Phase shift analysis of pion-4He scattering by optimal polynomial expansion

A novel method of phase shift analysis for the scattering of charged pion from⁴He nuclei is proposed. The nuclear amplitudef _N (ϑ) has been parametrized in terms of a polynomial expansion in a conformally mapped variable, which is obtained by optimally exploiting the analytic property off _N . The method exhibits a significant reduction in the number of free parameters required for the fixed energy phase shift analysis of the differential cross-section data. The nuclear amplitude thus constructed is then used to obtain phase shifts and inelastic parameters of all possible orders. Reliable values of the real and imaginary parts of the forward amplitude are also obtained.     

A Dissymmetry Ratio Optical Technique as Applied to Scattering Pattern Recognition of Differently Shaped Soot Aggregates

We investigated the shape of soot aggregates as retrieved from light scattering measurements. In particular, the ratios of scattered light intensities at two angles, called the dissymmetry ratios (DRs), will be considered. These are attractive diagnostic tools as they are insensitive to variations in the complex refractive index (m = n + i k) and to the electromagnetic effect of self-interaction that each individual scatterer in the aggregate produces with itself depending on its finite size. The aim of the paper is both to correlate the DRs with the information about the aggregate shape and to establish what is the minimum number of scattering measurements to be performed to characterize the aggregate scattering patterns. The main results can be summarized as follows: (a) an independent evaluation of the primary spherule size is required in order to interpret the scattering data correctly; (b) some of the DRs can share common values for different morphologies when the number of primary spherules per aggregate is sufficiently high; in this respect, we demonstrate the significance of the dissymmetry ratio R_vv(10°/90°) for the identification of the prevailing morphology of aggregates at different levels of agglomeration; (c) the information about light intensities scattered at three angles seems to suffice for the recognition of prevailing aggregate morphology.     

A Re-Examination of the Arguments for Baryon Parity Doublets

The arguments for baryon parity doubling are re-examined by use of a spin formalism developed by the author together with B. E. LAURENT . It is shown that the transformation between good parity amplitudes and helicity flip and non-flip amplitudes in πN scattering is ambiguous. It is further shown that the unitary condition for boson-fermion scattering gives no information of the parity of intermediate states contributing to a good parity amplitude. These ambiguities follow from the fact that for boson-fermion scattering the CPT transformation of an amplitude does not commute with the projection on a definite parity. It is finally shown how a Regge pole model with linear trajectories without parity doubling can be constructed without any specific dynamical assumptions or artifices. The constraints on the residues needed in this case do not violate any general principles.     

On the Regge-pole description of nucleus-nucleus scattering

The properties of the Regge poles of theS-matrix for scattering of strongly-absorbed nuclear particles are considered. Simple formulae are obtained for describing the Regge trajectories in terms of the nuclear radius, the quasi stationary levels in the combined nuclear-Coulomb-potential and the widths of these levels. The predictions of these formulae are compared with the Regge trajectories obtained previously, for a Woods-Saxon potential, and with those required to fit¹⁶O-¹²C backward scattering.     

Towards a Theory of Transition Paths

We construct a statistical theory of reactive trajectories between two pre-specified sets A and B, i.e. the portionsof the path of a Markov process during which the path makes a transition from A to B. This problem is relevant e.g. in the context of metastability, in which case the two sets A and B are metastable sets, though the formalism we propose is independent of any such assumptions on A and B. We show that various probability distributions on the reactive trajectories can be expressed in terms of the equilibrium distribution of the process and the so-called committor functions which give the probability that the process reaches first B before reaching A, either backward or forward in time. Using these objects, we obtain (i) the distribution of reactive trajectories, which gives the proportion of time reactive trajectories spend in sets outside of A and B; (ii) the hitting point distribution of the reactive trajectories on a surface, which measures where the reactive trajectories hit the surface when they cross it; (iii) the last hitting point distribution of the reactive trajectories on the surface; (iv) the probability current of reactive trajectories, the integral of which on a surface gives the net average flux of reactive trajectories across this surface; (v) the average frequency of reactive trajectories, which gives the average number of transitions between A and B per unit of time; and (vi) the traffic distribution of reactive trajectories, which gives some information about the regions the reactive trajectories visit regardless of the time they spend in these regions.     

