High Energy Phase Shifts Research Articles

Are low-energy nuclear observables sensitive to high-energy phase shifts?

Conventional nucleon–nucleon potentials with strong short-range repulsion require contributions from high-momentum wave function components even for low-energy observables such as the deuteron binding energy. This can lead to the misconception that reproducing high-energy phase shifts is important for such observables. Interactions derived via the similarity renormalization group decouple high-energy and low-energy physics while preserving the phase shifts from the starting potential. They are used to show that high-momentum components (and high-energy phase shifts) can be set to zero when using low-momentum interactions, without losing information relevant for low-energy observables.

Analytic expressions for phase shifts in partially screened Coulomb potentials with ionic long range Coulomb tails

Analytic expressions for the high energy phase shifts of an electron moving in a partially screened spherically symmetric potential corresponding to an atomic ion have been obtained using methods developed previously for phase shifts in neutral atom potentials. Comparison with numerical calculation shows that the ionic phase shift formula is accurate in the case of a self-consistent potential of the Hermann-Skillman type, provided the electron energy is large and the angular momentum is small. The effect of the ionic tail on the phase shift (as compared with the short-range case) becomes substantial at lower energies, higher ionicities or larger angular momenta. It is conclude that use of neutral atom high energy analytic phase shift expressions is justified even in the presence of ionic tails.

Analytic expressions for high energy full three-dimensional continuum wave functions and phase shifts in screened Coulomb potentials: A. Bechler, Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland; and R. H. Pratt, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Analytic expressions for high energy full three-dimensional continuum wave functions and phase shifts in screened Coulomb potentials: A. Bechler, Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland; and R. H. Pratt, Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

On the sensitivity of the trinucleon binding energy to the repulsive core range of the nucleon-nucleon interaction

Abstract A direct relation between the trinucleon binding energy, EB, and the repulsive core range, rc, of the nucleon-nucleon interaction has been extracted from three-body bound state calculations. The nuclear force is constructed in such a way as to allow for a change of high-energy phase shifts only (and thus of rc), while leaving the off-shell behavior and the low-energy observables unchanged. It is found that EB is most sensitive in the region 0.30

Half shell reaction matrices and high energy phase shifts for the Paris potential

We have calculated high energy phase shifts for the Paris potential for Elab ≥ 330 MeV and compared these with experimental results for all channels with L ≤ 3. The effect of the momentum dependence on these phase shifts is studied. The half shell reaction matrices for these channels are also presented.

Padé phenomenology forNNscattering:S01phase shifts

Recently developed Pad\'e approximant techniques are applied to two sets of $^{1}S_{0}\mathrm{NN}$ scattering data. In the first, the unconstrained $^{1}S_{0}\mathrm{np}$ phase shifts of MacGregor et al. are used to generate a scattering function, $F({k}^{2})=kcot({\ensuremath{\delta}}_{0})$, which is fitted with high precision. A six-parameter [3/2] Pad\'e fit gives four terms of the effective range expansion; the resulting Marchenko-type potential is expressible as the sum of a Yukawa one-pion-exchange potential and a shorter range part, the repulsion peaking at the origin at near 4 GeV. In a second application, Pad\'e fits are made to the scattering function of the Reid soft-core potential. The [3/2] approximant which fits $F({k}^{2})$ through the wave numbers consistent with the Lambert, Corbella, and Thom\'e criterion, to $k=2.5$ ${\mathrm{fm}}^{\ensuremath{-}1}$, leads to a potential with a core height of 4.6 \ifmmode\times\else\texttimes\fi{} ${10}^{4}$ GeV. In both [3/2] potentials the volume integrals are large and negative, and cannot be made positive by adjoining more repulsive high energy phase shifts. By application to the Reid soft-core potential the Pad\'e formalism is shown to generate useful [$\frac{L}{L\ensuremath{-}1}$] Pad\'e approximants with increasing $L$. The analytic structure of $F({k}^{2})$ beyond $k=224$ ${\mathrm{fm}}^{\ensuremath{-}1}$ is used in the construction of higher Pad\'e approximants that (a) satisfy the Lambert, Corbella, and Thom\'e criterion and (b) might lead to saturation.NUCLEAR REACTIONS Pad\'e approximants used to solve inverse scattering problem for $\mathrm{NN}^{1}S_{0}$ phase shifts; effective range expansion and short range repulsion computed.

High-energy phase-shifts and off-shell reaction matrices from local and nonlocal nucleon-nucleon potential models

Potential models are usually fitted to phase-shifts up to 350 MeV laboratory energy. The differences between such potentials show up in (i) high-energy phase-shifts predicted by them and (ii) half-off-shell reaction matrix elements derived from them. The authors have studied both aspects up to 750 MeV for the Reid soft-core potential, the super-soft-core potential of de Tourreil, Rouben and Sprung (1975) and several separable potentials.

