多维Kramers公式的研究

本文研究了鞍点附近多维的位能曲面及鞍点所在位置;并用Werner Wheeler及无旋液体等两种方法计算了多维的质量系数与粘滞系数,然后用多维Kramers公式计算了裂变速率.发现裂变速率随着维数的增加而适当增大.不同的形变参量以及不同的计算质量和粘滞系数方法对计算核裂变速率影响不大.从结果看,采用三维计算裂变几率已足够准确.     

用福克-普朗克方程严格解裂变速率问题

本文应用数值方法严格求解二维福克-普朗克(Fokker-Planck)方程,研究在鞍点上的速度分布、坐标和速度的二次矩以及核裂变速率随时间的演变.在相当大的粘滞性范围内,研究核裂变速率与粘滞性的依赖关系,观察到在一定粘滞性下出现裂变速率极大值的现象.对计算的各种结果进行了解释。     

布朗粒子越过位垒的逃逸速率

本文用Reichl解Smoluchowski方程的方法, 计算了布朗粒子越过位垒的逃逸速率. 并模拟了复合核的一维裂变位能曲线, 计算了核裂变速率随时间变化的规律, 并与其它方法计算的结果作了比较.     

84.0MeV16O轰击238U核的裂变碎片角关联的测量

使用两块大面积位置灵敏双栅雪崩计数器,测量了84.0MeV¹⁶O轰击²³⁸U核的裂变碎片角关联及角分布.用裂变碎片折叠角技术区分了熔合裂变反应中的复合核裂变和转移裂变的两种成份.在总裂变截面中,转移裂变的贡献约为10%.由于转移裂变碎片角分布的各向异性较小,扣除转移裂变贡献后,纯复合核裂变碎片各向异性提高5%左右.裂变碎片异性异常不可能仅仅来源于转移裂变的贡献.     

从布朗运动观点研究核裂变的速率问题

本文用布朗运动的观点研究了核裂变的速率问题。以简便的求速率本征值方法解福克-普朗克方程。将粘滞张量、惯量系数、温度作为变形坐标的函数,研究了它们对裂变速率的影响。     

垒下16O+232Th裂变碎片角关联模拟

使用Monte-Carlo模拟计算了垒下¹⁶O+²³²Th系统转移裂变和复合核裂变碎片角分布及角关联.转移过程、熔合过程和裂变过程分别用半经典模型、耦合道模型及鞍点过渡态统计模型进行模拟.考虑了各物理量分布产生的运动学效应及裂前中子发射和裂后碎片粒子蒸发对碎片角分布及角关联的影响.模拟结果和实验测量的分布相一致.使用折叠角技术借助Monte-Carlo模拟区分转移裂变和复合核裂变是可能的.考虑了转移裂变和裂前中子发射的影响,复合核裂变碎片角分布各向异性异常仍然存在.     

核裂变——未尽的探索

核裂变的发现深刻地影响了人类社会。核裂变的研究还在不断深入,一方面核裂变有新的应用需求,另一方面核裂变是一个复杂的量子多体动力学过程。近年来,核裂变理论和实验研究有很大进展,人们对核裂变几率、裂变产物和裂变机制都获得了新的认识,这有助于澄清一些唯象模型的经验假设。此外,机器学习的应用为发掘利用不精确不完整的核数据提供了可能。期待未来更精确更自洽的核裂变理论可以更好地支撑应用创新。     

核裂变中的Overshooting现象与中子多重性

本文采用扩散模型来讨论核裂变中的瞬态过程.研究结果表明在Kramers区域(T/E_f<1)和高温区域((T/E_f>1)瞬态过程的行为差别很大.高温区域瞬态过程中的Overshooting现象会使裂变几率增大,从而使通常认为的裂变速率的瞬态行为引起中子多重性增强效应在这一区域减弱甚至消失.     

