Correlated hyperspherical harmonics

The expansion of the wavefunction for a bound three particle state in the five-dimensional hyperspace of hyperspherical harmonics in some cases suffers bad convergence, especially for weakly bound states. For this reason correlated hyperspherical harmonics are proposed, of which the ordinary hyperspherical harmonics are one special choice. The “best” suited correlated hyperspherical harmonics are chosen from an infinite set of complete orthogonal systems by a Ritz variational calculation.     

Ground state wave functions in the hyperspherical formalism for nuclei with A>4

The general formulation of a technically advantageous method to find the ground state solution of the Schrödinger equation in configuration space for systems with a number of particles A greater than 4 is presented. The wave function is expanded in pair-correlated hyperspherical harmonics beyond the lowest order approximation and then calculated in the Faddeev approach. A recent efficient recursive method to construct antisymmetric A-particle hyperspherical harmonics is used. The accuracy is tested for the bound state energies of nuclei with A = 6–12. The high quality of the obtained results becomes evident from a comparison with other approaches.     

Trinucleon system with Reid soft core potential by hyperspherical harmonics expansion method

The hyperspherical harmonics expansion method has been used to solve the trinucleon system where the nucleons interact through Reid soft core potential. The binding energy of triton, both for extreme adiabatic approximation and uncoupled adiabatic approximation, and theS-state,S′-state andD-state probabilities are calculated and compared with the results by the Faddeev method.     

Calculation of geometrical coupling coefficients for the hyperspherical harmonics approach

An elegant and fast method for the calculation of geometrical structure coefficients needed for an expansion of a few-body wavefunction and interaction in hyperspherical harmonics has been proposed. A sum rule for the GSC has also been derived, which is useful for an independent check of the coefficients. The proposed method of computation is many orders of magnitude faster than conventional methods.     

How to build optimal subsets of hyperspherical harmonics

After a short revue of the resolution of few body problems with the hyperspherical harmonics formalism, we develop a method to generate an “optimal subset” of basis functions that approximate the exact wavefunction up to third order of perturbations. Examples are given for three-body systems, with emphasis on the hypertriton. In this latter case, numerical results show that our optimal subset gives an energy some 40 keV higher than that found using a complete set of hyperspherical harmonics.     

Effect of the three-body force on triton asymptotic normalization constants by the hyperspherical harmonics expansion method

We investigate the change in the calculated value of asymptotic normalization constant (ANC) by the hyperspherical harmonics expansion method with the inclusion of three nucleon force (3BF) in addition to two nucleon force. We see that ANC does not change very much with the inclusion of 3BF indicating that the 3BF does not alter the asymptotic behaviours of HHE wavefunction significantly.     

Application of Huang-Yang pseudopotential to a few-body system

Huang and Yang replace a hard core of radius c by their pseudopotential (HYPP), which can be used in perturbation theory. I show that HYPP and boundary value perturbation theory give the same energy shift, to first order in c. I model a two-body potential as an oscillator potential (angular frequency ω) and a hard core. For an A-body system, the ratio of the first order energy correction to the unperturbed energy is 0.448 A^3/4 c a, where a = (M ω/2h)^1/2.     

Effective two-mode description of a few ultra-cold bosons in a double-well potential

We present a construction of an improved two-mode model for modeling the dynamics of interacting ultra-cold bosons confined in a one-dimensional double well trap. Unlike in the typically used two-mode model based on the lowest single-particle eigenstates of the external potential, the improved model uses a basis of properly chosen effective wave functions originating in the many-body model. Accuracy of the improved model is examined and it is shown that within a certain limit of inter-particle interaction strength, the model recovers an exact evolution of the wells' populations much more closely than the traditional two-mode model.     

Quality of potential harmonics expansion method for dilute Bose-Einstein condensate

We present and examine an approximate but ab initio many-body approach, viz., potential harmonics expansion method (PHEM), which includes two-body correlations for dilute Bose-Einstein condensates. Comparing the total ground state energy for three trapped interacting bosons calculated in PHEM with the exact energy, the new method is shown to be very good in the low density limit which is necessary for achieving Bose-Einstein condensation experimentally.      

Recurrence relations between transformation coefficients of hyperspherical harmonics and their application to moshinsky coefficients

Closed formulae and recurrence relations for the transformation of a two-body harmonic oscillator wave function to the hyperspherical formalism are given. With them Moshinsky or Smirnov coefficients are obtained from the transformation coefficients of hyperspherical harmonics. For these coefficients the diagonalization method of Talman and Landéreduces to simple recurrence relations which can be used directly to compute them. New closed formulae for these coefficients are also derived : they are needed to compute the two simplest coefficients which determine the sign for the recurrence relation.     

