On the Yangian Y $$(\mathfrak{g}\mathfrak{l}_{m|n} )$$ and its quantum Berezinian

Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y of the general linear Lie algebra . In this article, we extend some of their ideas to consider the Yangian Y of the Lie superalgebra . In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

基态Bn(n=2, 3)结构与完全解析势能函数

使用Gaussian03程序包, 采用全电子单双取代耦合簇(CCSD(full))方法, 选择基组6-311+g(2df) , 对B2分子的基态进行优化计算, 采用十一参量Murrell-Sorbie函数, 运用最小二乘法拟合得到B2分子基态解析势能函数, 给出与实验值符合很好的光谱常数; 使用同样的方法和基组, 对B3分子的基态结构进行优化计算, 得到B3分子基态平衡结构. 采用多体项展式法, 利用B3分子平衡结构C2v的几何参数、力常数和离解能, 以及七个线性系数Ci(i=1, 2, 3, 4, 5, 6, 7)与两个非线性系数的函数关系, 进行非线性优化拟合得到两个非线性系数, 进而得到七个线性系数, 得到B3分子基态完全解析势能函数. 势能面静态特征表明, 该势能函数准确再现了B3分子基态全部平衡结构特征.     

Laplace-Beltrami operator on symmetric space X ≡ SOo(2, 3)/SO(2) × SO(3) of rank 2 and the related 2-body one dimensional quantum systems

The explicit form of the Laplace-Beltrami operator Δ_LB on symmetric space X  SO₀(2,3)/SO(2) xSO(3) of rank 2 is given. Using the representation of SO₀(2,3) the eigenfunctions of δ_LB, i.e. plane waves on X are constructed. The integral representation of the zonal spherical functions of the group SO_o(2, 3) is presented and the related 2-body one-dimensional quantum systems are considered.     

基态Bn(n=2,3)结构与完全解析势能函数简

使用Gaussian03程序包,采用全电子单双取代耦合簇(CCSD(full))方法,选择基组6-311+g(2df),对B2分子的基态进行优化计算,采用十一参量Murrell-Sorbie函数,运用最小二乘法拟合得到B2分子基态解析势能函数,给出与实验值符合很好的光谱常数;使用同样的方法和基组,对B3分子的基态结构进行优化计算,得到B3分子基态平衡结构.采用多体项展式法,利用B3分子平衡结构C2v的几何参数、力常数和离解能,以及七个线性系数Ci(i=1,2,3,4,5,6,7)与两个非线性系数的函数关系,进行非线性优化拟合得到两个非线性系数,进而得到七个线性系数,得到B3分子基态完全解析势能函数.势能面静态特征表明,该势能函数准确再现了B3分子基态全部平衡结构特征.     

14MeV中子引起的185Re(n,2n)184g,mRe和191Ir(n,2n)190Ir的核反应截面测量

利用活化方法测量了1?4MeV中子引起的¹⁸⁵Re(n,2n)^184gRe,¹⁸⁵Re(n,2n)^184mRe和¹⁹¹Ir(n,2n)¹⁹⁰Ir核反应的截面.中子能量E_n=(14.7±0.2)MeV时的实验结果分别为:(1817±85)mb,(390±18)mb和(2038±82)mb.并利用HFTT程序计算了中子能量在7—18MeV范围内的截面值,给出了其中两个核反应的激发函数曲线.     

Cross-section measurement for the ~(93)Nb(n,2n)~(92g)Nb reaction at the neutron energy of 14.6 MeV by the AMS method

The cross-section for the~(93)Nb(n,2n)~(92g)Nb reaction has been measured at the neutron energy of 14.6 Me V using neutron activation and accelerator mass spectrometry(AMS)determination of the long-lived product nuclide~(92g)Nb.The neutron energy was generated from the D+T neutron source at the China Institute of Atomic Energy(CIAE).The neutron flux was monitored by measuring the activity of~(92m)Nb produced in the competing reaction channel of~(93)Nb(n,2n)~(92m)Nb.At the neutron energy of 14.6 MeV,the~(93)Nb(n,2n)~(92g)Nb reaction cross-section of(736±220)mb was obtained for the first time.     

