Three-body coulomb effects in one-particle transfer reactions

The behaviour of the DWBA amplitudes in the vicinity of the nearest singularity in the cosθ-plane for the neutron and charged particle transfer reactions is investigated. It is shown that Coulomb interactions transform the pole singularity into a branch point. The main singular terms of the complete and the post-approximation DWBA cross sections are compared with the exact three-body results. They differ only by the Coulomb renormalization factors (CRF), which define the renormalization of the singularity strength generated by the Coulomb interactions. In the case of neutron transfer it is shown that the complete DWBA and exact CRFs practically coincide and slightly differ from CRF obtained in post-approximation DWBA. For charged particle transfer reactions the exact CRF may differ considerably from the one obtained in DWBA and especially in the post-approximation DWBA. Our conclusion therefore is that in order to obtain a reliable value of the vertex constant by extrapolating the differential cross-section to the nearest singularity, the exact three-body approach should be used.     

X-ray studies on muon transfer reactions from hydrogen to helium

We have experimentally studied the muon transfer reactions from hydrogen to helium in liquid hydrogen with helium impurity concentration around 100–1000 ppm. The X-ray from the decay of (d⁴He) molecule was clearly observed in the D₂-⁴He system, whereas the corresponding X-ray was very weak in other systems such as D₂-³He and H₂-⁴He. This is well explained by the particle decay mode of the muonic molecule.     

A comparison of differential and integral equations of radiative transfer

The equations of radiative transfer and of statistical equilibrium of a two-level atom are solved by means of differential and integral equations for a one-dimensional medium. The numerical solutions are compared to the analytic solution. It is found that the integral equation for piecewise quadratic source functions gives more accurate results than does the differential equation.     

Reduction of radiative transfer problems in semi-infinite media to linear Fredholm integral equations

Linear Fredholm integral equations are derived for the Stokes vector of polarized radiation, emergent from a scattering plane parallel semi-infinite medium, by means of the full range orthogonality and completeness properties of Case's eigensolutions. A renormalization concerning the eigenmode with the greatest discrete eigenvalue is applied, which permits us to obtain a new integral equation for the zeroth Fourier component of the radiation field. The kernel of the integral equations is given in terms of Case's eigenfunctions or of the Green's function matrix for an infinite medium. For isotropic scattering, it is shown that the integral equation can be solved by means of a very rapidly convergent Neumann series. Physical arguments lead to the conclusion that the renormalized Fredholm integral equations are well suited also for arbitrary phase matrices.     

Systematic study of muon transfer to sulphur dioxide

In a systematic study of the transfer process to sulphur dioxide, in seven different H₂ + SO₂ gas mixtures, the time spectra of the muonic sulphur X-rays yield muon transfer rates to the SO₂ molecule, deduced from the lifetimes of the p atoms, which agree all well with each other. The muonic oxygen time spectra show an additional structure as if p atoms of another kind were present. Reduced transfer rates_O are reproducible if one uses the model of ephemeral p atoms. The intensity ratios between the different kinds of p atoms are also discussed in the framework of this model and the one of black and white p atoms.     

Radiative transfer in finite cylindrical media using transformed integral equations

A modified direct integration method is presented to solve three-dimensional radiative transfer in emitting, absorbing and linear-anisotropic scattering finite cylindrical media. This scheme effectively avoids an integral singularity in the coupled Fredholm type integral equations of radiative transfer. The scheme leads to faster and more accurate results, which are needed in combined mode and non-gray problems. The calculated incident radiation and heat fluxes agree well with published results by discrete ordinates method. Using the transformed integral equations, the effects of boundary emission and reflection can also be easily handled.     

Bloch方程的精细时程积分及其在射频脉冲设计中的应用

射频脉冲的频率选择性直接影响磁共振成像的质量，而射频脉冲的优化设计又归结为对Bloch方程的求解.尽管在某些情况下Bloch方程存在解析解，但由于其缺乏通用性而且形式上过于复杂而难于得到实用.本文提出一种Bloch方程的精细时程积分算法，并结合全局优化算法给出一个完整的射频脉冲设计方案.精细积分算法具有高效、高精度的特点，对于射频脉冲的设计很有裨益.数值算例表明，设计所得的射频脉冲具有较好的频率选择性. 关键词： 磁共振成像 射频脉冲 Bloch方程 精细时程积分     

On the nonuniqueness of solutions for nonlinear integral equations in radiative transfer theory

The nonuniqueness problem is considered for the nonlinear integral equations satisfied by the reflection and transmission matrices of homogeneous plane-parallel atmospheres. The analysis of the problems for semi-infinite and finite atmospheres is based on a recently developed biorthogonolity concept. Explicit expressions for nonphysical solutions are derived. The structure of these solutions reveal that iterative solution procedures may easily yield nonphysical results, if no proper attention is paid to certain linear constraints.     

