Initial Bound State Research Articles

Electron emission in collisions of highly charged ions with atoms and diatomic molecules

A short review of theoretical models previously used to study single and multiple electron ionization in collisions of bare fast highly charged ions with atomic and diatomic molecular targets is given. Electron emission with simultaneous electron capture by the projectile is also considered. The principal mechanisms producing the different reactions are revisited. It is emphasized that two-center descriptions are necessary for an adequate description of the existing experimental data. The role of electron correlation in the initial bound state and during the collision process is analyzed as well as the presence of effects associated with the two-center character of diatomic molecular targets.

Semi-inclusive nonleptonic decaysB→Ds(*)X

We calculate the total and differential decay rates for the semi-inclusive nonleptonic decays $B\to D_s^{(*)} X_q$ ($q=c$ or $u$) under the factorization hypothesis. The initial bound state effect is treated using the light-cone expansion and the heavy quark effective theory. We investigate the contribution of the penguin amplitude for the decay mode $B\to D_s^{(*)} X_c$ and find that it is small but non-negligible. The resulting decay rates for $B\to D_s^{(*)} X_c$ agree with the measurements. The use of the decay mode $B\to D_s^{(*)} X_u$ to determine $|V_{ub}|$ is discussed.

Resonance effects in simultaneous electron-impact ionization-excitation of helium

Using a second-order perturbative model for a ``fast'' incident projectile, together with a convergent R matrix with pseudostates close-coupling model for the initial bound state and the scattering of a ``slow'' ejected electron in the field of the ion, we found a substantial effect of autoionizing resonances in simultaneous ionization-excitation of the $n=2$ states in ${\mathrm{He}}^{+}.$ Although widely ignored to date, we show that the effect must be accounted for in a meaningful comparison between theoretical predictions and the available experimental data.

Resonance effects in electron-impact ionization ofhelium

We have extended our recent work on electron-impact ionizationand ionization-excitation of helium (Fang Yand Bartschat K 2001 J. Phys. B: At. Mol. Opt. Phys. 34 L19) to investigateresonance structures in the ejected-electron-residual-ioninteraction. The calculations were performed using asecond-order perturbative model for a `fast' incident projectiletogether with a convergent R-matrix with pseudo-statesclose-coupling model for the initial bound state and thescattering of a `slow' ejected electron in the field of the ion.The agreement with previous calculations by Marchalant et al using a similar model is satisfactory and confirms the importanceof the `two-step' mechanism in these processes. However,significant discrepancies remain with experimental data by Lowerand Weigold and, to a lesser extent, by McDonald and Crowe.

Semi-inclusiveB→K(K*)Xdecays with initial bound state effects

The effects of initial $b$ quark bound state for the semi-inclusive decays $B\to K(K^*) X$ are studied using light cone expansion and heavy quark effective theory methods. We find that the initial bound state effects on the branching ratios and CP asymmetries are small. In the light cone expansion approach, the CP-averaged branching ratios are increased by about 2% with respect to the free $b$-quark decay. For $\bar B^0 \to K^- (K^{*-}) X$, the CP-averaged branching ratios are sensitive to the phase $\gamma$ and the CP asymmetry can be as large as 7% (14%), whereas for $B^-\to \bar K^0 (\bar K^{*0})X$ the CP-averaged branching ratios are not sensitive to $\gamma$ and the CP asymmetries are small ($< 1%$). The CP-averaged branching ratios are predicted to be in the ranges $(0.53 \sim 1.5)\times 10^{-4}$ [$(0.25 \sim 2.0)\times 10^{-4}$] for $\bar B^0 \to K^- (K^{*-})X$ and $(0.77 \sim 0.84)\times 10^{-4}$ [$(0.67 \sim 0.74)\times 10^{-4}$] for $B^-\to \bar K^0 (\bar K^{*0}) X$, depending on the value of the CP violating phase $\gamma$. In the heavy quark effective theory approach, we find that the branching ratios are decreased by about 10% and the CP asymmetries are not affected. These predictions can be tested in the near future.

