基于重离子输运理论对超重核合成及非对称核物质状态方程的研究

本论文基于重离子输运理论模型对当前人们感兴趣的超重核合成及非对称核物质状态方程做了研究。基于双核系统概念建立了一个描述超重核合成的理论模型。这个模型中通过求解Fokker-Planck方程来描述重离子碰撞过程的能量、角动量以及形变等的弛豫过程，从而合理地包含了重离子熔合过程中的动力学效应。在求解弹靶的质量扩散时采用了数值求解主方程的方法，避免对势能面做任何近似，因此能够充分地体现重离子熔合过程中弹靶的结构效应。本文利用这一模型计算了重离子熔合形成超重元素的最佳激发能、熔合几率、复合核的存活几率以及蒸发剩余核截面等，并给出了合成超重核的最佳弹靶组合。计算了超重核形成的最佳激发能，在符合已有最佳激发能实验数据的基础上预言了基于冷熔合反应合成114，116和118号元素的最佳激发能。计算了重离子熔合反应的熔合几率。结果表明，随着反应系统变得越来越重，重离子的熔合几率呈指数规律下降，准裂变变得越来越严重。这解释了实验上观测到的超重剩余核截面随体系的变重而急剧下降的现象。研究了重离子熔合截面的弹靶相关性。结果表明弹靶的质量非对称度越高越有利于熔合生成复合核，同时重离子熔合截面还强烈地依赖于弹靶结构。重离子的熔合过程是合成超重元素的关键因素之一，另一个影响超重核合成的因素是超重复合核的存活几率。基于统计模型，系统的研究了超重复合核存活几率的质量、能量、角动量等相关性。计算了基于冷熔合反应的蒸发剩余截面，得到的结果与实验基本符合，并预言了基于冷熔合反应生成114，116和115号元素的截面。在研究超重核蒸发剩余截面的弹靶相关性的基础上给出了合成超重核的最佳弹靶组合。计算表明，在挑选弹靶组合时使得合成的超重复合核是奇A核则会得到更高的奇数中子蒸发剩余核截面。计算给出了超重复合核的自旋布居及其对裂变位垒和鞍点态形变的依赖性。发现超重复合核的自旋布居强烈地依赖于复合核的裂变位垒，高的裂变位垒会给出宽的自旋布居；而超重复合核的自旋布居对鞍点态形变不是很敏感。另外研究了多核子转移反应合成超重元素的可能性。结果表明基于多核子转移反应合成大于108号的元素是很困难的。非对称核物质状态方程由于其对天体物理及理解奇异核结构的重要性，因此是人们长期以来一直感兴趣的研究内容，然而直到现在人们对核物质状态方程特别是高密核物质和非对称核物质状态状态方程仍了解甚少。基于Skyrme-Hartree-Fock理论以及同位旋相关的量子分子动力学（IQMD）模型研究了非对称核物质的化学不稳定性，结果表明非对称核物质可以发生化学不稳定性，且化学不稳定性发生的条件依赖于单粒子势能的密度相关形式。同时计算表明化学不稳定性是可以发生在真实的重离子碰撞过程中的，且在入射能量较高时化学不稳定性会消失。另外首次研究了高密核物质的化学不稳定性及其发生的条件。由于实验室很难达到很高密度的核物质，而中子星是由致密的极丰中子物质组成，因此提供了研究高密非对称核物质的自然实验室。基于Skyrme-Hartree-Fock理论研究了两种典型的非对称核物质状态方程（软对称势和硬对称势）对中子星中质子百分比的影响。另外研究了热中子星中质子百分比的温度相关性，发现热中子星中质子百分比随温度的升高而减小。基于IQMD模型研究了同位旋相分化现象的产生机制。通过与MSU的实验数据比较指出核物质应该有软的对称势。研究了重离子碰撞过程中的径向流现象，及其同位旋效应。计算了径向流产生的能量闭，并给出了实验上利用径向流产生的能量闭来提取非对称核物质状态方程的方法。

