Nucleon-alpha elastic scattering analyses: (II). 0 to 21 MeV energy-dependent n-α analysis

An energy-dependent phase-shift analysis of 0–21 MeV n-α scattering is presented and compared to the previous 0–23 MeV p-α analysis. The error matrix and inverse error matrix for both the n-α and the p-α analyses are given.     

Galactic potentials

The information contained in galactic rotation curves is examined under a minimal set of assumptions. If emission occurs from stable circular geodesic orbits of a static spherically symmetric field, with information propagated to us along null geodesics, observed rotation curves determine galactic potentials without specific reference to any metric theory of gravity. Given the potential, the gravitational mass can be obtained by way of an anisotropy function of this field. The gravitational mass and anisotropy function can be solved simultaneously in a Newtonian limit without specifying any specific source. This procedure, based on a minimal set of assumptions, puts very strong constraints on any model of the "dark matter."     

Lambda-nucleon interaction potentials

Two-body S-wave, spin dependent, central Λ-N interaction potentials of the form first given by Ram and Downs are constructed to fit the zero energy scattering lengths a_s = −2.25 fm, a_t = −2.08 fm of Herndon and Tang. When assumed to be effective in even-parity states with full strength and in odd-parity states with zero strength, these potentials fit the Λ-p scattering cross section data very well. The binding energy D of the Λ-particle in nuclear matter using these potentials is calculated by the method of independent pair approximation. The potentials that best fit the scattering data give values for D which are only 3–4 MeV lower than that obtained previously with a potential of Hemdon and Tang. It is concluded that the three-body ΛNN forces may be quite important in the calculations of D.     

Hydrodynamic vector potentials

Solving the Navier-Stokes equation for incompressible fluids is greatly simplified by the solution of the vorticity equation. To accomplish this for three-dimensional flows requires vector potentials. These potentials are not only useful to take care of the incompressibility. Their modes are suitable also as test functions since the familiar Galerkin procedure does not work. The new method is checked by examples with known results and its relation to the classical approach with the stream function is clarified. The principle demonstration, however, concerns the transition to turbulence in plane shear flows. A simple layer of long rolls with axes parallel to the basic flow incites the transition. Received 20 August 2001     

Complex absorbing potentials

We review the construction and use of complex potentials in reactive scattering and other molecular collisions to calculate continuum quantities (such as state-to-state transition probabilities, cumulative reaction probabilities, or resonance characteristics) with finite grid or finite basis methods. The success of the approach is greatly based on its simplicity. In general these potentials are adjusted phenomenologically or optimized for achieving an absorptive and non-reflecting boundary. For further progress the conceptual and formal framework of the complex potentials and the efficiency of their numerical implementation must be investigated more deeply. We present along this line a formal theory of scattering for complex potentials in one dimension, as well as a detailed account of the functional forms and construction methods proposed. We also demonstrate that part of the acquired knowledge may be transferred to “physical” absorbing potentials, i.e., effective interactions that can be tailored physically (rather than numerically) to accomplish e.g. an improved atomic detection by fluorescence.     

Stable potentials I

We discuss a conjecture of Ruelle concerningstable potentials on a group. For the groupsZ ₂,Z ₃, ₄, andZ ₆ any stable potential can be written as the sum of a non-negative function and a function of non-negative type. This is not true for the groupsZ _k (k odd, 5). For the Euclidean groupR ^v the question is open.Supported by NSF GP 7946.     

Generalized Bargmann potentials

Conditions are found for the coefficient functions of a linear ordinary differential equation of the kth order ^(k)+u₁^(k-2)+...+u_k-1=^k, when its solution has the following analytical dependence on the parameter: =exp(z _i=1 ⁿ (+a_i)(a_ja_j(Z)). The problem is closely related to the finding of n-soliton solutions of the simplest form for the periodic Toda system, corresponding to A _nand C _nseries.     

Generalized Rosenbluth potentials

It is shown that the coefficients of friction and diffusion of the Balescu-Lenard equation can be derived from two “generalized Rosenbluth potentials”, which reduce to the standard Rosenbluth potentials if wave effects are neglected. The potentials are evaluated explicitly in the case of Maxwellian field particles. The dominant contribution of wave effects to the potentials is due to the interaction of electron field particles with ion sound waves.     

On stable potentials

Examples are given of one- and two-dimensional stable potentials which cannot be decomposed into the sum of a non-negative function and a continuous stable potential.     

Logistic map potentials

We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x?sx(1−x) for 0<s?4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s>2. We illustrate the methods numerically for the cases s=5/2 and s=10/3.     

