An Empirical Formula Approach to Total Cross Sections for Electron Scattering on Polyatomic Molecules

Considering the real experimental process of e-molecule scattering a new empirical formula has been developed to calculate the total cross sections （TOSs） for electron scattering on polyatomic molecules （CH4, C2H2, CH3OH and CH3F）. The present results are compared with other available theoretical results and experimental data. The new formula incorporates an energy factor f（E） to represent the elastic and inelastic changing process during experiments. It depends on no adjustable parameters and has also extended the validity of the empirical approaches to lower energy range further.     

A New Semi-Empirical Method for Total Cross Sections of Electron Scattering from Spherical Polyatomic Molecules at 30-5000 eV

Electron scattering from spherical polyatomic molecules in the intermediate and high energy range is studied by employing the developed semi-empirical formula for electron scattering from simple diatomic molecules. The total cross sections of electron scattering from CF4 and CC14 are obtained over the incident energy range 30-5000 eV. The quantitative total cross sections are compared with the measurements and with the other calculations wherever available including the results derived from the additivity rule model and the correlated optical potential [Chin. Phys. Left. 21 (2004) 474], and good agreement is obtained over the incident energy range 30-5000eV. It is shown that the calculations derived from the semi-empirical formula are much closer to the measurements than other calculations. Finally, some quantitative information of the single Yukawa potential is also obtained.     

A Correlation Potential Method for Electron Scattering Total Cross Section Calculations on Several Diatomic and Polyatomic Molecules over Energy Range 10 ～ 5000 eV

A complex optical model potential correlated by the concept of bonded atom, which considers the overlapping effect of electron clouds between two atoms in a molecule, is firstly employed to calculate the total cross sections for electron scattering on several molecules (NH₃, H₂O, CH₄, CO, N₂, O₂, and C₂H₄) over the energy range 10～5000 eV using the additivity rule model at Hartree-Fock level. The difference between the bonded atom and the free one in states is that the overlapping effect of electron clouds of bonded atoms in a molecule is considered. The quantitative total cross sections are compared with the experimental data and with the other calculations wherever available and good agreement is obtained over the energy range 10～5000 eV. It is shown that the correlated calculations are much closer to the available experimental data than the uncorrelated ones at lower energies, especially below 500 eV. Therefore, considering the overlapping effect of electron clouds in the complex optical model potential could be helpful for the better accuracy of the total cross section calculations of electron scattering from molecules.     

Total Cross Sections for Electron Scattering from the Isoelectronic （Z = 14） Molecules （C2H2, CO, HCN and N2） at 100－5000eV

A complex optical model potential correlated by the conception of bonded atom, which considers the overlapping effect of electron clouds between the two atoms in a molecule, is firstly employed to calculate the total cross sections for electron scattering from the isoelectronic (Z = 14) molecules (C2H2, CO, HCN, and N2) at 100-5000 eV using the additivity rule at the Hartree-Fock level. The difference between the bonded atom and the free one is that the overlapping effect of electron clouds of bonded atoms in molecules is considered. The quantitative molecular total cross section results are compared with the experimental data and with the other calculations wherever available and good agreement is obtained above 100 eV. It is shown that the additivity rule along with the complex optical model potential considering the overlapping effect of electron clouds can give the results better than that uncorrelated by it. The correlating calculations are much closer to the experiments than the spherical-complex-optical-potential results in the lower energy region [Phys. Rev. A 45 (1992) 202]. Therefore,considering the overlapping effect of electron clouds in the complex optical potential could be helpful for the better accuracy of the total cross section calculations of electron scattering from molecules.     

A Modified Potential Method for Electrons Scattering Total Cross Section Calculations on Several Molecules at 30 ～ 5000 eV: CF4, CCl4, CFCl3, CF2Cl2, and CF3Cl

A complex optical model potential modified by the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds between two atoms in a molecule, is employed to calculate the total cross sections (TCSs) for electrons scattering from several molecules (CF4, CCl4, CFCl3, CF2 Cl2, and CF3 Cl) over an incident energy range 30 ～ 5000 eV using the additivity rule model at Hartree-Fock level. The quantitative TCSs are compared with those obtained by experiments and other theories wherever available, and good agreement is obtained above 100 eV.It is shown that the modified potential can successfully calculate the TCSs of electron-molecule scattering over a wide energy range, especially at lower energies.     

Absolute Differential Cross Sections for Elastic Scattering of Electrons from CO at Intermediate and High Energies

The additivity rule model together with the complex optical model potential correlated by the concept of bonded atoms, which considers the overlapping effect of electron clouds between two atoms in a molecule, is firstly employed to calculate the absolute differential cross sections for electrons scattered by carbon monoxide at intermediate and high energies at the Hartree-Fock level. A comparison of elastic differential cross section results, obtained by using the correlated complex optical model potential, with the available experimental data,shows a significant improvement over the uncorrelated ones. The differential cross sections obtained by using thecorrelated complex optical model potential are in very good agreement with the experimental data. It is shown that the additivity rule model together with the correlated complex optical model potential is suitable for the calculations of the absolute differential cross sections of e-CO scattering.     

