Partition function for an electron in a random potential

We compute the average partition function for an electron moving in a Gaussian random potential. A path integral formulation is used, with a trial action like that in Feynman's polaron theory. We compute the variational bound as well as the first correction in a systematic cumulant expansion. The results are checked against exact formulas for the onedimensional white noise problem. The density of states in the low-energy tail has the correct exponential energy dependence, and energy-dependent prefactor to within a few percent. In addition, the partition function goes over smoothly to the perturbation theory result at high temperatures.Work supported by the National Science Foundation.     

Prompt neutron multiplicity distribution for 235U(n,f) at incident energies up to 20 MeV

For the n+<'235>U fission reaction, the total excitation energy partition of the fission fragments, the average neutron kinetic energy <ε>(A) and the total average energies E<,γ>(A) removed by γ rays as a function of fission fragment mass are given at incident energies up to 20 MeV. The prompt neutron multiplicity as a function of the fragment mass, ν(A), for neutron-induced fission of <'235>U at different incident neutron energies is calculated. The calculated results are checked with the total average prompt neutron multiplicities ν and compared with the experimental and evaluated data. Some prompt neutron and γ emission mechanisms are discussed.     

角动量对基于裂变截面探测核耗散的影响（英文）

核耗散降低了裂变截面值(σdrop f)。基于Langevin模型,研究了角动量对σdrop f作为鞍点前摩擦强度β函数的影响。发现在低自旋,摩擦对σdrop1f的影响显著增强。通过考察系统95Bi,201Bi和207Bi的σdrop f随β的演化,发现摩擦效应随着Bi核中质比(N/Z)的增加而变大。这些结果建议,为了更好地在实验上用裂变截面探测β,应产生那些具有低自旋、高N/Z的热核系统。     

The Periodicity of Persistent Currents in Mesoscopic Rings

In a tight-binding model, we find that the equation of the Green's function in a onedimensional mesoscopic ring threaded by a Aharonov-Bohm (AB) flux can be exactly solved. From the poles of the Green's function, the eigenvalues are obtained and are periodic in the AB flux with period h/e. However, the periodicity of the persistent currents is determined by the number of electrons in the ring.     

Effects of N/Z on survival probability of heavy nuclei

The excitation functions of the evaporation residue formation probability of three heavy nuclei 194Pb, 200Pb and 206Pb are calculated by using a Langevin equation coupled with a statistical decay model.The results show that the neutron-to-proton ratio (N/Z) of a compound nucleus has an effect on survival probability and this effect becomes larger with increasing N/Z. This is because the fission barrier and the pre-saddle particle emission depend on the N/Z ratio of the system.     

重核存活几率的N/Z效应

用Langevin方程计算了重核 194Pb, 200Pb和206Pb的蒸发残余形成几率。结果表明系统中质比(N/Z）影响了该几率大小,并且高的N/Z增加了重核存活几率。这是由于裂变位垒和鞍点前粒子发射依赖于系统N/Z的缘故。     

Pressure-dependent partition functions

It is shown that the partition functions relating to statistical ensembles can be classified as cumulative, distributive or differential with regard to any of the extensive thermodynamic variables. The Laplace transforms involved in the general formulation of transformed partition functions, when extensive parameters are replaced by their conjugate intensive variables, are two-sided and appear in different forms according to the classification mentioned.

The petit partition function at constant pressure can be defined for both classical and quantal systems as a Stieltjes integral or dimensionless Laplace transform over the volume-dependent partition function. This expression contains no arbitrary external parameters and satisfies all the conditions formulated by Münster; it can be interpreted as the ratio of two partition functions, the one relating jointly to the system and a macroscopic boundary, and the second to the boundary alone.

It is known that the constant pressure grand partition function as defined by Guggenheim diverges for all thermodynamically compatible values of its independent variables. It is shown that the Gibbs-Duhem relation, and hence all the statistical properties of the system, except its size, can be derived by differentiating the reciprocal of this, or a similarly defined, function, not its logarithm as with other partition functions.

The mathematical differences arising out of the various proposed definitions are illustrated in a number of simple examples.     

