Effective potentials and threshold anomaly

The strongE andL dependence of the effective elastic channel potentials is shown to be an implicit radial kinetic energy (ε) dependence. It is also shown that this effective potential satisfies the dispersion relation inε variable at the strong absorption radius. Further, the experimental data for both elastic and fusion channels are consistent with thisL-dependence of the corresponding effective potentials. The effective transfer channel potentials derived using CRC code FRESCO are shown to exhibit strong energy dependence as a result of couplings. The energy dependence of effective transfer strength for¹⁶O+²⁰⁸Pb and¹⁶O+²³²Th systems is determined using the experimental transfer angular distributions.     

Sub-barrier fusion of35, 37Cl+58, 64Ni evidence of effects of proton transfer channels

Sub-barrier fusion excitation functions of^35,37Cl+^58,64Ni have been measured. They are discussed in comparison to similar data of^34,36S+^58,64Ni with the aim of revealing the influence of coupled proton transfer channels. Using the simplified coupled channel code CCFUS, differences in the effects of inelastic channels are eliminated in an approximative manner to stress the differences in the effects of transfer channels. Signatures of positiveQ-value transfer channels coupled to fusion are clearly identified.     

12C induced transfer reactions on 56Fe

Transfer reactions ⁵⁶Fe(¹²C, xN) have been investigated. Angular distributions of particles following elastic scattering, one neutron and one proton transfer reaction channels leading to low lying states in respective residual nuclei have been measured. These are analysed using the coupled reaction channel (CRC) formalism. Starting with a double folded real potential, the elastic scattering angular distribution is calculated using the computer code FRESCO. Inclusion of couplings to first excited states in both the target and the projectile already tends to describe the experimental elastic scattering distribution. Additional coupling of one neutron transfer reaction to first five excited states in ⁵⁵Fe and one proton transfer reaction to first three low lying states in ⁵⁷Co improves fit to the elastic scattering angular distribution. Further refinement in fit is brought about by addition of a weak imaginary potential to the complex potential calculated by ERESCO to simulate the absorption effects due to those channels whose coupling is not included explicitly. Such a potential describes the experimental angular distributions for elastic, one neutron and one proton transfer channels correctly in shape and magnitude without any arbitrary normalisation.     

Structure information from fusion barriers

It is shown that the analysis of fusion barrier distributions is not always an unambiguous test or a ‘fingerprint’ of the structure information of the colliding nuclei. Examples are presented with same fusion barrier distributions for nuclei having different structures. The fusion excitation functions for ¹⁶O+²⁰⁸Pb, using the coupled reaction channel (CRC) method and correct structure information, have been analysed. The barrier distributions derived from these excitation functions including many of the significant channels are featureless, although these channels have considerable effects on the fusion excitation function. However, a simultaneous analysis of the fusion, elastic and quasi-elastic channels would fix the structure and the reaction unambiguously.     

近垒能区6Li+208Pb熔合激发函数测量

测量了6Li+208Pb熔合反应近垒能区全熔合截面,并与考虑非弹道耦合和不考虑耦合的CCFUS程序计算做了比较. 结果表明在垒上能区,破裂使熔合截面减小,在垒下能区,破裂对熔合截面的影响基本上可以忽略.     

Accuracy in the detemination of fusion barriers

Although there is no proof of the validity of the method, in a lot of papers, one computes the Second derivative of the the experimental fusion cross section multiplied by the energy to extract the fusion barriers directly from the experiment. The purpose of this paper is to check the consistency of the method, as experimental points are sandwiched inside their error bars. We therefore analysed the validity, by giving ourselves a cross section σ(E), resulting from the coupled channel calculation code ECIS, upon which, in spite of the complexity of the calculations, we have full control. We took these calculated points as the “experimental” ones and we altered them by multiplication by small random numbers. This is intended to simulate the error bars, of which we want to examine the influence on the fusion barriers. We find that in spite of the rough predictions yielded by the second derivative method, this task requires data with a precision difficult to reach. Furthermore, a careful check of the predictions of this method for coupled channels calculations shows that, due to the errors bars, this approach adds spurious results. Received: 6 January 1999 / Revised version: 30 March 1999     

Static versus energy-dependent nucleus–nucleus potential for description of sub-barrier fusion dynamics of _8~(16)O+_(50)~(112,116,120)Sn reactions

The static and energy-dependent nucleus–nucleus potentials are simultaneously used along with the Wong formula for exploration of fusion dynamics of168O+112,116,12050 Sn reactions. The role of internal structure degrees of freedom of colliding pairs, such as inelastic surface vibrations, are examined within the context of coupled channel calculations performed using the code CCFULL. Theoretical calculations based on the static Woods–Saxon potential along with the one-dimensional Wong formula fail to address the fusion data of168O+112,116,12050 Sn reactions.Such discrepancies can be removed if one uses couplings to internal structure degrees of freedom of colliding nuclei.However, the energy-dependent Woods–Saxon potential model(EDWSP model) accurately describes the sub-barrier fusion enhancement of168O+112,116,12050 Sn reactions. Therefore, in sub-barrier fusion dynamics, energy dependence in the nucleus–nucleus potential governs barrier modification effects in a closely similar way to that of the coupled channel approach.     

