Validity of the two-determinantal deformed Hartree-Fock approximation

The two-fold degeneracy of the deformed Hartree-Fock (HF) solutions in thes-d shell suggests the use of a two-determinantal intrinsic state. The validity of this two-determinantal variational method is established in the case of the exactly solvable Lipkin Hamiltonian, for which the usual HF solution is known to be 2 fold degenerate. The approximation of using a two-determinantal intrinsic state turns out to be an exceedingly good one and in general as the particle number and the strength of the interaction increase, the exact solution is rapidly approached. The states of positive (negative) parity which are obtained by projection from the intrinsic two-determinantal state are found to reproduce the exact ground (first excited) state with a high accuracy.     

A band mixing shell model calculation for 47Ti

A shell model calculation for ⁴⁷Ti is done. The state with definite angular momenta projected from the prolate and oblate Hartree-Fock states and a few other intrinsic states obtained from these two HF states by 1 particle — 1 hole excitations were used as basis states. The calculated spectrum agrees well with the experimental one.     

采用MSDI严格角动量投影46Ti、48Cr形变HF谱

采用修正的表面δ相互作用(MSDI),以球形壳模型单粒子态作基矢,对fp壳层区偶偶核⁴⁶Ti、⁴⁸Cr进行形变Hartree–Fock(HF)计算,并用形变HF单粒子态构造Slater行列式波函数,即形变HF内禀态,然后对其实施严格角动量投影程序,得到比较合理的结果.     

Angular Momentum Projected Deformed HF Spectra of 46Ti and 48Cr With MSDI

Taking the modified surface delta interaction (MSDI) and using a spherical shell model basis set, we carry out the deformed Hartree-Fock (HF) calculation for the even-even nuclei ⁴⁶Ti and ⁴⁸Cr in the fp shell, and construct the deformed HF intrinsic states which are the Slater determinants from the HF single-particle states.The angular momentum projection program is then carried out and the reasonable results are obtained.     

铍原子基态交换-相关能的多体理论计算

到目前为止,几乎所有的关于原子基态的多体计算都是以Hartree-Fock(HF)模型为零级近似。本文将零级哈密顿量取为Hartree-Fock-Slater(HFS)型的,在双激发(两体)近似下,对Be原子基态交换-相关能进行了多体理论计算,得到了与实验及别的作者以HF模型为零级近似所作多体计算相符合的结果。计算表明,以HFS模型为零级近似,对闭合壳层原子基态亦可成功地进行多体计算。 关键词：     

Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

Study of doubly evens d-shell nuclei in the Multi-Configuration-Hartree-Fock model

A theory in the spirit of the Hartree-Fock (HF) model is formulated which takes into account general types of correlation effects. This theory, dubbed as Multi-Configuration Hartree-Fock (MCHF) model, makes use of a multideterminantal trial wave function. In the present work the intrinsic ground state wave functions obtained in this theory have been studied. Doubly evenN=Z andN=Z + 2 nuclei in thesd-shell have been treated and the results have been compared against the HF-predictions. While the HF-approximation is found to be quite good forN=Z nuclei, correlations are found to play a strikingly significant role in theN=Z +2 nuclei.     

Time-dependent Gutzwiller approximation for the Hubbard model

We develop a time-dependent Gutzwiller approximation (GA) for the Hubbard model analogous to the time-dependent Hartree-Fock (HF) method. This new formalism incorporates ground state correlations of the random phase approximation (RPA) type beyond the GA. Static quantities like ground state energy and double occupancy are in excellent agreement with exact results in one dimension up to moderate coupling and in two dimensions for all couplings. We find a substantial improvement over traditional GA and HF+RPA treatments. Dynamical correlation functions can be computed and are also substantially better than HF+RPA ones and obey well behaved sum rules.     

Investigation of native-oxide growth on HF-treated Si(111) surfaces by measuring the surface-state distribution

The evaluation of the surface state distribution of differently HF-treated Si(111) surfaces during the native-oxide growth in air is investigated by the large-signal field-modulated photovoltage technique. The surface state distribution consisting of intrinsic and extrinsic Si dangling bond defects is directly related to the state of oxidation of the Si surface. It is shown that the kind of HF treatment strongly influences the concentration of extrinsic defects with a lower state of oxidation. Special HF preparations for H termination of the Si(111) surface result in a nearly intrinsic surface state distribution. During the oxidation process three typical phases can be distinguished each characterized by specific defect structures. It was found that native-oxide growth is highly sensitive to the concentration of extrinsic defects directly after HF treatment.     

TFD extension of a self-consistent RPA to finite temperatures

The self-consistent RPA (SCRPA) developed by Schuck and coauthors is extended to finite temperatures. The corresponding equations are derived by using the formalism of thermofield dynamics. The intrinsic energy of a system is calculated as the expectation value of the Hamiltonian with respect to a T-dependent thermal vacuum state for a thermal-phonon operator. A nonvanishing number of thermal quasiparticles in the vacuum state are assumed. By virtue of the assumption, the thermal Hartree-Fock (HF) equations appear to be coupled to the equations of motion for phonon variables. The thermal occupation numbers are also calculated in a consistent way with the energies of the HF quasiparticles. The approximation is applied to the two-level Lipkin model. Advantages of the thermal SCRPA (TSCRPA) are most obvious at temperatures near the phase-transition point. In the TSCRPA, the phase transition occurs at lower T than in other approximations. Moreover, within the TSCRPA, a statistical behavior of the Lipkin model is described with an appropriate accuracy at any T even if the HF transformation parameter is kept fixed at a value corresponding to the “spherical” phase of the HF field.     

