非线性Schrdinger方程基态解的一致集中

本文讨论一类非线性Schrdinger方程-ε~2△v+V(z)v=K(x)v~p,x∈R~N,v∈W~(1,2)(R~N),v(x)>0,势函数V(x)有正下界和在无穷远处为零两种情形.通过强最大值原理我们证明方程的基态解关于充分小的ε>0一致集中.     

△-Resonances in Ground State Properties of ^40 20Ca Spherical Cold Finite Nucleus at Equilibrium and under Compression

The ground state properties of the spherical nucleus ^40Ca have been investigated by using constrained spherical Hartree Fock （CSHF） approximation at equilibrium and under high radial compression in a six major shells. The effective baryon-baryon interaction that includes the △（1236） resonance freedom degrees to calculate nuclear properties is used. The nucleon-nucleon （N-N） interaction is based on Reid soft core （RSC） potential. The results of calculations show that much of increase in the nuclear energy generated under compression is used to create the massive △ particles. The number of △ ＇s can be increased to about 2.1% of constituents of nucleus when nuclear density reaches about 1.34 times of normal density. The single particle energy levels are calculated and their behavior under compression is also examined. △ good agreement has been found between current calculations and phenomenological shell model for low lying single-particle spectra. The gap between shells is very clear and L-S coupling become stronger as increasing the static load on the nucleus. The results show a considerable reduction in compressibility when freedom degrees of △＇s are taken into account. It has been found that the total nuclear radial density becomes denser in the interior and less dense in the exterior region of nucleus. The surface of nucleus becomes more and more responsive to compression than outer region.     

Influence of Rashba SOI and Polaronic Effects on the Ground-State Energy of Electrons in Semiconductor Quantum Rings

The influence of Rashba spin-orbit interaction （SOI） and polaronic effect on the ground-state energy of electrons in semiconductor quantum rings （QRs） are studied by means of the Lee-Low-Pines variational method. Numerical calculations for GaAs QRs are performed and the results show that the ground-state energy of electrons splits into two branches as E（↑） and E（↓） under the Rashba SOI, which correspond to the spin-up state and spin-down state, respectively. The contribution of the Rashba SOI effect to the ground-state energy of electrons is related to the spin state of electrons and is closely linked to the inner and outer radii of a QR. However, it is independent of the height of the QR. The ground-state energy of electrons decreases due to the polaronic effect in QRs. The energy shift ＆#8710;Ee-LO of the ground-state of the electron induced by the polaronic effect decreases monotonically with increase of the height of a QR and fluctuates with the changes of the radii of QRs. The amplitude of the fluctuation is very sensitive and remarkable to the changes of the inner radius R1 and the outer radius R2.     

二氧化钚分子的多体展式势能函数

从导出基态PuO2分子的电子状态X5Σ g正确地判断其离解极限出发,采用MP2方法,应用相对论有效原子实模型(RECP)优化出PuO2(X5Σ g)分子稳定构型为线性OPuO(D∞h),其平衡核间距Re=0.18004nm.同时也计算出振动频率,并优化出存在亚稳态的Pu-O-O(C∞v)构型.使用多体项展式理论方法,导出了基态PuO2分子的分析势能函数.该势能表面准确地再现了O-Pu-O(D∞h)平衡结构和亚稳态的Pu-O-O(C∞v)构型.然后根据势能函数等值图讨论了O(3Pg) PuO反应的势能面静态特征.     

双拉盖尔-高斯腔光力系统中的腔内压缩冷却研究

机械振子的冷却是腔光力学研究的重要方向之一。计算光力噪声谱和稳态的最终声子数,对基于耦合光学参量放大器（OPA）的双拉盖尔-高斯腔光力系统中的腔内压缩冷却问题进行研究。在弱耦合条件下,利用微扰近似理论方法得出系统的光力噪声谱,基于费米黄金法则的理论计算出稳态下的最终声子数的解析表达式。利用入射泵浦光驱动腔场内耦合的OPA,使腔场内形成强烈的非线性压缩效应,量子反作用加热过程得到有效抑制,系统净冷却率得到显著提高。此外,讨论了其他系统参数对机械振子冷却的影响。最后研究了系统的稳态声子数,声子数可以在较大参数范围内小于1。该方案能有效地降低机械振子的冷却极限。     

类硼离子基态的精细结构(英文)

以多电子精细结构哈密顿的球张量形式为基础,借助不可约张量理论,建立了类硼离子基态精细结构能量的解析表达式.完成了所有角向积分和自旋求和计算,使精细结构能量表示为若干个径向积分之和.在此基础上计算了类硼体系(Z=5~8)基态精细结构能量,计算结果与实验数据符合得较好.     

类碳体系基态能量的相对论修正(英文)

以Breit-Pauli哈密顿的球张量形式为基础,借助不可约张量理论,将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形,导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体迭尔文修正项、自旋-自旋接触相互作用项)的解析表达式,完成了所有角向积分和自旋求和计算.利用所建立的理论,对类碳体系基态能量的相对论修正进行了具体计算.     

氦原子及类氦离子基态的二参数变分法研究

提出了一种计算氦原子及类氦离子基态能量和波函数的二参数变分法,包括试探波函数的设计和基态能量表达式的推导,并用Mathematica 5.0软件的优化计算功能方便快捷地计算出基态能量,将计算结果与实验结果和部分所列文献的结果进行对比.结果表明,本文所得精度较高,变分参数个数较少.同时强调交换对称性和量子态的交缠在双电子原子体系问题中的重要性.     

102Ru核振动到转动演化的微观研究

基于微观sdIBM-2方案和实验单粒子能量值,在最普遍的哈密顿量下,用两组不同的核子.核子等效相互作用参数,分别很好地再现了102Ru核的振动带能谱和转动带能谱及其演化过程.微观和唯象的研究指认:1)这两种激发模式的共存区是能态81 -121 (即Ex=2.500-4.000 MeV);态81 是振动模式占据优势的能态,态121 是转动模式占据优势的能态,而状态101 则是两种模式的中立能态;2)态121 是141 态退耦到态101 辐射光子相变后的中间能态;3)从基态起直到201 态的yrast态全都是集体态,而以后出现的第一个拆对顺排态很可能就是中子h11/2的两准粒子态;4)这种结构的过渡不是很剧烈的,而是通过玻色子结构常数在过渡区中不大的改变来实现的.