Inelasticity Parameter Research Articles

Quark Jet Model Study of Forward and Backward Multiplicities inνp and \barνp Interactions

Based on the quark jet model we calculate the forward and backward multiplicities in νp and \barνp interactions. In these calculations the observed rapidity distributions of particles produced in e + e - annihilations are used as input data to determine the rapidity distribution of secondary particles in the quark jet. The model describes the ν(\barν)p forward and backward multiplicities successfully, if we choose the inelasticity parameter η to be 0.46. This result suggests that the inelasticity parameter takes different values for leptonic and hadronic interactions.

Leading Particle Effect and Multiplicity Relationsamong Hadron and Lepton Induced Reactionsin Quark Jet Model

We show that in quark jet model various multiplicities in hadron and lepton induced reactions are directly related to e + e - multiplicity. In these relations only adjustable parameter is the inelasticity parameter η, which expresses the leading nucleon effect. We tested these multiplicity relations, using the data on the average multiplicities of nondiffractive pp and πp, νp and \barνp interactions and those of e + e - -annihilations. The data seem to satisfy these relations at high energies.

Single-particle widths induced by axially symmetric vibrations in extended fermion matter

We examine the single-particle widths in extended fermion matter originated in the coupling to a harmonic vibration that presents axial symmetry. This is a primary model for the broadening in the nucleon spectrum in an axially symmetric nucleus where a giant collective mode becomes excited. We resort to the Quantal Brownian Motion model of the coupled dynamics of collective and intrinsic degrees of freedom in fermion systems and propose a modified kinetic equation for the particle density operator. This equation is solved in the relaxation time approximation from where the single-particle widths are extracted as the collision rates in the fermionic environment. The geometry and dynamics of the collisions are analyzed, as well as the relevance of those sources of energy spread other than the interaction between the particles and the oscillation, such as the temperature and the inelasticity parameter.

Relativistic three-body approach to NN scattering at intermediate energies.

The Bethe-Salpeter equation for coupled-channel N-\ensuremath{\Delta} scattering is extended to satisfy unitarity in the NN and NN\ensuremath{\pi} sectors. The procedure eliminates the unitarity violations characteristic of the standard ladder Bethe-Salpeter equation in the inelastic region, and improves the description of pion production near threshold. Results are presented for the NN phase shifts and a number of observables up to 1 GeV. In particular, the $^{1}\mathrm{D}_{2}$ inelasticity is found to be considerably smaller than found from phase shift analysis. In this context, the importance of the pion deuteron channel for the inelasticity parameter is pointed out.

Kinetic grain flow in a vertical channel

A self-consistent kinetic grain flow model proposed earlier has been applied in detail to the description of rapid flow in a verticad channel. The equations of motion reduce to an ordinary differential equation for the fluctuation velocity ν , which is solved numerically. Boundary conditions on ν are derived which incorporate the nature of grain-wall collisions. The overall flow pattern is found to depend significantly upon the grain inelasticity parameter γ ( γ = 0 for elastic grains) and upon the grain diameter d. The flow velocity profile is rounded for very elastic grains and for large grains, but becomes more blunt as grain diameter decreases or γ increases. For large enough γ, a region of plug flow develops in the central region of the channel, corresponding to a vanishing grain fluctuation velocity. In this case the region of dispersed or “thermalized” grains, within which all shearing occurs, is restricted to a thin layer near each wall.

Buckling Approximations for Inelastic Beams

Hand methods of calculating buckling loads of inelastic moment gradient beams are developed. An inelastic parameter, the stiffness modification factor, j, is used to estimate equivalent uniform tangent modulus rigidities for partially yielded simply supported beams. From this is developed a buckling moment equation. For laterally continuous beams, a step‐by‐step procedure which allows for interaction between adjacent segments is proposed. The structure is reduced to a critical subassemblage of beam segments. The stiffness modification factor is used to quantify segment end interaction and an effective length factor, k, is found for the critical segment. The buckling moment equation is used to estimate the beam capacity. A worked example and comparisons with theoretical and experimental results show that the proposals are accurate and simple to apply.

Computer studies of the energy spectra and reflection coefficients of light ions

Abstract A new computer code, i.e., the ACAT code, has been developed to simulate atomic collisions in amorphous targets using binary collision approximation, where random targets are simulated employing the so-called cell model which is successfully used in the liquid theory. The ACAT code is used to study the backscattering and the implantation of 0.01-10 keV hydrogens on Au and on Cu. In comparing the calculated results of the ACAT code with those of the MARLOWE and TRIM codes, as a whole, an agreement between these three codes is satisfactory, and the ACAT and TRIM codes give almost the same results for energy spectra of backscattered particles and other related quantities. Using the ACAT computer code, it was found that in light ion backscattering the potential parameter as well as the inelastic energy loss parameter has an appreciable influence on the particle and energy reflection coefficients.

Mathematically Allowed Nonphysical Phase-Shift Solutions

An angular distribution for $^{12}\mathrm{C}(\ensuremath{\alpha},\ensuremath{\alpha})^{12}\mathrm{C}$ near the center of a resonance can be fitted with any value for the real part of the resonating nuclear phase shift. This surprising result is in agreement with resonance theory and occurs because the elastic width of the resonance is \textonehalf{} of the total width. In general, in a phase-shift analysis the real part of the nuclear phase shift will be indeterminate whenever the inelastic parameter is zero.

