Effective Range Parameters Research Articles

Percolation-like behavior of the spin wave stiffness in amorphous (FepNi1−p)80P20

The spin wave stiffness D and the phase diagram have been determined for the series of amorphous (FepNi1−p)80P20 alloys, from magnetization data. For applied fields greater than 1 kOe, the magnetization follows the Bloch T3/2 law when corrected for field-induced gap. The coefficient of the T3/2 term diverges as the concentration is reduced towards the critical concentration pc. The effective range parameter D/Tc is also found to diverge, as (p−pc)−1/2. This is consistent with current models for the spin wave stiffness in percolating magnets.

Effective range parameters in nucleon-nucleon scattering

We have calculated effective range parameters for the $S$ and $P$ states for proton-proton and neutron-proton scattering and compared them with results from other authors. The calculations were done in the framework of a phase shift analysis. Different effective range expansions (with and without inclusion of the one-pion-exchange cut) were investigated. Taking into account features of the deuteron and of one pion exchange we give a low energy parametrization for the mixing parameter ${\ensuremath{\epsilon}}_{1}$.

The NN-potential with forbidden state suggested from a six-quark model with one-pion exchange

A new, realistic NN-potential is proposed which is suggested from a six-quark model with dominant quark configuration s 4p 2 and includes the one-pion exchange mechanism in the 1S 0 and coupled 3S 1 − 3D 1 channels. The potential is purely attractive on the mass shell and includes a deep-lying forbidden state instead of a repulsive core. A very small number of free parameters is sufficient to succesfully describe both the 3S 1 − 3D 1 NN-phase shifts, the mixing parameter ε and the singlet 1S 0 phase shifts in a broad energy range from 0 to 400 MeV (alongside with effective range parameters) and also basic deuteron parameters (i.e. binding energy, RMS charge radius, quadrupole moment, etc.). The deuteron wave function components ( u and w) have an inner node at the place of the hard core of the conventional realistic NN potentials.

Nucleon-deuteron low energy parameters

Momentum space Faddeev equations are solved for nucleon-deutron scattering and effective range parameters are calculated. A reverse trend is found in the two spin states by 4a nd < 4a pd and 2a pd < 2a nd which is in agreement with a configuration space calculation, but in conflict with all existing experiments. The Coulomb contributions to the effective range are small in quartet but sizeable in doublet scattering.

Low-energy parameters in nonrelativistic scattering theory

Low-energy quantities like the scattering length and effective range parameter range parameter are direetly derived from the threshold behavior of the scattering amplitude for Schrödinger Hamiltonians with short-range and Coulomb-type interactions. The possibility of zero-energy resonances and zero-energy bound states of the underlying Hamiltonian is explicitly taken into account. No spherical symmetry of the interaction is assumed.

Comments on Recent Progress in Few Particle Physics

Status of the present understanding of multiparticle reaction mechanism is summarized. Lesson derived from the studies of the reaction D(p,2p)n is that mechanism can be very imoortant even if not easily noticeable in a particular representation. E.g. even a deep minimum is understood as a destructive interference between neutron-proton and proton-proton quasifree scattering. Information about nuclear interaction derived from few particle studies is discussed. The correct neutron-neutron effective range parameters are those extracted from the D(?-,?)2n reaction. Values extracted from the D(n,p)2n reaction are influenced by the three body force. Evidences for the three body force are summarized.

The meson and quark-gluon degrees of freedom in NN-interaction at low and intermediate energies

A set of nonsingular integral equations has been formulated to calculate the partial amplitudes of hadron-hadron scattering at low and intermediate energies making allowance for the meson and quark-gluon degrees of freedom. The results are presented of the calculations of the np effective range parameters and of the np scattering 1S 0- and 3S 1-phase shifts at incident nucleon energies ranging from 1 to 1050 MeV.

Are there bound A=2 hyperon states?

One-boson-exchange potentials for ΛN, Σ + p, ΛΛ and ΞN elastic scattering at E lab ≲ 150 MeV are calculated including renormalizations due to two-boson exchanges. The model is derived from a quark pairing mechanism that has previously been tested for elastic NN scattering. The resulting phase shifts and effective range parameters are compared with data and other phenomenological potentials for ΛN and Σ +p systems, and reasonable agreement is achieved. In the ΛΛ and ΞN channels, deuteron-like bound states may exist.

