the same particles in ternary fission. It is concluded that in quaternary fission, as in ternary fission, light particles escape from the neck of the fissioning nucleus much earlier than scission of the nucleus into heavy fragments occurs.