Energy and angular distributions in 6He photodisintegration

Energy and angular distributions of the neutrons and the α particle from the reaction ⁶He(γ, 2n)⁴He is examined in the minimal approximation of the hyperspherical-function method in the algebraic version of the resonating-group method. The differential cross section for ⁶He photodisintegration is calculated as a function of the energies of the product particles, the angles between their momenta, and their emission angles with respect to the incident-photon momentum.     

Generalized numerical differentiation in the turbidity spectrum method

The validity of the choice of the geometric mean wavelength in the differential version of the turbidity spectrum method is analyzed by numerical simulation. It is found that this choice can introduce errors, as large as 5–35%, in the estimated values of parameters of a colloid system. It is proposed to construct the calibrations n=n(α, m) by using the realistic (instrument-dependent) differentiation method, generalized in a way that provides for the monotonic nature of the calibrations.     

α8Be cluster model for the 0 2 + resonance in the 12C nucleus

The 0 ₂ ⁺ resonance in the ¹²C nucleus is treated on the basis of the α+⁸Be two-cluster model. An equation for the function describing the relative motion of the clusters is derived by using the s-wave differential Faddeev equations for the 3α system and by relying on the simplest version of the resonating-group method. A phenomenological potential is taken to simulate the pair αα interaction. A three-body potential binding three alpha particles together gives rise to a resonance in two-cluster α+⁸Be scattering. The calculated resonance features and the calculated parameters of the wave function of the system are compared with the results obtained by other authors.     

Interference of isovector and isoscalar giant quadrupole resonances in Y and Pb

We present the calculations of the fore-aft asymmetry of γ-rays in fast nucleon capture reactions ⁸⁹Y(n, γ)⁹⁰Y, ²⁰⁸Pb(n, γ)²⁰⁹Pb and ²⁰⁸Pb(p, γ)²⁰⁹Bi which are based on a consistent version of the direct-semi-direct (DSD) capture model. The results are in good agreement with observed differential cross sections.     

Gaussian estimation of electron scattering cross sections on the basis of a Feynman path integral

A version of Gaussian estimation of a Feynman path integral is considered and its validity for a scattering problem is investigated. Test calculations of the differential and total cross sections are performed for the scattering of a plane wave by a three-dimensional spherically symmetric Gaussian potential and for the electron impact excitation of the 1s → 2s transition in the hydrogen atom. The data on the scattering by a potential are compared with the analogous results obtained using the first Born approximation and the method of phase functions (which gives almost exact results). The excitation cross sections for the transition in the hydrogen atom are compared with those obtained by the convergent close-coupling method. The validity of this approach is demonstrated. The accuracy of the method proposed is acceptable for many cases. For total cross sections, the result obtained in terms of the density matrix formalism turned out to be more exact than that derived from differential cross sections. Among all the above approaches using path integration to solve problems of scattering of electrons by atoms, the method proposed here.     

On the separation of the direct reaction contribution in fluctuating cross sections by the use of polarized particles

A method to determine the direct reaction contribution y_D to the differential cross section in the presence of Ericson fluctuations is proposed. For the scattering of polarized $\text{spin}\text{-}\text{1}\text{2}$ particles from spinless nuclei the statistical analysis of the differential cross section dσ/dΩ and of the differential analyzing power $\text{(}\text{d}\text{σ/}\text{d}\text{Ω)A}$ allows an unambiguous and model independent extraction of y_D. The method is applied to the elastic scattering of polarized protons from ²⁶Mg, ⁸⁸Sr and ⁹⁰Zr; the results are in agreement with Hauser-Feshbach calculations.     

An accurate multislice method for low-energy transmission electron microscopy

The conventional multislice method (CMS), originally proposed by Cowley and Moodie (1957), is an important algorithm for image and electron diffraction calculations in transmission electron microscopy. Nevertheless, this method is based on the so-called high-energy approximation, which neglects the second differential term ?²φ(r)/?z² to greatly simplify the calculation without severe loss of accuracy. In the current study, we show that for low-energy transmission electron microscopy (LE-TEM) (<100 kV), the high-energy approximation error becomes large and the accurate multislice method, proposed by Chen and Van Dyck (1997), can be used as an alternative method to obtain more accurate calculations. The accurate multislice method, called the revised real space method (RRS) in this paper, can be realized by treating the propagation and scattering as an entirety in real space. A detailed comparison of the numerical results of the RRS and CMS at different accelerating voltages, Debye–Waller factors, and beam tilts is performed. Results show that for image and diffraction simulations in LE-TEM, CMS is no longer sufficiently accurate and the RRS procedure can be used as an alternative method with reasonable computing time.     