三体核力影响下的核物质状态方程及中子星物质中的中子质子超流性

本论文介绍了极端条件下核物质研究的现状以及目前常用的几种核多体方法，系统描述了冷、热非对称核物质的状态方程和刀稳定中子星物质中的15。态中子和质子超流性，特别是微观三体核力对此所产生的影响。通过引入微观三体核力，扩展了有限温度的BI．tleclcller-Hal'tree-Fock（FTBHF）理论。利用这一扩展的理沦，详细研究了同位旋非对称热核物质的状态方程、液气相变临界现象以及三体核力对此所产生的影响。在不同的中质比条件下，重点讨论了热核物质液气相变的临界温度和动力学不稳定区域的温度、同位旋相关性。由此表明，三体核力的引入在一定程度上降低了液气相变的临界温度值，在固定的温度和密度下，非对称核物质的压弧随同位旋非对称度的增加而单调的增力日，而且随着核物质温度的升高和非对称度的增加，动力学不稳定区域逐渐缩小。通过与其它理论模型（特别是Di1'ac-BHF方法）所预言的结果相比较，就目前扩展的包含三体核力修正的FTBHF理论与Dilac-BHF方法所计算的临界温度的差异问题，文中给出一种可能的解释。通过计算热核物质的单粒子结合能，给出了有限温度条件下对称能的计算方式，并且细致研究了不同温度、密度下的对称能以及三体核力在高密度区域对对称能的影响。结果表明，微观三体核力强烈影响着高密度区域的对称能，使其对温度的变化更加明显。此外，其它重要物理量（例如中子和质子的单粒子势能、有效质量等）的同位旋依赖性和温度、密度相关性在文中也被详细的讨论。利用质量算子的空穴线展井，表明了在基态关联所导致的对单核子势的重排修正项影响下的HLlgenholtz-VanHove(HVH)定理的恢复程度，并且进一步计算了中子和质子化学势。并且以包含兰体核力的FTBI-方法为基础，研究了热核物质中重排项的密度和温度依赖性并讨论了三体核力对重排项的影响。通过计算不同温度和密度下的核物质中单核子势和核子有效质量，特别是研究和讨论了基态关联效应和三体核力贡献对热核物质中单核子势的影响，表明了基态关联和三体核力对单核子势修正的重要性。利用BHF和BCS的理论方法，计算了β稳定中子星物质中处于150态的中子和质子的对关联能隙，着重研究和讨论了三体核力的影响。结果表明，三体核力对刀稳定物质中｛s0态中子超流性的影响相对较小，但是对，S0态质子超流性具有重要影响，其效应随核子数密度的增大而迅速增强。三体核力的主要作用是强烈地抑制了高密度区刀稳定中子星物质中的150态质子超流性，而且三体核力对中子星物质中，So态超流相的抑制效应主要是通过质子或中子的有效对相互作用而起作用的。

非相对论重离子碰撞动力学的两体关联输运理论

论文系统地介绍和分析了当前几类描述重离子碰撞动力学过程输运理论的优点和缺点，并针对这些理论的不足作为建立我们理论模型的出发点。例如BUU（Boltzmann-Uehling-Uhlenbeck）系列的输运过程，可以通过不同方法从量子多体理论依照扩展的时间相关的Hartree-Fock（ETDHF）的基本思想推导出来，并对重离子碰撞过程中有关平均场物理量给出了合理的描述。但由于推导中采用了一些半经典近似和参数化近似，破坏了平均场合碰撞项之间的动力学自洽耦合。特别是数值计算中采用了实验粒子系综平均法，从而丢失了多体关联和涨落，使其无法直接描述重离子碰撞中基本的碎块形成和多重碎裂过程。而量子分子动力学（QMD）系列的理论能够给出重离子碰撞过程中碎块形成的动力学描述，但至今无法从量子多体理论推导出有关QMD的输运方程。碰撞项是在数值计算中通过Monte Carlo抽样技术人为地加入的。那么，如何从量子多体理论出发推导出描述重离子碰撞动力学过程的，可将时间相关的平均场，多体关联进行自洽耦合描述的量子输运理论就成了本论文工作的中心目的。 基于王顺金等人建立的多体关联动力学理论，选用时间相关的相干态单粒子基矢作为新理论的工作表象，对两体关联动力学中的一体密度矩阵和两体关联函数进行轨道展开，推导出了描述非相对论重离子碰撞动力学过程的两体关联输运理论TBCTT（Two-Body Correlation Transport Theory）。TBCTT是一组包括时间相关的平均场，两体关联和Pauli原理的自洽耦合的动力学方程组。其中时间相关的相干单粒子基矢是该理论的一个关键问题。其时间演化的动力学可由多种不同的方法得到，如时间相关的Hartree-Fock方法，时间相关的变分方法等。但作为建立TBCTT工作的第一步，为了计算简便，我们采用经典的Hamilton方程来描述相干单粒子基矢中相空间参数的时间演化，然后通过与两体关联动力学的耦合而恢复TBCCT基本的量子特征。 利用TBCTT对几组轻的碰撞系统进行了数值计算和分析。计算结果表明：TBCTT可以给出重离子碰撞过程中的有关物理量时间演化过程的合理描述，得到了在不同入射道条件下与QMD模型的可比性结果。同时也在组态空间的有限截断和两体关联函数不同的等级截断下均得到了碰撞系统总动量，总能量和总粒子数的近似守恒结果，特别是能量守恒，这是一般半经典输运理论中一个重要的困难问题。另外还得到了两体关联函数不同的等级截断近似对碰撞动力学方面不同的描述。所用这些数值计算结果充分表明：TBCTT是一个有希望和有发展前途的能够描述重离子碰撞动力学的量子输运理论。最后我们对当前计算中所采用的近似和存在的问题进行了分析和讨论，提出了进一步改进和完善TBCTT的途径和方案。 我们在开始TBCTT的研究之前还对QMD进行了仔细的研究和改进。通过在平均场中引入Pauli势和对称势并利用摩擦冷却方法构造原子核基态，得到了一种改进的量子分子动力学MQMD。利用这种MQMD研究了12C+12C反应多重碎裂过程中的核结构效应，得到了与AMD和实验数据基本一致的结果。对QMD的改进和应用为开展TBCTT的研究工作创造了必要条件和准备。