B→φKandB→φXsin the heavy quark limit

We study $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}K$ and $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}{X}_{s}$ decays in the heavy quark limit using perturbative QCD. The next leading order corrections introduce substantial modifications to the naive factorization results (more than 50%). The branching ratio $Br(\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}K)$ is predicted to be in the range $[{F}_{1}^{\stackrel{\ensuremath{\rightarrow}}{B}K}{(m}_{\ensuremath{\varphi}}^{2})/0.33{]}^{2}(3.2\ensuremath{-}4.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ that is within the one \ensuremath{\sigma} allowed region from the central value of $6.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ measured by CLEO Collaboration, but outside the one \ensuremath{\sigma} allowed region from the central value of $17.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ measured by BELLE Collaboration for reasonable ${F}_{1}^{\stackrel{\ensuremath{\rightarrow}}{B}K}.$ For the semi-inclusive decay $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}{X}_{s}$ we also include initial bound state effects in the heavy quark limit that decreases the branching ratio by about 10%. $Br(\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}{X}_{s})$ is predicted to be in the range $(4.8\ensuremath{-}6.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}.$

Double ionization of helium in fast ion collisions: comparative study of model wavefunctions

Recently, the doubly differential cross section for double ionization of helium by fast bare carbon ions has been measured as a function of the longitudinal momentum components of both electrons (see Bapat et al 2000). These data show that the two electrons are preferentially emitted back to back. In this work we investigate the influence of various forms for the initial and final state wavefunctions on the calculated doubly differential cross sections in the first Born approximation. It is found that both an appropriate representation of the derivative discontinuities of the initial bound state wavefunction at the two-particle coalescence points and of the Coulomb repulsion of the electrons in the final continuum state are necessary to reproduce this experimental feature. The accuracy of the calculated initial helium atom binding energy is not a reliable criterion for an adequate description of correlation effects in a collisional situation.

Interpretation of high-order harmonic generation in terms of transitions between quantum Volkov states

A theoretical perspective of high-order harmonic generation is presented in which transitions between quantum Volkov states\char22{}stationary solutions to Schr\odinger's equation for an electron interacting with a quantized optical field\char22{}are the dominant mechanism for producing radiation. The picture proposed here is one in which the interaction of an intense optical field with an electron forms a photon-electron ``quasiatom'' and the stationary states of this complex can be viewed as the high optical field analog of bound states of an atom. Consequently, although momentum conservation for the overall harmonic generation process requires that an electron eventually return to the parent atom, the electron and fundamental optical field are treated as an isolated system with well-defined energy and momentum. To introduce a secondary photon (harmonic) field, the matrix element describing the electron-photon field interaction through quantum Volkov states is modified in a perturbative manner. The result is the production of harmonic photons by Volko$\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$Volkov-state transitions, a process which has no classical counterpart. The generation of odd harmonics of the fundamental field and the requirement that the final state of the electron be the initial bound state of the atom follow directly from the theory. A clear connection between harmonic generation and above-threshold ionization (ATI) is drawn by maintaining the discrete, nonzero energies of photoelectrons injected into the driving optical field by ATI. For experiments in which the laser pulse width is \ensuremath{\gtrsim}100\char21{}150 fs, only the lowest ATI photoelectron orders contribute significantly to harmonic generation, whereas higher-energy electrons escape from the parent atom during the pulse risetime. As the duration of the fundamental field is decreased, however, the rapid rise of the field intensity to its peak value effectively traps more energetic photoelectrons, thereby extending the harmonic response to shorter wavelengths. An analytic expression for the transition matrix for the harmonic generation process is derived and is compared with the predictions of semiclassical theory and published experimental results, including harmonic spectra and polarization data.

Initial State Dependence of Low-Energy Electron Emission in Fast Ion Atom Collisions

Single and multiple ionization of neon and argon atoms by 3.6 MeV/u ${\mathrm{Au}}^{53+}$ impact has been explored in kinematically complete experiments. Doubly differential cross sections for low-energy electron emission have been obtained for a defined charge state of the recoiling target ion and the receding projectile. Observed target specific structures in the electron continuum are attributable to the nodal structure of the initial bound state momentum distribution. The experimental data are in excellent accord with continuum-distorted-wave eikonal-initial-state single ionization calculations if multiple ionization is considered appropriately.