Charge-exchange reaction pd → n(pp) within the Bethe-Salpeter approach

The charge-exchange reaction pd → n(pp) at low momentum transfers and low excitation energies of the pp pair is considered within the Bethe-Salpeter approach. The method is proposed for calculating observables in the case where the pp pair is in the ¹ S ₀ state. The results of methodological numerical calculations for the differential cross sections and the tensor analyzing power T ₂₀ are presented. The possibility of using the reaction in question as a basic reaction for creating a deuteron tensor polarimeter at high energies and for obtaining additional information about the elementary amplitude for nucleon-nucleon charge-exchange is predicted.     

Measurement of the differential cross sections for π − p charge-exchange scattering in the region of the low-lying P 11, S 11, and D 13 resonances

The differential cross sections for the reaction π ^? p → π ⁰ n were measured for scattering angles in the backward hemisphere. The experiment was performed by using the pion channel of the synchrocyclotron installed at the Petersburg Nuclear Physics Institute (PNPI, Gatchina), the momenta of incident pions being varied in the range between 456 and 710 MeV/c. The measurements were performed by recording the recoil neutron in coincidence with one of the photons from the decay process π ⁰ → 2γ. The experimental facility used is described, and the results of the measurements are presented. These new results are characterized by a statistical accuracy higher than that of all results published previously and are in better agreement with the predictions of the partial-wave analysis (SM-95 version) performed by a group from Virginia Polytechnic Institute.     

General triplectic quantization

The general structure of the Sp(2)-covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism, the so-called triplectic quantization, as presented in our previous paper with A.M. Semikhatov is further generalized and clarified. We present new unified expressions for the generating operators which are more invariant and which yield a natural realization of the operator V^a and provide for a geometrical explanation for its presence. ThisV^a operator provides then for an invariant definition of a degenerate Poisson bracket on the triplectic manifold being non-degenerate on a naturally defined submanifold. We also define inverses to non-degenerate antitriplectic metrics and give a natural generalization of the conventional calculus of exterior differential forms which, e.g., explains the properties of these inverses. Finally we define and give a consistent treatment of second class hyperconstraints.     

Numerical analysis of energy-minimizing wavelengths of equilibrium states for diblock copolymers

We present a robust and accurate numerical algorithm for calculating energy-minimizing wavelengths of equilibrium states for diblock copolymers. The phase-field model for diblock copolymers is based on the nonlocal Cahn–Hilliard equation. The model consists of local and nonlocal terms associated with short- and long-range interactions, respectively. To solve the phase-field model efficiently and accurately, we use a linearly stabilized splitting-type scheme with a semi-implicit Fourier spectral method. To find energy-minimizing wavelengths of equilibrium states, we take two approaches. One is to obtain an equilibrium state from a long time simulation of the time-dependent partial differential equation with varying periodicity and choosing the energy-minimizing wavelength. The other is to directly solve the ordinary differential equation for the steady state. The results from these two methods are identical, which confirms the accuracy of the proposed algorithm. We also propose a simple and powerful formula: h = L¹/m, where h is the space grid size, L¹ is the energy-minimizing wavelength, and m is the number of the numerical grid steps in one period of a wave. Two- and three-dimensional numerical results are presented validating the usefulness of the formula without trial and error or ad hoc processes.     

The source galerkin method for scalar field theory

This is part I of a two-part series on the Source Galerkin method. This approach is based on the differential formulation of quantum field theory. On a finite lattice, the functional differential equations for a theory in the presence of an external source becomes a set of coupled differential equations for the generating functional Z. Systematic approximations to these equations are found using the Galerkin method. Calculations are straightforward to perform, and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. In addition, bosons and fermions are treated in a symmetric manner. In this paper, we consider power series solutions for scalar field theory in D = 2, 3,4. Propagators and mass gaps are calculated for a number of systems. The calculations in this paper were made on a work station of modest power using a fourth order polynomial expansion for lattices of size 8², 4³, 2⁴ in 2D 3D, and 4D. In part II we consider the fermionic formulation.     

Inclusive spectra of protons and α particles from reactions induced by protons with an energy of 30.0 MeV on the 209Bi nucleus

Inclusive spectra of protons and α particles resulting from the interaction between 30.0-MeV protons and the ²⁰⁹Bi nucleus are investigated. Double differential and integral cross sections for the (p,xp) and (p,xα) reactions are obtained and total partial cross sections for these reactions are subsequently determined. The experimental spectra are analyzed using a modified version of the exciton model of preequilibrium decay and the PRECO-2006 code. Contributions from the compound and direct mechanisms to the formation of integral cross sections are calculated.     