Total cross sections of electron scattering by molecules NF3, PF3, N(CH3)3, P(CH3)3, NH(CH3)2, PH(CH3)2, NH2CH3 and PH2CH3 at 30–5000 eV

Total cross sections of electron scattering by eight molecules NF₃, PF₃, N(CH₃)₃, P(CH₃)₃, NH(CH₃)₂, PH(CH₃)₂, NH₂CH₃ and PH₂CH₃, which have some structural similarities, are calculated at the Hartree-Fork level by the modified additivity rule approach [D.H. Shi, J.F. Sun, Z.L. Zhu, H. Ma, Y.F. Liu, Eur. Phys. J. D 45, 253 (2007); D.H. Shi, J.F. Sun, Y.F. Liu, Z.L. Zhu, X.D. Yang, Chin. Opt. Lett. 4, 192 (2006)]. The modified additivity rule approach takes into considerations that the contributions of the geometric shielding effect vary as the energy of incident electrons, the dimension of target molecule, the number of electrons in the molecule and the number of atoms constituting the molecule. The present investigations cover the impact energy range from 30 to 5000 eV. The quantitative total cross sections are compared with those obtained by experiments and other theories. Excellent agreement is observed even at energies of several tens of eV. It shows that the modified additivity rule approach is applicable to carry out the total cross section calculations of electron scattering by these molecules at intermediate and high energies, in particular over the energy range above 80 eV or so. It proves that the microscopic molecular properties, such as the geometrical size of the target and the number of atoms constituting the molecule, are of crucial importance in the TCS calculations. The new results for PH(CH₃)₂ and PH₂CH₃ are also presented at energies from 30 to 5000 eV, although no experimental and theoretical data are available for comparison. In the present calculations, the atoms are still represented by the spherical complex optical potential, which is composed of static, exchange, polarization and absorption terms.     

Measurements of the Cross Sections and A y for D(p, n) Inclusive Breakup Reaction at 170 MeV

The effects of three-nucleon force (3NF) has been actively studied by using the nucleon–deuteron (Nd) scattering states. The differential cross sections of the elastic Nd scattering at the energy below 150 MeV can be well reproduced by incorporating 3NF in the Faddeev calculation based on modern nucleon–nucleon (NN) interactions. On the other hand, the differential cross sections of Nd elastic and inelastic scatterings at 250 MeV show large discrepancies between the data and the Faddeev calculations with 3NF. It indicates the presence of the missing features of the three nucleon system at this energy region. For the systematic study about the energy dependence of this large discrepancies, we measured the differential cross sections and the vector analyzing power A _y for the ²H(p, n) inclusive breakup reaction at 170 MeV. The experiment was carried out at RCNP by detecting scattered neutrons by using the neutron detector NPOL3. The data was compared with the results of the Faddeev calculations with and without the 3NF.     

Differential Cross Sections for High-Lying Vibrational Excitations （v= 0→v′=1,2,... , 9, 10） of e-H2 Scattering

A theoretical investigation on the differential cross section （DCS） from low-energy electron scattering of high-lying vibrational excited H2 molecules is reported. The body-frame vibrational close-coupling （BFVCC） approach is used to solve the scattering equations. Quantum scattering potentials include static, exchange, and polarization contributions based on ab initio calculations. By including the contributions of 9 partial waves （Nt = 9）, 18 Morse vibrational states （Nv = 18）, and 16 molecular symmetries （A = 0, 1,..., 7）, the calculated DCSs have good agreement with available experimental measurements and theoretical studies, and show that high angular momenta and good vibrational wavefunctions are necessary to better describe the scattering physics of electronmolecule vibrational excitation collisions.     

Production of CH （A2△） by multi-photon dissociation of （CH3）2CO,CH3NO2, CH2Br2, and CHBr3 at 213 nm

In order to realize electrostatic Stark deceleration of CH radicals and study cold chemistry, the fifth harmonic of a YAG laser is used to prepare CH(A2△) molecules through using the multi-photon dissociation of(CH3)2CO, CH3NO2, CH2Br2,and CHBr3 at ～ 213 nm. The CH product intensity is measured by using the emission spectrum of CH(A2△→ X2Π). The dependence of fluorescence intensity on laser power is studied, and the probable dissociation channels are analyzed. The relationship between the fluorescence intensity and some parameters, such as the temperature of the beam source, stagnation pressure, and the time delay between the opening of pulse valve and the photolysis laser, are also studied. The influence of three different carrier gases on CH signal intensity is investigated. The vibrational and rotational temperatures of the CH(A2△) product are obtained by comparing experimental data with the simulated ones from the LIFBASE program.     

