The crossed beams scattering dynamics of the F+HD→HF+D reaction have been studied at collision energies ranging from 8.19 k J/tool to 18.98 k J/tool using the high resolution H-atom Rydberg tagging time-of-flight m...The crossed beams scattering dynamics of the F+HD→HF+D reaction have been studied at collision energies ranging from 8.19 k J/tool to 18.98 k J/tool using the high resolution H-atom Rydberg tagging time-of-flight method. Product rotational state-resolved differential cross sections have been measured. Most of the DF products are backward scattered at low collision energies and then gradually shift to the sideway as the collision energy increases. In addition to the backward and sideway scatterings, we have also observed the DF(v'=4) product in the forward direction for the first time for this reaction. The forward scattering DF(v=4) product also increases with the collision energy. Angular and collision energy dependence of the product energy disposals in different degrees of freedom have been determined. Collision energy dependence of the vibrational branching ratios has also been examined. Possible dynamical origins of the forward scattering DF(v'=4) products were discussed.展开更多
The dynamics of F+HD→HF+D reaction has been studied at ten collision energies ranging from 5.43 kJ/mol to 18.73 kJ/mol using high-resolution H/D atom Rydberg tagging time-of-flight method. Product vibrational and r...The dynamics of F+HD→HF+D reaction has been studied at ten collision energies ranging from 5.43 kJ/mol to 18.73 kJ/mol using high-resolution H/D atom Rydberg tagging time-of-flight method. Product vibrational and rotational state-resolved differential cross sections have been determined. The intensity of the HF(v1=2) forward products decreases as the collision energy increases, suggesting that the resonance contribution is reduced as the collision energy increases. The forward peak of HF(vl=3) product has also been observed above the threshold of this product channel. Product energy disposals in different degrees of freedom have been analyzed. The collision energy dependence of the HF vibrational product branching was also determined. This work presents a comprehensive dynamic picture of this resonance mediated reaction in a wide collision energy regime, providing a good test ground for theoretical understandings of this interesting reaction at higher collision energies.展开更多
We presented an experimental apparatus combining the H-atom Rydberg tagging time-of-flight technique and the laser detonation source for studying crossed beam reactions at hyperthermal collision energies. The prelimin...We presented an experimental apparatus combining the H-atom Rydberg tagging time-of-flight technique and the laser detonation source for studying crossed beam reactions at hyperthermal collision energies. The preliminary study of the F+D2→DF+D reaction at hyperthermal collision energy of 23.84 kJ/mol was performed. Two beam sources were used in this study: one is the hyperthermal F beam source produced by a laser detonation process, and the other is D2 beam source generated by liquid-N2 cooled pulsed valve. Vibrational state-resolved di erential cross sections (DCSs) of product for the title reaction were determined. From the product vibrational state-resolved DCS, it can be concluded that products DF(v'=0, 1, 2, 3) are predominantly distributed in the sideway and backward scattering directions at this collision energy. However, the highest vibrational excited product DF(v'=4), is clearly peaked in the forward direction. The probable dynamical origins for these forward scattering products were analyzed and discussed.展开更多
Let TΩ be the singular integral operator with kernel Ω(x)/|x|n where is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn-1. In this paper, by Fourier transform estimates, L...Let TΩ be the singular integral operator with kernel Ω(x)/|x|n where is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn-1. In this paper, by Fourier transform estimates, Littlewood-Paley theory and approximation, the authors prove that if Ω∈(lnL)2 (Sn- 1), then the commutator generated by TΩ and CMO(Rn) function, and the corresponding discrete maximal operator, are compact on LP(Rn, |s|γp) for p∈ (1, ∞) and γp ∈ (-1, p-l)展开更多
Let T_σ be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ∈Z∥σ_κ∥W^s(R^(2n))< ∞ for some s ∈ (n, 2n]. In this paper, it is proved that th...Let T_σ be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ∈Z∥σ_κ∥W^s(R^(2n))< ∞ for some s ∈ (n, 2n]. In this paper, it is proved that the commutator generated by T_σ and CMO(R^n) functions is a compact operator from L^(p1)(R^n, w_1) × L^(p2)(R^n, w_2) to L^p(R^n, ν_w) for appropriate indices p_1, p_2, p ∈ (1, ∞) with1 p=1/ p_1 +1/ p_2 and weights w_1, w_2 such that w = (w_1, w_2) ∈ A_(p/t)(R^(2n)).展开更多
基金This work was supported by the Chinese Academy of Sciences, the National Natural Science Foundation of China, and the Ministry of Science and Technology of China.