Cluster models of light nuclei and the method of hyperspherical harmonics: Successes and challenges

Hyperspherical-harmonics method to investigate the lightest nuclei having three-cluster structure is discussed together with recent experiments. Properties of bound states and methods to explore three-body continuum are presented. The challenges created by large neutron excess and halo phenomena are highlighted. Astrophysical aspects of the ⁷Li + n → ⁸Li + γ reaction and the solar-boron-neutrinos problem are analyzed. Three-cluster structure of highly excited states in ⁸Be is shown to be responsible for extreme isospin mixing. Progress in studies of ⁶He- and ¹¹Li-induced inclusive and exclusive nuclear reactions is demonstrated, providing information on the nature of continuum structures of Borromean nuclei. The text was submitted by the authors in English.     

Spatial harmonics modelling of planar periodic segmented waveguides

A theoretical approach based on Bloch theorem and spatial harmonics has been used to investigate the propagation characteristics in planar periodic segmented waveguides. This analytical method allows to evaluate the field distribution, the effective index and the propagation losses of these structures, taking into account both the propagating and the counterpropagating field components, thus evidencing all the phenomena which can take place in: Bragg reflections, leaky waves, etc. Results for TE fields are presented and compared with those obtained using a paraxial 2D FD-BPM method and a Padé based one, showing that no more than (1, 1) order approximants are needed to provide good estimates of the device characteristics.     

激光脉宽对谐波频移和振幅强度的影响

数值研究了激光脉宽对H_2~+和T_2~+谐波辐射的影响.计算结果表明:(i)对于谐波频移现象:在少周期激光场下,H_2~+和T_2~+谐波辐射呈现红移.随着激光脉宽增大,H_2~+谐波辐射呈现蓝移; T_2~+谐波辐射红移减弱.(ii)对于谐波振幅强度:H_2~+和T_2~+谐波辐射强度会随着激光脉宽增大而增强.但是,在少周期激光场下,H_2~+谐波截至能量附近的强度要大于T_2~+.在多周期激光场下,T_2~+谐波截至能量附近的强度要大于H_2~+.     

介质的非均匀性对高次谐波影响的研究

讨论了气体介质的非均匀性对飞秒激光高次谐波产生过程的可能影响.计算结果表明,采用喷阀技术所提供的气体介质的密度梯度和气体原子运动速度的影响很小,不会产生实验上可观测的效果.这一结果支持了喷气靶在高次谐波产生中的广泛应用 关键词： 高次谐波 气体介质 各向异性 飞秒激光     

Orientation dependence in high harmonics of ZnO with polarization corrections to counteract the birefringent effect

We investigate the influence of the birefringence on the high-order harmonics in an a-cut Zn O crystal with midinfrared laser pulses. The high harmonics exhibit strong dependence on the alignment of the crystal with respect to the laser polarization. We introduce the Jones calculus to counteract the birefringent effect and obtain the harmonics with polarization corrections in Zn O. We show that the birefringent effect plays an important role in the orientation dependence of HHG.     

交直交型机车的高频谐波混沌分析

针对典型的交直交型动车组CRH2车型,推导出其在正弦脉宽调制下的参数方程,并建立一套新的非线性参数模型.通过混沌原理分析了高次谐波的分形情况,并针对典型的牵引变电站,进行了计算和仿真,依托实际录波的数据验证,证实高频谐波能够导致系统谐振,为混沌分析方法拓展了新的应用.     

核运动对非奇次谐波产生的影响

理论研究了H2+、D2+、T2+辐射高次谐波的特点.结果表明,在核运动影响下,不仅奇次谐波呈现红移现象,而且谐波光谱呈现非奇次谐波.随着核质量增大,奇次谐波频移和非几次谐波强度都减弱.但是随着激脉宽增大,非奇次谐波的产生明显被增强.理论分析表明,谐波频移是由谐波辐射在激光上升和下降区间的非对称性导致的;非奇次谐波是由于分子对称性在较大核间距离处遭破坏产生的.     

激光场中H原子高次谐波

建立了激光与原子相互作用的伪分立态模型 ,并用此模型计算了激光场中H原子的高次谐波 ,得到了与实验和其它理论计算相符的结果     

Theory of higher harmonics imaging in tapping-mode atomic force microscopy

The periodic impact force induced by tip-sample contact in tapping mode atomic force microscope (AFM) gives rise to non-harmonic response of a micro-cantilever. These non-harmonic signals contain the full characteristics of tip-sample interaction. A complete theoretical model describing the dynamical behaviour of tip--sample system was developed in this paper. An analytic formula was introduced to describe the relationship between time-varying tip--sample impact force and tip motion. The theoretical analysis and numerical results both show that the time-varying tip--sample impact force can be reconstructed by recording tip motion. This allows for the reconstruction of the characteristics of the tip--sample force, like contact time and maximum contact force. It can also explain the ability of AFM higher harmonics imaging in mapping stiffness and surface energy variations.