微观描述热核裂变寿命（英文）

有关热核裂变的研究与反应堆中的诱发裂变,天体环境中的裂变,以及超重元素的合成等密切相关。热核裂变的研究通常是基于Bohr-Wheeler 的统计裂变理论。而统计模型的研究十分依赖唯像的能级密度和位能面。因此,提出基于微观的有限温度的能量密度泛函理论计算热核的裂变寿命。可以微观自洽地计算出温度相关的裂变位垒高度,曲率,集体质量参数。基于虚自由能法,从低温到高温的裂变寿命可以由一个统一的框架给出。展示了在裂变研究中温度相关裂变位垒的重要性,并讨论了微观描述热核裂变的前景。The studies of thermal fission rates are relevant to novel reactors, astrophysical environments, and survival probabilities of compound superheavy nuclei. This has been conventionally studied by the Bohr-Wheeler statistical model that depends on phenomenological level densities and fission barriers. In this context, we propose to study the thermal fission rates based on microscopic temperature dependent nuclear energy density functional theory. The microscopic temperature dependent fission barrier heights and curvatures, and collective mass parameters can be self-consistently obtained. The fission lifetimes from low to high temperatures can be given by the imaginary free energy method in a consistent framework. Microscopic temperature dependent fission barriers play an essential role in fission studies.     

核裂变中的Overshooting现象与中子多重性

本文采用扩散模型来讨论核裂变中的瞬态过程。研究结果表明在Kramers区域(T/E_f<1)和高温区域(T/E_f>1)瞬态过程的行为差别很大。高温区域瞬态过程中的Overshooting现象会使裂变几率增大,从而使通常认为的裂变速率的瞬态行为引起中子多重性增强效应在这一区域减弱甚至消失。     

Kramers rate formula with coordinate-dependent mass

We study in this paper the classical stationary fission rate including a coordinate-dependent mass and a realistic potential. The results show that our numerical rate formula is a good approximation to the realistic Langevin simulation even if the nuclear temperature is not smaller than the fission barrier.     

Prediction of ion channel transport from Grote—Hynes and Kramers theories

Generalized Langevin equation based Grote—Hynes (GH) theory and Langevin equation based Kramers theory are used to calculate the transmission coefficient for K⁺ diffusion through a model of the biological potassium ion channel IRK1, which contains a high potential barrier in the selectivity filter. The ion friction kernel is determined from a molecular dynamics (MD) simulation of the force on a stationary ion at the barrier top. The GH and Kramers estimates of the transmission coefficient are compared with those obtained from MD simulations of ion diffusion at the barrier top of the IRK1 channel. It is found that the GH estimate agrees with the value determined by rigorous MD, but the Kramers estimate is about 40% too small. The success or failure of GH and Kramers theories for various other systems is discussed and compared with these results.     

Inverse Kramers formula and fusion dynamics of heavy ions

Fusion probability of colliding heavy ions is evaluated by exactly solving a Langevin equation with a parabolic potential barrier. The model, which accommodates dissipation in the approaching phase, leads to an inverse Kramers formula and an expression of the extra-push energy. In the very specific case of an overdamped regime, an Arrhenius-type formula is obtained.Received: 27 January 2003, Published online: 18 November 2003PACS: 02.50.Ey Stochastic processes - 05.40.Jc Brownian motion - 25.70.Jj Fusion and fusion-fission reactions     

Precision of approximate kramers formulas for the fission rate: Canonical and microcanonical ensembles

The precision of the Kramers formulas, which are frequently used to calculate the rate of fission of excited nuclei, is studied quantitatively bymeans of a numerical simulation. The deformation dependence of the level-density parameter is taken here into account in contrast to what was done in previous studies on this subject. It turns out that, as the excitation energy becomes lower, the error in the integral Kramers formula decreases monotonically, reaching 2% (precision of dynamical simulation) for a potential-barrier height three to four times greater than the temperature. The approximate Kramers formula obtained from the aforementioned integral formula is in substantially poorer agreement with the results of the dynamical simulation. In the same region of the controlling parameter, its typical error may change sign and reaches 5 to 15%.     

