Multichannel Coupling Research Articles

Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for the Feshbach resonance

A new type of supersymmetric transformations of the coupled-channel radial Schroedinger equation is introduced, which do not conserve the vanishing behavior of solutions at the origin. Contrary to usual transformations, these ``non-conservative'' transformations allow, in the presence of thresholds, the construction of potentials with coupled scattering matrices from uncoupled potentials. As an example, an exactly-solvable potential matrix is obtained which provides a very simple model of Feshbach-resonance phenomenon.

A theoretical study on the photoionization of the valence orbitals of phosphine

We report a theoretical study on the photoionization of phosphine in the static-exchange level and frozen core approximation, using the method of continued fractions. The main subject of the present study is to investigate in which extent the Hartree-Fock description of the target applied to molecular photoionization is valid. Also, the role played by multichannel coupling is analysed. Our study shows that single-channel Hartree-Fock calculations can provide reliable results except for photon energies near the photoionization threshold.

Fabrication of a V-groove on the optical fiber connector using a miniaturized machine tool

As optical communication is being substituted for telecommunication, the demand of a large variety of fiber optic components is increasing. V-groove substrates, one of the module components, are used to connect optical fibers to optical planar circuits and to arrange fibers. Their applications are multi-channel optical connectors and optical wave-guide fiber coupling, etc. Because these substrates are a critical part of the splitter in a multiplexer and a multi-fiber connector, precise and reliable fabrication process is required. For precisely aligning core pitch between fibers, machined core pitch tolerance should be within submicrons. In general, these are produced by state-of-the-art micro-fabrication. However, most of the process equipment is very expensive. Also, it is difficult to change the process line for custom designs to meet specific requirements using various materials. For various design specifications such as different values of the V angle and for low-priced products, the fabrication method should be flexible and low cost. To achieve this goal, a miniaturized machine tool with high accuracy positioning was developed. It is shown in this present work, that this cutting process can be efficiently used to produce V-groove subtracts.

Kondo Effect in Unconventional Superconductors

A new type of Kondo effect in unconventional superconductors is studied theoretically by using the Wilson's numerical renormalization group method. In this case, orbital degrees of freedom of a Cooper pair play an important role. It produces multichannel exchange couplings with a magnetic impurity, although the impurity is just a local spin. Here we focus on a p x +i p y -wave state which is a fully gapped system. In this case, the ground state is always a spin doublet in all the T K /Δ region, and the local spin is shrunk by the Kondo effect in the strong coupling region ( T K /Δ→∞). Here T K and Δ are the Kondo temperature and the superconducting energy gap, respectively. It indicates that the spin of the ground state is generated by the orbital effect of the Cooper pairs. This is completely different from the s -wave pairing case where a Kondo singlet is stabilized for large T K /Δ values. This type of Kondo effect reflects the symmetry of the conduction electron system.

Orbital effect of Cooper pairs on the Kondo effect in unconventional superconductors

A type of Kondo effect peculiar to unconventional superconductors is studied theoretically by using Wilson's numerical renormalization group method. In this case, the angular momentum of a Cooper pair plays an important role in the Kondo effect. It produces multichannel exchange couplings with a local spin. Here we focus on a ${p}_{x}{+ip}_{y}$-wave state which is a full-gap system. The calculated impurity susceptibility shows that the local spin is almost quenched by the Kondo effect in the strong-coupling region ${(T}_{\mathrm{K}}/\ensuremath{\Delta}\ensuremath{\rightarrow}\ensuremath{\infty}),$ while the ground state is always a spin doublet over all the ${T}_{\mathrm{K}}/\ensuremath{\Delta}$ region. Here ${T}_{\mathrm{K}}$ and $\ensuremath{\Delta}$ are the Kondo temperature and the superconducting energy gap, respectively. This is different from the s-wave pairing case where the Kondo singlet is realized for large ${T}_{\mathrm{K}}/\ensuremath{\Delta}$ values. The strong-coupling analysis shows that the ${p}_{x}{+ip}_{y}$-wave Cooper pair is connected to the Kondo singlet via the orbital dynamics of the paired electrons, generating the spin of the ground state. This type of Kondo effect reflects the symmetry of the conduction electron system.