基于回音壁模式微球腔的PDH稳频技术

光学微球腔因其回音壁模式可获得极高的品质因数而受到广泛关注.本文分析了Fabry-Perot腔和微球腔的基本原理,通过CO2激光熔融光纤实验制得了直径为1.2 mm的微球腔,并测试了微球腔和锥形光纤耦合结构的耦合特性.采用典型的PDH稳频系统设计了基于微球腔的稳频系统,分析了用于鉴频的误差曲线的吸收特性和色散特性,对比了不同调制频率、微球腔直径、耦合损耗、传输损耗下与误差曲线斜率的关系.结果表明:耦合状态下最大Q值可达到1.1×108,调节微球腔内横磁模和横电模的转换可优化耦合效率,匹配微球腔和锥形光纤的尺寸得到了径向二阶模式的透射谱,误差曲线效率达到15.4A mW/MHz.球腔在提高PDH稳频技术灵敏度上具有巨大潜力.     

Decomposition of the equation of state of asymmetric nuclear matter into different spin-isospin channels

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin ST channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force（TBF） . It is shown that the potential energy per nucleon in the isospinsinglet T = 0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities,the TBF effect on the isospin-triplet T = 1 channel contribution turns out to be much larger than that on the T =0 channel contribution. At low densities around and below the normal nuclear matter density,the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T = 1 component is almost independent of isospin asymmetry. As the density increases,the T = 1 channel contribution becomes sensitive to the isospin asymmetry and at high enough densities its isospin dependence may even become more pronounced than that of the T = 0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in a nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories.     

Sub-barrier fusion excitation function data and energy dependent Woods–Saxon potential

This paper analyzed the role of intrinsic degrees of freedom of colliding nuclei in the enhancement of sub-barrier fusion cross-section data of various heavy ion fusion reactions. The influences of inelastic surface vibrations of colliding pairs are found to be dominant and their couplings result in the significantly larger fusion enhancement over the predictions of the one dimensional barrier penetration model at sub-barrier energies. The theoretical calculations are performed by using energy dependent Woods–Saxon potential model (EDWSP model) in conjunction with the one dimensional Wong formula. The effects of dominant intrinsic channels are entertained within framework of the coupled channel calculations obtained by using the code CCFULL. It is quite interesting to note that the energy dependence in Woods–Saxon potential simulates the effects of inelastic surface vibrational states of reactants wherein significantly larger value of diffuseness parameter ranging from a = 0.85fm to a = 0.95fm is required to address the observed fusion excitation function data of the various heavy ion fusion reactions.     

A 3-D radiation model for non-grey gases

A three-dimensional radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) coupled with spectral line-based weighted sum of grey gases (SLW) model for radiative heat transfer in non-grey absorbing-emitting media for use in conjunction with a computational fluid dynamics (CFD) code based on the same approach was developed. The code was applied to three test problems: two containing isothermal homogenous/non-homogenous water vapor and one non-isothermal water vapor/carbon dioxide mixture. Predictive accuracy of the code was evaluated by benchmarking its steady-state predictions against accurate results, calculated by ray tracing method with statistical narrow band model, available in the literature. Comparative testing with solutions of other methods is also provided. Comparisons reveal that MOL solution of DOM with SLW model provides accurate solutions for radiative heat fluxes and source terms and can be used with confidence in conjunction with CFD codes based on MOL.     

Decomposition of the equation of state of asymmetric nuclear matter into different spin-isospin channels

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin ST channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force (TBF). It is shown that the potential energy per nucleon in the isospin-singlet T=0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities, the TBF effect on the lsospin-triplet T=1 channel contribution turns out to be much larger than that on the T=0 channel contribution. At low densities around and below the normal nuclear matter density, the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T=1 component is almost independent of isospin asymmetry. As the density increases, the T=1 channel contribution becomes sensitive to the isospin asymmetry and at high enough densities its isospin dependence may even become more pronounced than that of the T=0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in a nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories.     

Modeling of nonlinear responses in BK7 glass under irradiation of femtosecond laser pulses

In this paper, the nonlinear response in BK7 glass sample is investigated under irradiation of 200 fs laser pulses at 800 nm wavelength by using of transmission measurement method. Nonlinear transmission is observed for incident pulse energies above 37μJ. A theoretical model based on simultaneously absorption of one, two and three-photon absorption is presented. The contribution of free-carriers absorption is also included on the model. The differential equation is solved analytically. The experimental results and predictions of theoretical model are in good agreement. The values of three-photon absorption coefficient and free-carriers absorption cross-section are reported.     

