Born Values Research Articles

Scattering amplitudes for dark and bright excitons

Using the composite boson many-body formalism that takes single-exciton states rather than free carrier states as a basis, we derive the integral equation fulfilled by the exciton-exciton effective scattering from which the role of fermion exchanges can be unraveled. For excitons made of -spin electrons and -spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude Δ, despite differences in the carrier exchanges involved. A brightness-changing channel also exists when two opposite-spin excitons scatter: dark excitons can end either in the same dark states with an amplitude , or in opposite-spin bright states , with a different amplitude , the number of carrier exchanges involved in these scatterings being even or odd, respectively. Another major result is that these amplitudes are linked by a striking relation, , which has decisive consequence on exciton Bose-Einstein condensation. By using Born values, we show that the exciton condensate can be optically observed through a bright part when excitons have large dipole only, that is, when the electrons and holes are in two well-separated layers, as in current experiments.

Pengaruh Variasi JarakKolom Kapur dalam Stabilisasi Tanah Lempung Lunak pada Tinjauan Nilai Indek Pemampatan Tanah(Cc)

<p>Numerousbuildingslocated in north area of Java Island encountersettlement problem. The settlementoccurs because most ofsoil in the areais soft clay soil. The behavior of this soilis characterized by the large value of coefficient compression (Cc) and small valueof bearing capacity. This condition causes potentially great consolidation settlement. In this research, limes column stabilization method will be applied to make soft clay soil better. Limes columns were expected to reduce Cc value therefore consolidation settlement decreases. This research was conducted throughlaboratory experiment, usingbox100 cm in lengths, 40 cm in wide, and 40 cmin height. Three variations of diameters (5 cm, 10 cm, 15 cm) and three variations of distance of sample taken from outside of the limes column mould (10 cm,20 cm, 30 cm) was applied in this research. Influence of limes column to the value of Ccwasexamined. The result of this research showsthat limescolumn couldsignificantlyreduceCcvalue. TheCc valuedecreases when thedistance of sample taking placedecreases. The average of Ccdeclineon three variationsdistance of column (10 cm, 20 cm, 30 cm)are 17.28%, 44.97%, 52.24%respectively. The most efficient distance of thelimes column is 20 cm.</p>

Positronium formation cross-sections in the ground and excited states ( $\mathsf{n=2}$ levels) in an $\mathsf{e^{+}}$ -He atom collision

The positronium formation cross-sections in the ground and excited n=2 levels have been studied in an -He atom collision in the framework of eikonal approximation. Both the differential and total formation cross-sections have been investigated in the intermediate- and high-energy regime. Present eikonal results are found to differ appreciably from the corresponding first Born values even at very high incident energies. The total cross-section results have been compared with available experiments due to different groups as well as with other existing theoretical results.

FIRST EVIDENCE FOR ELECTROWEAK RADIATIVE CORRECTIONS FROM THE NEW PRECISION DATA

The analysis of the newest data on the leptonic Z-decays and mW appears to reveal the first manifestations of electroweak radiative corrections. In fact, these data differ, at the level of 2σ, from their electroweak Born values, while they agree, to within 1σ, with the theoretical values which take the electroweak radiative corrections into account. Previous data were within 1σ in agreement with both sets of values.

The values of mt and [formula omitted] derived from the non-observation of electroweak radiative corrections at LEP: global fit

A set of equations representing the W/ Z mass ratio and various observables of Z decays in terms of g ̄ a ≡ α(m z), G μ, m z, m t, m H, g ̄ a s ≡ α s (m z), m b and m τ (all other fermion masses being neglected) are compared with the latest data of the four LEP detectors, which at the level of one standard deviation coincide with their Born values. Our global fit gives: m t = 161 −16−22 +15+16, g ̄ a s = 0.119±0.006±0.002 , where the central values correspond to m H = 300 GeV, the first errors are statistical and the second ones represent shifts of the central values corresponding to m H = 1000 GeV(+) and 60 GeV(−). The predicted mass of the top is smaller than in the recent fits by 4 GeV. The predicted values of m w / m z and the LEP observables, based on the fitted values of m t and g ̄ a s , show a weak dependence on m H and differ by several predicted standard deviations from the corresponding Born values. The uncertainties of the predicted values and their deviations from the corresponding Born values determine the experimental accuracy required to observe electroweak radiative corrections.

