D. van der Knijff

An algebraic solution of the multichannel problem applied to low energy nucleon-nucleus scattering

This is a pre-print version published in Nuclear Physics A

A critical examination of software science

The claims that software science could provide an empirical basis for the rationalization of all forms of algorithm description are shown to be invalid from a formal point of view. In particular, the conjectured dichotomy between operators and operands is shown not to hold over a wide class of languages. An experiment that investigated discrepancies between the level measure and its estimator is described to show that its failure was due to shortcomings in the theory. One cannot obtain reliable results without tampering with both measure and estimator definitions.

Role of the Pauli principle in collective-model coupled-channel calculations.

A multichannel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. By tracking the results in the zero coupling limit, a correct interpretation of the subthreshold and resonant spectra of the compound system can be made. As an example, the neutron-12C system is studied defining properties of 13C to 10 MeV excitation. Accounting for the Pauli principle in collective coupled-channels models is crucial to the outcome.

Collective-coupling analysis of spectra of mass-7 isobars : 7He, 7Li, 7Be, and 7B

A nucleon-nucleus interaction model has been applied to ascertain the underlying character of the negative-parity spectra of four isobars of mass seven, from neutron-- to proton--emitter driplines. With one single nuclear potential defined by a simple coupled-channel model, a multichannel algebraic scattering approach (MCAS) has been used to determine the bound and resonant spectra of the four nuclides, of which ^7He and ^7B are particle unstable. Incorporation of Pauli blocking in the model enables a description of all known spin-parity states of the mass-7 isobars. We have also obtained spectra of similar quality by using a large space no-core shell model. Additionally, we have studied ^7Li and ^7Be using a dicluster model. We have found a dicluster-model potential that can reproduce the lowest four states of the two nuclei, as well as the relevant low-energy elastic scattering cross sections. But, with this model, the rest of the energy spectra cannot be obtained.

Linking the exotic structure of 17C to its unbound mirror 17Na

Abstract The structure of 17C is used to define a nuclear interaction that, when used in a multichannel algebraic scattering theory for the n + C 16 system, gives a credible definition of the (compound) excitation spectra. When couplings to the low-lying collective excitations of the 16C-core are taken into account, both sub-threshold and resonant states about the n + C 16 threshold are found. Adding Coulomb potentials to that nuclear interaction, the method is used for the mirror system of p + Ne 16 to specify the low excitation spectrum of the particle unstable 17Na. We compare the results with those of a microscopic cluster model. A spectrum of low excitation resonant states in 17Na is found with some differences to that given by the microscopic cluster model. The calculated resonance half-widths (for proton emission) range from ∼2 to ∼ 672 keV .

Compound and quasicompound states in low-energy scattering of nucleons from {sup 12}C

A multichannel algebraic scattering theory has been used to study the properties of nucleon scattering from {sup 12}C and of the subthreshold compound nuclear states. The theory accounts for properties in the compound nuclei to {approx}10 MeV. All compound and quasicompound resonances observed in total cross-section data are matched, and, on seeking solutions of the method at negative energies, all subthreshold states in {sup 13}C and {sup 13}N are predicted with the correct spin-parities and with reasonable values for their energies. A collective-model prescription has been used to define the initiating nucleon-{sup 12}C interactions and, via use of orthogonalizing pseudopotentials, account is made of the Pauli principle. Information is extracted on the underlying structure of each state in the compound systems by investigating the zero-deformation limit of the results.

Coupled-channel evaluations of cross sections for scattering involving particle-unstable resonances.

How does the scattering cross section change when the colliding bound-state fragments are allowed particle-emitting resonances? This question is explored in the framework of a multichannel algebraic scattering method of determining nucleon-nucleus cross sections at low energies. Two cases are examined, the first being a gedanken investigation in which n + 12C scattering is studied with the target states assigned artificial widths. The second is a study of neutron scattering from 8Be, a nucleus that is particle unstable. Resonance character of the target states markedly varies evaluated cross sections from those obtained assuming stability in the target spectrum.

Evaluation of length and level for simple program schemes

Several examples of simple program schemes are used to study the influence of basic con structs on measures of Software Science. A min imal low level language is used in order to build examples which contain large numbers of the constructs under study. The measures are expressed as functions depending on the number of con ceptually unique input-output operands. They may therefore be evaluated and compared to their estimators analytically rather than statistically.

Low-energy neutron-{sup 12}C analyzing powers: Results from a multichannel algebraic scattering theory

Analyzing powers in low-energy neutron scattering from {sup 12}C are calculated in an algebraic momentum-space coupled-channel formalism, that is, a multichannel algebraic scattering (MCAS) theory. The results are compared with recently obtained experimental data. The channel-coupling potentials have been defined previously to reproduce the total cross section and subthreshold bound states of the compound system. Without further adjustment, good agreement with data for the analyzing powers is obtained.

Comparison between two methods of solution of coupled equations for low-energy scattering

Cross sections from low-energy neutron-nucleus scattering have been evaluated using a coupled-channel theory of scattering. Both a coordinate-space and a momentum-space formalism of that coupled-channel theory are considered. A simple rotational model of the channel-interaction potentials is used to find results using two relevant codes, ECIS97 and MCAS, so that they may be compared. The very same model is then used in the MCAS approach to quantify the changes that occur when allowance is made for effects of the Pauli principle.