An intrinsic state generating the ground state rotational band of a deformed nucleus and its approximate equivalence to an algebraic-variational treatment: Illustration by an exactly soluble model

We construct a class of intrinsic or trial states to generate the ground state band of a rotating nucleus in a highly schematized shell model possessing R(5) symmetry. This model is described in the preceding paper. The exponential form of the state links this work to a line of recent developments tracing back ultimately to the work of Jancovici and Schiff on the generator coordinate method. For the present case the state is a product of BCS states and is seen to contain more general (four-particle) correlations than a single deformed BCS state. A technique for the construction of the states is described. The major result of this paper is the proof that the cranking variational principle associated with the trial state is essentially equivalent (exactly equivalent in the thermodynamic or large system limit) to the algebraic-variational method described in the preceding paper, when the latter is restricted to the oneband approximation. The existence of sharp phase transitions in the model is then investigated analytically. A spherical to deformed transition is thus confirmed, as well as an anti-pairing transition. As explained, this is unrelated to the Coriolis anti-pairing phenomena.     

The influence of state dependent short range correlations on the depletion of the nuclear Fermi sea

The inlfuence of state dependent short range correlations on the occupation numbers of the single particle shell model orbits of the doubly closed shell nuclei¹⁶O and⁴⁰Ca is examined. The study shows that the effect of the state dependence of the short range correlations is rather small. The total depletion of the nuclear Fermi sea changes slightly compared with the one calculated by considering state independent short range correlations.     

Random phase approximation and continuum states

For scattering of nucleons the possibilities of including ground state correlations are investigated in a formalism similar to the usual shell model formalism. It is shown that the effect of the ground state correlations may be considerable.     

Intrinsic Structure of Light Nuclei in Monte Carlo Shell Model Calculation

Wavefunctions obtained from the Monte Carlo shell model (MCSM) calculation are investigated. It has been difficult to discuss the intrinsic structure of nuclei in conventional shell-model calculations. We propose a way to describe an intrinsic state in the MCSM and demonstrate the appearance of two-α-cluster structure in the ⁸Be ground state. The changes of cluster shape with respect to the number of major shell and basis is discussed. The shape of the ¹⁰Be ground state is also investigated. The behavior of valence neutron is consistent with the picture of molecular orbit state. The method is also applied to the ⁶He ground state, which is expected to have the asymmetric distribution of valence neutrons.     

The effect of neutron-proton pairing correlations on the transfer of a neutron-proton pair

A theory of neutron-proton pairing interaction is developed considering bothJ=0T=1 andJ≠0T=0 correlations. The model of a singlej-shell is investigated explicitly forN=Z nuclei. Instead of solving the full HFB (Hartree Fock Bogoliubov) problem a variational method is used for determining the ground state energy and wavefunction. Our model shows that the best solutions contain either onlyT=0 or onlyT=1 correlations. A solution mixingT=0 andT=1 is energetically worse. It is estimated in PWBA (Plane Wave Born Approximation) that for ground state transitions at light nuclei in the transfer of a neutron-proton pair the cross section is enhanced up to a factor 3 by pairing correlations compared with shell model calculations.     

Quartet states in the sd and fp shells

Two-proton-two-neutron correlations are studied in psd and fp shell nuclei in the frame of the aligned scheme approximation. Four-particle rotational states are obtained in terms of linear combinations of projected aligned Slater determinants and the resulting excitation energies and wave functions are compared with those of elaborate shell-model calculations. The close agreement obtained both for single j-shell and complete shell configuration spaces shows that rotational or quasi-rotational states are almost entirely generated by aligned configurations. The lowest four-particle states obtained in one j-shell can be explained as the rotational spectrum of an oblate intrinsic state. The lowest four-particle states of ¹⁶O, ²⁰Ne, ⁴⁴Ti and ⁶⁰Zn, calculated in a major shell, correspond to the rotational spectrum of a prolate intrinsic state and fit the existing data. Higher states are the result of a mixed deformation.     

CORRELATION EFFECTS ON THE GROUNDSTATES OF THREE-ELECTRON QUANTUM DOTS IN A STRONG MAGNETIC FIELD

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Renormalization for collective motion within a truncated space of the spherical shell model. I. Intrinsic frame in a schematic model

Using schematic Hamiltonians in the ²⁰Ne example, the series of perturbation terms for effective interactions and operators in a truncated space of a spherical shell model is found that, when summed, yields the results for intrinsic moments and energy of the unrestricted deformed Hartree-Fock state. Black-box and random phase approximation diagrams are shown to be important as is another (little used and to be called IBG) diagram and the ladder diagrams. A black-dot vertex renormalization is introduced corresponding to consistent renormalization of every transformation within the model space. The black-dot corresponds exactly to the self consistency of deformed Hartree-Fock.     

Charge Correlations in a Harmonic Trap

A system of N classical Coulomb charges trapped in a harmonic potential displays shell structure and orientational ordering. The local density profile is well understood from theory, simulation, and experiment. Here, pair correlations are considered for this highly inhomogeneous system for both the fluid and ordered states. In the former, it is noted that there is a close relationship to pair correlations in the uniform one component plasma. For the ordered state, it is shown that the disordered “tiling” is closely related to the ground state Thomson sites for a single sphere (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)