2p Sigma Research Articles

Spectroscopic evidence for the interaction between shallow hydrogenic donors in GaAs, InP and CdTe

Spectroscopic studies of the shallow donor impurities in compensated samples of n-GaAs, InP and CdTe are made using the technique of photothermal excitation of photoconductivity. In addition to the usual 1s-2p line of the isolated donors, other features are observed which connot be explained in terms of the hydrogenic model of isolated impurities. The most prominent line consists of a relatively sharp peak observed at 60 per cent of the impurity Rydberg in all three materials. The position of this line is independent of impurity concentration but the line increases in intensity with increasing doping. Several models suggesting an explanation involving interacting donor impurities are considered. The most plausible explanation appears to be an analogue of the ionized hydrogen molecule in which the line arises from electronic transitions between the 2p sigma u and 3p sigma g states where the transition energy is almost independent of internuclear separation for a range from six to thirteen Bohr radii.

K X-ray production by 90-360 keV Ar and Ne collisions with Si. A comparison between gas and solid target experiments

K X-ray production in the collisions Ne+, Ne++ to SiH4; Si+, Si++ to Ne and Ar++ to SiH4 has been studied in the energy range 90-360 keV. Ar(K) and Si(K) X-rays were looked for but not observed, and the production cross sections must be less than 10-26 cm2, but Ne(K) X-rays were found and the corresponding cross section increases between 10-24 and 3*10-22 in the energy range studied, which agrees with expectations according to the electron promotion model of Fano and Lichten (1965). Comparison has been made of these ion-gas target results, with the previous ion-solid target results of Brandt and Laubert (1970) and Taulbjerf et al. (1973), and comment is made on the interpretation in terms of 'solid effects'. Within the framework of the Fano-Lichten model a rotational coupling of the 2p sigma MO to levels at or near the continuum is required to explain our observation of Ne(K) X-rays.

Photodissociation of H2+: variation with temperature

Theoretical results are presented for the photodissociation cross section of H2+ from the 1s sigma g ground electronic state to the vibrational continuum of the 2p sigma u state. Values of the cross section have been calculated for rotational states 0 or=10000K, the total cross section would be improved by including more rotational states. An empirical extrapolation procedure is proposed using the available results to obtain cross sections accurate at high temperatures.

Gas target experiments of K-shell vacancy sharing in asymmetric ion-atom collisions

K-shell vacancy sharing was measured using 200 to 500 keV Ne incident on Na, Ne, O2 and N2 gas targets. The experimental results are in good agreement with a previous theory assuming radial coupling between the 2p sigma and 1s sigma molecular orbitals.

Multistate molecular treatment of H+-H collisions

The low-energy direct and charge exchange, elastic and inelastic proton-hydrogen collisions were studied in an impact parameter eikonal approximation, employing a molecular expansion on the 1s sigma g, 2p sigma u, 2p pi u, 3p sigma u and 3p pi u states of the H2+ molecule. Results for the 1s, 2s, 2p0, 2p+or-1 and n>or=3 states are presented and compared with other theoretical and experimental values. The influence on the final results of the relevant coupling matrix element between the 2p sigma u and 2p pi u is analysed.

Translational factors in eikonal approximation and their effect on channel couplings

The coupled equations of the adiabatic-state expansion formulated in the context of the stationary-state scattering theory are examined. The translational factors are introduced in the eikonal approximation through coordinate transformation. The equations are consistent with those of Chen and Watson (1968) in that they are free from the spurious long-range interaction even in the absence of the translational factors. The cancellation of the spurious R-1 long-range interaction of the 2p sigma u-2p pi u rotational coupling in the (p+,H) system is given as an example. The effect of the translational factor on the channel coupling interaction is discussed.