Near-barrier fusion, breakup and scattering for the Be + Sm system

Fusion, breakup and scattering for the ⁹Be + ¹⁴⁴Sm system at near barrier energies are investigated by different approaches. We show that at energies above the barrier there is a small complete fusion suppression when compared with predictions from a double folding potential and with a similar tightly bound system. At sub-barrier energies there is no significant deviation from the predictions using coupled channel calculations that do not include the breakup channel. The energy dependence of the optical potential does not show the usual threshold anomaly found in tightly bound systems. From a simultaneous analysis of fusion and scattering data we estimate the distance where breakup starts to occur.     

Coupled channel description of O+Nd scattering around the Coulomb barrier using a complex microscopic potential

Angular distributions of elastic scattering and inelastic scattering from 2⁺₁ state are measured for ¹⁶O+^142,144,146Nd systems at several energies in the vicinity of the Coulomb barrier. The angular distributions are systematically analyzed in coupled channel framework. Renormalized double folded real optical and coupling potentials with DDM3Y interaction have been used in the calculation. Relevant nuclear densities needed to generate the potentials are derived from shell model wavefunctions. A truncated shell model calculation has been performed and the calculated energy levels are compared with the experimental ones. To simulate the absorption, a ‘hybrid’ approach is adopted. The contribution to the imaginary potential of couplings to the inelastic channels, other than the 2⁺₁ target excitation channel, is calculated in the Feshbach formalism. This calculated imaginary potential along with a short ranged volume Woods–Saxon potential to simulate the absorption in fusion channel reproduces the angular distributions for ¹⁶O+¹⁴⁶Nd quite well. But for ¹⁶O+^142,144Nd systems additional surface absorption is found to be necessary to fit the angular distribution data. The variations of this additional absorption term with incident energy and the mass of the target are explored.     

Slow neutron scattering parameters for stable nuclei with nucleon numbers betweenA=79 andA=96

The relation between the method of coupled channels for rearrangement reactions (CRC) and the bound state approximation to the channel coupling array formalism (BSCCA), advocated in recent years, is investigated in detail for a simple 3-body system expressed in terms of truncated component wavefunctions of Faddeev type. The system is described by coupled differential or integral equations that are truncated into a model space of strongly-coupled channels. It is shown that CRC can be derived from the truncated coupled equations, either in differential or integral form, provided care is taken to use the entire model space. The corresponding BSCCA in this model space can be obtained from a restrictive condition on the integral from of the coupled equations, while it cannot be obtained consistently from the differential form of the coupled equations. The boundary conditions for the component functions are discussed in detail.     

In-plane free vibration analysis of combined ring-beam structural systems by wave propagation

This paper presents a systematic, wave propagation approach for the free vibration analysis of networks consisting of slender, straight and curved beam elements and complete rings. The analysis is based on a ray tracing method and a procedure to predict the natural frequencies and mode shapes of complex ring/beam networks is demonstrated. In the wave approach, the elements are coupled using reflection and transmission coefficients, and these are derived for discontinuities encountered in a MEMS rate sensor consisting of a ring supported on an array of folded beams. These are combined, taking into account wave propagation and decay, to provide a concise and efficient method for studying the free vibration problem. A simplification of the analysis that exploits cyclic symmetry in the structure is also presented. The effects of decaying near-field wave components are included in the formulation, ensuring that the solutions are exact. To illustrate the effectiveness of the approach, several numerical examples are presented. The predictions made using the proposed approach are shown to be in excellent agreement with a conventional FE analysis.     

Escape factors for laser-plasmas

A method of parameterizing escape factors (transmission factors and net radiative brackets) for conditions typical of laser-produced plasmas is introduced. The assumptions of planar geometry, exponentially decreasing emissivity and absorption coefficient with distance with a step rise at a particular point, and spatially constant Doppler broadened line profiles have been made. The effect of velocity gradients in spectrally shifting the absorption and emission line profiles relative to each other is taken into account assuming linear velocity gradients with distance. A parameter R representing the ratio of the spatial scale-length of the absorption coefficient to the Doppler decoupling length is introduced. Fitting formulae for transmission factors and net radiative brackets are given which are valid for all R and all optical depths. In the limit of small R (large Doppler decoupling length), the escape factors asymptotically approach formulae developed originally by, for example, Holstein assuming negligible plasma velocities. For large R (small Doppler decoupling length), the escape factors have been shown to asymptotically approach the Sobolev approximation. The parameterized net radiative bracket has been used in the hydrodynamic and atomic physics code ‘EHYBRID’ for the calculation of the effect of radiation trapping on population densities in laser-produced plasmas. The output of the modified EHYBRID code has then been post processed using the parameterised transmission factors to simulate 123 Ne-like and 399 F-like germanium resonance line intensities emitted in typical X-ray laser experiments. We obtain an agreement between the simulated and experimental spectra.