Total Elastic Cross Sections Research Articles

Calculation of the elastic collision properties of Na and Li atoms at ultracold temperature

This paper firstly reports a theoretical study of elastic scattering properties in a mixture of 23Na and 7Li atoms at cold and ultracold temperatures in detail. Based on the new constructed accurate singlet X1 Σ+g and the triplet α3Σ+u states interatomic potentials for 23Na7Li mixture, it calculates the scattering lengths and the effective ranges by three computational methods, and obtains good agreements. Using the mass scaling method, it also calculates 23Na6Li scattering lengths and s-wave and total elastic cross sections, whose rich resonance structures were found and interpreted in terms of quasibound diatomic levels trapped behind a centrifugal barrier.

Elastic collision between S and D atoms at low temperatures and accurate analytic interaction potential and molecular constants of the SD(X2Π) radical

The equilibrium internuclear separations, harmonic frequencies and interaction potentials have been calculated by employing the CCSD（T） theory in combination with the series of the correlation- consistent basis sets, cc-pVnZ and aug-cc-pVnZ （n=2, 3, 4, 5）, of Dunning and co-workers. The potential energy curves are all fitted to the Murrell-Sorbie functions, which are used to determine the spectroscopic parameters. At the CCSD（T）/aug-cc-pV5Z level of theory, the values of D0, De, Re, ωe, αe, B0 are 3.65730 eV, 3.77669 eV, 0.13424 cm－1, 1938.372 cm－1, 0.09919 cm－1, 4.88585 cm－1 and 4.8872 cm－1, respectively, which conform almost perfectly with the available measurements. With the analytic interaction potential obtained at the CCSD（T）/aug-cc-pV5Z level of theory, a total of 23 vibrational states has been predicted for the first time when the rotational quantum number J is set to equal zero （J=0） by solving the radial Schrdinger equation of nuclear motion. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are reproduced from the SD（X2Π） potential when J=0 The total and various partial-wave cross sections are calculated for the elastic collisions between the ground-state S and D atoms at energies from 1.0×10-11 to 1.0×10-4 a.u. when the two atoms approach each other along the SD（X2Π） interaction potential. No shape resonances can be found in the total elastic cross sections. The results show that the shape of the total elastic cross sections is mainly dominated by the s-partial wave at very low temperatures. Because of the weakness of the shape resonances coming from various partial waves, they are all covered up by the strong total elastic cross sections.

Elastic collisions between O and D atoms at low temperature and accurate analytic potential energy function and molecular constants of the OD（X2Π） radical

Interaction potential of the OD（X2Π） radical is constructed by employing the CCSD（T） theory in combination with the correlationconsistent quintuple basis set, augccpV5Z, in the valence range. Using the potential, the spectroscopic parameters are accurately determined. The present D0, De, Re, ωe, ωeχe and Be values are of 44574, 46225 eV, 009702 nm, 2724923, 453534 and 100096 cm-1, respectively, which are in excellent agreement with the recent measurements wherever available. A total of 23 vibrational states have been found when J = 0 by solving the radial Schrdinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good agreement with the available experimental results. The total and various partialwave cross sections are calculated for the elastic collisions of O and D atoms in their ground states at low and ultralow temperatures when the two atoms approach each other along the OD（X2Π） potential energy curve. The impact energy range covers a vange from 10×10-11 to 10 ×10-3a.u.. One shape resonance has been found in the total elastic cross sections. Contribution to the total elastic cross sections by each partial wave is investigated carefully. The results show that the shape of the total elastic cross sections is mainly dominated by the s partial wave. The shape resonances coming from the higher partial waves are covered up by the strong s partial wave cross sections.

Screening-corrected electron impact total and ionization cross sections for boron trifluoride (BF3) and boron trichloride (BCl3)

In this paper, we report modified calculations for total elastic, total ionization and total (complete) cross sections for boron trifluoride (BF3) and boron trichloride (BCl3) upon electron impact at energies from around threshold to 2000 eV. We have proposed a model which allows screening correction due to the overlapping of atoms as seen by incident electrons in a complex molecule. We have employed the well-known spherical complex optical potential (SCOP) formalism to evaluate total elastic and total inelastic cross sections and hence total (complete) cross sections. The ionization cross sections were derived using the complex optical potential–ionization contribution (CSP-ic) method developed by us. The present results are compared with available experimental and other theoretical data wherever available and overall good agreement is observed. The present screening-corrected model shows improvement over the previous method especially at low energies. We also predict total elastic cross sections for these targets using this method.