AB(~1∏,J)+C(~(s_1)l_(1j_1))→AB(~1∏,J′)+C(~(s_1)l_(1j_1)′)+C(~(s_2)l_(2j_2)′)电子和转动传能的电子量子干涉

在我们以前的理论研究中,给出了AB(1∏,J) C(sli)→AB(1∏,J′) C(slj′)碰撞诱导电子和转动传能的理论模型.为了进一步在理论上研究AB(1∏,J) C(s1l1j1)→AB(1∏,J′) C(s1l1j1′) C(s2l2j2′)的电子和转动传能的电子量子干涉,以波恩奥本海默近似为基础,考虑各项异性Lennard-Jones相互作用势,给出了其理论模型.得出了衡量干涉程度的干涉角,对完全干涉的情况进行了讨论,得出了决定几率比的因素,此理论模型对理解和进行这种类型的实验是很重要的.     

R-matrix formulation of the quantum inhomogeneous groups ISO q,r (N) and ISp q,r (N)

The quantum commutationsRTT=TTR and the orthogonal (symplectic) conditions for the inhomogeneous multiparametricq-groups of theB _n ,C _n ,D _n type are found in terms of theR-matrix ofB _n+1 ,C _n+1 ,D _n+1 .A consistent Hopf structure on these inhomogeneousq-groups is constructed by means of a projection fromB _n+1 ,C _n+1 ,D _n+1 .Real forms are discussed; in particular, we obtain theq-groups ISO _q,r (n+1,n–1), including the quantum Poincaré group. The inhomogeneusq-groups do not contain dilatations when the parameters satisfy certain conditions. For example, we find a dilatation-freeq-Poincaré group depending on one real parameterq.     

On the mechanism of the (n, 2n) reaction with 14MeV projectiles on127I and209Bi

The angular and spectral distributions of coincident neutrons from the reactions¹²⁷I(n, 2n)¹²⁶I and²⁰⁹Bi(n, 2n)²⁰⁸Bi have been measured with two time-of-flight detectors at the incident energy 14.1 MeV. Neutron emission has been studied for reaction anglesθ _lab between 10° and 150° (relative angles from 60° to 270°). Energy spectra, angular distributions and coincidence yields are compared with statistical model calculations including preequilibrium decay modes, and nuclear level density and spin cut off parameters are derived.     

替代反应法测量锕系核(n,f)和(n,xn)截面

对于某些中子反应截面,在直接测量上存在困难。为了获得那些对核能发展极其重要的核数据,人们提出替代反应法,即利用带电粒子代替中子进行反应,从而实现中子反应截面间接测量的方法。现有替代反应一般采用非弹激发、转移等周边反应,涉及的角动量远比中子反应的大,需要理论修正,这造成了一定的困难。有鉴于此,提出利用轻带电离子的俘获反应作为替代反应,其复合核自旋与中子反应的相当,有效避免了自旋修正的困难。根据这个思路,采用236U的（α,f）和（α,2n）反应作为替代反应,成功提取了239Pu的（n,f）和（n,2n）反应截面,与ENDFB7评价库数据在误差范围内符合较好,表明了替代反应法的优越性,可以在核数据测量中推广应用。There are always difficulties in the direct measurement of reactions induced by neutron, in order to obtain the neutron induced nuclear reaction data which are extremely important for nuclear power development, the surrogate reaction method, which uses charged particles instead of neutron, was proposed. The existing surrogate reaction method generally chooses peripheral reaction as the surrogate reaction, such as inelastic scattering excitation or transfer reaction. As a result, the angular momentum involved is always far larger than the neutron induced reaction, which causes difficulties in the theoretical calculation. Because of this, we proposed to use light-ion capture reaction as the surrogate reaction, the compound nuclei spin is similar with that of the neutron induced reaction, so that the difficulties in spin correction can be effectively avoided. Based on this idea, the 239Pu(n, f) and (n, 2n) reaction cross sections were successfully extracted using 236U(α,f) and (α,2n) reactions as the surrogate reaction. The results coincide well with the data of ENDFB7 within the error range, which shows that the surrogate reaction method has its own superiority, and it can be applied in the measurement of nuclear data.     