A novel hierarchy of differential integral equations and their generalized bi-Hamiltonian structures

With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 x 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy.     

Transition factor method for discrete master equations; and application to chemical reactions

We introduce transition factors and derive equations for them which are equivalent to the originalN-dimensional discrete master equation. After transition to continuous variables we obtain nonlocal partial differential equations for these transition factors which are slowly varying variables. Finally we consider a chemical reaction system. Using this method the corresponding master equation is exactly solvable in a very simple manner.     

Experimental investigation of the muon transfer reaction from deuterium to helium isotopes

Muon transfer from the ground state of muonic deuterium to a helium atom proceeds mainly via the formation of a muonic molecule in an excited state. A large number of decay X rays ( 6.8 keV) from these (dµHe)^* molecules were observed for the⁴He as well as for the³He case. The time distributions of these X rays allow the determination of the ground state transfer rate. The simultaneous employment of Ge/Si-detectors and CCDs for the same target conditions allows the determination of the branching ratio of radiative to nonradiative decay for the first time.     

Linear integral equations and nonlinear difference-difference equations

This paper studies the dynamics of members of the two-parameter family of maps x → μx(1 ? x^v), emphasizing the evolution from snapback repeller to crisis bifurcations. The example of the square root map $\text{v =}\text{1}\text{2}$ is taken to represent the subfamily where v is fixed and taken from the range $\text{1}\text{2}\text{≤ v ≤ 1}$. A map from such a subfamily is shown to be conjugate with a map with negative Schwarzian derivative. This allows a characterization of crisis as the demise of a snapback repeller on a proper subinterval.     

Method of integral transforms to calculate reactions

A method to calculate reactions in quantum mechanics is outlined. It is advantageous, in particular, in problems with many open channels of various nature, i.e., when energy is not low. In the difference with more conventional approaches the dynamics calculations to be performed are bound-state type-calculations. Continuum spectrum states never enter the game. In the course of calculations there is no need to consider reaction channels, as well as reaction thresholds. Reaction channels and thresholds come into play at merely the kinematics level and only after a dynamics calculation is done.     

Isotopic effects in the muon transfer from pmu and dmu to heavier atoms

The results of accurate hyperspherical calculations of the muon-transfer rates from muonic protium and deuterium atoms to nitrogen, oxygen, and neon are reported. Very good agreement with measured rates is obtained and, for the three systems, the isotopic effect is perfectly reproduced. The transfer rate is higher for deuterium in the cases of nitrogen and neon due to constructive interferences between two transfer paths. The lower transfer rate for deuterium in the case of oxygen results from a large resonant contribution.     

Symmetric integral equations derived from the Faddeev equations

A way is shown to transform the Faddeev equations of the atomic three-body problem into a set of integral equations with symmetric kernel. The method is treated in more detail for total angular momentumJ=0 and applied to calculating the binding energy of theH ^? ion.     

Applications of the first integral method to nonlinear evolution equations

<正>In this paper,we establish travelling wave solutions for some nonlinear evolution equations.The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations.The obtained results include periodic and solitary wave solutions.The first integral method presents a wider applicability to handling nonlinear wave equations.     

Three-body calculations of elastic Deuteron-helium-4-scattering with faddeev equations

The Faddeev equations are applied to the Deuteron-⁴He system. For the interactions between the particles squarewell potentials are used. In order to solve the Faddeev equations, thet-matrix is approximated by one separable term. The phaseshifts of the elastic Deuteron-⁴He scattering are calculated. It is shown, that the separable approximation by only one term is insufficient for such calculations.     

Laser control of intramolecular hydrogen transfer reactions: A real-time path integral approach

Different pulse shapes realizing photo isomerization via laser driven tunnelling or vibrational transitions are studied here. Particular attention is paid to the investigation of their robustness with respect to the influence of dissipative processes introduced by the interaction with an environment. An iterative scheme for propagation of the reduced density matrix in the path integral representation is used to take into account arbitrary system-environment coupling strengths as well as the effect of non-Markovian dynamics.     

Three-body Coulomb Green function and the reactions with charged particles at low energies

It has been shown that the inclusion of all possible Coulomb rescatterings of three charged particles in intermediate state results in an infinite series of diagrams which have a pole located at the same place as the pole of the pole diagram. The contribution of the pole terms of such infinite series has explicitly been singled out and summed-up. Renormalization of the pole diagram amplitude due to all the possible Coulomb rescatterings of particles in intermediate state has been found. The result obtained means that the three-body Coulomb Green function entering the expression for the reaction amplitude may be written in the form of the renormalized free Green function plus the residue which behaves as in the case of short-range interactions.Presented at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.