Pre-formation Probability of 5He Cluster in Pre-equilibrium Mechanism

The possibility of 5He cluster emission has been affirmed theoretically. In order to describe the emission probability of 5He cluster, the pre-formation probability of 5He cluster in pre-equilibrium emission process is needed to be established. In terms of Iwamoto-Harada model, the theoretical formula of pre-formation probability of 5He cluster including 1p shell nucleon in pre-equilibrium mechanism has been established and calculated. In the case of low incident energies, the configuration of [1, m] for 5He cluster is the dominant part in the nuclear reaction. The calculated results indicate that pre-formation probability of configuration [1, m] for the unstable 5He cluster is much smaller than those of d, t, 3He, and 4He, i.e. the light stable composite particles, which are consisted of only 1s shell nucleons. However, it is propitious to the emission of 5He from the point of view on threshold energies, since the binding energies of 5He are generally lower than that of 3He in compound nucleus. The corresponding model formula has been given in this paper for described pre-formation probability of 5He cluster in pre-equilibrium mechanism.     

Probability Collectives for Unstable Particles

Unstable particles, together with their stable decay products, constitute probability collectives that are defined as Hilbert spaces with dimension higher than one, nondecomposable in a particle basis. Their structure is considered in the framework of Birkhoff-von Neumann's Hilbert subspace lattices. Bases with particle states are related to bases with a diagonal scalar product by a Hilbert-bein involving the characteristic decay parameters (in some analogy to the n-bein structures of metrical manifolds). Probability predictions as expectation values, involving unstable particles, have to take into account all members of the higher dimensional collective. For example, the unitarity structure of the S-matrix for an unstable particle collective can be established by a transformation with its Hilbert-bein.     

Analysis of Neutron Double-Differential Cross Sections for n + 12C Reaction Below 30 MeV

Based on the light nucleus reaction model (Nucl. Sci. Eng. l33 (1999) 218), four aspects (neutron incident energy region, reaction channel analysis, the renewed level schemes and the optical model parameters) of n 12 C reaction are improved to calculate total outgoing neutron double-differential cross sections with modified LUNF code below 30 MeV. The calculated results agree fairly well with the experimental data at En = 14.1 MeV and 18 MeV. The analysis shows that the pre-equilibrium mechanism, which is exactly considered the conservation of energy, momentum and parity, dominates the whole reaction process. The contribution of the neutron emission from 5He to total energyangular spectra is also considered properly. This modified LUNF code will be a useful tool to set up the file of neutron double-differential cross sections below 30 MeV in the neutron evaluation nuclear data library.     

Determination of γ Factor of Kalbach-Mann Systematics for Energy Balance

Kalbach Mann systematics is a very useful formula to discrete the double-differential cross sections of emitted particles. However, the energy balance by using this systematics is still a task to be studied. In the form of Legendre polynomial expansion the energy balance has been proved analytically. In terms of this approach, the formula to determine the prc-equilibrium fraction r factor of Kalbach Mann systematics has been obtained for keeping energy balance strictly. This formula could be straightforwardly applied for describing the double-differential cross sections of all projectile types in the eontinuum spectrum emissions. It indicates that Legendre expansion coefficient with l= 1 is the key term in the energy balance.     

微粒形体特征概率分布函数的光散射频谱分析法

针对微粒(包括生物微粒)光散射测量中微粒形体对测量结果的影响以及形体分布不能实时测量的问题,本文根据光散射测量原理,从微粒群的统计性出发,对散射脉冲的脉宽、脉峰分布及其与微粒大小和形体分布物理动态特征的相互关系进行了系统的分析,得到了微粒形体、微粒大小分布与其散射谱分布的特征关系,提出了等值概率面积确定法则,并据此建立了一种实时由散射谱一体分析获取微粒形体特征分布的方法,得到了较好的实验验证,由此可有效地修正因微粒形体变化而对测量精度的影响,从而为粒度分析仪以及以光散射原理为测量理论的流式细胞仪技术的提升提供了有力的基础。     

Determination of r Factor of Kalbach-Mann Systematics for Energy Balance

Kalbach-Mann systematics is a very useful formula to discrete the double-differential cross sections of emitted particles. However, the energy balance by using this systematics is still a task to be studied. In the form of Legendre polynomial expansion the energy balance has been proved analytically. In terms of this approach, the formula to determine the pre-equilibrium fraction r factor of Kalbach-Mann systematics has been obtained for keeping energy balance strictly. This formula could be straightforwardly applied for describing the double-differential cross sections of all projectile types in the continuum spectrum emissions. It indicates that Legendre expansion coefficient with l=1 is the key term in the energy balance.     