SOLVENT AND SUBSTITUENT EFFECTS ON THE INTRAMOLECULAR AMIDE HYDROLYSIS OF N-METHYLMALEAMIC ACID

Intramolecular amide hydrolysis of N-methylmaleamic acid is revisited at the B3LYP/6-311G(2df,p)//B3LYP/6-31G(d,p)+ZVPE level, including solvent effects at the CPCM-B3LYP/6-311G(2df,p)//Onsager-B3LYP/6-31G(d,p)+ZPVE level. The concerted reaction mechanism is energetically favorable over stepwise reaction mechanisms in both the gas phase and solution. The calculated reaction barriers are significantly lower in solution than in the gas phase. In addition, it is concluded that the substituents of the four N-methylmaleamic acid derivatives considered herein have a significant effect on the gas-phase reaction barriers but a smaller, or little, effect on the barriers in solution.

Structural stability and electronic state of transition metal trimers

Ground state geometries were searched for transition metal trimers Sc-3, Y-3, La-3, Lu-3, Ti-3, Zr-3, and Hf-3 by density functional methods. For all the studied trimers, our calculation indicates that the ground state geometries are either equilateral triangle (Zr-3 and Hf-3) or near equilateral triangle (Ti-3, Sc-3, Y-3, La-3, and Lu-3). For rare earth trimers Sc-3, Y-3, La-3, and Lu-3, isosceles triangle (near equilateral triangle) at quartet state is the ground state. Isosceles triangle at doublet state is the competitive candidate for the ground state. For Zr-3 and Hf-3, equilateral triangle at singlet state is the most stable. For Ti-3, isosceles triangle (near equilateral triangle) at quintet state gives the ground state. For Sc-3, Zr-3, and Hf-3, where experimental results are available, the predicted geometries are in agreement with experiment in which the ground state is equilateral triangle (Zr-3) or fluxional (Sc-3 and Hf-3). For Y-3, the calculated geometry is in agreement with experimental observation and previous theoretical study that Y-3 is a bent molecule for the ground state.

Gas-phase ion-molecule reactions of C-60 with the plasma of methyl acrylate

The gas-phase ion-molecule reactions of C-60 with the plasma generated from methyl acrylate under self-chemical ionization conditions were studied by use of a triple-quadrupole mass spectrometer. The adduct cation [C60C3H3O](+) and protonated molecular ion [C60H](+) were observed as the major product ions. The former adduct ion is formed by electrophilic reaction of C-60 with the ion [CH2=CHCO](+), a main fragment ion resulting from the methyl acrylate molecular ion [CH2=CHCOOCH3](+) through alpha cleavage. The latter ion is generated by proton transfer from protonated methyl acrylate to C-60. Semi-empirical quantum chemical calculations have been performed for the eight possible isomers of [C60C3H3O](+) at the Hartree-Fock level by use of the AMI method. The results show three types of cycloadducts as the most stable structures among the possible isomers.