Elastic collisions of sulfur and hydrogen in their ground states at low temperatures and spectroscopic parameters of SH(X2∏) radical

This paper constructs the interaction potential of the SH(X2∏) radical by using the coupled-cluster singles-doubles-approximate-triples theory combining the correlation-consistent quintuple basis set augmented with the diffuse functions, aug-cc-pV5Z, in the valence range. Employing the potential, it accurately determines the spectroscopic parameters. The present De, Re, ωe, ωeχe, αe and Be values are of 3.7767eV, 0.13424 nm, 2699.846 cm−1, 47.7055cm−1, 0.2639cm−1 and 9.4414cm−1, respectively, which are in excellent agreement with those obtained from the measurements. A total of 19 vibrational states has been found when J = 0 by solving the radial Schrödinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the experimental results. The total and various partial-wave cross sections are computed for the elastic collisions of sulfur and hydrogen in their ground states at low temperatures when two atoms approach each other along the SH(X2∏) potential energy curve. Over the impact energy range from l.0 × 10−11 to 1.0 × 10−4 a.u., eight shape resonances have been found in the total elastic cross sections. For each shape resonance, the resonant energy is accurately calculated. Careful investigations have pointed out that these resonances result from the l = 0, 1, 2, 3, 4, 6, 7, 8 partial-wave contributions.

Strong resonances in low-energy electron elastic total and differential cross sections for Hf and Lu atoms

Very low-energy electron elastic total and differential cross sections for Hf and Lu atoms exhibit dramatically sharp resonances, whose energy positions are identified with their electron affinities, which are comparable in magnitude with those of Ca and Sr atoms, thus making Hf and Lu atoms suitable candidates for use in the quenching of Rydberg states. The calculation used the recent Regge-pole methodology which embeds the crucial electron correlation effects, with a Thomas-Fermi-type potential incorporating the vital core-polarization interaction. The near-threshold total cross sections for Hf and Lu are contrasted with those of Yb, Ca, and Sr atoms.

Positron scattering fromC20

Ab initio calculations of 0.01--10 eV collisions of positrons with fullerene ${\text{C}}_{20}$ are performed using a single-center expansion of the total wave function and a model potential to represent the positron-molecule interaction. Total elastic cross sections and eigenphase sums are generated and analyzed, while bound states and possible long-lifetime scattering resonances are explored, particularly those which are found to reside within the cage structure defined by the carbon atoms of the cluster.

Elastic scattering of two H(2Sg) and N(4Su) atoms at low temperatures and accurate spectroscopic parameters of NH (X3Σ−) radical

This paper reports that the interaction potential for the X3Σ− state of NH radical is constructed at the CCSD(T)/cc-PV6Z level of theory. Using this potential, this paper calculates the spectroscopic parameters (De, Re, ωe, ωeχe, αe and Be) and their values are of 3.578eV, 0.10368 nm, 3286.833cm−1, 78.433cm−1, 0.6469cm−1 and 16.6735cm−1, respectively, which are in excellent agreement with the experiments. Then the total of 14 vibrational states has been found when J = 0 by solving the radial Schrodinger equation of nuclear motion. For each vibrational state, the vibrational manifolds are reported for the first time. And last, the total cross sections, s-wave, p-wave and d-wave cross sections are computed for the elastic collisions between two ground-state atoms (hydrogen and nitrogen) at low temperatures. It finds that the total elastic cross sections are dominated by s-wave scattering when the collision energy is below 10−6 a.u. The pronounced shape resonance is found at energy of 6.1 × 10−6 a.u. Calculations have shown that the shape resonance comes from the p-wave contributions.

Theoretical electron impact elastic, ionization and total cross sections for silicon hydrides, SiHx (x = 1, 2, 3, 4) and disilane, Si2H6 from threshold to 5 keV

In this article we report comprehensive calculations of total elastic (Qel), and total ionization cross sections, (Qion), on silicon hydrides SiHx (x = 1–4) and disilane, Si2H6 on electron impact at energies from circa threshold to 2000 eV and total (complete) cross sections (QT) up to 5 keV. Spherical complex optical potential (SCOP) formalism is employed to evaluate Qel and QT. Total ionization cross sections, Qion, are derived from total inelastic cross sections, Qinel, using our complex spherical potential – ionization contribution (CSP-ic) method. Dependence of QT on the dipole polarizability of the target and incident energy is presented for these targets through analytical formula, using which calculation of QT is extended up to 5 keV. Comparison of QT for all these targets is carried out to present a general theoretical picture of collision processes and also to visualize the dependence of QT on the total number of electrons in the target and hence on the geometrical size of the target. Present calculations also provide information on the excitation processes of these targets. Present results are compared with available experimental and other theoretical data wherever available and overall good agreement is observed. There is probably no data for total elastic and total (complete) cross sections for SiHx (x = 2-3) in the present energy range and hence reported for the first time.

