Channel Wave Functions Research Articles

Perey-effect in continuum-discretized coupled-channel description of (d, p) reactions

The Perey effect in two-body channels of (d, p) reactions has been known for a long time. It arises when the nonlocal two-body deuteron-target and/or proton-target problem is approximated by a local one, manifesting itself in a reduction of the scattering channel wave functions in the nuclear interior. However, the (d, p) reaction mechanism requires explicit accounting for three-body dynamics involving the target and the neutron and proton in the deuteron. Treating nonlocality of the nucleon-target interactions within a three-body context requires significant effort and demands going beyond the widely-used adiabatic approximation, which can be done using a continuum-discretized coupled-channel (CDCC) method. However, the inclusion of nonlocal interactions into the CDCC description of (d, p) reactions has not been developed yet. Here, we point out that, similarly to the two-body nonlocal case, nonlocality in a three-body channel can be accounted for by introducing the Perey factors. We explain this procedure and present the first CDCC calculations to our knowledge including the Perey effect.

Constrained Correlated-Gaussians for Hyperspherical Calculations

We formulate a hyperspherical approach within standard configuration interaction calculations aiming at a description of large-scale dynamics of $N$-particle system. The channel wave function and the adiabatic channel energy are determined by solving a hyperradius-constrained eigenvalue problem of the adiabatic Hamiltonian. The needed matrix elements are analytically evaluated using correlated Gaussians with good orbital angular momentum and parity. The feasibility of the approach is tested in three-$\alpha$ system. A spectrum of the adiabatic channel energies is determined depending on the degree of localization of the basis functions.

The Faddeev-Merkuriev Differential Equations (MFE) and Multichannel 3-Body Scattering Systems

Numerical implementation of the modified Faddeev Equation (MFE) is presented in some detail. The Faddeev channel wave function displays unique properties of each and every open channel, respectively. In particular, near resonant energies, the structures of the resonances are beautifully displayed, from which, the life-time of the resonances can be determined by simply using the uncertainty principle. The phase shift matrix, or the K-matrix, provides unique information for each and every resonance. This information enables the identification of the physical formation mechanism of the Gailitis resonances. A few of these resonances, previously known as the mysterious shape resonances, have occurred in a number of different collision systems. The Gailitis resonances are actually produced by a quantized Stark-effect within the various collision systems. Since the Stark-effect is a universal phenomenon, the Gailitis resonances are expected to occur in much broader classes of collision systems. We will present the results of a precision calculation using the MFE method in sufficient detail for interested students who wish to explore the mysteries of nature with a powerful theoretical tool.

Direct excitation near the thresholds for alkali-like ions impacted by electrons

A new method is described for solving the multi-channel equation, in which channel wave functions are expressed in terms of the homogeneous solutions analytically. By using the method, direct excitations of and ions impacted by electrons are calculated for the energies close to their thresholds. The calculated results are compared with the experimental results and previous theoretical calculations. The lack of orthogonality between the channel wave functions and the orbital wave functions of the target ions is considered.

Understanding the structure of d*(2380) in chiral quark model

The structure and decay properties of d* have been detailedly investigated in both the chiral SU(3) quark model and the extended chiral SU(3) quark model that describe the energies of baryon ground states and the nucleon-nucleon (NN) scattering data satisfactorily. By performing a dynamical coupled-channels study of the system of ΔΔ and hidden-color channel (CC) with quantum numbers I(J P ) = 0(3+) in the framework of the resonating group method (RGM), we find that the d* has a mass of about 2.38-2.42 GeV and a root-mean-square radius (RMS) of about 0.76-0.88 fm. The channel wave function is extracted by a projection of the RGM wave function onto the physical basis, and the fraction of CC component in the d* is found to be about 66%-68%, which indicates that the d* is a hexaquark-dominated exotic state. Based on this scenario the partial decay widths of d* → d π 0 π 0 and d∗ → d π + π − are further explicitly evaluated and the total width is then obtained by use of the branching ratios extracted from the measured cross sections of other possible decay channels. Both the mass and the decay width of d* calculated in this work are compatible with the data (M ≈ 2380 MeV, Γ ≈ 70 MeV) reported by WASA-at-COSY Collaboration.