Formulas for theδ-shell-plus-Coulomb potential for all partial waves

Closed forms are given for a large number of quantities occurring in the theory of potential scattering in an arbitrary partial-wave state $l$ for the cases (i) the $\ensuremath{\delta}$-shell potential $V(r)=\ensuremath{-}\ensuremath{\lambda}{R}^{\ensuremath{-}2}\ensuremath{\delta}(r\ensuremath{-}R)$, and (ii) the $\ensuremath{\delta}$-shell plus Coulomb potential. Furthermore, the trajectories of the poles of the total $T$ operator in the complex $k$ plane, with varying complex $\ensuremath{\lambda}$, are investigated in detail for zero, repulsive, and attractive Coulomb force, respectively. Expressions are given for the effective-range parameters, and the Coulomb-modified effective-range parameters, for all $l$, with application to the $\mathrm{NN}$ system, and the $N\ensuremath{\alpha}$ system, respectively. The connection between Coulomb-level shifts and effective-range parameters is considered. Improvements on the standard small-shift approximation, which is relatively poor, are suggested.NUCLEAR REACTIONS Charged-particle scattering. $\ensuremath{\delta}$-shell plus Coulomb potential. Effective-range parameters for all $l$. Application to $\mathrm{NN}$ and $N\ensuremath{\alpha}$. Coulomb-level shifts.

Padé phenomenology for two-body bound states

Pad\'e approximants in the squared momentum variable, recently used for elastic scattering, are employed in generating accurate analytic approximants for bound states. Through iteration, [$\frac{L}{L+1}$] approximants yield the lowest eigenstate of the homogeneous Lippmann-Schwinger equation for Yukawa, Malfliet-Tjon, and Reid soft core central potentials with, respectively, $L=1, 2, \mathrm{and} 3$. Higher eigenstates are readily obtained; the second is given for the Yukawa potential. Analytic separable expansions and scattering expressions result.NUCLEAR STRUCTURE Pad\'e approximants in ${k}^{2}$, analytic two-body bound states, separable expansions, effective range parameters.

Comment on "Three-Body Forces and Neutron-Neutron Effective Range Parameters"

The difficulty of separating charge-exchange processes from three-body forces in the analysis of the reaction (D(n,2n)p is discussed.(AIP)

Separable potential for the neutron-proton system

A separable potential is proposed for the $n\ensuremath{-}p$ interaction in $^{1}S_{0}$ and $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ partial waves. In the singlet $S$ state the potential fits new phenomenological phases rather accurately in the laboratory kinetic energy range 0-600 MeV; it is also capable of reproducing singlet effective-range parameters in close agreement with experiment. In the coupled state $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ the potential provides a correct description of the deuteron data (${E}_{D}$, ${p}_{D}$, $Q$, $\ensuremath{\eta}$), while at the same time it adequately fits modern phenomenological phases up to ${E}_{\mathrm{lab}}\ensuremath{\gtrsim}500$ MeV in both the $S$ and the $D$ wave; triplet effective-range parameters are also in agreement with experimental data. Only the mixing parameter ${\ensuremath{\epsilon}}_{1}$ deviates from predictions of phase-shift analyses. In the construction of the potential care was taken that its off-shell behavior be reasonable. As an eminent property it thus exhibits an off-shell behavior similar to the one of the Paris potential. In particular the $^{3}S_{1}\ensuremath{-}^{3}D_{1}$ potential yields a deuteron $S$-state wave function, which in momentum space shows a zero like the Paris potential. Still the model is simple enough to be of good use in modern computer codes for few-body systems and other nuclear applications.NUCLEAR REACTIONS Separable potential proposed for $n\ensuremath{-}p$ interaction; fits new on-shell data; off-shell behavior compared to Paris potential.

Three-Body Forces and Neutron-Neutron Effective-Range Parameters

It is suggested that the difference which presently exists between neutron-neutron effective-range parameters extracted from the reactions $\mathrm{D}({\ensuremath{\pi}}^{\ensuremath{-}},\ensuremath{\gamma})2n$ and $\mathrm{D}(n, 2n)p$ can be explained by the same three-body force which describes $^{3}\mathrm{H}$, $^{3}\mathrm{He}$, and $^{4}\mathrm{He}$. The effects of the three-body force are different for neutron pickup and proton knockon processes in the reaction $\mathrm{D}(n, 2n)p$.