Near-threshold resonances in electron elastic scattering cross sections for Au and Pt atoms: identification of electron affinities

The recent Regge-pole methodology has been employed together with a Thomas–Fermi type potential which incorporates the vital core-polarization interaction to investigate the near-threshold electron attachment in Au and Pt as Regge resonances. The resultant stable negative ion states are found to have the discernible characteristic of very small imaginary parts of the Regge poles, which translate into long-lived resonances. The near-threshold electron elastic total cross sections are characterized by multiple resonances from which we extract the electron affinity (EA) values through the scrutiny of the imaginary part of the relevant complex angular momentum. For the Au− and Pt− negative ions the extracted binding energies of 2.262 eV and 2.163 eV, respectively are in excellent agreement with the most recently measured EA values for Au and Pt. Ramsauer–Townsend minima, shape resonances and the Wigner threshold behaviour are identified in both Au− and Pt− ions.

Hydrogen molecule – antihydrogen scattering at very low energies

We consider the low-energy scattering of antihydrogen (H¯) by the simplest molecule, H2. This preliminary treatment applies a generalisation of the Kohn variational method to the calculation of total elastic cross section at low energies. The scattering wavefunction calculated by the generalised Kohn method is used to estimate the antiproton annihilation in flight using a delta function pseudo potential introduced in the treatment of antiproton annihilation in H–H¯ scattering.

Near-Threshold Electron Attachment as Regge Resonances: Cross Sections for K, Rb, and Cs Atoms

We investigate the near-threshold formation of negative ions as Regge resonances in electron-atom scattering, with specific results obtained for e--K, e--Rb, and e--Cs. The complex angular momentum method, implemented within the Mulholland formulation of the total elastic cross sections, is employed. We demonstrate that for e--K, e--Rb, and e--Cs scattering, the near-threshold electron attachment cross sections are characterized by the Wigner threshold behavior, Ramsauer-Townsend minima, and Regge resonances, all discernible only through Regge partial cross section scrutiny. Regge partial, differential, and total elastic cross sections are presented and contrasted, as well as the differential cross section critical minima.

Calculations of elastic, ionization and total cross sections for inert gases upon electron impact: threshold to 2 keV

In this paper we report comprehensive calculations of total elastic (Qel), total ionization (Qion) and total (complete) cross sections (QT) for the impact of electrons on inert gases (He, Ne, Ar, Kr and Xe) at energies from about threshold to 2000 eV. We have employed the spherical complex optical potential (SCOP) formalism to evaluate Qel and QT and used the complex spherical potential-ionization contribution (CSP-ic) method to derive Qion. The dependence of QT on polarizability and incident energy is presented for these targets through an analytical formula. Mutual comparison of various cross sections is provided to show their relative contribution to the total cross sections QT. Comparison of QT for all these targets is carried out to present a general theoretical picture of collision processes. The present calculations also provide information, hitherto sparse, on the excitation processes of these atomic targets. These results are compared with available experimental and other theoretical data and overall good agreement is observed.

Proton–proton interaction in constituent quarks model at LHC energies

In this paper we consider the soft processes at LHC energies in the framework of the Constituent Quark Model (CQM). We show that this rather naive model is able to describe all available soft data at lower energies and to predict the behavior of the total cross section, elastic and diffractive cross sections at the LHC energy. It turns out that the ''input'' Pomeron, which has been used in this approach, has parameters that are close to so called ''hard'' Pomeron with rather large intercept $\Delta \approx 0.12$ and small value of the slope $\alpha'_P \approx 0.08 GeV^{-2}$. We show that the elastic amplitude has a minimum at impact parameter $b =0$ and a maximum at $b \approx 2 GeV^{-1}$. Such a behavior is a result of overlapping the parton clouds that belong to different quarks in the hadron.