Theoretical resolution of theH−resonance spectrum up to then=5 threshold: States of3Posymmetry

The spectrum of resonance states of ${\mathrm{H}}^{\ensuremath{-}}$ of ${}^{3}{P}^{o}$ symmetry up to the $n=5$ Hydrogen threshold has been resolved by identifying all the complex eigenvalues of the corresponding Schr\"odinger equation with widths down to about ${10}^{\ensuremath{-}9}$ a.u. In order to achieve this spectral resolution inside the continuous spectrum, we employed the previously described polyelectronic complex-eigenvalue Schr\"odinger-equation theory, with special choices of large trial two-electron spaces, constructed in terms of real and complex one-electron Slater-type orbitals. Electron correlation and multistate and multichannel couplings characteristic to the problem were accounted for with high numerical accuracy. The basis set of real orbitals constituting the localized part of the resonances, were chosen systematically so as to cover in a regular manner the configuration space from 3 a.u. up to about ${10}^{4}$ a.u. In this way, both the inner and the outer (very diffuse) orbitals as well as the possible cases of medium-range intrashell states were represented reliably. Energies, widths, and wave-function characteristics were computed and analyzed for 83 resonances below the $n=2,$ 3, 4, and 5 Hydrogen levels. The essence of these results is presented numerically as well as in special figures, whose purpose is to demonstrate the degree to which these complex eigenvalues fall into series according to the Gailitis-Damburg theory of dipole resonances. The existence of series of dipole resonances with characteristic energy and width scaling is used as the zero-order reference model. We found that, in general, the resonances indeed follow the regularity predicted by the Gailitis-Damburg model. At the same time, there are a few irregularities, caused by interseries perturbations. They appear especially strongly in regions where overlapping resonances exist. Using our previous results for the resonance spectrum of ${}^{1}{P}^{o}$ symmetry, similarities and differences are discussed. Finally, the existence of a shape resonance lying above the $n=3$ threshold, which has been predicted in earlier work, is confirmed. On the contrary, our calculations did not confirm the appearance of a shape resonance above the $n=2$ threshold, which has also been predicted before in the literature.

Theoretical resolution of theH−resonance spectrum up to then=4threshold. II. States of1Sand1Dsymmetries

The resonance spectrum of ${\mathrm{H}}^{\ensuremath{-}}$ for ${}^{1}S$ and ${}^{1}D$ symmetries up to the $n=4$ threshold has been computed by solving the corresponding complex eigenvalue Schr\odinger equation in terms of basis functions of real and complex coordinates. These functions are chosen and optimized judiciously and systematically in order to account for the specific details of electronic structure, electron correlation, and multistate and multichannel couplings characterizing the problem. Large sets of Slater orbitals, extending in a regular manner to about 8000 atomic units, were employed in order to describe properly the full range and especially the large-$r$ behavior of the localized part of these resonances, as their energy approaches their corresponding threshold. Energies, widths, and wave-function characteristics are presented for $33{}^{1}S$ states and $37{}^{1}D$ states having widths down to about $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\mathrm{a}.\mathrm{u}.$ Of this total of 70 states, only 32 have been identified before via the application of different theoretical approaches, or, for very few of them, in scattering experiments. By adopting the Gailitis-Damburg model of dipole resonances as the relevant zero order model, we identify unperturbed and perturbed spectral series, in analogy with the well-known spectra of neutral atoms or positive ions, where the zero-order model is based on the Rydberg spectrum of the $1/r$ Coulomb potential. For perturbed spectra, only rough correspondence can be made with the smooth series predictions of the zero-order model. By achieving many-digit numerical precision for our results, we demonstrate the occasional presence of unique irregularities associated with each threshold, such as the existence of overlapping resonances and of ``loner'' resonances (i.e., not belonging to any series) below and above threshold. An example for the latter is a ${}^{1}D$ shape resonance above the $n=3$ threshold. This state was already identified by Ho and Bhatia [Phys. Rev. A 48, 3720 (1993)]. However, our values for the energy above threshold $(\ensuremath{\Delta}E=0.49497\mathrm{meV})$ and for the width $(\ensuremath{\Gamma}=8.632\mathrm{meV})$ differ significantly from theirs $(\ensuremath{\Delta}E=116.94\mathrm{meV}$ and $\ensuremath{\Gamma}=157\mathrm{meV}).$