Structures and vibrational spectra of C-2 and LaC2+ clusters

C-2 and LaC2+ were studied using Hartree-Fock(HF), B3LYP (Becke 3-paremeter-Lee-Yang-Parr) density functional method, second-order Moller-Plesset perturbation (MP2) and coupled cluster singles and doubles with non-iterative triples(CCSD(T)) methods. The basis set employed was LANL1DZ. Geometries, vibrational frequencies and other quantities were reported. The results showed that for C-2, all the methods performed well for low spin state (singlet), while only HF and B3LYP remained so for high spin state (triplet). For LaC2+, four isomers were presented and fully optimized. The results suggested that linear isomers with C-infinity v and D-infinity h symmetries were predicted to be saddle points on the energy surface for all the methods, while for isomers with C-2 upsilon and C-s symmetries, they were local minima except C-2 upsilon at B3LYP level, and were isoenergetic at HF, MP2 and CCSD(T) levels, near isoenergetic at B3LYP level. From the differences between HOMO and LUMO, it is also known that the isomers with C-2 upsilon and C-s symmetries offer the largest values and therefore correspond to the most stable structure. For La-C bond lengths, B3LYP gives the shortest, the order is B3LYP

Theoretical investigation of LaC2 and LaC2+ clusters

LaC2 (with doublet and quartet states) and LaC2+ (with singlet and triplet states) cluster have been studied by using the B3LYP (Becke three-parameter/Lee-Yang-Parr) density functional method and the HF (Hartree-Fock) method with LANLIDZ basis set. For each cluster, four possible isomers in C-2v, C-s, C-proportional to v and D-proportional to h symmetries have been investigated. The results indicate that structures in C-s symmetry are local minima in all cases and, in most cases (particularly for high spin states), our initial guess in C-s symmetry converges to structures in C-2v symmetry. For the isomers in C-2v, C-proportional to v and D-proportional to h symmetries, local minima were found to be dependent on the method and spin state. The two clusters may also exist as linear chains. The ordering of the binding energies for the isomers in all spin states is C-s similar to C-2v < C-proportional to v < D-proportional to h. The ionization potential of LaC2 is reported as well. (C) 1998 Elsevier Science B.V.

Theoretical investigation of LaCn+ (n=2-8) clusters

LaCn+ (n = 2-8) have been studied using Hartree-Fock (HF) and B3LYP density functional method. The results indicated that at both levels, isomers with C-2v, C-s symmetry for n = 2, and edge insertion isomer for n = 4, 6, 8, as well as edge binding isomer for n = 3, 5, 7 were found as ground states. This is in good agreement with experimental results. The exceptional case is for n = 6 at B3LYP level, in which edge insertion and edge binding isomers were computed to be near isoenergetic. (C) 1997 Elsevier Science B.V.

Gas-phase ion-molecule reactions of C-60 and theoretical studies of [C60C2H3O](+) adduct cations

Gas-phase ion-molecule reactions of buckminsterfullerene (C-60) with the acetyl cation CH3-C-+=O (m/z 43) and formylmethyl cation (CH2)-C-+-CH=O (m/z 43, or oxiranyl cation), generated from the self-chemical ionization of acetone and vinyl acetate, respectively, were studied in the ion source of a mass spectrometer. Adduct cations [C60C2H3O](+) (m/z 763) and protonated C-60, [C60H](+) (m/z 721), were observed as the major products. AM1 semiempirical molecular orbital calculations on the possible structures, stabilities and charge locations of the isomers of the adducts [C60C2H3O](+) were carried out at the restricted Hartree-Fock level. The results indicated that the sigma-addition product [C-60-COCH3](+) is the most stable adduct for the reaction of C-60 with CH3-C-+=O rather than that resulting from the [2+2] cycloaddition. The [2+3] cycloadduct and the sigma-adduct [C60CH2CHO](+) might be the most possible coexisting products for the reactions of C-60 with (CH2)-C-+-CH=O or oxiranyl cation. Other [C60C2H3O](+) isomers are also discussed. (C) 1997 by John Wiley & Sons, Ltd.