Multiple scattering theory for pion-nucleus elastic scattering and the in-medium piN amplitude

Elastic scattering of positive and/or negative pions (pi+ and/or pi-) by nuclei has been studied by means of Glauber's multiple scattering theory (GMST). The differential, total and total elastic cross sections using both the full series expansion and the first order correction (called optical limit results, OLA) of the Glauber amplitude, have been calculated. The in-medium pN amplitude (sigmaeff., sigmaeff.) as well as the free piN one (sigmafree, sigmafree) are invoked into the full series calculations of the Glauber amplitude and our results were compared with the corresponding experimental data. These calculations are carried out for the elastic collisions, pi-- 2He4 at incident energy 180 MeV, pi±- 3Li6 at 240 MeV, pi-- 6C12 at incident energies 180, 200 and 260 MeV, pi+- 8O16 at 240 and 270 MeV and pi±- 20Ca40 at energy 292.5 MeV. The comparisons reflect that, except around the minima, the full series calculations with the in-medium pN amplitude are better in describing the scattering data than those using the free piN one and both are better than the optical limit results.

INELASTIC COLLISIONS OF POSITRONS WITH BERYLLIUM AND MAGNESIUM IONS

The collision of positrons with beryllium and magnesium positive ions is treated for the first time as a three-channel problem with the assumption that the elastic, ground-positronium and excited-positronium formation channels are open. A one-valence-electron model for the targets, based on the Clementi–Roetti Slater basis functions, as well as an improved coupled-static approach allowing for the polarization of the excited positronium, are used for calculating the partial cross-sections of eight partial waves (corresponding to 0≤ℓ≤7, where ℓ is the total angular momentum of the scattering problem considered). The calculations are carried out, in each case, at 19 values of the incident energy lying above the excited positronium formation threshold (i.e. above 16.42 eV in e+– Be+scattering and above 13.02 eV in e+– Mg+scattering). The total elastic cross-sections of e+– Mg+scattering show a peak around the ionization threshold of Mg+(at 14.723 eV) but for e+– Be+scattering, display a peak at 90 eV (remember that the ionization threshold of Be+is 18.2 eV). Although the resulting total collisional positronium formation cross-sections are smaller than the elastic ones, their relatively large values should draw the attention of experimental and theoretical physicists to the field of positron–ion collisions.

ELASTIC AND INELASTIC SCATTERING OF POSITRONS BY POTASSIUM ATOMS

The investigations of the elastic and inelastic collisions of positrons with potassium atoms, K (1s2, 2s2, 2p6, 3s2, 3p6, 4s), are presented. The potassium target atoms are described using Clementi–Roetti wavefunctions within the framework of the one-valence-electron model. The total cross-sections which correspond to eight partial cross-sections are calculated at 34 values of the incident energy [Formula: see text] using the coupled-static approximation. The resulting total elastic, ground- and excited-positronium formation cross-sections are compared with experimental results and those calculated by other authors. In the vicinity of 6 eV, and consistent with the measurements of Parikh et al.,2our total cross-section displays a pronounced peak. We support the conclusion of McAlinden et al.15and Hewitt et al.14that above about 4 eV, positronium formation is mainly into excited states. Good agreement is obtained with the total cross-section measurements of Kwan et al.1and Parikh et al.2Positronium formation is not important above about 50 eV.

What can one do with Regge poles?

We briefly review recent applications of the Regge pole analysis to light- and heavy particle collisions. These include interpretation of resonance structures observed in elastic, inelastic and reactive angular distributions as well as in total elastic cross-sections of atom–atom and electron–atom collisions. Simple models as well as realistic reactive systems are used as examples.

Strong similarities between small cluster anions and electrons colliding with argon

Total destruction cross sections for negative aluminum clusters $\mathrm{Al}^{\ensuremath{-}}{}_{n}$ with $n=2--4$, and total detachment cross sections of the aluminum anion ${\mathrm{Al}}^{\ensuremath{-}}$, incident on Ar are measured. These values, and previously measured cross sections of $\mathrm{C}^{\ensuremath{-}}{}_{n}$ and $\mathrm{Si}^{\ensuremath{-}}{}_{n}$ with $n=1--4$, are compared with total (elastic plus inelastic) cross sections for electron impact on the same target. Similarities between the experimental cross sections for anions and electrons, observed in the velocity range of $0.2\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1.8\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$, led to a model in which the overall shape of the dependence on velocity of the anionic cross sections is well described by a convolution of the anion's outermost electron momentum distribution with the free electron-impact cross sections, and their absolute values obtained by fitting a cluster-size dependent additive constant. A geometrical interpretation is then proposed.

Theoretical calculations of the total and ionization cross sections for electron impact on some simple biomolecules

In this paper we report total cross sections TCS, QT, total elastic cross sections, Qel, and total ionization cross section, Qion for electron impact on water, formaldehyde, formic acid, and the formyl radical from circa 15 eV to 2 KeV. The results are compared where possible, with previous theoretical and experimental results and, in general, are found to be in good agreement. The total and elastic cross sections for HCHO, HCOOH, and CHO radical are reported.