Model calculations for the two-fragment electro-disintegration of4He

Differential cross sections for the electro-disintegration process $e + {^4He} \longrightarrow {^3H}+ p + e'$ are calculated, using a model in which the final state interaction is included by means of a nucleon-nucleus (3+1) potential constructed via Marchenko inversion. The required bound-state wave functions are calculated within the integrodifferential equation approach (IDEA). In our model the important condition that the initial bound state and the final scattering state are orthogonal is fulfilled. The sensitivity of the cross section to the input $p{^3H}$ interaction in certain kinematical regions is investigated. The approach adopted could be useful in reactions involving few cluster systems where effective interactions are not well known and exact methods are presently unavailable. Although, our Plane-Wave Impulse Approximation results exhibit, similarly to other calculations, a dip in the five-fold differential cross-section around a missing momentum of $\sim 450 MeV/c$, it is argued that this is an artifact of the omission of re-scattering four-nucleon processes.

Non-relativistic momentum transfer in free-free absorption processes

We consider the non-relativistic free-free absorption of a photon in the presence of a Coulomb field and calculate the momentum transferred to the resulting ion for polarized photons and isotropic initial electron angular distributions. Our calculations, carried to the quadrupolar order, end in an integral which is solved numerically. We show that the final ion always recoils in the opposite direction to the incident photon and that the transferred momentum may be much greater than the photon momentum. Our results are consistent with those of bound-free absorption processes in the limit where the initial bound state tends to the ionization threshold.

Initial-state, final-state and higher-order effects in electron impact ionization of helium atoms

An approximate method to include second-order effects in the treatment of electron impact ionization processes within a combined distorted wave Born approximation -matrix approach is presented. The sensitivity of the results for triple differential cross sections for electron impact ionization of helium to the description of the initial and final states, and to the inclusion of second-order effects within the R-matrix box, is analysed. It is found that changes in the representation of the initial bound state have the strongest effect on the theoretical predictions.

Mechanisms of double ionization of atoms by electron impact

Recent high-energy $(e,3e)$ experiments indicate that the one-step mechanism (shake-off process) is insufficient. We have performed an ab initio calculation that takes into account all the two-step mechanisms of double ionization. This calculation uses the second Born approximation and correlated wave functions for the initial bound state. We show that the two-step processes are not negligible and must be added to the one-step process with the production of interference terms.

A study of the two-step mechanism in the double ionization of helium by fast electrons

In view of recent experiments it can be suggested that the two-step process is not negligible even at high impact energy. An ab initio calculation has been performed on the basis of the second Born approximation using different correlated wavefunctions for the initial bound state. This calculation also shows that the contribution of the two-step process must be included at any impact energy.

Recoil-induced electronic excitation and ionization in one- and two-electron ions

The electronic redistribution of an ion or atom induced by a sudden recoil of the nucleus occurring during the emission or capture of a neutral particle is theoretically investigated. For one-electron systems, analytical expressions are derived for the electronic transition probabilities to bound and continuum states. The quality of a B-spline basis set approach is evaluated from a detailed comparison with the analytical results. This numerical approach is then used to study the dynamics of two-electron systems (neutral He and ) using correlated wavefunctions for both the target and daughter ions. The total transition probabilities to discrete states, autoionizing states and direct single- and double-ionization probabilities are calculated from the pseudospectra. Sum rules for transition probabilities involving an initial bound state and a complete final series are discussed.

Significant hydrogen exchange protection in GroEL‐bound DHFR is maintained during iterative rounds of substrate cycling

An unresolved key issue in the mechanism of protein folding assisted by the molecular chaperone GroEL is the nature of the substrate protein bound to the chaperonin at different stages of its reaction cycle. Here we describe the conformational properties of human dihydrofolate reductase (DHFR) bound to GroEL at different stages of its ATP-driven folding reaction, determined by hydrogen exchange labeling and electrospray ionization mass spectrometry. Considerable protection involving about 20 hydrogens is observed in DHFR bound to GroEL in the absence of ATP. Analysis of the line width of peaks in the mass spectra, together with fluorescence quenching and ANS binding studies, suggest that the bound DHFR is partially folded, but contains stable structure in a small region of the polypeptide chain. DHFR rebound to GroEL 3 min after initiating its folding by the addition of MgATP was also examined by hydrogen exchange, fluorescence quenching, and ANS binding. The results indicate that the extent of protection of the substrate protein rebound to GroEL is indistinguishable from that of the initial bound state. Despite this, small differences in the quenching coefficient and ANS binding properties are observed in the rebound state. On the basis of these results, we suggest that GroEL-assisted folding of DHFR occurs by minor structural adjustments to the partially folded substrate protein during iterative cycling, rather than by complete unfolding of this protein substrate on the chaperonin surface.