Strong coupling limit of gφ4 theory: General formalism and applications

A method, independently proposed by Kaiser and by us, to study the strong coupling limit of the Green functions is described and discussed. Although its quantum mechanical version exhibits unusual features, an application to the anharmonic oscillator indicates that the method is able to reproduce correctly known numerical results. In spite of difficulties in the setting up of a renormalization program for the theory, a preliminary study of the CS β function for the gφ⁴ interaction shows that $\text{β(g}{}_{\mathrm{<mtext>r</mtext>}}$ is asymptotically linear in the renormalization coupling constant. Evidence is given for the compatibility of this behaviour with the information that can be drawn from the known perturbative expansion.     

Elastic and charge exchange scattering of pions on3He in the (3,3)-resonance region

The elastic scattering of pions from³He and the single charge exchange reaction³He(π ^?,π ⁰)³H are calculated in the energy domain of the (3,3)-resonance within the framework of Glauber's theory, including spin and isospin degrees of freedom in all orders. It is pointed out that, from the first minimum on, the differential cross section strongly depends on the parametrization of theπN amplitude, especially on its continuation into the unphysical region of momentum transfer. Single and double spin flip contributions prove to be very important in the charge exchange reaction. Within a modified version of Glauber's formalism, directly usingπN phase shifts rather than amplitudes, the³He charge exchange scattering is reexamined. Whereas the shape of the angle-integrated cross section as a function of pion energy is confirmed, the magnitude is still uncertain within a factor of 2.     

Quartic oscillator potential in the γ-rigid regime of the collective geometrical model

A prolate γ-rigid version of the Bohr-Mottelson Hamiltonian with a quartic anharmonic oscillator potential in β collective shape variable is used to describe the spectra for a variety of vibrational-like nuclei. Speculating the exact separation between the two Euler angles and the β variable, one arrives at a differential Schrödinger equation with a quartic anharmonic oscillator potential and a centrifugal-like barrier. The corresponding eigenvalue is approximated by an analytical formula depending only on a single parameter up to an overall scaling factor. The applicability of the model is discussed in connection to the existence interval of the free parameter, which is limited by the accuracy of the approximation, and by comparison with the predictions of the related X(3) and X(3)-β ² models. The model is applied to qualitatively describe the spectra for nine nuclei which exhibit near-vibrational features.     

Simulation of euclidean quantum field theories by a random walk process

A new Monte Carlo method for euclidean lattice field theory is introduced by writing the Boltzmann distribution e^?s as a solution of a diffusion type equation and constructing the associated random walk process. It is practically tested for a quantum mechanical model and a non-compact version of lattice QCD. It is explained where the main interest in this algorithm lies: the diffusion process coming from an action that can be generalized to include non-conservative forces. This possibility is exploited in our QCD version to implement gauge fixing without Faddeev-Popov ghosts.     

Effective dielectric theory from QCD

New effective fields are defined in QCD by averaging the phase factor P exp∫_x0^x₀+?iA_μdx^μ in small four-dimensional boxes. Their effective lagrangian is constructed explicitly for G=SU(2). It is a version of the dielectric theory proposed by 't Hooft, Kogut and Susskind. The classical electric flux-tube solution is analyzed quantitatively.     

Chaos in numerical analysis of ordinary differential equations

The discretisation of the ordinary nonlinear differential equation $\text{d}\text{y}\text{d}\text{t}\text{= y(1?y)}$ by the entral difference scheme is studied for fixed mesh size. In the usual numerical computation, this method produces some “ghost solution” for the long range calculation. Regarding this discretisation as a dynamical system in R², these pathological behaviors are shown to be a kind of “chaos” in the dynamical system for any mesh size. Moreover, some combination of the central difference scheme and the Euler's scheme is studied for the above equation. It gives some motivation for Hénon's model. The usual discretisation of a second order differential equation are studied also. It gives some chaotic behaviors numerically which is similar to the behavior of the orbits of the system of differential equations proposed by Hénon-Heiles.     

Determination of the interaction potential of the Li+-He system relative to the experimental differential cross sections

Reassessment of the interaction potential relative to the experimental differential scattering cross sections of Li⁺ ions by He at energies from 3.64 to 218 eV is carried out in this present report by the method published in 1970 by L. G. Yakovlev and É. M. Bashirov. The numerical values obtained for the potential are approximated by the formula (in eV)V(r)=398·exp(-4.90r) ?8.47 exp(?3.31r) eV. This formula gives values of the potential over the range of spacing from 0.5 to 1.5 Å. Comparison with other well-known data shows the excellent agreement of the results, but the use of the proposed method permits the potential to be determined over a wider range of spacings.