Positronium formation in the ground and n=2 levels in an e+-H collision.

The positronium formation processes in the ground and excited n=2 levels have been investigated in ${e}^{+}$-H atom collision using the Glauber eikonal approximation. Both the differential and total formation cross sections have been studied in the intermediate- and high-energy regime. Present eikonal results are found to differ appreciably from the corresponding first-order Born values even at very high energies. The total-cross-section results have been compared with other existing theoretical values as well as with the corresponding Born cross sections.

Cross sections for excitation and ionization in e-He(21,3S) collisions

Cross sections for the 23S-n3L(n=2-5, L=S-F) excitations and for single ionization in e-He(21,3S) collisions are determined by using the Born approximation. For a given n, the 23S-n3D transitions dominate at intermediate energies and this trend is continued for transitions to the near continuum. For larger energies epsilon of the ejected electron, higher angular momentum l waves progressively dominate. While up to nine partial waves are in general required for convergence of the bound-free form factor, as many as 30 are needed when momentum changes are in the vicinity of the Bethe ridge for large epsilon . Binary-encounter results for ionization are also obtained and agree with the Born values at intermediate energies.

Measurement of total cross sections (e+, Ne) and (e+, Ar)

The total cross sections for positrons on neon and argon atoms have been measured in the energy ranges 15 eV to 272.5 eV and 25 eV to 300 eV respectively. The cross sections indicate clearly that Born values will not be reached until at least 3 KeV. Interpolating between the measured and the valid Born regions has allowed an application of the sum rule which connects scattering length. Born forward scattering amplitude, and the momentum-integral over the total cross section. This procedure gives scattering lengths as = −0.53 ± 0.15 Bohr radii for neon and as = −2.8 ± 0.7 Bohr radii for argon; the errors include maximum credible uncertainties in the interpolations.

E−−Hscattering for a wider range of energy

An integral form of the close-coupling approximation has been applied to the scattering of electrons by hydrogen atoms with the retention of only the $1s$ state, the effect of exchange being included. Results for the differential and the total cross sections have been obtained from 1 to 500 eV. The calculated results have been compared with the experimental findings and other theoretical results and are found to be fairly reliable throughout the entire energy range. The present results differ from Born values by about 4% even at 500 eV.

A high energy approximation. III. Helium excitation by electrons

For Pt II see abstr. A75744 of 1971. The cross sections for the direct excitation of the 21S and 21P states of helium by electron impact are evaluated in a first order approximation in which the interaction between the incident electron and target nucleus is represented by a coulomb wave final state in the T matrix. The results obtained for the differential cross sections are much greater than those of the Born approximation for large scattering angles, and the present results are in much better agreement with experiment. The present calculation predicts inelastic differential cross sections which have the asymptotic energy dependence of E-3 for all nonzero angles of scattering. The total cross sections converge to the Born values at high energy.

Étude des niveaux d'énergie de 47Sc au moyen de la réaction 48Ti(t, α)47Sc

Abstract The energy levels of 47 Sc are investigated through the 45 Sc(t, p) 47 Sc reaction using 11.8 MeV incident tritons and a multigap magnetic spectrograph with nuclear emulsions to analyse the resulting protons. Seventy states are excited in 47 Sc up to 6.9 MeV. The data are analysed using the distorted wave Born approximation and values of the orbital angular momentum L of the transferred neutron pair are derived for 28 levels. Good agreement with previous results is generally obtained, new states in 47 Sc are detected and more precise information on the spins of some levels in 47 Sc are deduced. The results are compared with shell model calculations. Strong L = 0 and mixed L = 0 + 2 transitions to 47 Sc levels other than the ground state are detected, and qualitative explanations for them are presented.