Theoretical study of thed*(2380)→dππdecay width

The decay widths of the $\ds\to d \pi^0\pi^0$ and $\ds\to d \pi^+\pi^-$ processes are explicitly calculated in terms of our chiral quark model. By using the experimental ratios of cross sections between various decay channels, the partial widths of the $\ds\to pn \pi^0\pi^0$, $\ds\to pn \pi^+\pi^-$, $\ds\to pp \pi^0\pi^-$, and $\ds\to nn \pi^+\pi^0$ channels are also extracted. Further including the estimated partial width for the $\ds\to pn $ process, the total width of the $\ds$ resonance is obtained. In the first step of the practical calculation, the effect of the dynamical structure on the width of $\ds$ is studied in the single $\Delta\Delta$ channel approximation. It is found that the width is reduced by few tens of MeV, in comparison with the one obtained by considering the effect of the kinematics only. This presents the importance of such effect from the dynamical structure. However, the obtained width with the single $\Delta\Delta$ channel wave function is still too large to explain the data. It implies that the $\ds$ resonance will not consist of the $\Delta\Delta$ structure only, and instead there should be enough room for other structure such as the hidden-color (CC) component. Thus, in the second step, the width of $\ds$ is further evaluated by using a wave function obtained in the coupled $\Delta\Delta$ and CC channel calculation in the framework of the Resonating Group Method (RGM). It is shown that the resultant total width for $\ds$ is about 69 MeV, which is compatible with the experimental observation of about 75 MeV and justifies our assertion that the $\ds$ resonance is a hexaquark-dominated exotic state.

Extracting partial decay rates of helium from complex rotation: autoionizing resonances of the one-dimensional configurations

Partial autoionization rates of doubly excited one-dimensional helium in the collinear Zee and eZe configuration are obtained by means of the complex rotation method. The approach presented here relies on a projection of back-rotated resonance wave functions onto singly ionized channel wave functions and the computation of the corresponding particle fluxes. In spite of the long-range nature of the Coulomb potential between the electrons and the nucleus, an asymptotic region where the fluxes are stationary is clearly observed. Low-lying doubly excited states are found to decay predomintantly into the nearest single-ionization continuum. This approach paves the way for a systematic analysis of the decay rates observed in higher-dimensional models, and of the role of electronic correlations and atomic structure in recent photoionization experiments.

Surface-integral formalism of deuteron stripping

The purpose of this paper is to develop an alternative theory of deuteron stripping to resonance states based on the surface integral formalism of Kadyrov et al. [Ann. Phys. 324, 1516 (2009)] and continuum-discretized coupled channels (CDCC). First we demonstrate how the surface integral formalism works in the three-body model and then we consider a more realistic problem in which a composite structure of target nuclei is taken via optical potentials. We explore different choices of channel wave functions and transition operators and show that a conventional CDCC volume matrix element can be written in terms of a surface-integral matrix element, which is peripheral, and an auxiliary matrix element, which determines the contribution of the nuclear interior over the variable $r_{nA}$. This auxiliary matrix element appears due to the inconsistency in treating of the $n-A$ potential: this potential should be real in the final state to support bound states or resonance scattering and complex in the initial state to describe $n-A$ scattering. Our main result is formulation of the theory of the stripping to resonance states using the prior form of the surface integral formalism and CDCC method. It is demonstrated that the conventional CDCC volume matrix element coincides with the surface matrix element, which converges for the stripping to the resonance state. Also the surface representation (over the variable $r_{nA}$ of the stripping matrix element enhances the peripheral part of the amplitude although the internal contribution doesn't disappear and increases with increase of the deuteron energy. We present calculations corroborating our findings for both stripping to the bound state and the resonance.