On the on- and off-shell proton-proton T matrix for the Graz separable interaction

The Coulomb-distorted nuclear transition matrix Tcs of the proton-proton system is considered for the separable Graz potential. Analytic expressions for its on- and off-shell matrix elements are given for partial waves with l<or=1. Numerical results are quoted for Coulomb-distorted nuclear phase-shifts and effective-range parameters. This thereby corrects erroneous formulae given in a previous work by R.J.W. Hodgson (1979).

N-n Effective range from the photon spectrum of the reaction π−d→ γnn

Notable improvements in the treatment of the reaction π − d→ γnn, extending the validity of the calculation to lower photon energies, permit a new analysis of a high statistics photon spectrum. A precise value of the effective range parameter γ nn = 2.83 ± 0.11 fm has been obtained. The theoretical uncertainty is 0.11 fm. The value of the scattering length previously extracted from the same spectrum is confirmed, with a nn = − 18.6 ± 0.5 fm.

Off-shell rescattering effects in the reactionπ−+d→2n+γ

We have reexamined the multiple scattering corrections to the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}+d\ensuremath{\rightarrow}2n+\ensuremath{\gamma}$ in order to extend the validity of previous calculations to a larger neutron-neutron relative momentum interval and to determine the effective range parameter. This extension has been carried out analytically by studying the off-shell properties and energy dependence of the pion-nucleon amplitude. The sensitivity of the photon spectral curves for various approximations is shown, and the importance of the different effects in the values of the neutron-neutron scattering length and effective range is indicated.NUCLEAR REACTIONS ${\ensuremath{\pi}}^{\ensuremath{-}}+d\ensuremath{\rightarrow}2n+\ensuremath{\gamma}$, analytical treatment of multiple scattering. Off-shell extension of pion-nucleon amplitude.

Exchange current corrections to the proton-proton reaction

The contribution from tau- and rho-meson exchange to the rate of the proton-proton reaction is found to be approximately 2%. For the one-body operator a good estimate is obtained directly from experimental effective-range parameters.

Phenomenological study of lambda-nucleon interaction

A joint fit has been made to the binding energy data of the $A=3\ensuremath{-}4$ hypernuclei (ground and excited states) together with the $\ensuremath{\Lambda}\ensuremath{-}p$ scattering data in order to deduce depth and range parameters of a phenomenological $\ensuremath{\Lambda}$-nucleon potential. Having determined the potential parameters we were able to infer the scattering lengths and effective ranges for the $\ensuremath{\Lambda}\ensuremath{-}p$ and $\ensuremath{\Lambda}\ensuremath{-}n$ systems.NUCLEAR REACTIONS $\ensuremath{\Lambda}$-nucleon potential inferred from the data; effective range parameters calculated.

2H(n, nn)p reaction at 21.5 MeV

A kinematically complete experiment that examines the 2H(n, nn)p reaction at several quasifree angles has been performed. The results are compared with the predictions of the Ebenhöh code which solves the Faddeev equations with separable two-body potentials. Assuming the “best value” for the 1S 0 neutron scattering length a nn of −16.3 ± 0.6 fm we determine a value for the effective range parameter r nn of 2.9 ± 0.4 fm , not including any theoretical uncertainties.

Suppression of the isospin-½, three-body photodisintegration ofHe3

The suppression of the isospin-1/2, three-body photodisintegration of /sup 3/He is shown to result from two facts: (1) For the S = 1/2, I = 1/2 states of three nucleons, the spin-isospin symmetries lead to integral equations dominated by a single effective interaction V/sup +/, which is the average of the NN s-wave spin-singlet and spin-triplet interactions and (2) This V/sup +/ supports a bound state due to the nature of the NN effective-range parameters. In the approximation that the (1/2,1/2) states are generated from V/sup +/ alone, it is clear that a fraction of the isospin-1/2 bremsstrahlung-weighted sum rule must come from two-body photodisintegration with a corresponding reduction of the three-body channel contribution, since the total isospin-1/2 sum rule is fixed. The substantial reduction of the actual physical isospin-1/2, three-body photodisintegration is directly related to the strength of V/sup +/.