arXiv subjects

D. van der Knijff

Publications and source records attributed to D. van der Knijff.

At least 19 recordsLinked to original sources

arXiv2017

Mass-15 nuclei and predicting narrow states beyond the proton drip line

In a previous letter (Phys. Rev. Lett. 96, 072502 (2006)), the multi-channel algebraic scattering (MCAS) technique was used to calculate spectral properties for proton-unstable $^{15}$F and its mirror, $^{15}$C. MCAS achieved a close match to the then-new data for $p+^{14}$O elastic scattering and predicted several unusually narrow resonances at higher energies. Subsequently, such narrow resonance states were found. New cross section data has been published characterising the shape of the $J^π=\frac{1}{2}^-$ resonance. Herein we update that first MCAS analysis and its predictions. We also study the spectra of the set of mass-15 isobars, ${}^{15}$C, ${}^{15}$N, ${}^{15}$O, and ${}^{15}$F, using the MCAS method and seeking a consistent Hamiltonian for clusterisation with a neutron and a proton, separately, coupled to core nuclei ${}^{14}$C and ${}^{14}$O.

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arXiv2017

Very low-energy nucleon + 16O coupled-channel scattering: results with a phenomenological vibrational model

We employ a collective vibration coupled-channel model to describe the nucleon-16O cluster systems, obtaining low-excitation spectra for 17O and 17F. Bound and resonance states of the compound systems have been deduced, showing good agreement with experimental spectra. Low energy scattering cross sections of neutrons and protons from 16O also have been calculated and the results compare well with available experimental data.

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arXiv2016

A multi-channel model for an α plus $^6$He nucleus cluster

A multi-channel algebraic scattering (MCAS) method has been used to solve coupled sets of Lippmann-Schwinger equations for the $α$+${}^6$He cluster system, so finding a model spectrum for ${}^{10}$Be to more than 10 MeV excitation. Three states of ${}^6$He are included and the resonance character of the two excited states taken into account in finding solutions. A model Hamiltonian has been found that gives very good agreement with the known bound states and with some low-lying resonances of ${}^{10}$Be. More resonance states are predicted than have as yet been observed. The method also yields $S$-matrices which we have used to evaluate low-energy ${}^6$He-$α$ scattering cross sections. Reasonable reproduction of low-energy differential cross sections and of energy variation of cross sections measured at fixed scattering angles is found.

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arXiv2016

A multichannel model for clusters of an $α$ and select $N=Z$ nuclei

A multi-channel algebraic scattering (MCAS) method has been used to solve coupled sets of Lippmann-Schwinger equations for $α$+nucleus systems to find spectra of the compound systems. Low energy spectra for ${}^{12}$C, ${}^{16}$O, and ${}^{20}$Ne are found with the systems considered as the coupling of an $α$ particle with low-excitation states of the core nuclei, ${}^8$Be, ${}^{12}$C, and ${}^{16}$O, respectively. Collective models have been used to define the matrices of interacting potentials. Quadrupole (and octupole when relevant) deformation is allowed and taken to second order. The calculations also require a small monopole interaction to provide an extra energy gap commensurate with an effect of strong pairing forces. The results compare reasonably well with known spectra given the simple collective model prescriptions taken for the coupled-channel interactions. Improvement of those interaction specifics in the approach will give spectra and wave functions suitable for use in analyses of cross sections for $α$ scattering and capture by light-mass nuclei; reactions of great importance in nuclear astrophysics.

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arXiv2016

Structure of $^{23}$Al from a multi-channel algebraic scattering model based on mirror symmetry

The proton-rich nucleus $^{23}$Al has a ground state just 123 keV below the proton drip-line, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering (MCAS) method to describe states as resonances of a valence proton coupled to a $^{22}$Mg rotor core. Six states with low-excitation energies and defined $J^π$ are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.

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arXiv2016

Importance of resonance widths in low-energy scattering of weakly-bound light-mass nuclei

What effect do particle-emitting resonances have on the scattering cross section? What physical considerations are necessary when modelling these resonances? These questions are important when theoretically describing scattering experiments with radioactive ion beams which investigate the frontiers of the table of nuclides, far from stability. Herein, a novel method is developed that describes resonant nuclear scattering from which centroids and widths in the compound nucleus are obtained when one of the interacting bodies has particle unstable resonances. The method gives cross sections without unphysical behavior that is found if simple Lorentzian forms are used to describe resonant target states. The resultant cross sections differ significantly from those obtained when the states in the coupled channel calculations are taken to have zero width, and compound-system resonances are better matched to observed values.