The unitary pole approximation for the binding energy of 4He

The sensitivity of the binding energy E α of 4He to the high-energy phase shift of the NN interaction, with a fixed deuteron wave function, is shown to be of the order of 6 MeV. This variation is compared to the one previously obtained for E α , if the short-range behaviour of the deuteron wave function is varied. In both cases a comparable broadening of the Tjon line results. A consequence of this result is that the accuracy of the unitary pole approximation in 4He is considerably less than was previously found for 3H.

Comparison of field theoretic and potential inverse problems in pion-nucleus scattering

The elastic scattering of ..pi../sup +/ on /sup 12/C in the P33 channel is examined for two different two-body interaction theories. A modified Chew-Low interaction and an energy dependent separable potential, both of which are solved as inverse problems to fit the on-shell two-body data exactly, are used to construct a first order optical potential. Differential cross sections are calculated in the impulse approximation at three energies; below, at, and above the energy of the ..pi..-nucleon resonance in the (3,3) channel. The differences between cross sections of the two models are compared to the differences made by varying the high energy phase shifts in the region where that are not well known experimentally (E/sub c.m./>1900 MeV) and found to be of the same order of magnitude. (AIP)

Intermediate-range potential and the 1S 0neutron-proton transition matrix

The half-shell transition matrix t( p, k) for the singlet s-wave neutron-proton interaction has been studied for a class of partly non-local potentials. The potentials have been generated from the experimental phase shifts by using inverse scattering theory. The non-uniqueness of the inversion solution has been exploited to construct potentials with different short-range behaviour. It is shown that the intermediate-range potential essentially determines t( p, k) for momenta p and k both less than 2fm −. Different short-range behaviour is reflected in t( p, k) for larger momenta. The unknown high-energy phase shifts imply, however, comparable variations in that region even if the on-shell momentum k is small. The implications for nuclear structure calculations are discussed.

Heavy-ion scattering at intermediate and high energies

We investigate the elastic scattering of two heavy ions. Elastic scattering gives us information on the heavy-ion optical potential and forms a basis for a further description of heavy-ion reactions using either the DWBA or the semi-classical approach to these processes. To extract the nuclear parameters from elastic scattering, one can use an exact phase-shift analysis, which at high energies is tedious and difficult (the Coulomb barrier sets the energy scale), or one can use various approximation schemes to compute the phase shifts. Here we investigate the validity of the WKB approximation and its high-energy eikonal limit (the “Glauber approximation”). The high-energy limit has the advantage that it is very simple and gives a useful picture of the scattering process in terms of straight-line eikonal trajectories. We also look at the systematic V / E corrections to the high-energy phase shift. The exact scattering amplitude is compared with the various approximations to it for an optical potential which fits 60 Ni( 16 O, 16 O) 60 Ni at low energies. The simple high-energy approximation is shown to provide an accurate description of the scattering process at energies and scattering angles of practical interest. We give some analytical expressions for the heavy-ion scattering amplitude in the high-energy approximation and also look at the model problem of heavy-ion scattering by a totally absorbing black sphere.

The sensitivity of the binding energies of the triton and nuclear matter to the high-energy phase shift

It is shown that using Srivastava's phase shifts and potential parameters one would also have come to the conclusion that the binding energy of the triton is nearly independent of the high-energy phase shift like he did for nuclear matter. This conclusion is however shown to be incorrect for the triton with different potentials and high-energy phase shifts.

Semiempirical Generalized One-Boson-Exchange Potentials

Four generalized one-boson-exchange-potential (GOBEP) models are examined. The first is a highly realistic model which includes only well-established mesons and which takes account of the resonance width of the isoscalar scalar $\ensuremath{\epsilon}$ meson. Two others are adaptions of this model, each containing a phenomenological term to help improve the fits to high-energy phase shifts. The final model does not assume charge independence of the nuclear force. Meson-nucleon form factors derived from a generalized field theory are used throughout, and a new fitting procedure is introduced which makes allowances for the uncertainties in the theoretical model. The models are compared and evaluated in terms of both the $F$ test for a fit to the phase shifts and the second-derivative matrix method for a fit to observable data. Our basic intention is to provide realistic GOBEP models suitable for nuclear-structure and nuclear-matter calculations.

The dependence of the triton binding energy on the high-energy phase shift

An investigation of the dependence of the binding energy of the model triton on the highenergy part of the phase shift has been made for an interaction consisting of a second-rank separable potential. For this investigation we used our previous exact solution of the inverse scattering problem for a second-rank separable potential. It is shown that for input phase shifts obtained from either a standard separable potential or a local potential with a repuslive core this high-energy dependence of the binding energy is rather small. However arbitrary modifications in the standard phase shift at high energies produce large effects in the binding energy, presumably resulting from the “unphysical” nature of such changes. It is also found that separable potentials reproducing the same two-body data as a local potential generally produce much higher triton binding energies than the local potential. The effect of the interaction between the high-energy on-shell phase shift and the off-shell behaviour of the potential on the triton binding energy is also discussed.

The dependence of nuclear matter binding energy on the high energy phase shifts

The dependence of the binding energy per particle in nuclear matter on the phase shifts beyond 350 MeV lab is investigated. Second rank separable potentials are used. It is found that the results are rather insensitive to the form of the phase shifts in the high energy region.