X-ray fluorescence from the element with atomic number Z=120

An atomic clock based on x-ray fluorescence yields has been used to estimate the mean characteristic time for fusion followed by fission in reactions 238U + 64Ni at 6.6 MeV/A. Inner shell vacancies are created during the collisions in the electronic structure of the possibly formed Z=120 compound nuclei. The filling of these vacancies accompanied by a x-ray emission with energies characteristic of Z=120 can take place only if the atomic transitions occur before nuclear fission. Therefore, the x-ray yield characteristic of the united atom with 120 protons is strongly related to the fission time and to the vacancy lifetimes. K x rays from the element with Z=120 have been unambiguously identified from a coupled analysis of the involved nuclear reaction mechanisms and of the measured photon spectra. A minimum mean fission time τ(f)=2.5×10(-18) s has been deduced for Z=120 from the measured x-ray multiplicity.     

Quantal Noether Identities and Their Applications

Based on the phase-space generating functional of the Green function for a system with a regular/singular Lagrangian, the quantal canonical Noether identities (NI) under the local and non-local transformation in extended phase have been derived, respectively. The result holds true whether the Jacobian of the transformation is equal to unity or not. Based on the configuration-space generating functional of the gauge-invariant system obtained by using Faddeev-Popov (FP) trick, the quantal NI under the local and non-local transformation in configuration space have been also deduced. It is showed that for a system with a singular Lagriangian one must use the effective action in the quantal NI instead of the classical action in corresponding classical NI. It is pointed out that in certain cases, the quantal NI may be converted into the quantal (weak) conservation laws by using the quantal equations of motion. This algorithm to derive the quantal conservation laws differs from the quantal first Noether theorem. The preliminary applications of this formulation to Yang-Mills (YM) fields and non-Abelian Chern-Simons (CS) theories are given. The quantal conserved quantities for non-local transformation in YM fields are obtained. The conserved BRS and PBRS quantities at the quantum level in non-Abelian CS theories are also found. The property of fractional spin in CS theories is discussed. PACS no11.10. Ef; 11.30.−j 11.15. −q.     

Calculation of prompt fission neutron spectrum for 233U（n,f）reaction by the semi-empirical method~

The prompt fission neutron spectra for the neutron-induced fission of ²³³U for low energy neutrons (below 6 MeV) are calculated using nuclear evaporation theory with a semi-empirical method, in which the partition of the total excitation energy between the fission fragments for the n_th+²³³U fission reactions is determined by the available experimental and evaluation data. The calculated prompt fission neutron spectra agree well with the experimental data. The proportions of high-energy neutrons of prompt fission neutron spectrum versus incident neutron energies are investigated with the theoretical spectra, and the results are consistent with the systematics. The semi-empirical method could be a useful tool for the prompt evaluation of fission neutron spectra.     

New type of asymmetric fission in proton-rich nuclei

A very exotic process of β-delayed fission of 180Tl is studied in detail by using resonant laser ionization with subsequent mass separation at ISOLDE (CERN). In contrast to common expectations, the fission-fragment mass distribution of the post-β-decay daughter nucleus 180Hg (N/Z=1.25) is asymmetric. This asymmetry is more surprising since a mass-symmetric split of this extremely neutron-deficient nucleus would lead to two 90Zr fragments, with magic N=50 and semimagic Z=40. This is a new type of asymmetric fission, not caused by large shell effects related to fragment magic proton and neutron numbers, as observed in the actinide region. The newly measured branching ratio for β-delayed fission of 180Tl is 3.6(7) × 10(-3)%, approximately 2 orders of magnitude larger than in an earlier study.     

Study of the Mo-Ba partition in 252Cf spontaneous fission

Measurements of fission fragment yields and neutron multiplicities have been carried out for the Mo-Ba fragment pairs in the spontaneous fission of ²⁵²Cf, using the γ-ray spectroscopy technique to analyze γ-γ-γ coincidence data. Prompt γ -ray multiplicities were also measured as a function of the number of neutrons emitted in the fission process leading to the Mo-Ba partition. We do not observe the enhancement in the yields of events with high neutron emission multiplicity (ν_n > 7) that has been associated to a second fission mode leading to the production of hyperdeformed Ba fragments, as reported in some earlier studies. The average γ-ray multiplicity is found to be rather weakly dependent on the number of neutrons emitted in the fission process. Received: 21 July 1999 / Revised version: 19 November 1999     

Measurements of Fission and Radioactive Capture Reaction Rates Inside the Fuel of the Ipen/MB-01