Hulthén势散射态的解析解

在任意l波的离心项1/r²用λ²e^-λr/(1-e^-λr)²近似表达的条件下,对Hulthén势的径向Schrdinger方程作自变量指数变换,使此转化为超几何微分方程,获得了Hulthén势s波散射态的精确解和非s波散射态的近似解析解.给出了相移的解析表达式和按“k/2π标度”归一化的用超几何函数表示的径向波函数.讨论了解析解的意义.     

Semiclassical scattering theory with complex trajectories. I. Elastic waves

The WKB approximation to the one-particle Schrödinger equation is used to obtain the wave function at a given point as a sum of semiclassical terms, each of them corresponding to a different classical trajectory ending up at the same point. Besides the usual, real trajectories, also possible complex solutions of the classical equations of motion are considered. The simplicity of the method makes its use easy in practical cases and allows realistic calculations. The general solution of the one-dimensional WKB equations for an arbitrary number of complex turning points is given, and the solution is applied to calculate the position of the Regge poles of the scattering amplitude. The solution of the WKB equations in three dimensions for a central analytical potential is also obtained in a way that can be easily generalized to N-dimensions, provided the problem is separable. A multiple reflection series is derived, leading to a separation of the scattering amplitude into a smooth “background” term (single reflection approximation) that can be treated using classical but complex trajectories and a second resonating term that can be treated using the Sommerfeld-Watson transformation. The physical interpretation of the complex solutions of the classical equations of motion is given: they describe diffractive effects such as Fresnel, Fraunhofer diffraction, or the penetration of the quantal wave into shadow regions of caustics. They arise also in the scattering by a complex potential in an absorptive medium. The comparison with exact quantal calculations shows an astonishingly good agreement, and establishes the complex semiclassical approximation as a quantitative tool even in cases where the potential varies rapidly within a fraction of a wavelength. An approximate property of classical paths is discussed. The general pattern of the trajectories depends only on the product ? = EΘ, and not on energy and angle separately. This property is confirmed by experiments and besides the signature it gives for the semiclassical behavior, it simplifies considerably the search for all trajectories scattering through the same angle. Finally, a general classification of the different types of elastic heavy ion cross sections is given.     

Polarization of slow electrons (100–2000 ev) elastically scattered from heavy atoms

The angular and energy dependence of the Mott polarization for slow electrons is explained in terms of the complex zeros of the scattering amplitudef(z), wherez is the cosine of the scattering angle. The trajectories in the complexz-plane, on which the zeros move if the energy is varied, are shown in the case of scattering from mercury atoms. The properties of these trajectories imply that there are, in fact, certain combinations of energy and angle, for which total polarization occurs. Calculations for target atoms lighter than mercury show, that the number of such combinations becomes smaller and the corresponding energy values are shifted to lower energies. The possibility is also discussed to extract the complex zeros and the other relevant parameters from the experimental data rather than from theoretical calculations, which to some extent are sensitive to the model of the atomic potential.     

Transport theory for a scalar quark & gluon model

A model for scalar quarks and gluons that successfully gives rise to a ln s behavior in high-energy qq scattering and which contains a non-trivial three-gluon vertex is used to study collision theory with the following aspects: i) A three-body interaction simulating QCD is present and ii) particle production and annihilation occur naturally. In this paper, the collision term in the model is examined in detail in the quasiparticle approximation. The construction of cross-sections in which self-energy terms are ordered according to a coupling constant expansion is undertaken. It is shown explicitly which terms of second order are required to obtain the scattering amplitudes that are two body in nature. Additional ordering in the number of colors shows that quark loop diagrams are suppressed and gluon production or scattering processes dominate. It is also shown that a consistent calculation of the scattering graphs at the two-loop level also simultaneously yields terms that renormalize one-loop level graphs. This can then be extended to arbitrary m↦n processes. We examine the constraint equation briefly, discussing the appearance of a width. The issue of pinch singularities is also addressed, and examples of the elimination of such singularities in equilibrium are given explicitly. Received: 7 November 2001 / Accepted: 12 June 2001     

Regge analysis of the ππ scattering amplitude

The theoretical predictions for the subtraction constants lead to a very accurate dispersive representation of the ππ scattering amplitude below 0.8 GeV. The extension of this representation up to the maximum energy of validity of the Roy equations (1.15 GeV) requires a more precise input at high energies. In this paper we determine the trajectories and residues of the leading Regge contributions to the ππ amplitude (Pomeron, f and ρ), using factorization, phenomenological parametrizations of the πN and NN total cross sections at high energy, and a set of sum rules which connect the high and low energy properties of ππ scattering. We find that nonleading Regge terms are necessary in order to achieve a smooth transition from the partial waves to the Regge representation at or below 2 GeV. We obtain thus a Regge representation consistent both with the experimental information at high energies and the Roy equations for the partial waves with ℓ≤4. The uncertainties in our result for the Regge parameters are sizable, but in the solutions of the Roy equations these only manifest themselves above the K[`]KK\hspace {0.03cm}\overline {\rule [0.7em]{0.6em}{0em}}\hspace {-0.8em}K threshold.     