Fission dynamics of hot nuclei

Experimental evidence accumulated during the last two decades indicates that the fission of excited heavy nuclei involves a dissipative dynamical process. We shall briefly review the relevant dynamical model, namely the Langevin equations for fission. Statistical model predictions using the Kramers’ fission width will also be discussed.     

Rate of excited-nucleus fission within a multidimensional stochastic approach

A stochastic approach to describing the dynamics of the nuclear-fission process is applied to study the effect of the number of dimensions on the fission rate within the dynamical model used. The time dependence of the fission rate is calculated on the basis of a multidimensional Langevin equation without taking into account particle evaporation. The one-, two-, and three-dimensional cases are considered for the example of the “c, h, α” parametrization of nuclear-surface shapes. The calculations are performed for a large number of compound nuclei whose parameter Z ²/A falls within the range 20 ≤ Z ²/A ≤ 40. The stationary level of the fission rate is found to increase considerably upon going over from the one- to the three-dimensional case. This increase is especially pronounced for light fissile nuclei in the vicinity of the Businaro-Gallone point. Also, the stationary fission-rate level obtained from our dynamical simulation is compared with its counterpart calculated by the Kramers formula generalized to the multidimensional case.     

Stochastic resonance in multidimensional periodic potential

We study the mobility and diffusion of an underdamped Brownian particle moving in a two-dimensional (2D) periodic potential which subjects to a thermal white noise and a weak external driving force. Both the signal power amplification and the diffusion rate are calculated via Langevin simulations. It is shown that the stochastic resonance (SR) can be observed in the two dimension, namely, the output quantities as functions of the temperature show a nonmonotonic behavior, however, the SR cannot be obtained in the one dimension (1D). In the 2D potential, the height of dynamical barrier is decreased effectively along the direction of transport if the curvature of the potential at the barrier is less than that at the local minima. This leads to the SR condition being obeyed, i.e., the Kramers frequency over the barrier roughly matches the frequency of external signal.     

Deformation parameter changes in fission mass yields within the systematic statistical scission-point model

The fission fragment mass-yields are evaluated for pre-actinide and actinide isotopes using a systematic statistical scission point model. The total potential energy of the fissioning systems at the scission point is presented in approximate relations as functions of mass numbers,deformation parameters and the temperature of complementary fission fragments. The collective temperature, Tcoll, and the temperature of fission fragments, Ti, are separated and the effect of collective temperature on mass yields results is investigated. The fragment temperature has been calculated with the generalized superfluid model. The sum of deformation parameters of complementary fission fragments has been obtained by fitting the calculated results with the experimental data. To investigate the transitions between symmetric and asymmetric modes mass yields for pre-actinide and heavy actinides are calculated with this model. The transition from asymmetric to symmetric fission is well reproduced using this systematic statistical scission point model. The calculated results are in good agreement with the experimental data with Tcoll= 2 Me V at intermediate excitation energy and with T_(coll)= 1MeV for spontaneous fission.Despite the Langevin model, in the scission point model, a constraint on the deformation parameters of fission fragments has little effect on the results of the mass yield.     

Application of the theory of open quantum systems to nuclear physics problems

Quantum diffusion equations with transport coefficients explicitly depending on time are derived from the generalized non-Markovian Langevin equations. The asymptotic behavior of the friction and diffusion coefficients is investigated in the case of the FC and RWA couplings between the collective and internal subsystems. An asymptotic expression is obtained for the propagator of the density matrix of the open quantum system with the general quadratic Hamiltonian, linearly coupled (in coordinate and momentum) to internal degrees of freedom. The effect of different sets of transport coefficients on the decoherence and decay rate of the metastable state is investigated using the master equation for the reduced density matrix of open quantum systems. The developed approach is used to study the capture of the projectile nucleus by the target nucleus at energies near the Coulomb barrier. Capture cross sections in asymmetric reactions are well described with allowance for the calculated capture probabilities. Particular cases where dissipation favors penetration through the potential barrier are found. The generalized Kramers formula for the quasi-stationary decay rate of the quantum metastable systems is analytically derived.     

Temperature dependent fission fragment distribution in the Langevin equation

The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.