Daniel S. Koltun

Pion-deutron scattering in the Δ(1236) energy region as a three-body problem☆

Abstract We study pion-deuteron scattering in the first π-N resonance energy region, in a three-body model based on Faddeevs equations. We discuss the effects of multiple scattering, nuclear binding, and virtual excitation of the target, on the energy behavior of the cross section.

ELASTIC PION-DEUTERON SCATTERING IN THE RESONANCE REGION AS A THREE-BODY PROBLEM *

Abstract We study elastic pion-deuteron scattering in the Δ(1236) energy region by means of the three-body Faddeev equations. We present a compact angular momentum reduction of the Faddeev integral equation for separable amplitudes, neglecting the nucleon spin, and solve the resulting coupled integral equations. We examine the dependence of the elastic scattering amplitude on the deuteron structure, on the pion-nucleon scattering amplitude, and on the various orders of multiple scattering. The differential cross section is very sensitive to multiple scattering effects at backward angles. We find that a number of conventional approximations do not well reproduce these multiple scattering effects in the resonance region.

Absorption of s-orbit π− mesons by 4He

Abstract The rate for absorption of s-orbit bound π − mesons by correlated nucleon pairs, and the distributions in momentum and lab angle of the emitted fast nn or np pair, are calculated for 4 He. The pion is assumed to be absorbed either directly by one nucleon, or by processes that involve exchange of the absorbed pion between the two nucleons in question. The absorbing nucleon pair is assumed to interact in the initial state through a harmonic-oscillator potential plus a short-range (Hamada-Johnston) interaction, and in the final state only through the short-range interaction.

The average effective interaction in linked cluster theory

Abstract We derive a theoretical method for calculating the averages (over J and T) of matrix elements of the nuclear effective interaction, in any order of the linked cluster expansion. We apply this to calculate all terms through fourth order in the G-matrix, for the averages in mass-6 and mass-18 nuclei. We find that the averages in fourth order are as large as in second and third order. This behavior is associated with a small number of terms, which suggests a partial summation method of improving the series. The relation to other work is discussed.

Pion excess, nuclear correlations, and the interpretation of ({rvec p},{rvec n}) spin transfer experiments

Conventional theories of nuclear interactions predict a net increase in the distribution of virtual pions in nuclei relative to free nucleons. Analysis of data from several nuclear experiments has led to claims of evidence against such a pion excess. These conclusions are usually based on a collective theory [random-phase approximation (RPA)] of the pions, which may be inadequate. The issue is the energy dependence of the nuclear response, which differs for theories with strong NN correlations from the RPA predictions. In the present paper, information about the energy dependence is extracted from sum rules, which are calculated for such a correlated, noncollective nuclear theory. The results lead to much reduced sensitivity of nuclear reactions to the correlations that are responsible for the pion excess. The primary example is ({rvec p},{rvec n}) spin transfer, for which the expected effects are found to be smaller than the experimental uncertainties. The analysis has consequences for deep inelastic scattering experiments as well. {copyright} {ital 1998} {ital The American Physical Society}

Behavior of the G-matrix expansion for the average effective interaction☆

Abstract A method is presented for calculating the spectroscopic average of higher-order terms in the G -matrix expansion of the nuclear effective interaction. Results for the 1d-2s and 1f-2p shells show that the expansion is well behaved on the average through third order, in contrast to earlier results for J , T = 0,1 states.

Sensitivity of inelastic pion scattering to non-local interactions

Abstract We show that the excitation of nuclear electric dipole states by small angle inelastic scattering of pions can be used to detect the degree of non-locality of pion nucleus scattering matrix.

Soft pion theorems, meson exchange currents, and pion double charge exchange

Abstract Meson exchange current (MEC) contributions to pion double charge exchange (DCX) scattering at low energies are studied using soft pion theorems. A general form for the scattering amplitude on any scalar-isovector target is derived and applied as a constraint on the pion-nucleus DCX scattering amplitude. One result is an estimate that for a nuclear target with two excess valence neutrons, the MEC amplitude is less than ∼ 10 −2 fm. Second, a consistency condition on different MEC contributions is obtained, which exhibits the requirement of cancellations among these, and leads to a sum rule for evaluating all contributions of one type of exchanged meson. Consequences for vector meson exchange are discussed.

Inelastic nucleon contributions in (e,e{sup {prime}}) nuclear response functions

We estimate the contribution of inelastic nucleon excitations to the (e,e{sup {prime}}) inclusive cross section in the CEBAF kinematic range. Calculations are based upon parameterizations of the nucleon structure functions measured at SLAC. Nuclear binding effects are included in a vector-scalar field theory, and are assumed to have a minimal effect on the nucleon excitation spectrum. We find that for q{approx_lt}1 GeV the elastic and inelastic nucleon contributions to the nuclear response functions are comparable, and can be separated, but with roughly a factor of 2 uncertainty in the latter from the extrapolation from data. In contrast, for q{approx_gt}2 GeV this uncertainty is greatly reduced but the elastic nucleon contribution is heavily dominated by the inelastic nucleon background. {copyright} {ital 1997} {ital The American Physical Society}

Relativistic Coulomb sum rules for (e,e').

A Coulomb sum rule is derived for the response of nuclei to ([ital e],[ital e][prime]) scattering with large three-momentum transfers. Unlike the nonrelativistic formulation, the relativistic Coulomb sum is restricted to spacelike four-momenta for the most direct connection with experiments; an immediate consequence is that excitations involving antinucleons, e.g., [ital N[bar N]] pair production, are approximately eliminated from the sum rule. Relativistic recoil and Fermi motion of target nucleons are correctly incorporated. The sum rule decomposes into one- and two-body parts, with correlation information in the second. The one-body part requires information on the nucleon momentum distribution function, which is incorporated by a moment expansion method. The sum rule given through the second moment (RCSR-II) is tested in the Fermi gas model, and is shown to be sufficiently accurate for applications to data.