13.5—14.6MeV中子能区镓的同位素反应截面的测量

报道了在13.5—14.6MeV中子能区用活化法以⁹³Nb(n,2n)^92mNb反应截面为中子注量标准测得的⁶⁹Ga(n,2n)⁶⁸Ga,⁶⁹Ga(n,p)^69mZn,⁷¹Ga(n,p)^71mZn和⁷¹Ga(n,n′α)⁶⁷Cu的反应截面值.由(13.5±0.2),(14.1±0.1)和(14.6±0.2)MeV中子引起的⁶⁹Ga(n,2n)68Ga反应截面值分别为(794±31),(869±35)和(986±39)mb,⁷¹Ga(n,n′α)⁶⁷Cu反应截面值分别为(1.3±0.1),(1.7±0.1)和(2.5±0.1)mb.在中子能量为(14.1±0.1)MeV能量点,⁶⁹Ga(n,p)^69mZn反应截面值为(21.5±1.0)mb,⁷¹Ga(n,p)^71mZn反应截面值为(12.4±0.7)mb.单能中子由T(d,n)⁴He反应获得.文中还列举了尽可能收集到的数据以作比较.     

Effect of electric field on the spectrum and the persistent current of a quantum ring with two electrons （II） additional effect of a charged impurity

This paper studies the effect of a charged impurity together with or without an external homogeneous electric field on a quantum ring threaded by a magnetic field B and containing two electrons. The potential caused by the impurity has been plotted which is helpful to the understanding of the electronic structures inside the ring. The deep valley appearing in the potential curve is the source of localization, which affects seriously the Aharonov-Bohm oscillation （ABO） of the energy and persistent current. It also causes the fluctuation of the total orbital angular momentum L of the pair of electrons. It is found that the appearance of the impurity reduces the domain of the fractional ABO. During the increase of B, the domain of the integral ABO may appear earlier when B is even quite small. The transition from the localized states to extended states has also been studied. Furthermore, it has deduced a set of related formulae for a transformation, by which an impurity with a charge ep placed at an arbitrary point Rp is equivalent to an impurity with a revised charge ep placed at the X-axis with a revised radial distance Rp. This transformation facilitates the calculation and make the analysis of the physical result clearer.     

Determination of the subthreshold state contribution in 13C(alpha,n)16O,the main neutron-source reaction for the s process

The reaction rate of the stellar reaction 13C(alpha,n)16O, which is currently considered to be the main neutron source for the slow (s) process at low energies, has been rederived using the direct alpha-transfer reaction 13C(6Li,d)17O leading to the subthreshold state at 6.356 MeV in 17O. The contribution of the subthreshold state is found to be much smaller than the currently accepted predictions for the main neutron source of the s process, indicating less of a role of this reaction as the neutron source for the s-process scenario in low-mass stars at the asymptotic giant branch.     

Energies of 1s2ng and 1s2nh (n = 5, 6, 7, and 8) States for Lithium Isoelectronic Sequence

The nonrelativistic energies for lithium isoelectronic sequence 1s²ng and 1s²nh (n=5, 6, 7, and 8) states from Z=3 to 8 are calculated by using a full core plus correlation (FCPC) method with multiconfiguration interaction wave functions. Relativistic and mass-polarization effects on the energy are evaluated as the first-order perturbation theory. Our predicted excitation energies are compared with previous experimental results in the literature.     

铥原子收敛于4f13(2F7/2o)6s(7/2,1/2)4o和4f13(2F7/2o)6s(7/2,1/2)3o偶宇称里德伯系列能级的电子关联效应

本文在多通道量子亏损理论框架下,利用相对论多通道理论,计算了铥原子收敛于4f¹³（²F_7/2^o）6s（7/2,1/2）₄^o和4f¹³（²F_7/2^o）6s（7/2,1/2）₃^o的三个偶宇称里德伯系列.通过将计算结果与美国国家标准与技术研究院数据进行比较,展示了两种类型的电子关联效应：1）里德伯系列之间的相互作用,导致里德伯系列的能级出现整体偏移;2）一个孤立的干扰态镶嵌在一个里德伯系列中,破坏了该里德伯系列能级的规则性.     

Binding energy of the donor impurities in GaAs-Ga_(1-x)Al_xAs quantum well wires with Morse potential in the presence of electric and magnetic fields

The behavior of a donor in the GaAs–Ga_(1-x)Al_xAs quantum well wire represented by the Morse potential is examined within the framework of the effective-mass approximation. The donor binding energies are numerically calculated for with and without the electric and magnetic fields in order to show their influence on the binding energies. Moreover, how the donor binding energies change for the constant potential parameters(De, re, and a) as well as with the different values of the electric and magnetic field strengths is determined. It is found that the donor binding energy is highly dependent on the external electric and magnetic fields as well as parameters of the Morse potential.