Theory of two-photon spectroscopy of autoionizing states in helium and beryllium

Two-photon ionization of helium and beryllium in the region of (2,n) and (3,n) autoionizing series is investigated in the perturbative regime. The problem involves above threshold ionization as well as multichannel coupling for series lying above the second ionization threshold. Our method is based on the Feshbach formalism in the context of L2-basis functions. It allows us to parametrize the ionization cross section in the region of resonances by generalizing the usual Fano and Starace forms to multiphoton processes. The resonance parameters are given for (2,n) and (3,n) series of helium and (3,n) series of beryllium lying below the Be+(3s) threshold. Symmetries 1Se and 1De are considered.

Efficient self-aligning multibeam coupling into a single-mode fiber

We present and demonstrate a method for efficient coupling of many beams into a single-mode fiber. Using the phase conjugating property for mutually incoherent beams of the double phase conjugate mirror (DPCM), we achieved coupling for a full 6/spl times/6 matrix of beams into a single-mode fiber. In principle, this number of input channels can be increased manyfold beyond the 36 used in our experiment. Of the phase conjugate generated by the DPCM in the direction of the fiber, over 97% (Fresnel corrected) entered the fiber, thus giving a highly accurate coupling. The DPCM transmission efficiency itself was measured at 40% (Fresnel corrected), thus giving an overall coupling efficiency of 39%. By optimizing the DPCM parameters, a significantly higher overall coupling could be achieved. An additional advantage of this method is that the DPCM will reconfigure if there are small changes in the system, thus making the system very robust. This multichannel coupling method can be of importance in the coupling of the output beams of a vertical cavity surface emitting laser (VCSEL) into a single-mode fiber where each channel may carry independently modulated information. This technique can be further generalized to a bidirectional multisingle-mode fiber interconnection system, of which a basic 3/spl times/2 system is demonstrated. >

Dependence of the steady state of a nonlinear degenerate molecular dimer on the character of dissipative coupling.

The dynamics of quasiparticle transport in a degenerate adiabatic molecular dimer with dissipative as well as nonlinear local site coupling has been analyzed. The dissipative part of the model is based on the Haken-Strobl type of Liouville equation for a density matrix that includes multichannel coupling to a dissipative environment and, moreover, the additional nonlinear term of polaronic type. The theory of positive semigroups has been applied in deriving equations of motion for components of the Bloch vector that satisfy requirements of a relaxing semigroup. The presence of only one decay channel, represented by local dissipative coupling, always leads to the long-time equalization of site-occupation probabilities. We have shown that whether the nonsymmetrical steady state is reached or not depends exclusively on the properties of the Haken-Strobl dissipative part of Liouvillian, regardless of the nonlinear coupling. Clearly, the magnitude of the asymmetry, if it occurs, is influenced by the strength of the nonlinear local site coupling.

Dynamics of transfer-ionisation processes in slow collisions of multicharged ions with atoms

The transfer-ionisation Auger processes involving two active electrons in slow collisions of multiply charged ions with atoms are considered. The corresponding multichannel coupling problem is approximately reduced to interaction of three quasistationary states. The three-state S matrix is constructed by assuming a weak overlap of the two-state non-adiabatic transition regions and applying a matching procedure. Closed-form expressions for transition probabilities are given for each transfer-ionisation channel for two typical configurations of the initial, one-electron and two-electron capture potential curves.

Multi three-cluster coupling model of nuclear reactions

Two alternative versions of practicable connected kernel theories of nuclear reactions are proposed. The state of a many-body system is approximated by a superposition of two- and three- cluster states. The transitions among these states are assumed to be either due to particle exchanges as in the Amado-Lovelace (AL) formalism, or due to multi-channel couplings within two-cluster subsystems. Via latter couplings, all important three-cluster partitions in addition to the original one are incorporated. The simpler of two models, the Multi Three-Cluster Coupling (MTCC) model, is the direct extension of the AL formalism to accomodate multi-channel couplings in two-cluster subsystems. An important process missing from both the Faddeev theory and the MTCC model is the sequential transfer. In the second model, which is the most extended MTCC model, and which is named the Multi Two- and Three-Cluter Coupling (MTTC) model, this shortcoming is remedied. Under the limitation of two- and three-cluster approximation, our theories can treat all reactions, elastic, inelastic, rearrangement and breakup, consistently within one formalism to all orders in compliance with the full unitarity requirement.