Ultracold O2 + O2 collisions in a magnetic field: On the role of the potential energy surface

The collision dynamics of (17)O(2)((3)Σ(g)(-)) + (17)O(2)((3)Σ(g)(-)) in the presence of a magnetic field is studied within the close-coupling formalism in the range between 10 nK and 50 mK. A recent global ab initio potential energy surface (PES) is employed and its effect on the dynamics is analyzed and compared with previous calculations where an experimentally derived PES was used [T. V. Tscherbul et al., New J. Phys 134, 055021 (2009)]. Compared to the results using the older PES, magnetic-field dependence of the low-field-seeking state in the ultracold regime is characterized by a very large background scattering length, a(bg), and cross sections exhibit broader and more pronounced Feshbach resonances. The marked resonance structure is somewhat surprising considering the influence of inelastic scattering but it can be explained by resorting to the analytical van der Waals theory, where the short-range amplitude of the entrance channel wavefunction is enhanced by the large a(bg). This strong sensitivity to the short range of the ab initio PES persists up to relatively high energies (10 mK). After this study and despite quantitative predictions are very difficult, it can be concluded that the ratio between elastic and spin relaxation scattering is generally small, except for magnetic fields which are either low or close to an asymmetric Fano-type resonance. Some general trends found here, such as a large density of quasibound states and a propensity toward large scattering lengths, could be also characteristic of other anisotropic molecule-molecule systems.

An asymptotic normalization coefficient for the loosely-bounded state of 17F nucleus in the orthogonality conditions model

A method for calculating an asymptotic normalization coefficient (ANC) is developed within an approximation of the resonating group model (RGM)-the orthogonality conditions model (OCM). An ANC for the 16O + p channel of the (1/2+, 495.3 keV) state of the 17F nucleus is calculated using different versions of the model. It is shown that the influence of the exchange terms on the values of the ANC is quite great and is not reduced to renormalizing the channel wave function as a whole.

Magnetic forces and stationary electron flow in a three-terminal semiconductor quantumring

We study stationary electron flow through a three-terminal quantum ringand describe effects due to deflection of electron trajectories by classicalmagnetic forces. We demonstrate that generally at high magnetic field (B) the current is guided by magnetic forces to follow a classical path, which forB > 0 leads via the left arm of the ring to the left output terminal. The transport to the leftoutput terminal is blocked for narrow windows of magnetic field for which the interferencewithin the ring leads to formation of wavefunctions that are only weakly coupled to theoutput channel wavefunctions. These interference conditions are accompanied by injectionof the current to the right arm of the ring and by appearance of sharp peaks of the transferprobability to the right output terminal. We find that these peaks at high magnetic fieldare attenuated by thermal widening of the transport window. We also demonstrate that theinterference conditions that lead to their appearance vanish when elastic scatteringwithin the ring is present. The clear effect of magnetic forces on the transferprobabilities disappears along with Aharonov–Bohm oscillations in a chaotic transportregime that is found for rings whose width is larger than the width of the channels.

Quantum theory of chemical reactions in the presence of electromagnetic fields

We present a theory for rigorous quantum scattering calculations of probabilities for chemical reactions of atoms with diatomic molecules in the presence of an external electric field. The approach is based on the fully uncoupled basis set representation of the total wave function in the space-fixed coordinate frame, the Fock-Delves hyperspherical coordinates, and the adiabatic partitioning of the total Hamiltonian of the reactive system. The adiabatic channel wave functions are expanded in basis sets of hyperangular functions corresponding to different reaction arrangements, and the interactions with external fields are included in each chemical arrangement separately. We apply the theory to examine the effects of electric fields on the chemical reactions of LiF molecules with H atoms and HF molecules with Li atoms at low temperatures and show that electric fields may enhance the probability of chemical reactions and modify reactive scattering resonances by coupling the rotational states of the reactants. Our preliminary results suggest that chemical reactions of polar molecules at temperatures below 1 K can be selectively manipulated with dc electric fields and microwave laser radiation.

