David R. Harrington

Correlation and isospin effects in high energy scattering of hadrons from nuclei

Abstract Correlation effects in high energy hadron-nucleus scattering are considered within the context of multiple diffraction theory. For Pauli and c.m. correlations a simple harmonic oscillator model is used for which the effects can be calculated exactly, even for fairly heavy nuclei. This model is used to test the convergence of a correlation expansion; a truncation of this expansion at pair correlations is found to give good results. Simple prescriptions are given for including these effects in realistic nuclei and are shown to be quite accurate. The effects of dynamical short-range correlations and isospin dependence of nucleon-nucleon interactions are also considered. The corresponding contributions to the second order optical potential are discussed. It is pointed out that neglect of Pauli and c.m. effects in most nuclei can lead to errors in extracting nuclear structure information from the data.

PRODUCTION OF ALIGNED DEUTERONS IN HIGH-ENERGY ELASTIC PROTON--DEUTERON SCATTERING.

Abstract It is shown that, because of spin-dependence resulting from the D-wave components of the deuteron, it should be possible to produce and analyze strongly aligned beams of high-energy deuterons by elastic scattering on protons.

Overlapping isospin-dependent interactions in high-energy pion-deuteron scattering

Abstract The complications introduced into Glauber theory by overlapping isospin-dependent interactions are discussed in the context of high-energy pion-deuteron scattering. The commonly used ordered form of the Glauber theory is exact only when the isospin-dependent potentials have zero overlap, or in the limit in which they are weak. A pair of coupled integrals equations is derived which should be useful for numerical calculations when the ordered form is inadequate. An exactly soluble one-dimensional overlapping slab model is also discussed; it gives some idea of the nature of the approximation made when the ordered form is used. Finally, an overlap expansion is developed for another one-dimensional model in which the potentials have more realistic exponential tails. Such expansions could be useful for estimating the magnitudes of the errors introduced through the use of the ordered form.

Corrections to the Glauber theory and nucleon-nucleus scattering

Abstract The leading corrections to the Glauber approximation are evaluated for a wide range of target nuclei. Near 1 GeV the corrections are small enough that the uncorrected theory should be quite reliable for determining the nucleon density distributions in target nuclei from proton scattering data. Effects arising from Pauli correlations and isospin dependence (charge exchange) are also considered.

Hadron-nucleon total cross section fluctuations from hadron-nucleus total cross sections

The extent to which information about fluctuations in hadron-nucleon total cross sections in the frozen approximation can be extracted from very high energy hadron-nucleus total cross section measurements for a range of heavy nuclei is discussed. The corrections to the predictions of Glauber theory due to these fluctuations are calculated for several models for the distribution functions, and differences of the order of 50 mb are found for heavy nuclei. The generating function for the moments of the hadron-nucleon cross section distributions can be approximately determined from the derivatives of the hadron-nucleus total cross sections with respect to the nuclear geometric cross section. The argument of the generating function, however, is limited to the maximum value of a dimensionless thickness function obtained at zero impact parameter for the heaviest nuclear targets: about 1.8 for pions and 3.0 for nucleons.

Test of correlation expansions for inelastic scattering of protons from 16O and 40Ca in Glauber theory

Abstract Two different versions of a correlation expansion for the A -body nuclear transition density required to evaluate the Glauber amplitude for inelastic proton-nucleus scattering are tested. Antisymmetrized oscillator wave functions, containing only Pauli correlations, are used to calculate the “exact” amplitude as well as various terms in the correlation expansions for the excitation of the 3 − (6.13 MeV) state of 16 O and the 5 − (4.49 MeV) state of 40 Ca. The leading term in both expansions, which ignores all correlations and corresponds to the Glauber theory version of the DWIA, leads to errors which are larger than present experimental errors, especially at large momentum transfers. In one version of the correlation expansion, due to Alkhazov et al. , the first-order correction contains both elastic and inelastic two-body correlations and leads to satisfactory results. In the other version, used by Abgrall et al. , the first-order correction contains only inelastic two-body correlations. In this case the first- and second-order corrections are needed to obtain accuracy comparable to that of the latest experiments.

Corrections to Glauber theory in the optical limit

Abstract In the optical limit the leading finite energy correction to Glauber theory for scattering from a composite system in the fixed scatterer approximation takes a form similar, but not identical, to the leading correction to scattering from an elementary system via the optical potential.

Spin-orbit and Pauli-correlation effects in intermediate-energy proton-nucleus inelastic scattering

Abstract The excitation of the 3− (6.13 MeV) state of 16O by 0.8 GeV protons is studied using Glauber theory with a spin-orbit NN amplitude. Two previously suggested approaches for handling the z-ordered non-commuting NN profile functions, γ, are compared and found to give nearly identical results for the usual observables. Transitions to certain LM substates which are forbidden in one approach are allowed in the other, but their cross sections are proportional to the fourth power of the strength of the NN spin-orbit amplitude and thus quite small. It is also shown that, in this energy region, an expansion in powers of the strength of the spin-orbit interaction converges rapidly and consequently any convenient ordering of the γs can be used without serious errors. Using this result an estimate of the effects of Pauli correlations on the cross section and the polarization is given.

Test of the DWIA for inelastic proton-nucleus scattering in glauber theory

Abstract An anti-symmetrized oscillator model is used to determine the accuracy of the DWIA for inelastic scattering of protons from nuclei in Glauber theory. The leading correction to the DWIA from the next term in a correlation expansion of the transition density is also tested. The DWIA for the profile function for 1ħω excitations of 40 Ca is accurate to about 10 % in this model, but the leading correction does not give significant improvement and in some cases increases the error.

Functional integral representation of Glauber theory for high-energy heavy-ion scattering

Abstract A functional integral representation is presented for the Glauber theory amplitude for high- energy heavy-ion scattering with arbitrary nucleon-nucleon interactions, closely related to that previously obtained by Winbow using Reggeon field theory. As in Winbows paper the amplitude can be evaluated in the large- A limit using a saddle point technique. The evaluation is carried out in a simple case: it predicts less absorption than does the double-folding model.