Multi three-cluster coupling model of nuclear reactions

Two alternative versions of practicable connected kernel theories of nuclear reactions are proposed. The basic assumption is that the state of a many-body system can be approximated by a superposition of two- and three-cluster states corresponding to various possible reaction processes. The approach is based on the concept of transitions due to particle exchange as in the AmadoLovelace (AL) formalism. All important three-cluster partitions can be incorporated via multichannel couplings in two-cluster subsystems. The simpler of two models, which is called the multi three-cluster coupling (MTCC) model, is a direct extension of the AL formalism. Using the separable representation of two-cluster potentials, the AL type coupled equations among reaction amplitudes are postulated. The MTCC equation is shown to be reduced to the equation with the same structure as the Faddeev equation. Thus, while the MTCC model can treat a much wider class of nuclear reactions than the Faddeev approach, the calculation is no more complicated than that. The basic assumption in this model, as well as in the AL and AGS theories, is shown to contain some degree of inconsistency regarding the treatment of bound state pole parts of interacting pairs. This is remedied in the other model, which we call the multi two- and three-cluster coupling (MTTC) model. This is the most extended MTCC model that is possible within the two- and three-cluster coupling model. In the MTTC treatment, it is shown that sequential (multi-step) transfers can also be accommodated in addition to all various processes that are possible in the MTCC approach.

A semiclassical approach to the dynamics of chemical reactions within the hyperspherical formalism

Semiclassical techniques are introduced within the hyperspherical coordinate approach, which allows the reduction of many-body problems to the multichannel close coupling formalism in terms of a single (hyper) radial variable. The theory, when applied to collinear chemical reactions, leads to the computation of adiabatic energy levels, and to estimates of nonadiabatic coupling elements. Comparisons are carried out with exact quantum results for the reactions H+H 2, I+HI, H+FH, and their isotopic variants. It is shown that the theory predicts accurately resonance properties and interference effects in reaction probabilities.

A semiclassical approach to the dynamics of chemical reactions within the hyperspherical formalism

Semiclassical techniques are introduced within the hyperspherical coordinate approach, which allows the reduction of many-body problems to the multichannel close coupling formalism in terms of a single (hyper)radial variable. The theory, when applied to collinear chemical reactions, leads to the computation of adiabatic energy levels, and to estimates of nonadiabatic coupling elements. Comparisons are carried out with exact quantum results for the reactions H+H 2, I+HI, H+FH, and their isotopic variants. It is shown that the theory predicts accurately resonance properties and interference effects in reaction probabilities.

Reciprocity relation for multichannel coupling kernels

Assuming time-reversal invariance of the many-body Hamiltonian, it is proven that the kernels in a general coupled-channels formulation are symmetric, to within a specified spin-dependent phase, under the interchange of channel labels and coordinates. The theorem is valid for both Hermitian and suitably chosen non-Hermitian Hamiltonians which contain complex effective interactions. While of direct practical consequence for nuclear rearrangement reactions, the reciprocity relation is also appropriate for other areas of physics which involve coupled-channels analysis.NUCLEAR REACTIONS Symmetry relation for multichannel coupling kernels. Non-Hermitian operators. Time-reversal invariance and reciprocity.

Studies of rotational predissociation of van der Waals molecule by the method of complex coordinate

A practical method is presented for calculating resonance energies and widths (lifetimes) of metastable states of van der Waals molecules, incorporating the use of complex coordinate transformation and square-integrable basis functions. The utility of the method is illustrated through a study of the level widths and energies of rotationally predissociating atom–diatom model systems. Satisfactory agreement with previous works was found. Besides involving only bound state calculations and being free from imposement of boundary conditions, the method can be readily extendable to multichannel coupling problems.

Quantitative evaluation of radioisotope distribution in vivo by isosensitive scanner plus 4096-word multi-channel analyzer coupling

Quantitative evaluation of radioisotope distribution in vivo by isosensitive scanner plus 4096-word multi-channel analyzer coupling