用类Li原子波函数对H52+团簇的正四面体中心结构与能量的研究

在单中心球模型近似下,选用类Li原子解析波函数,用变分法计算了H52 团簇正四面体中心结构与能量.结果表明当中心氢原子核到顶角氢原子核之间的距离R=1.93a0时,体系能量有一极小值E=-4.3792 Hartree(a0=0.529177×10-10m,1 Hartree=27.2 eV).这表明H52 团簇的正四面体中心结构是稳定的结构,H52 团簇是可能存在的.     

用类B原子波函数对H7^2＋团簇的正八面体中心结构与能量的研究

在单中心球模型近似下,选用类B原子解析波函数,用变分法计算了H27 团簇正八面体中心结构与能量.结果表明当中心氢原子核到顶角氢原子核之间的距离R=2.83a0时,体系能量有一极小值E=-3.918h0(a0=0.529177×10-10m,h0=27.2 eV).这表明H72 团簇的正八面体中心结构是稳定的结构,H27 团簇是可能存在的.     

用类氧原子波函数计算H7^—团簇正八体中心结构的能量曲线

选用类氧原子波函数,在单中心球模型近似下,利用变分法计算了Ｈ７＾－团簇正八面体中心结构的能量曲线。结果表明,当中心Ｈ原子核能顶角Ｈ原子核之间的距离Ｒ＝１．５８ａ０时,体系能量有一极小值－４．０８９９４５３ｈ．ａ．ｕ．。这表明Ｈ７的正八面体中心结构是可能稳定存在的。计算结果与用ＭＡＣＱＭ法计算的结果基本相符,表明提出的物理模型及其计算方法是合理的。     

H9团簇的电子结构与能量计算

对氢原子团簇H9的电子结构提出了一个物理模型 .认为其电子结构类似于氟原子的电子结构 ,具有 2个 1s电子 ,2个 2s电子和 5个 2p电子 .其基态可写为H9(1s2 2s2 2p5) 2 P .用电子波函数计算出该团簇的总能量为E =- 4 .99(Har.atomicunit) ,键长为R =1.5 9a0 ,与过去用改进的量子力学排列通道法计算的结果非常吻合 .这表明所提出的物理模型是合理的 ,而且所提出的电子波函数对研究H9团簇的物理性质很有用. The electronic structure of H 9 cluster is proposed. The total energy of this cluster is calculated by using its electron wave functions. The results are in good agreement with the value calculated by using of the modified arrangement channel quantum mechanics method in a previous paper. The results also indicate that the electronic structure of H 9 cluster is similar to that of fluorine atom.     

用类O原子波函数对H+9团簇的体心立方结构与能量的研究

在单中心球模型近似下,选用类O原子解析函数,用变分法计算了H+9团簇体心立方结构与能量。结果表明当中心氢原子核到顶角氢原子核之间的距离R=1.97a0时,体系能量有一极小值E=-4.376h0(a0=0.529177×10-10m,h0=27.2eV)。这表明H+9团簇的体心立方结构是稳定的结构,H+9团簇是存在的。     

Cluster-variational calculations for extended nuclear systems

The energy as a function of density is calculated for neutron matter and for symmetrical nuclear matter, based on Jastrow trial wave functions. The energy expectation value is truncated in low cluster order. A detailed analysis of the two- and three-body cluster contributions and a special portion of the four-body contribution is given. Variation of a parameterized two-body correlation function is subjected to constraints designed to confine the trial wave function to the domain corresponding to rapid cluster convergence. Results are presented for a variety of model central potentials containing hard cores, for different sets of constraints, and for two- and three-parameter correlation functions. Calculations constrained by the “average Pauli condition” are found to yield results very close to those constrained by the “normalization” or “unitarity” condition, and the two-parameter correlation function appears to be quite adequate. The convergence of the cluster expansion, as reflected in the low orders, is good except at the highest densities considered. The three-body cluster contribution displays, in all cases, a remarkable internal cancellation between its “two-correlation-line” addends.     

Multipole expansion of non-local coupling potentials for cluster transfer and application to 16O(16O, 12C)20Ne

When the transfer of clusters and the symmetrization (antisymmetrization) of scattering wave functions is described by cluster models within the coupled-channel formalism, non-local coupling potentials arise. We suggest a procedure to calculate these potentials by a multipole expansion of all potentials and wave functions which depend on sums of vectors. The expansion coefficients are found by least-squares fit. The method is applied to the ¹⁶O(¹⁶O, ¹²C)²⁰Ne reaction, which is treated in the cluster model with two inert ¹²C- and α-clusters as constituents.     

Compact and loosely bound structures in light nuclei

The role of various components in the wave function of loosely bound light nuclei is considered in terms of the cluster model by taking into account orbital polarization. We show that several structures corresponding to particular modes of nucleon motion can be concurrently important for such structures. Specific examples of simple and fairly flexible trial wave functions are given for the ⁸Be and ⁶He nuclei. Explicit expressions are derived for the microscopic wave functions of these nuclei and employed to calculate basic nuclear parameters for commonly used central exchange NN potentials.     

A correlated-basis-functions approach to realistic nuclear matter

The method of correlated basis functions is adapted to the nuclear-matter problem with two-nucleon potentials containing tensor as well as central components. Procedures are described for evaluating through three-body cluster order the energy expectation value with respect to a constrained trial ground-state wave function incorporating tensor and central correlations, and for calculating in two-body cluster approximation the second-order perturbation correction in a basis of likewise-correlated functions. Results for the 5100, 5200, Gammel-Christian-Thaler and Hamada-Johnston potentials are presented and dissected.     