Absolute cross sections for excitation of helium by electrons (20–2000 eV) and the polarization of the emitted radiation

Absolute cross sections for excitation by electrons from the ground state of helium to 4 1S, 5 1S, 6 1S, 3 1P, 4 1D, 5 1D, 6 1D, 4 3S and 3 3P states of helium have been determined by observing the resulting light emission. The energy region covered extends from 20 to 2000 eV. Two devices were used, one for electron energies from threshold up to 100 eV and another for higher impact energies. All line-intensity measurements were corrected for the polarization of the radiation, the polarizing effect of the monochromator and space-charge effects. In the evaluation of the excitation cross sections cascading effects were taken into account. The energy dependence of the 1 1S-3 1P cross section is in very good agreement with theoretical calculations above about 200 eV. The experimental values for the n 1S and 3 1P levels are in the asymptotic high-energy region about 10% larger than the theoretical ones according to the Born approximation. The energy dependences of the n 1S and 3 1P cross sections are in good agreement with the results of Moustafa Moussa et al.. Our n 1D cross sections are, although 14 to 35% larger than the theoretical values, closer to the Born values than previous experimental results. In a plot of cross section times electron energy against the logarithm of the electron energy the n 1D curves exhibit a maximum. This effect becomes less pronounced for higher principal quantum numbers. The energy dependences of the 4 3S and 3 3P cross sections do not agree with the E −3 el law as predicted by Ochkur. For energies larger than 100 eV we find a decrease proportional to E −2.0 el for the 4 3S level and to E −2.4 el for the 3 3P level. The polarization results for the 3 1P-2 1S light emission show very good agreement with the Born theory. The energy dependence of the polarization degree of the radiation of n 1D-2 1P transitions is over a large energy range (150–1000 eV) in agreement with theoretical calculations; however, the magnitude of the polarization degree differs with theory which is also the case in previous experiments of other investigators.

The 21S and 21P excitations of helium by proton and electron impact

The 2 1S and 2 1P excitations of helium by electron and proton impact are considered by use of Born, two-state and four-state versions of the impact-parameter treatment. The cross sections so obtained are modified by a transformation that takes account (in a plane-wave approximation) of the maximum and minimum momentum changes that occur during the collision. Agreement with the accurate Born values of Bell et al. (1968- 9) is found, while comparison with the proton-impact cross sections of Van den Bos (1969) suggests that the 2s-2p dipole coupling is more sensitive to the choice of the 2 1S helium wave function than is the Born 1s-2s short-range coupling. The inclusion of wavelength distortion, back-couplings, 2p-2s couplings and rotational coupling between the magnetic substates affects the proton-impact excitations more than it does the electron-impact excitations.

Approximate Cross-Sections for Inelastic Collisions of Electrons with Atoms. II. Forbidden Transitions.

view Abstract Citations (11) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Approximate Cross-Sections for Inelastic Collisions of Electrons with Atoms. II. Forbidden Transitions. Scanlon, Joseph H. ; Milford, S. N. Abstract A previous method for finding very simple approximate electron-atom cross-sections for allowed transitions is extended to forbidden transitions. From the high-energy properties of cross-sections and the form of the cross-section at its maximum, an expression is obtained for the momentum cutoff in terms of O , the energy at which the maximum occurs. The multipole expansion gives a simple approximate formula for the cross-section (T, in the region 0 o , in terms of the quadrupole moment determined from experiment or calculation; the threshold shape is adopted for e < E The curve for (T(E,) is found to cross the Born curves within 10 per cent of the Born maxima for several forbidden transitions in hydrogen With the particular method used for estimating o,, in the region 0 > o, the simple (T(o) formula satisfactorily reproduces the Born values for the An = 1, but not the An = 2, transitions considered. For use in this and other approximation methods, Born and Bethe cross-sections were calculated for seven forbidden and three allowed transitions in hydrogen, namely, 1s-2s, 3s; 2s-3s, 3p, 3d, 4s; 2p-3s, 3p, 3d, 4f. Publication: The Astrophysical Journal Pub Date: November 1961 DOI: 10.1086/147198 Bibcode: 1961ApJ...134..724S full text sources ADS | Related Materials (1) Part 1: 1960ApJ...131..407M