5Li resonances above the 3He-d threshold

Starting from a soft-core nucleon-nucleon potential the scattering states of 5Li above the 3He-d threshold are calculated using the refined cluster model. Apart from the well-known 3 2 + resonance a quartet of S = 3 2 , L = 2 3He-d resonances is found. Furthermore 3 2 − and 1 2 − resonances appear in phase-shift and inelastic parameter curves; they are shown to be due to three-body break-up channels connected with an intermediate α ∗-p structure, α ∗ being the first excited state of the 4He nucleus.

Multichannel potential model of πN scattering in theI=1/2,J=1/2+ state

A multichannel-potential model, which incorporates some relativistic kinematics, correct threshold behaviors, space-time symmetries and coupling to channels containing unstable particles is developed. The model is a generalization of the separable-potential model of Yamaguchi. It is applied to πN scattering in theI=1/2,J=1/2+ state. The πN and σN (where σ is an unstableI=0,J=0+ two-pion state) channels are taken into account. The parameters of the model are adjusted to give 1) a nucleon bound state at the physical nucleon mass, 2) a zero in the πN amplitude at a pion laboratory kinetic energy of 150 MeV, 3) the πN Roper resonance at a pion laboratory kinetic energy of 600 MeV and 4) the experimental inelasticity parameter. We then find theN coupling constant\(g\frac{2}{\pi }\) /4π=15.2 and the πNI=1/2,J=1/2+ scattering lengtha11=−0.06 in units of the cube of the pion Compton wavelength, in fair agreement with the experimental values\(g\frac{2}{\pi }\) /4π=15.1±0.006 anda11=−0.101±0.007, respectively. The πN coupling constant\(g\frac{2}{\pi }\) /4π was found to be ∼7 in comparison with estimates of ∼ 4÷5 from the analysis of nucleon-nucleon scattering.

Modified Phase Representation and Effects of Inelasticity inNDCalculation ofp-Wave Pion-Pion Scattering

An $\frac{N}{D}$ formalism based on a modified phase representation is used to study the effects of inelasticity on the $p$-wave pion-pion amplitude. The effects of high-energy inelasticity are introduced in terms of the assumed behavior of the high-energy phase (not phase shift) of the partial-wave amplitude. Using a $\ensuremath{\rho}$-exchange input force with the experimental $\ensuremath{\rho}$ mass and a $\ensuremath{\rho}$ width of about 100 MeV, and the assumption that the average phase is $\frac{1}{2}\ensuremath{\pi}$, for total c.m. energies greater than about $8{M}_{\ensuremath{\pi}}$, we find that there is no appreciable reduction in the width of the calculated $p$-wave resonance. We also investigate the effects of low-energy inelastic channels that may contribute through the inelasticity parameter $\ensuremath{\eta}$ for $E<~{E}_{i}$, where ${E}_{i}$ is the energy above which the phase assumption is made. None of the forms for $\ensuremath{\eta}$ that were used resulted in an output width less than about 280 MeV.

Faddeev Equations with Inelastic Processes

Starting from the general Lippmann-Schwinger equation, we study the effect of inelastic processes on the scattering of three-body states. We show that it is possible to incorporate the inelastic effects into Faddeev-type equations in two different ways. The first approach is a straightforward generalization of the single-channel Faddeev equations to the multichannel form. However, we have to introduce the concepts of position and particle labeling in order to obtain a meaningful generalization. The second approach, which is derived from an extension of the concept of a complex potential, yields single-channel Faddeev equations with a modified input. The essential difference between this input and the input for the elastic case is the presence of a completely connected term. The two approaches are shown to be equivalent in their common region of validity. Under the resonance approximation, both approaches yield one-dimensional equations. The structure of the completely connected term is investigated for certain specific models and further simplifications on it are obtained. We also observe that the concept of the inelasticity parameter in the two-body case does not seem to have a natural generalization.

Asymptotic Behavior of the Inelasticity Parameter

We examine the asymptotic behavior of the inelasticity parameter $\ensuremath{\eta}$ under the assumption that an infinite number of 2-particle channels open up as energy becomes infinite. We investigate in detail three specific models, which can be handled analytically, and find that in general $\ensuremath{\eta}(\ensuremath{\infty})=1$ in these models. We speculate that this may in fact be the general asymptotic behavior of $\ensuremath{\eta}$ in the physical situations. We also observe that a purely imaginary elastic-scattering amplitude can be realized even as $\ensuremath{\eta}\ensuremath{\rightarrow}1$.

The effect of inelastic processes on theP 11 phase shift inπN scattering

Assuming that the nucleon is a bound state in the πN system we derive the approximate formula for a phase shift in theP11 wave. The left-hand cut is approximated by two poles and the effect of inelastic processes on the scattering amplitude of the partial waveP11 is discussed in terms of Froissart's method. The values of the inelastic parameter are taken from the experimental data. In this way the agreement with the experimental values of the phase shift in theP11 wave for low energies can be obtained.

Inelastic Unitarity Contributions toS12,T=12Pion-Nucleon Scattering Length

Inelastic unitarity contribution to the pion-nucleon ${S}_{\frac{1}{2}}$, $T=\frac{1}{2}$ zero-energy scattering length has been determined following the modified $\frac{N}{D}$ formalism due to Froissart. The fixed-energy dispersion relations and the experimental information for the $s$-wave inelastic parameter have been used to solve the resulting dispersion equations in the effective-range approximation method of Bal\'azs. We find a large positive scattering length, indicating that the inclusion of inelastic effects generates an attractive interaction in the $s$ wave.