Elongation factor Tu, a GTPase triggered by codon recognition on the ribosome: mechanism and GTP consumption.

The mechanism of elongation factor Tu (EF-Tu) catalyzed aminoacyl-tRNA (aa-tRNA) binding to the A site of the ribosome was studied. Two types of complexes of EF-Tu with GTP and aa-tRNA, EF-Tu.GTP-aa-tRNA (ternary) and (EF-Tu.GTP)2.aa-tRNA (quinternary), can be formed in vitro depending on the conditions. On interaction with the ribosomal A site, generally only one molecule of GTP is hydrolysed per aa-tRNA bound and peptide bond formed. The second GTP molecule from the quinternary complex is hydrolyzed only during translation of an oligo(U) tract in the presence of EF-G. The first step in the interaction between the ribosome and the ternary complex is the codon-independent formation of an initial complex. In the absence of codon recognition, the aa-tRNA-EF-Tu complex does not enter further steps of A site binding and remains in the initial binding state. Despite the rapid formation of the initial complex, the rate constant of GTP hydrolysis in the noncognate complex is four orders of magnitude lower compared with the cognate complex. This, together with the results of time-resolved fluorescence measurements, suggests that codon recognition by the ternary complex on the ribosome initiates a series of structural rearrangements that result in a conformational change of EF-Tu, presumably involving the effector region, which, in turn, triggers GTP hydrolysis and the subsequent steps of A site binding.

Laser-induced degeneracies involving autoionizing states in complex atoms.

An initial bound state and an autoionizing state of a complex atom (or ion) which are resonantly coupled by a radiation field can both be characterized in a Floquet approach by complex quasienergies. For certain values of the field's intensity and frequency, the two quasienergies become equal, giving rise to laser-induced degenerate states (LIDS). This phenomenon is demonstrated by applying the ab initio, fully nonperturbative $R$-matrix Floquet theory to Ar, ${\mathrm{H}}^{\ensuremath{-}}$, and He. The general case is considered by constructing models containing discrete states and continua. Results for one- and for two-photon resonances are presented and suggestions for experimental observation are given.

Theory of one- and two-photon dissociation with strong laser pulses

The theory of one- and two-photon dissociation processes with strong laser pulses for slowly varying multiple continua (‘‘direct’’ dissociation) is developed. Closed form expressions for the state preparation and evolution during and after the excitation pulse are derived. We show how saturation of the photodissociation process as a function of the laser power sets in. We also show that for direct dissociation, the fragment state distribution is independent of the laser power. The dependence of spontaneous emission during dissociation (continuum Raman and resonance fluorescence) on the pulse intensity is studied. The formulation is extended to treating resonantly enhanced two-photon dissociation with strong laser pulses. Closed-form expressions for slowly varying pulses and slowly varying continua are derived. Using these expressions, the existence of adiabatic passage to the continuum (APC) by which a system executes a complete population transfer from an initial bound state to the continuum by following two guiding light pulses is established. A simple iterative scheme for going beyond the adiabatic approximation is introduced.

Electron emission induced by resonant coherent interaction in ion-surface scattering at grazing incidence.

The resonant coherent interaction of an ion with an oriented crystal surface, under grazing-incidence conditions with respect to a special direction of the crystal, gives rise to electron loss to the continuum from electronic bound states of the ion. The calculations presented below predict large probabilities for electron emission due to this mechanism. The electrons are emitted with well defined energies, expressed in terms of the condition of resonance. Furthermore, the emission takes place around certain preferential directions, which are determined by both the latter condition and the symmetry of the surface lattice. Our calculations for MeV He[sup +] ions scattered at a W(001) surface along the [l angle]100[r angle] direction with glancing angle of 0--2 mrad indicate a yield of emission close to 1. Using heavier projectiles, one obtains smaller yields, but still large enough to be measurable in some cases (e.g., [approx]0.9 for 53 MeV B[sup 4+] and an angle of incidence of 1 mrad). Besides, the initial bound state is energy shifted due to the interaction with both the crystal potential and the velocity-dependent image potential. This results in a slight shift of the peaks of emission, which suggests a possible spectroscopy for analyzing the dynamical interactionmore » of electronic bound states with solid surfaces.« less