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arXiv2014

Coupling to two target-state bands in the study of the n+22Ne system at low energy

One theoretical method for studying nuclear scattering and resonances is via the multi-channel algebraic scattering (MCAS) formalism. Studies to date with this method have used a simple collective-rotor prescription to model target states with which a nucleon couples. While generally these target states all belong to the same rotational band, for certain systems it is necessary to include coupling to states outside of that main band. Here, we extend MCAS to allow coupling of different strengths between such states and the rotor band. This is an essential consideration in studying the example examined herein, the scattering of neutrons from 22Ne.

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arXiv2011

Nuclear mass systematics and nucleon-removal thresholds; application to 17-Na

A survey of known threshold excitations of mirror systems suggests a means to estimate masses of nuclear systems that are uncertain or not known, as does a trend in the relative energies of isobaric ground states. Using both studies and known mirror-pair energy differences, we estimate the mass of the nucleus 17-Na and its energy relative to the p+16-Ne threshold. This model-free estimate of the latter is larger than that suggested by recent structure models.

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arXiv2010

Scattering of nucleons from nuclei with couplings to particle-unstable excited states

The physics of radioactive ion beams implies the description of weakly-bound nuclear systems. One key aspect concerns the coupling to low-lying collective-type excited states, which for these systems might not be stable levels, but particle emitting resonances. In this work we describe how the scattering cross section and compound spectra change when the colliding fragments have such collective excitations featuring particle emission. We explore this question in the framework of a multi-channel algebraic scattering method of determining nucleon-nucleus cross sections at low energies. For a range of light-mass, particle-unstable nuclear targets, scattering cross sections as well as the spectra of the compound nuclei formed have been determined from calculations that do and do not consider particle emission widths for nuclear states. Assuming a resonance character for target states markedly varies evaluated cross sections from those obtained assuming the target spectrum to have entirely discrete states.

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arXiv2008

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 multi-channel 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 + carbon-12 scattering is studied with the target states assigned artificial widths. The second is a study of neutron scattering from beryllium-8; 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.

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arXiv2007

Multi-channel algebraic scattering theory and the structure of exotic compound nuclei

A Multi-Channel Algebraic Scattering (MCAS) theory is presented with which the properties of a compound nucleus are found from a coupled-channel problem. The method defines both the bound states and resonances of the compound nucleus, even if the compound nucleus is particle unstable. All resonances of the system are found no matter how weak and/or narrow. Spectra of mass-7 nuclei and of {}^{15}F, and MCAS results for a radiative capture cross section are presented.

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arXiv2007

Particle-unstable light nuclei with a Sturmian approach that preserves the Pauli principle

Sturmian theory for nucleon-nucleus scattering is discussed in the presence of all the phenomenological ingredients necessary for the description of weakly-bound (or particle-unstable) light nuclear systems. Currently, we use a macroscopic potential model of collective nature. The analysis shows that the couplings to low-energy collective-core excitations are fundamental but they are physically meaningful only if the constraints introduced by the Pauli principle are taken into account. The formalism leads one to discuss a new concept, Pauli hindrance, which appears to be important to understand the structure of weakly-bound and unbound systems.

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arXiv2006

Collective-coupling analysis of spectra of mass-7 isobars: ^7He, ^7Li, ^7Be, ^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.

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arXiv2005

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

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

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arXiv2005

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.

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arXiv2005

Solution of multi-channel problems using MCAS for spectra and scattering cross sections

A multi-channel 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. Positive (scattering) and negative (sub-threshold) solutions can be found to predict both the compound nucleus sub-threshold spectrum and all resonances due to coupled-channel effects that occur on a smooth energy varying background. The role of the Pauli principle is crucial in defining what interaction potentials are required to fit data. The theory also gives an algebraic form for the dynamic polarization potential which adds to the ground state interaction to define the optical potential that gives the same elastic scattering cross sections.

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arXiv2005

Low energy nuclear scattering and sub-threshold spectra from a multi-channel algebraic scattering theory

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arXiv2005

Role of the Pauli principle in collective-model coupled-channels calculations

A multi-channel 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 sub-threshold 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.

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