Electron-ion recombination rate coefficients and photoionization cross-sections for Al XI, Al XII, Si XII, Si XIII for UV and X-ray modeling

Results are presented from detailed study of inverse processes of photoionization and electron-ion recombination of ( hν + Al XI ⇋ Al XII + e), ( hν + Al XII ⇋ Al XIII + e), ( hν + Si XII ⇋ Si XIII + e), and ( hν + Si XIII ⇋ Si XIV + e) using ab initio unified method. These are the first results on photoionization cross-sections ( σ PI( nSLJ)) with autoionizing resonances and level-specific recombination rate coefficients, incorporating both the radiative and dielectronic recombination, for these ions. All fine structure levels with n ⩽ 10 and 0 ⩽ l ⩽ 9 are considered. A total of 98 fine structure levels with 1/2 ⩽ J ⩽ 17/2 for Al XI and Si XII, and 190 for Al XII and 189 for Si XIII with 0 ⩽ J ⩽ 10 are found. σ PI( nSLJ) show background enhancements due to core excitations and narrow high-peak resonances. Level-specific recombination rates show smooth decay with a small bump at high temperature. Present total recombination rate coefficients with temperature ( α R( T)) show good agreement with available rates. Recombination rates over photoelectron energy ( α R( E)) are presented for astrophysical and laboratory plasma applications. Total recombination rates for H-like Al XIII and Si XIV are given for completeness. Calculations are carried out in the relativistic Breit-Pauli R-matrix method using coupled channel wavefunctions. Inclusion of important atomic effects such as radiation damping, channel couplings, interference of DR and RR, and relativistic fine structure effects should provide accuracy within 10–15%. The comprehensive datasets are applicable for various models such as for ionization balance and recombination-cascade for UV and X-ray lines.

대전입자형 디스플레이 소자의 측정시스템 및 광학특성

We fabricated the 4 channel wave function generator with variable frequency, pulse width, amplitude and rising/falling slope to develop driving method of charged particle type display. The selective sell driving is ascertained by fabricated panel with black and yellow particles. To measure CIE point, reflectivity, contrast ratio and viewing angle, experimental apparatus is integrated with optical circular moving emitting/receiving part and spectrometer connected to emitting part. The yellow particles in glass have reflectivity of and wavelength of 571.2nm and black one has reflectivity of in case of only 1 layer of particle, and the case of 3 layer the optical property is promoted.

The interaction of antihydrogen with simple atoms and molecules

In this paper, we describe calculations that we have carried out of cross sections for rearrangement processes in very low-energy helium+antihydrogen (H¯) scattering that result in He+p¯+Ps or Hep¯+e+ or αp¯+Ps-. A significantly more accurate method from that used previously [E.A.G. Armour, S. Jonsell, Y. Liu, A.C. Todd, Nucl. Instr. and Meth. B 247 (2006) 127] is used to calculate the He+H¯ entrance channel wave function. Results are presented for the first two processes. Mention is made of the use of the method in calculations of low-energy e+H2 scattering.

Shift equations iteration solution to n-level close coupled equations, and the two-level nonadiabatic tunneling problem revisited

The shift equations iteration (SEI) solves the n-level quantum scattering problem in one dimension, i.e., the close-coupled equations, free from exponential instability arising from closed channels. SEI provides exponential-instability-free transmission and reflection coefficients, and is well suited to two-sided scattering problems such as conduction in molecular wires. Our most efficient implementation of SEI utilizes an adaptation of the log-derivative symplectic integrator described by Manolopoulos and Gray in (J Chem Phys 102:9214, 1995). The two-level nonadiabatic tunneling system is investigated—in the tunneling regime, above the barrier, and at resonance. Nonadiabatic components in the upper channel wavefunction (and lower channel wavefunction at resonance energies) are found to be non-adiabatic, i.e., not describable by WKB functions. Their behavior is characterized in terms of an empirical model relating these components to adiabatic components in the lower (upper) channel and the potential energy coupling.

Electron‐Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. X. Ne viii and Ne ix for Ultraviolet and X‐Ray Modeling