Variational approximations to the 2pσuand 2pπuwavefunctions of the hydrogen molecule ion

It is shown that trial wavefunctions for the 2p sigma u and 2p pi u states of H2+ with three variational parameters, separable in elliptic coordinates give excellent results for the energy eigenvalues as functions of the internuclear coordinate. It is also seen that there are two minima for the energy as a function of the parameters. Earlier results for the same trial function used for the 2p sigma u state in error because the optimization has not always been carried out for the absolute minimum.

Photoionization of the helium metastable states above the n=2 threshold

Differential cross sections for the photoelectric transitions He(21S0,23S1)+h(cross) omega to He+(1s,2s,2p,3s,3p,3d)+e- have been calculated for incident photon energies above the n=2 threshold using Hylleraas bound state wavefunctions and close coupling final state wavefunctions. Particular attention has been given to the angular distribution of the photoelectrons ejected in the transitions to the excited states of the residual He+ ion. When the partial cross sections are transformed to a representation which diagonalizes the long range r-2 interactions coupling degenerate final state channels, it is found that some linear combination of the degenerate channels is preferentially excited over a range of incident photon energies from the threshold to several times the threshold value. At higher energies the calculated ( sigma 2s+ sigma 2p)/ sigma 1s and ( sigma 3s+ sigma 3p+ sigma 3d)/ sigma 1s ratios approach the asymptotic values predicted by the theory of Kabir and Salpeter.

Photoionization of helium: study of He+H nu =He+(n=2)+e

Simultaneous excitation and ionization of helium to the n=2 state has been studied between 100 and 200 eV, at angles theta =54 degrees 44' and theta =90 degrees between photon and photo-electron. The cross section ratio ( sigma 2s+ sigma 2p)/ sigma 1s agrees well with the theoretical prediction by Jacobs and Burke; also the theoretical values of sigma 1s/ sigma 2p and asymmetry parameter beta 2p are consistent with experimental data.

The production of K shell vacancies in symmetric ion-atom collisions

The electron-promotion model of Fano and Lichten (1965) has been applied to the calculation of the cross section for production of K shell vacancies in symmetric ion-atom collisions. The promotion is assumed to occur via rotational coupling between the 2p sigma and 2p pi molecular orbitals. Certain statistical factors which govern the probability of a vacancy occurring initially in the 2p pi molecular orbital have been derived. A peak in the vacancy production probability at small impact parameters is predicted and is shown to correspond to deflection through 90 degrees . Good agreement with experiment is obtained when the method is applied to the Ne+-Ne system and an approximate scaling law is suggested by which the cross section for K shell vacancy production in other symmetric collisions may be deduced.

On the asymmetry in the angular distribution of the fragments produced from the collision induced dissociation of HD+ion

The recently observed asymmetry in the forward and backward scattering of the fragments produced from the collision induced dissociation of heteronuclear molecular ions has been explained by considering their dipole moments. For simplicity, the electron impact dissociation of the HD+ ion for the 1s sigma 2 Sigma g+ to 2p sigma 2 Sigma u+ transition has been considered by applying the Born-Oppenheimer approximation. To include the effect of the dipole moment of the molecular ion, exchange scattering has also been considered. The results show that the inclusion of the electron-dipole interaction term in the Hamiltonian cannot explain the observed asymmetries. It is suggested that the asymmetry is due to the preferential orientation of the molecular ions due to the effect of the accelerating field on the dipole moment of the ions in the ion source chamber.

Differential cross sections for elastic scattering, resonant charge exchange and excitation in low energy proton-hydrogen collisions

The H+-H collision is investigated using the three-state molecular expansion, which takes account of the coupling between 2p sigma and the 2p pi states of the H2+ quasi-molecule. Differential cross sections for direct elastic scattering, resonant charge exchange and direct and exchange excitation of H(2p) have been computed for a range of incident proton energies from 150 eV to 2.84 keV and for a range of scattering angles from 0 to 10 degrees (in laboratory system). The agreement with the experimental results is excellent. The nature of non-adiabatic effects in low energy H+-H collisions is discussed in detail.