The Novel Cluster States in 10Be

We have investigated the cluster structures in ¹⁰Be by using ⁶He+α cluster wave functions and dineutron condensate wave functions. We suggested two kinds of exotic cluster states which have not been confirmed experimentally yet. One of them has a gas-like structure of two alphas and one dineutron, and another has ⁶He and an extremely developed α.     

Electronic properties of silicon with ultrasmall germanium clusters

The electronic states of silicon with a periodic array of spherical germanium clusters are studied within the pseudopotential approach. The effects of quantum confinement in the energies and wave functions of the localized cluster states are analyzed. It is demonstrated that clusters up to 2.4 nm in size produce one localized s state whose energy monotonically shifts deep into the silicon band gap as the cluster size increases. The wave function of the cluster level corresponds to the single-valley approximation of the effective-mass method. In the approximation of an abruptly discontinuous potential at the heterointerface, the quantities calculated using the effective-mass method for clusters containing more than 200 Ge atoms are close to those obtained by the pseudopotential method. For smaller clusters, it is necessary to take into account the smooth potential at the interface.     

A convenient analytical form for the triton wave function

The triton wave function obtained by solving the Faddeev equations with the Reid softcore potential is parametrized in a symmetrized cluster form. As a test the ³He charge form factor is calculated for the exact and the parametrized wave functions and reasonable agreement between the two is found.     

Scattering of hadrons by Li isotopes in the diffraction theory

Elastic and inelastic scattering of protons and mesons by ^{6, 7, 8}Li nuclei is analyzed on the basis of the Glauber diffraction theory. Several versions of the wave functions of the nuclei, obtained within the two- and three-particle potential cluster models, are used in our calculations. It is demonstrated that the use of these wave functions in the diffraction theory enables us to adequately describe the experimental differential cross sections for hadron scattering at energies of 0.6 and 1.0 GeV. Considerable attention is devoted to to nuclear structure and the mechanism of nucleon interaction in elastic scattering.     

Separation of a Slater Determinant Wave Function with a Neck Structure into Spatially Localized Subsystems

A method of separating a Slater determinant wave function with a two-center neck structure into spatially localized subsystems is proposed, and it is applied to α + α Margenau–Brink cluster wave functions and antisymmetrized molecular dynamics wave functions of the ground state in ¹⁰Be and a negative-parity largely deformed state in ³⁵S.     

Correlated basis functions for the many-electron problem

The method of correlated basis functions is applied to the electron system in a metal. To overcome the twofold difficulty of large particle number and long-range Coulomb interaction in metals, a new optimal cluster decomposition for arbitrary correlated wave functions is derived. With this method, not only ground-state properties, but also thermal averages and response functions can be calculated from a given set of correlated basis functions. The appropriate synthesis of correlated wave functions including physically expected properties of subsystems as for instance partially filled inner shells in transition metals is discussed in detail.     

Semi-microscopic analysis of multi-nucleon transfer and the 40Ca(α, p)43Sc reaction

A semi-microscopic model for analyzing multi-nucleon transfer reactions in the distorted-wave Born approximation is presented. This model, which is shown to be compatible with other semi-microscopic models, employs cluster form factors. The cluster spectroscopic factors are calculated using shell-model wave functions. Data from the ⁴⁰Ca(α, p)⁴³Sc reaction are presented and used to test the model. The relative cluster spectroscopic factors for a number of levels are found to be in agreement with those calculated using wave functions in an $\text{(}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^3$ basis.     

Model independent bounds on reaction cross-sections in heavy-ion scattering

The coupled cluster equations first proposed by Coester and Kümmel and developed by Kümmel, Lührmann, and Zabolitsky are derived explicitly from the variational principle for the ground state energy (the “true” energy) using a new set of simple formulas relating density matrices (equal time limits of Green functions) to the coupled cluster functions. In this respect a simplification appears to be achieved by working with a normalized ground state wave function. The further transformation of the variational equations into the standard forms given by the previous authors differs mainly in its pedagogical aspects from ideas found in the existing literature.     

Short-range correlations in high-energy hadron collisions

High-energy collisions of hadrons on nuclei are studied by means of Glauber multiple scattering theory, using Jastrow correlated wave functions. To this end a cluster expansion is derived, and its convergence properties are studied. Calculations have been carried out for ⁴He and ¹⁶O nuclei, and they are compared with experimental data.     

Fine structure in the alpha-cluster radioactivity of the255Fm nucleus

Within the one level R-matrix approach several hindrance factors for the radioactive decay of the²⁵⁵Fm nucleus in which are emitted alpha-nuclei are calculated. The interior wave functions are supposed to be given by the shell model with effective residual interactions. The exterior wave functions are calculated from a cluster-nucleus double-folding model potential obtained with the Michigan 3-Yukawa (M3Y) interaction. As example of the cluster decay fine structure we analyzed the case of alpha-decay of²⁵⁵Fm nucleus. Good agreement with the experimental data is obtained.The author would like to thank Dr. O. Dumitrescu for fruitful discussions concerning different parts of this work and help in computing different quantities entering the expressions of the hindrance factors.