Canonical supergravity potentials

We investigate the potentials of supergravity models with canonical kinetic energy and derive several properties. If the model isR-invariant with non-negativeR-charges, we prove that the potential is strictly positive and vanishes without finetuning if and only if supersymmetry is unbroken. Allowing for negativeR-charges we present a model where supersymmetry is broken in the absolute minimum which is finetuned toV _min=0.     

Some torsion potentials

Using the notion of torsion potentials, the duality between antisymmetric tensor fields and scalar fields is discussed. First-order actions with these fields, the connection and the metric as independent variables are presented.     

Electrodynamics without potentials

We construct a Lagrangian formulation of classical and quantum electrodynamics with-out using potentials.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.5, pp. 67–73, May, 1989.     

Singular perturbation potentials

This is a perturbative analysis of the eigenvalues and eigenfunctions of Schrödinger operators of the form ?Δ + A + λV, defined on the Hilbert space L²(Rⁿ), where $\text{Δ = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{n}}\text{?}{}^2\text{?X}{}_{\mathrm{i}}{}^2$, A is a potential function and V is a positive perturbative potential function which diverges at some finite point, conventionally the origin. λ is a small real or complex parameter. The emphasis is on one-dimensional or separable problems, and in particular the typical example is the “spiked harmonic oscillator” Hamiltonian, $\text{?d}{}^2\text{dx}{}^2\text{+ x}{}^2\text{+}\text{l(l + 1)}\text{x}{}^2\text{+ λ|x|}{}^{\mathrm{?\alpha }}$, where α is a positive constant. When this kind of perturbation is very singular, the first-order Rayleigh-Schrödinger perturbative correction, (u₀, Vu₀), where u₀ is the unperturbed eigenfunction, diverges. This analysis constructs explicitly calculable terms in a modified perturbation series to a finite order, by using linear operator theory in concert with approximation methods for differential equations. Along the way a connection between a W-K-B type approximation and Bessel functions is exploited.     

Equivalent two-body potentials

The consequences of the existence of a bound state in a local nuclear two-body potential for charge distribution, inelastic scattering, photodisintegration and saturation are investigated.     

Dynamics and potentials

A dynamics (i.e. a one-parameter group of automorphisms) of a system described by a C*-algebra with a local structure in terms of C*-subalgebras A(I) for local domains I of the physical space (a discrete lattice) is normally constructed out of potentials P(I), each of which is a self-adjoint element of the subalgebra A(I), such that the the first time derivative of the dynamical change of any local observable A is i times the convergent sum of the commutator [P(I), A] over all finite regions I. We will invert this relation under the assumption (obviously assumed in the usual approach) that local observables all have the first time derivative, i.e. we prove the existence of potentials for any given dynamics satisfying the above-stated condition. Furthermore, by imposing a further condition for the potential P(I) to be chosen for each I that it does not have a portion which can be shifted to potentials for any proper subset of I, we also show (1) the existence, (2) uniqueness, (3) an automatic convergence property for the sum over I, and (4) a quite convenient property for the chosen potential. The so-obtained properties (3) and (4) are not assumed and are very useful, though they were never noticed nor used before.     

Integrable cosmological potentials

The problem of classification of the Einstein–Friedman cosmological Hamiltonians H with a single scalar inflaton field \(\varphi \), which possess an additional integral of motion polynomial in momenta on the shell of the Friedman constraint \(H=0\), is considered. Necessary and sufficient conditions for the existence of the first-, second- and third-degree integrals are derived. These conditions have the form of ODEs for the cosmological potential \(V(\varphi )\). In the case of linear and quadratic integrals we find general solutions of the ODEs and construct the corresponding integrals explicitly. A new wide class of Hamiltonians that possess a cubic integral is derived. The corresponding potentials are represented in parametric form in terms of the associated Legendre functions. Six families of special elementary solutions are described, and sporadic superintegrable cases are discussed.     

Some nucleon-nucleonS-wave potentials

A number of solvableS-wave potentials are presented which match theS-wave nucleon-nucleon phase shifts. The calculation shows that for simple, four parameter potentials there are many rather different parameter sets which yield nearly the same scattering data. We give furthermore some parameter sets which are especially suited for the low energy region. The possibility of fitting the phase shifts with an energy-dependent repulsion was examined phenomenologically. We also calculated a Scott-Moszkowski version of the potentials.     

New hydrogen-like potentials

Using the modified factorization method employed in [5], we construct a new class of radial potentials whose spectrum for l=0 coincides exactly with that of the hydrogen atom. A limiting case of our family coincides with the potentials previously derived by Abraham and Moses [6].