文摘The crossed beams scattering dynamics of the F+HD→HF+D reaction have been studied at collision energies ranging from 8.19 k J/tool to 18.98 k J/tool using the high resolution H-atom Rydberg tagging time-of-flight method. Product rotational state-resolved differential cross sections have been measured. Most of the DF products are backward scattered at low collision energies and then gradually shift to the sideway as the collision energy increases. In addition to the backward and sideway scatterings, we have also observed the DF(v'=4) product in the forward direction for the first time for this reaction. The forward scattering DF(v=4) product also increases with the collision energy. Angular and collision energy dependence of the product energy disposals in different degrees of freedom have been determined. Collision energy dependence of the vibrational branching ratios has also been examined. Possible dynamical origins of the forward scattering DF(v'=4) products were discussed.
基金This work was supported by the Chinese Academy of Sciences, the National Natural Science Foundation of China, and the Ministry of Science and Technology of China.
文摘The dynamics of F+HD→HF+D reaction has been studied at ten collision energies ranging from 5.43 kJ/mol to 18.73 kJ/mol using high-resolution H/D atom Rydberg tagging time-of-flight method. Product vibrational and rotational state-resolved differential cross sections have been determined. The intensity of the HF(v1=2) forward products decreases as the collision energy increases, suggesting that the resonance contribution is reduced as the collision energy increases. The forward peak of HF(vl=3) product has also been observed above the threshold of this product channel. Product energy disposals in different degrees of freedom have been analyzed. The collision energy dependence of the HF vibrational product branching was also determined. This work presents a comprehensive dynamic picture of this resonance mediated reaction in a wide collision energy regime, providing a good test ground for theoretical understandings of this interesting reaction at higher collision energies.
基金supported by the National Natural Science Foundation of China (No.21473015, No.21203016, No.41574101, No.21673232, No.21773213)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No.201222)
文摘We presented an experimental apparatus combining the H-atom Rydberg tagging time-of-flight technique and the laser detonation source for studying crossed beam reactions at hyperthermal collision energies. The preliminary study of the F+D2→DF+D reaction at hyperthermal collision energy of 23.84 kJ/mol was performed. Two beam sources were used in this study: one is the hyperthermal F beam source produced by a laser detonation process, and the other is D2 beam source generated by liquid-N2 cooled pulsed valve. Vibrational state-resolved di erential cross sections (DCSs) of product for the title reaction were determined. From the product vibrational state-resolved DCS, it can be concluded that products DF(v'=0, 1, 2, 3) are predominantly distributed in the sideway and backward scattering directions at this collision energy. However, the highest vibrational excited product DF(v'=4), is clearly peaked in the forward direction. The probable dynamical origins for these forward scattering products were analyzed and discussed.
基金supported by National Natural Science Foundation of China(Grant No.11371370)
文摘Let TΩ be the singular integral operator with kernel Ω(x)/|x|n where is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn-1. In this paper, by Fourier transform estimates, Littlewood-Paley theory and approximation, the authors prove that if Ω∈(lnL)2 (Sn- 1), then the commutator generated by TΩ and CMO(Rn) function, and the corresponding discrete maximal operator, are compact on LP(Rn, |s|γp) for p∈ (1, ∞) and γp ∈ (-1, p-l)
基金supported by the National Natural Science Foundation of China(No.11371370)
文摘Let T_σ be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that sup κ∈Z∥σ_κ∥W^s(R^(2n))< ∞ for some s ∈ (n, 2n]. In this paper, it is proved that the commutator generated by T_σ and CMO(R^n) functions is a compact operator from L^(p1)(R^n, w_1) × L^(p2)(R^n, w_2) to L^p(R^n, ν_w) for appropriate indices p_1, p_2, p ∈ (1, ∞) with1 p=1/ p_1 +1/ p_2 and weights w_1, w_2 such that w = (w_1, w_2) ∈ A_(p/t)(R^(2n)).