Electron paramagnetic resonance of the two-dimensional system Mn(CH3COO)2·4H2O

A single crystal Electron Paramagnetic Resonance (EPR) study of manganese acetate tetrahydrate was carried out at Q-band and room temperature. The EPR spectrum always reduces to a Lorentzian singlet with g=2.008. The maximum of linewidth observed along a¹ reveals the spin diffusion effects in this two-dimensional system. The maximum of linewidth observed along b reveals the exchange narrowed dipolar interactions in the linear trimers, as well as the contribution of the fine structure terms.     

Ni(C3H10N2)2NO2(ClO4)晶体的ESR研究

报道了Ni(C₃H₁₀N₂)₂NO₂(ClO₄)晶体在T=1.5K温度和W波段的ESR实验.建立了d⁸离子基态³A₂(F)的零场分裂参量D,E,和g因子与斜方对称晶场势参量间的关系,并应用于Ni(C₃H₁₀N₂)₂NO₂(ClO₄)晶体.计算值与实验数据符合很好,表明所给关系式是合理的.     

Total cross sections for electrons scattering from C_2F_4 and SO_2 at 30-5000 eV: considering the geometric shielding effect

Considering the changes of the geometric shielding effect in a molecule as the incident electron energy varing, an empirical fraction, which is dependent on the incident electron energy, is presented. Using this empirical fraction, the total cross sections (TCSs) for electrons scattering from complex polyatomic molecules C2F4 and SO2 are calculated over a wide energy range from 30 to 5000 eV together with the additivity rule model at Hartree-Fock level. In the TCS calculations, the atoms are presented by the spherical complex optical potential, which is composed of static, exchange, polarization and absorption contributions. The quantitative TCSs above 100 eV are in good agreement with those obtained by experiments and other theories. It is proved that the empirical fraction, which exhibits the TCS contributions of shielded atoms in a molecule at different energies, is reasonable.     

Electron impact total(elastic+inelastic) cross sections with simple molecules consisting of N & O atoms at 100-1600eV

A model complex optical potential rewritten by the conception of bonded atom, which considers the overlapping effect of electron cloud, is employed to calculate the total (elastic + inelastic) cross sections with simple molecules (N2, O2, NO2, NO, N2O) consisting of N & O atoms over an incident energy range of 100 - 1600 eV by the use of additivity rule at Roothaan-Hartree-Fock level. In the study, the complex optical potential composed of static, exchange, correlation polarization plus absorption contributions firstly uses bonded-atom conception. The qualitative results are compared with experimental data and other calculations wherever available and good agreement is obtained. The total cross sections of electron-molecule scattering above 100 eV can be successfully calculated.     

Cross Section Measurements for (n,2n),(n,p)and (n,α) Reactions on Strontium Isotopes at the Neutron Energy About 14MeV

Cross-sections for ⁸⁴Sr(n, 2n)⁸³Sr, ⁸⁶Sr(n, 2n)^{85mSr,86Sr(n, 2n)85Sr,88Sr(n, 2n)87mSr,84Sr(n, p)84Rb,86Sr(n, p)86Rb, 88Sr(n, p)88Rb and 88Sr(n,α)85mKr reactions were measured at neutron energies from 13.5 to 14.6MeV using activation technique and γ-ray spectrometry. The neutron flux was determined using the monitor reaction 93Nb(n, 2n)92mNb and the neutron energies were measured by the method of cross section ratios for $^{90}$Zr(n, 2n)$^{89m+g}$Zr to $^{93}$Nb(n, 2n)$^{92m}$Nb reactions. The results of present work were compared with data published previously.}     

Finite size scaling for O(N) φ4-theory at the upper critical dimension

A finite size scaling theory for the partition function zeroes and thermodynamic functions of O(N) φ⁴-theory in four dimensions is derived from renormalization group methods. The leading scaling behaviour is mean-field like with multiplicative logarithmic corrections which are linked to the triviality of the theory. These logarithmic corrections are independent of N for odd thermodynamic quantities and associated zeroes and are N dependent for the even ones. Thus a numerical study of finite size scaling in the Ising model serves as a non-perturbative test of triviality of φ⁴₄-theories for all N.     

Study of (e, 2e) process on potassium at 6 eV—60 eV above threshold in second-order Born approximation

The standard distorted wave Born approximation (DWBA) method has been extended to second-order Born amplitude in order to describe the multiple interactions between the projectile and the atomic target. Second-order DWBA calculations have been preformed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e, 2e) collisions for alkali target potassium at excess energies of 6 eV-60 eV. Comparing with the first-order DWBA calculations before, the present theoretical model improves the degree of agreement with experiments, especially for backward scattering angle region of TDCS. This indicates that the present second-order Born term is capable to give a reasonable correction to DWBA model in studying coplanar symmetric (e, 2e) problems in low and intermediate energy range.