This work presents the measures of the nuclear reaction rates along the radial direction of the fuel pellet by irradiation and posterior gamma spectrometry of a thin slice of fuel pellet of UO₂ at 4.3% enrichment. From its irradiation, the rate of radioactive capture and fission had been measured as a function of the radius of the pellet disk using a Ortec GMX HPGe detector. Lead collimators had been used for this purpose. Simulating the fuel pellet in the pin fuel of the IPEN/MB-01 reactor, a thin UO₂ disk is used, being inserted in the interior of a dismountable fuel rod. This fuel rod is then placed in the central position of the IPEN/MB-01 reactor core and irradiated during 1 h under a neutron flux of 5 ×10⁸ n/cm² s. In gamma spectrometry, 10 collimators with different diameters have been used; consequently, the nuclear reactions of radioactive capture that occurs in atoms of ²³⁸U and the fission that occurs on both ²³⁵U and ²³⁸U are measured in function of 10 different regions (diameter of collimator) of the UO₂ fuel pellet disk. Nuclear fission produces different fission products such as ¹⁴³Ce with a yield fission of 5.9% which decay is monitored in this work. Corrections in geometric efficiency due to introduction of collimators on HPGe detection system were estimated using photon transport of MCNP-4C code. Some calculated values of nuclear reaction rate of radioactive capture and fission along the radial direction of the fuel pellet obtained by Monte Carlo methodology, using the MCNP-4C code, are presented and compared to the experimental data showing very good agreement.     

Systematic study of survival probability of excited superheavy nuclei

The stability of excited superheavy nuclei (SHN) with 100 Z 134 against neutron emission and fission is investigated by using a statistical model. In particular, a systematic study of the survival probability against fission in the 1n-channel of these SHN is made. The present calculations consistently take the neutron separation energies and shell correction energies from the calculated results of the finite range droplet model which predicts an island of stability of SHN around Z = 115 and N = 179. It turn...     

The Asymptotic Functional integrals and Critical Temperature of the Dicke Model

A corrective effective action of the Dicke model is derived by means of the operator determinant identity. An asymptotic expression of functional integral (Z/Z₀) is obtained at critical temperature T_c. The error of the partition function is estimated.     

离线测量钍快中子裂变反应率方法

钍快中子裂变反应率是钍铀燃料循环中的重要数据.为了测量基于聚变-裂变混合能源堆包层概念设计的钍样品在宏观中子学装置中的钍快中子裂变数据,发展了钍快中子裂变率的离线活化γ测量方法.通过测量232Th裂变碎片85mKr的β衰变产物85Rb发射的151.16 keV特征γ射线,并结合钍裂变产额数据,获得了钍样品装置中232Th裂变反应率的分布.详细介绍了此方法的原理和影响因素,并利用14 MeV的D-T中子源在贫铀球壳中开展了校验实验,实验不确定度为5.3%—5.5%.采用MCNP5程序和ENDF/B-VI及ENDF/B-VII数据库模拟计算的结果与实验结果在实验不确定度内基本符合,这证明该方法能够有效地模拟装置中232Th裂变反应率.     

Quantal Poincaré-Cartan Integral Invariant for Field Theory

On the basis of the phase-space generating function of Green function for a system with a regular/singular Lagrangian, the quantal Poincaré-Cartan integral invariant (PCII) for field theory is derived. This PCII is equivalent to the quantal canonical equations. For this case in which the Jacobian of the transformation does not equalto unity, the quantal PCII can still be derived. This case is different from the quantal first Noether theorem. The quantal PCII connected with canonical equations and canonical transformation is also discussed.     

Disappearance of shell effects and persistence of an even-odd staggering in the fragment production in nuclear reactions at relativistic energies

The isotopic distributions of fragments produced in the spallation of uranium are strongly influenced by the fission of the excited prefragments, highly fissile nuclei. The competition between fission and evaporation around the doubly-magic nucleus Pb is discussed. The light fragments from Fe beam are produced with a strong enhancement of even-even nuclei compared to the odd-odd in the region of nuclei with equal number of neutrons and protons, N ～ Z. This staggering in the production of light fragments is not observed in the production of heavy fragments, and is in contradiction with the basis of the statistical model of deexcitation of a hot nucleus. Pairing interaction as a function of the excitation energy and as a function of the isospin of the nucleus are questioned.