Study of Survival Probability of Super Heavy Nuclei

The survival probability of super heavy nuclei produced in cold fusion reactions is studied by using thestandard Fermi gas level density formula and analyzed with fission and neutron evaporation characteristics predicted indifferent theoretical models. The level density formula used in this letter suppresses the ratio of neutron emission widthalso investigated.     

Analysis of Neutron Double-Differential Cross Sections for n ＋ ^12 C Reaction Below 30 MeV

Based on the light nucleus reaction model （Nucl. Sci. Eng. 133 （1999） 218）, four aspects （neutron incident energy region, reaction channel analysis, the renewed level schemes and the optical model parameters） of n＋ ^12 C reaction are improved to calculate total outgoing neutron double-dilferential cross sections with modified LUNF code below 30 MeV. The calculated results agree fairly well with the experimental data at En = 14.1 MeV and 18 MeV. The analysis shows that the pre-equilibrium mechanism, which is exactly considered the conservation of energy, momentum and parity, dominates the whole reaction process. The contribution of the neutron emission from 5He to total energy- angular spectra is also considered properly. This modified LUNF code will be a useful tool to set up the file of neutron double-differential crass sections below 30 Me V in the neutron evaluation nuclear data library.     

Study of Survival Probability of Super Heavy Nuclei

The survival probability of super heavy nuclei produced in cold fusion reactions is studied by using the standard Fermi gas level density formula and analyzed with fission and neutron evaporation characteristics predicted in different theoretical models. The level density formula used in this letter suppresses the ratio of neutron emission width to fission width, Гn/Гf. The dependence of Гn/Гf on the saddle point level density parameter and excitation energy is also investigated.     

超重复合核的存活概率

考虑角动量相关性的情况下计算了超重核259Db的裂变位垒Bf.计算了258Rf,259Db,266Hs和267Mt 4个超重核单中子蒸发的存活概率Wsur及其随角动量分波的变化关系.给出了中子蒸发宽度、裂变宽度和超重核蒸发一个中子的概率对激发能与角动量分波的依赖关系. Considering the dependence on angular momentum， the fission barriers of super heavy nuclei 259Db have been calculated. The survival probability for 258Rf， 259Db，266Hs，267Mt compound and its relation with angular momentum have been estimated. The neutron emission width， the fission width and the realization probability for one neutron emission and their relation with excitation energy and angular momentum are also presented.     

^5He Emission in Neutron-Induced ^10B Reactions

In n ＋^10B reactions, ^5He cluster emission has been discussed with the updated level scheme and the new optical model parameters. In this paper the reaction channels related to ^5He emission are listed in detail. By using the new reaction model for light nuclei, the double-differential cross sections of total outgoing neutrons for n ＋ ^10 B reactions at En= 14.2 MeV have been calculated, and the results agree fairly well with the measurements. Particularly, in the energy-angular spectra the contribution from the 5He-emission to the total outgoing neutron double-differential cross sections has also been analyzed, and the partial energy-angular spectra of 60° at En= 14.2 MeV have been given. The calculated results indicate that once the 5He emission is taken into account, the fitting with the double-differential measurements of total outgoing neutrons at the low energy region could be improved. Therefore, to consider the ^5He emission properly in the reaction processes of light nuclei is necessary.     