Results are presented for the inverse processes of photoionization and electron-ion recombination of (hν + Ne ↔ Ne + e) and (hν + Ne ↔ Ne + e) using the self-consistent unified method. The method employs an identical wave function expansion for both photoionization and recombination, and it includes both radiative and dielectronic recombination. Total, as well as level-specific, photoionization cross sections, σPI(E; nSLJ), and recombination rate coefficients, αR(T; nSLJ), are presented for all fine-structure levels up to n ≤ 10. These correspond to a total of 98 bound fine-structure levels of Ne VIII with 1/2 ≤ J ≤ 17/2, and 178 bound levels of Ne IX with 0 ≤ J ≤ 10. Total recombination cross sections and rates as functions of electron energy are also presented. The coupled channel wave function expansions for the core ions include 17 levels of Ne IX and 16 levels of Ne X. Relativistic fine structure is considered through the Breit-Pauli R-matrix (BPRM) method. The photoionization and recombination cross sections include important atomic effects such as radiation damping, channel coupling, and interference and should be of definitive accuracy. Level-specific σPI(nSLJ) and αR(T; nSLJ) are calculated for the first time. In addition, we describe the applicability of these comprehensive data sets to not only ionization balance and recombination-cascade models for astrophysical and laboratory plasmas, but also to (1) models of UV and X-ray lines in He-like ions from C V to Ne IX involving the 2 3P → 2 3S1 allowed triplet transitions in the UV, and 2(1P, 3P, 3S1) → 1 1S0 allowed, intercombination, and forbidden transitions in the X-ray, and (2) calculation of dielectronic satellite intensities from the highly resolved resonances in the unified recombination cross sections of He-like and Li-like ions through straightforward integration over a Maxwellian or other electron distribution functions.

Properties of nearly one-electron molecules. I. An iterative Green function approach to calculating the reaction matrix

An ab initio R-matrix method for determining the molecular reaction matrix of scattering theory is introduced. The method makes use of a principal-value Green function to compute the collision channel wave functions for the scattered electron, in combination with the Kohn variational scheme for the evaluation of R-matrix eigenvalues on a spherical boundary surface at short range. This technique permits the size of the bounded volume in the variational calculation to be reduced, making the computations fast and efficient. The reaction matrix is determined in a form that minimizes its energy dependence. Thus the procedure does not require modification or an increase in the computational effort to study the electronic structure and dynamics in Rydberg molecules with extremely polar ion cores. The analysis is specialized to examine the bound-state and free-electron scattering properties of nearly one-electron molecular systems, which are characterized by a Rydberg/scattering electron incident on a closed-shell ion core. However, it is shown that the treatment is compatible with all-electron/ab initio representations of open-shell and nonlinear polyatomic ion cores, emphasizing its generality. The introduced approach is used to calculate the electronic spectrum of the calcium monofluoride molecule, which has the extremely polar (Ca+2F-)+e- closed-shell ion-core configuration. The calculation utilizes an effective single-electron potential determined by M. Arif, C. Jungen, and A. L. Roche [J. Chem. Phys. 106, 4102 (1997)] previously. Close agreement with experimental data is obtained. The results demonstrate the practical utility of this method as a viable alternative to the standard variational approaches.

Singly differential electron emission cross sections for ionization of helium by protons

Angular differential cross sections are calculated for electrons emitted in proton–helium collisions within the framework of the time-dependent coupled channel-method. The channel wave functions are constructed from Slater functions and Coulomb wave packets. As projectiles we consider protons with energies between 0.3 and 1.5 MeV. We compare our results with experimental data and other theoretical calculations using the first Born approximation, different distorted wave models and classical trajectory Monte Carlo simulations.

Radial and angular correlations and the classification of intershell2l2l′3l″triply excited states of atoms

We analyzed radial and angular correlations of 50 ${2l2l}^{\ensuremath{'}}{3l}^{\ensuremath{''}}$ triply excited states of atoms. Using hyperspherical coordinates, we examined channel wave functions in the body-fixed frame to identify elementary normal modes of the correlated motion of the three electrons. For these states, we showed that the bending vibrational modes characterizing the angular correlations are the same as those in ${2l2l}^{\ensuremath{'}}{2l}^{\ensuremath{''}}$ and ${3l3l}^{\ensuremath{'}}{3l}^{\ensuremath{''}}$ intrashell states, but additional ``$+$'' or ``$\ensuremath{-}$'' quantum numbers are needed to distinguish the symmetric or antisymmetric stretch of the outer electron with respect to the two inner ones for the ${2l2l}^{\ensuremath{'}}{3l}^{\ensuremath{''}}$ intershell states.