arXiv subjects

P. R. Fraser

Publications and source records attributed to P. R. Fraser.

14 recordsLinked to original sources

arXiv2022

Coupled-channel description for mirror mass-11 nuclei compared to shell-model structures

The spectra of mass-11 nuclei are unusual, and so pose a challenge for theoretical models of their structure. The set of isobars range from being well bound to nucleon emission (11B,11C) through weakly bound (11Li, 11Be), with the former taking the form of a two neutron halo, to being proton unstable (11N,11O). A self-consistent approach to understand this set of nuclei is especially important as the mirror pair 11Be-11N exhibit a parity-inverted ground state compared to their neighbouring nuclei. Herein the Multi-Channel Algebraic Scattering (MCAS) method has been used to describe the low excitation spectra of those isobars in terms of nucleon-nucleus clusters. A collective model description of the low-excitation states of the mass-10 core nuclei has been used to form the coupled-channel interactions required in the method. For comparison, and to understand the underlying configurations, a shell model approach has been used to obtain those spectra with no-core (0+2+4)hw and (0+2)hw shell-model spaces for the mass 10 and mass 11 nuclei respectively.The results of the calculations suggest the need of a strong coupling in the collective coupled-channel vibrational model. In particular, the strong coupling of the collective 2+_1 state of 10Be to the valence neutron plays a decisive role in forming the positive parity ground state in11Be.

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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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arXiv2017

An effective two-body model for spectra of clusters of ${}^2$H, ${}^3$H, ${}^3$He, and $^4$He with $^4$He, and $^2$H-$^4$He scattering

Four light-mass nuclei are considered by an effective two-body clusterisation method; $^6$Li as $^2$H$+^4$He, $^7$Li as $^3$H$+^4$He, $^7$Be as $^3$He$+^4$He, and $^8$Be as $^4$He$+^4$He. The low-energy spectrum of each is determined from single-channel Lippmann-Schwinger equations, as are low-energy elastic scattering cross sections for the $^2$H$+^4$He system. These are presented at many angles and energies for which there are data. While some of these systems may be more fully described by many-body theories, this work establishes that a large amount of data may be explained by these two-body clusterisations.

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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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arXiv2012

Renormalization of coherent state variables, within the geometric mapping of algebraic models

We investigate the geometrical mapping of algebraic models. As particular examples we consider the Semimicriscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model (PACM), which also contains the vibron model, as a special case. In the geometrical mapping coherent states are employed as trial states. We show that the coherent state variables have to be renormalized and not the interaction terms of the Hamiltonian, as is usually done. The coherent state variables will depend on the total number of bosons and the coherent state variables. The nature of these variables is extracted through a relation obtained by comparing physical observables, such as the distance between the clusters or the quadrupole deformation of the nucleus, to their algebraic counterpart.

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arXiv2011

Phenomenological and microscopic cluster models I. The geometric mapping

The geometrical mapping of algebraic nuclear cluster models is investigated within the coherent state formalism. Two models are considered: the Semimicroscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model (PACM), which is a special limit of the SACM. The SACM strictly observes the Pauli exclusion principle while the PACM does not. The discussion of the SACM is adapted to the coherent state formalism by introducing the new SO(3) dynamical symmetry limit and third-order interaction terms in the Hamiltonian. The potential energy surface is constructed in both models and it is found that the effects of the Pauli principle can be simulated by higher-order interaction terms in the PACM. The present study is also meant to serve as a starting point for investigating phase transitions in the two algebraic cluster models.

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arXiv2011

Phenomenological and microscopic cluster models II. Phase transitions

Based on the results of a previous paper (Paper I), by performing the geometrical mapping via coherent states, phase transitions are investigated and compared within two algebraic cluster models. The difference between the Semimicroscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model (PACM) is that the former strictly observes the Pauli exclusion principle between the nucleons of the individual clusters, while the latter ignores it. From the technical point of view the SACM is more involved mathematically, while the formalism of the PACM is closer to that of other algebraic models with different physical content. First- and second-order phase transitions are identified in both models, while in the SACM a critical line also appears. Analytical results are complemented with numerical studies on α-cluster states of the neon-20 and magnesium-24 nuclei.

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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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