恒星氦燃烧关键反应12C(α,γ)16O天体物理S因子及其反应率

恒星氦燃烧阶段3α反应和12C（α,γ）16O反应相互竞争,两者的反应率共同决定了氦燃烧结束后12C与16O的丰度比,该比值是大质量恒星后继演化以及伴随的元素核合成过程的初始条件。目前,氦燃烧12C（α,γ）16O反应起始T₉=0.2处,天体物理模型要求的反应率的精确度要低于10%,然而尚未有实验或理论给出满足要求的结果。最为直接和可靠地获取12C（α,γ）16O反应率的方法,就是尽可能往低能区测量其天体物理S因子,然后通过理论外推到感兴趣的能区。为此基于经典的R-矩阵理论,建立了适用于低能核反应的多道、多能级的约化R-矩阵理论来拟合几乎所有可用的16O系统的实验数据。配合使用协方差统计和误差传播理论,拟合外推得到了客观的、内部自恰的和唯一性好的12C（α,γ）16O反应天体物理S因子。总的外推S因子STOT（0.3 MeV）=162.7±7.3 keV·b,理论上首次给出达到恒星演化与元素核合成模型的最低要求的S因子。基于计算给出的全能区的S因子,数值积分给出了温度位于0.04 6 T₉ 6 10的12C（α,γ）16O天体物理反应率。在T₉=0.2处,推荐的反应率为（7.83 ±0.35）×10-15 cm3mol-1s-1。During stellar helium burning, the rates of 3α and the 12C(α,γ)16O reaction, in competition with one another, determine the relative abundances of 12C and 16O in a massive star. The abundance ratio is the beginning condition of the following nucleosynthesis and star evolution of massive stars, which are extremely sensitive to the rate of 12C(α,γ)16O reaction at T₉=0.2. The most direct and trustworthy way to obtain the reaction rate of the 12C(α,γ)16O reaction is to measure the S factor for that reaction to as low energy as possible, and to extrapolate to energies of astrophysical interest. Based on a new multilevel and multichannel reduced R-matrix theory for applications in nuclear astrophysics, we have obtained an accurate and self-consistent astrophysical S factor of 12C(α,γ)16O, by a global fitting for almost all available experimental data of 16O system, with the coordination of covariance statistics and error-propagation theory. The extrapolated S factor of 12C(α,γ)16O was obtained with a recommended value STOT (0.3 MeV)=162.7±7.3 keV·b. And the reaction rates of 12C(α,γ)16O for stellar temperatures between 0.04 6 T₉ 6 10 are provided. At T₉=0.2, the reaction rate is (7.83 ±0.35)×10-15 cm3mol-1s-1, where stellar helium burning occurs.     

Quantum Integrable Toda-Like Systems in Deformation Quantization

We define and discuss the notion of quantum integrability of a classically integrable system within the framework of deformation quantization, i.e. the question whether the classical conserved quantities (which are already in involution with respect to the Poisson bracket) commute with respect to some star product on the phase space after possible quantum corrections. As an example of this method, we show by means of suitable 2 by 2 quantum R-matrices that a list of Toda-like classical integrable systems given by Y. B. Suris is quantum integrable with respect to the usual star product of the Weyl type in flat 2n-dimensional space.     

里德堡钠原子抗磁谱的模型势计算

用B样条基组展开方法结合模型势计算了里德堡钠原子抗磁谱和相应的振子强度谱.径向和角向均采用高阶B样条基组.计算结果与已有的R-矩阵和多通道量子亏损理论相结合(R-matrix MQDT)法及其他理论计算结果作了比较,几种理论结果在我们所研究的能区内符合得非常好.本文方法较R-ma-trix MQDT法简单,易于推广到交叉电磁场中里德堡原子的精确谱的计算中.     

Double quantization of CP type orbits by generalized Verma modules

It is known that symmetric orbits in g^* for any simple Lie algebra g are equipped with a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to the “canonical” R-matrix. We realize quantization of the Poisson pencil CPⁿ type orbits (i.e. orbits in sl(n + 1)^* whose real compact form is CPⁿ) by means of q-deformed Verma modules.     

The crystal commutor and Drinfeld’s unitarized <Emphasis Type="Italic">R</Emphasis>-matrix

Drinfeld defined a unitarized R-matrix for any quantum group . This gives a commutor for the category of representations, making it into a coboundary category. Henriques and Kamnitzer defined another commutor which also gives representations the structure of a coboundary category. We show that a particular case of Henriques and Kamnitzer’s construction agrees with Drinfeld’s commutor. We then describe the action of Drinfeld’s commutor on a tensor product of two crystal bases, and explain the relation to the crystal commutor. P. Tingley was supported by the RTG grant DMS-0354321.     

锂原子激发态光电离的R—矩阵计算

使用Ｒ－矩阵方法,采用三态密耦图象计算了锂原子激发态１ｓ＾２２ｐ＾２Ｐ的光电离截面,并给出了不同分波及不同过程的截面,计算结果揭示了光电离过程中的Ｒｙｄｂｅｒｇ系列共振,并指出在非共振区光电离截面不是单调变化的。     

Majid conjecture: quantum Kac-Moody algebras version

Based on the n-fold tensor product version of the generalized double-bosonization construction, we prove the Majid conjecture of the quantum Kac-Moody algebras version. Particularly, we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types G_2^{(1)} , E_2^{(1)},and Tp,q,r, and in this way, we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category. This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside.     

Ionization Potentials and Quantum Defects of ls^2np^2p Rydberg States of Lithium Atom

Abstract In this work, ionization potentials and quantum effects of ls^2 np^2 P Rydberg states of lithium are calculated based on the calibrated quantum defect function. Energy levels and quantum defects for ls^2np^2P bound states and their adjacent continuum states are calculated with the R-matrix theory, and then the quantum defect function of the ls^2np （n ≥ 7） channel is obtained, which varies smoothly with the energy based on the quantum defect theory. The accurate quantum defect of the ls^2 7p^2P state derived from the experimental data is used to calibrate the original quantum defect function. The new function is used to calculate ionization potentials and quantum effects of ls^2np ^2P （n ≥ 7） Rydberg states. Present calculations are in agreement with recent experimental data in whole.     

运用R矩阵方法研究低能电子与NO_2分子的散射

基于静电-交换和密耦合两种模型,采用R矩阵方法,研究了低能电子与二氧化氮自由基分子的积分散射截面和动量迁移散射截面,包括弹性散射和从电子基态到电子激发态的非弹性散射.采用aug-cc-pVTZ基组进行靶分子结构优化和散射研究.在密耦合模型中,包含6个电子的最低三个占据轨道1b_2,1a_1,2a_1被冻结,其余17个电子自由运动在活化空间中,并给活化空间增加了2b_1和7a_1两个虚轨道.包含了所有垂直激发能小于20 eV的靶分子电子组态,得到了收敛的散射截面,并与最新理论和实验值进行了比较.当入射能量小于4 eV时,本文结果与实验值符合得更好,校正了以往部分理论结果在极低能量处过高的现象,表明关联效应对于极低能量散射是非常重要的.