Model Calculation of n 6Li Reactions Below 20 MeV

Based on the unified Hauser-Feshbach and exciton model for light nuclei, the calculations of reaction cross sections and the double-differential cross sections for n 6Li are performed. Since all of the first-particle emissions are from the compound nucleus to the discrete levels, the angular momentum coupling effect in pre-equilibrium mechanism must be taken into account. The fitting of the measured data indicates that the three-body break-up process needs to be involved, and the pre-equilibrium reaction mechanism dominates the reaction processes. In light nucleus reactions the recoil effect must be taken into account.``     

Effect of pre-equilibrium emission on probing postsaddle nuclear dissipation with neutrons

Using the stochastic Langevin model coupled with a statistical decay model, we study the influence of pre-equilibrium(PE) emission on probing postsaddle friction(β) with neutrons. A postsaddle friction value of(14-16.5) ×10~(21)s~(-1) and(11-13) ×10~(21)s~(-1) is obtained from comparing calculated and measured prescission neutron multiplicities of heavy fissioning systems248 Fm and256Fm in the absence and presence of the deformation factor.Moreover, it is found that a larger β is required to fit multiplicity data after the PE effect is accounted for, and that the effect becomes stronger when more energy is removed by PE particles. Our findings suggest that, to more accurately determine the postsaddle friction strength through the measurement of prescission neutrons, in addition to incorporating the contribution of PE evaporation source into the experimental multi-source analysis for particle energy spectra in coincidence with fission fragments, on the theoretical side, it is very important to make a precise evaluation of the energy that PE emission carries away from excited compound systems produced in heavy-ion fusion reactions.     

Model Calculation of n+6Li Reactions Below 20 MeV

Based on the unified Hauser-Feshbach and exciton model for light nuclei, the calculations of reaction cross sections and the double-differential cross sections for n+⁶Li are performed. Since all of the first-particle emissions are from the compound nucleus to the discrete levels, the angular momentum coupling effect in pre-equilibrium mechanism must be taken into account. The fitting of the measured data indicates that the three-body break-up process needs to be involved, and the pre-equilibrium reaction mechanism dominates the reaction processes. In light nucleus reactions the recoil effect must be taken into account.     

Probability Density and Statistical Properties for a Three-State Markovian Noise and Escape of Particles for a System Driven by This Noise

A three-state Markovian noise is investigated. Its probability density and statistical properties are obtained. Escape of particles for a system with potential barrier only driven by this noise is investigated. It is shown that, in some circumstances, this noise can make the particles escape over the potential barrier; but in other circumstances, it cannot. Resonant activation phenomenon appears for the system considered by us.     

Probability and Joint Probability Distributions for Systems Driven by Correlated Colored Noises

This paper deals with systems driven by correlated colored noises. The evolution equations for both the single and joint probability distribution functions are derived. It is shown that both the stationary and dynamical properties of the systems are affected by correlated colored noises. These results are obtained by means of the systematic use of the ordered cumulant-expansion technique.     

Quantum Mechanics and Imprecise Probability

An extension of the Born rule, the quantum typicality rule, has recently been proposed [B. Galvan in Found. Phys. 37:1540–1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into non-overlapping wave packets, the particle stays approximately inside the support of one of the wave packets, without jumping to the others. In this paper a formal definition of this rule is given in terms of imprecise probability. An imprecise probability space is a measurable space endowed with a set of probability measures ℘. The quantum formalism and the quantum typicality rule allow us to define a set of probabilities on (X ^T ,ℱ), where X is the configuration space of a quantum system, T is a time interval and ℱ is the σ-algebra generated by the cylinder sets. Thus, it is proposed that a quantum system can be represented as the imprecise stochastic process , which is a canonical stochastic process in which the single probability measure is replaced by a set of measures. It is argued that this mathematical model, when used to represent macroscopic systems, has sufficient predictive power to explain both the results of the statistical experiments and the quasi-classical structure of the macroscopic evolution.     

重离子反应中核子前平衡发射的同位旋效应

考虑了同位旋相关的对称能、库仑能及核子—核子碰撞截面，对反应４０Ａｒ＋４０Ａｒ（Ｅ＝２５ＭｅＶ／ｕ，ｂ＝０）进行了量子分子动力学模拟，讨论了同位旋效应对核子发射的影响．观察到前平衡发射的中子和质子的比率大于反应系统的中质比，发现对称能有利于中子的发射而阻碍质子的发射，而同位旋相关的核子—核子碰撞截面对中子和质子的发射都有利，但似乎更有利于质子的发射。