Properties of molecules in tunnel junctions

Molecular tunnel junctions involve studying the behaviour of a single molecule sandwiched between metal leads. When a molecule makes contact with electrodes, it becomes open to the environment which can heavily influence its properties, such as electronegativity and electron transport. While the most common computational approaches remain to be single particle approximations, in this thesis it is shown that a more explicit treatment of electron interactions can be required. By studying an open atomic chain junction, it is found that including electron correlations corrects the strong lead-molecule interaction seen by the ΔSCF approximation, and has an impact on junction I − V properties. The need for an accurate description of electronegativity is highlighted by studying a correlated model of hexatriene-di-thiol with a systematically varied correlation parameter and comparing the results to various electronic structure treatments. The results indicating an overestimation of the band gap and underestimation of charge transfer in the Hartree-Fock regime is equivalent to not treating electron-electron correlations. While in the opposite limit, over-compensating for electron-electron interaction leads to underestimated band gap and too high an electron current as seen in DFT/LDA treatment. It is emphasised in this thesis that correcting electronegativity is equivalent to maximising the overlap of the approximate density matrix to the exact reduced density matrix found at the exact many-body solution. In this work, the complex absorbing potential (CAP) formalism which allows for the inclusion metal electrodes into explicit wavefunction many-body formalisms is further developed. The CAP methodology is applied to study the electron state lifetimes and shifts as the junction is made open.

Latest development of the combinatorial model of nuclear level densities

The combinatorial model of nuclear level densities has now reached a level of accuracy comparable to that of the best global analytical expressions without suffering from the limits imposed by the statistical hypothesis on which the latter expressions rely. In particular, it provides, naturally, non-Gaussian spin distribution as well as non-equipartition of parities which are known to have an impact on cross section predictions at low energies [1, 2, 3]. Our previous global models developed in Refs. [1, 2] suffered from deficiencies, in particular in the way the collective effects - both vibrational and rotational - were treated. We have recently improved this treatment using simultaneously the single-particle levels and collective properties predicted by a newly derived Gogny interaction [4], therefore enabling a microscopic description of energy-dependent shell, pairing and deformation effects. In addition for deformed nuclei, the transition to sphericity is coherently taken into account on the basis of a temperature-dependent Hartree-Fock calculation which provides at each temperature the structure properties needed to build the level densities. This new method is described and shown to give promising results with respect to available experimental data.

Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

Role of Landau quantization on the neutron-drip transition in magnetar crusts

The role of a strong magnetic field on the neutron-drip transition in the crust of a magnetar is studied. The composition of the crust and the neutron-drip threshold are determined numerically for different magnetic field strengths using the experimental atomic mass measurements from the 2012 Atomic Mass Evaluation complemented with theoretical masses calculated from the Brussels-Montreal Hartree-Fock-Bogoliubov nuclear mass model HFB-24. The equilibrium nucleus at the neutron-drip point is found to be independent of the magnetic field strength. As demonstrated analytically, the neutron-drip density and pressure increase almost linearly with the magnetic field strength in the strongly quantizing regime for which electrons lie in the lowest Landau level. For weaker magnetic fields, the neutron-drip density exhibits typical quantum oscillations. In this case, the neutron-drip density can be either increased by about 14% or decreased by 25% depending on the magnetic field strength. These variations are shown to be almost universal, independently of the nuclear mass model employed. These results may have important implications for the physical interpretation of timing irregularities and quasiperiodic oscillations detected in soft gamma-ray repeaters and anomalous x-ray pulsars, as well as for the cooling of strongly magnetized neutron stars.

Radiative lifetimes of metastable states of negative ions

We present a technique for measuring the radiative lifetimes of metastable states of negative ions that involves the use of a heavy-ion storage ring. The method has been applied to investigate the radiative decay of the np3 2P1/2 levels of Te–(n=5) and Se–(n=4) and the 3p3 2D state of Si– for which the J=3/2 and 5/2 levels were unresolved. All of these states are metastable and decay primarily by emission of E2 and M1 radiation. Multi Configuration Dirac-Hartree-Fock calculations of rates for the transitions in Te– and Se– yielded lifetimes of 0.45 s and 4.7 s, respectively. The measured values agree well with these predicted values. In the case of the 2D state of Si–, however, our measurement was only able to set a lower limit on the lifetime. The upper limit of the lifetime that can be measured with our apparatus is set by how long the ions can be stored in the ring, a limit determined by the rate of collisional detachment. Our lower limit of 1 min for the lifetime of the 2D state is consistent with both the calculated lifetimes of 162 s for the 2D3/2 level and 27.3 h for the 2D5/2 level reported by O'Malley and Beck and 14.5 h and 12.5 h, respectively, from our Breit-Pauli calculations.