Large N expansion for strongly-coupled boson–fermion mixtures

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson–fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.     

A semi-empirical formula for the neutron total cross section and the interpretation of the empirical formula forA ⩾ 40

Weaknesses in Angeli and Csikai’s interpretation of their empirical formula for the neutron total cross section (σ _T) are pointed out. Using the Fourier-Bessel re-presentation of the scattering amplitude a semi-empirical formula forσ _T is obtained which has greater applicability and also explains the success of the empirical formula for mass numberA ⩾ 40 in terms of the established trends in neutron optical potential parameters.     

Asymptotic Properties of Solutions to 3-Particle Schrödinger Equations

We construct a generalized Fourier transformation ℱ(λ) associated with the 3-body Schr?dinger operator H=−Δ+Σ ^a V ^a (x ^a ) and characterize all solutions of (H−λ)u= 0 in the Agmon–H?rmander space ℬ^* as the image of ℱ(λ)^*. These stationary solutions admit asymptotic expansions in ℬ^* in terms of spherical waves associated with scattering channels. Received: 20 September 2000 / Accepted: 20 May 2001     

Elastic Scattering of Electrons by a Cut-Off Coulomb Potential at Low Energies

Elastic scattering of electrons by cut-off Coulomb potential U_c(r) is investigated, where U_c(r) = 0, for r > r_c and U_c(r) = ?1/r + 1/r_c for r ≦ r_c. This is first considered in terms of classical, and later quantum mechanical (partial wave) methods in the low energy range 0 ≦ ? ? 1/r_c, where ? is the energy of the free electron. Scattering in this energy region displays a number of particular characteristics, such as back scattering, at certain energies. It can be concluded that some agreement does exist between the classical and quantum mechanical results.     

The potential energies of the Na** + He quasi-molecule

The special features of the behavior of the potential energy surfaces of the system comprising a highly excited A** atom and a neutral B atom with a filled electronic shell were thoroughly analyzed. This was done using the integral variant of theory combined with the generalized finite radius potential method correctly describing the scattering of a weakly bound electron by the B atom. The method allows P scattering to be taken into account. This scattering causes the additional splitting of potential energy surfaces into separate groups of interacting terms classified according to the projection m of the electron angular momentum l onto the quasimolecular axis. Calculations of the nl(^{2s + 1}Λ) state potential curves of the Na** + He quasi-molecule (n, l, and Λ are the principal quantum number, angular momentum, and its projection onto the molecular axis, and s is the spin of the system) were performed. The calculation results were compared to those obtained by other authors.     

The first three pomerons...

A model of a three pomeron contribution to high energy elastic pp and scattering is proposed. The data are well described for all momenta ( GeV) and energies ( GeV) (). The model predicts the appearance of two dips in the differential cross-section which will be measured at LHC. The parameters of the pomeron trajectories are . Received: 11 July 2001 / Published online: 20 December 2001     

Levinson's theorem for the Klein-Gordon equation in one dimension

In terms of the modified Sturm-Liouville theorem, the Levinson theorem for the one-dimensional Klein-Gordon equation with a symmetric potential V(x) is established. It is shown that the number N₊ (N_-) of bound states with even (odd) parity is related to the phase shift of the scattering states with the same parity at zero momentum as and The solution of the one-dimensional Klein-Gordon equation with the energy M or -M is called as a half bound state if it is finite but does not decay fast enough at infinity to be square integrable. Received 22 December 1999     

Fundamental constants and higher-dimensional universe

In order to study the origin of the fundamental constants and Dirac's large number, a cosmological solution in vacuum is presented in a seven-dimensional universe which is defined by adding extra three coordinates (e ² G/c ⁴)^1/2, (hG/c ³)^1/2 and (Gm/c ²) to the four-dimensional spacetime coordinates. It has common features with Chodos-Detweiler's solution. The parameters appearing in this theory are estimated to meet the conditions required by the cosmological first-order phase transition and Dirac's large number hypothesis.