# Dr Paul Stevenson

## Senior Lecturer

Qualifications: MA (Oxon) D.Phil. (Oxon) CSci MInstP FHEA

Email:
Phone: Work: 01483 68 6796
Room no: 12 BB 03

## Biography

Paul was born in Glasgow on the day President Nixon announced his resignation.  He grew up in Glasgow, Bristol, London and Bishop's Stortford. After graduating from the University of Oxford in 1999 with a D.Phil in theoretical nuclear structure physics he spent a year as a Postdoctoral Research Associate at the University of Tennessee in Knoxville. From there he was appointed as a Research Fellow at Surrey, a job he held for two years, which was followed by being appointed a Lecturer in 2002, and a Senior Lecturer in 2008. He is the chair of the Physics Department Board of Studies and deputy warden of International House and Twyford Court

## Research Interests

Paul's research centres around the solution of the quantum-mechanical many-body problem. Mostly this is applied in the case of atomic nuclei, but he has also looked at metal clusters, Bose-Einstein condensates and neutron stars, where similar techniques to those used in nuclear problems may be applied. In the nuclear case he has developed a new approach for going beyond the mean-field approximation based on perturbation theory. Currently he is looking at time-dependent solutions of the Hartree-Fock equations and the connection with the Random-Phase Approximation. In addition, he supports experimentalists at Surrey and elsewhere by applying a variety of models to look at experimental results to help in their interpretation and also in evaluation of the models.

He is also intrerested in the foundations of quantum mechanics and econo- and socio-physics

## Research Collaborations

Paul is involved with collaborations with many of the experimental nuclear physics groups in UK universities, and additionally with physicists from Beijing (China), Frankfurt and Erlangen (Germany), and Oak Ridge (USA).

## Publications

### Highlights

• . (2015) 'Fission dynamics within time-dependent Hartree-Fock: Deformation-induced fission'. PHYSICAL REVIEW C, 92 (5) Article number ARTN 054610
• . (2014) 'The TDHF code Sky3D'. Computer Physics Communications, 185 (7), pp. 2195-2216.

#### Abstract

The nuclear mean-field model based on Skyrme forces or related density functionals has found widespread application to the description of nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The code Sky3D solves the static or dynamic equations on a three-dimensional Cartesian mesh with isolated or periodic boundary conditions and no further symmetry assumptions. Pairing can be included in the BCS approximation for the static case. The code is implemented with a view to allow easy modifications for including additional physics or special analysis of the results. © 2014 Elsevier B.V. All rights reserved.

• . (2013) 'Charge radius isotope shift across the N=126 shell gap'. Physical Review Letters, 110 (3)

#### Abstract

We revisit the problem of the kink in the charge radius shift of neutron-rich even isotopes near the N=126 shell closure. We show that the ability of a Skyrme force to reproduce the isotope shift is determined by the occupation of the neutron 1i orbital beyond N=126 and the corresponding change it causes to deeply-bound protons orbitals with a principal quantum number of 1. Given the observed position of the single-particle energies, one must either ensure occupation is allowed through correlations, or not demand that the single-particle energies agree with experimental values at the mean-field level. © 2013 American Physical Society.

• . (2012) 'Skyrme interaction and nuclear matter constraints'. PHYSICAL REVIEW C, 85 (3) Article number 035201

#### Abstract

This paper presents a detailed assessment of the ability of the 240 Skyrme interaction parameter sets in the literature to satisfy a series of criteria derived from macroscopic properties of nuclear matter in the vicinity of nuclear saturation density at zero temperature and their density dependence, derived by the liquid-drop model, in experiments with giant resonances and heavy-ion collisions. The objective is to identify those parametrizations which best satisfy the current understanding of the physics of nuclear matter over a wide range of applications. Out of the 240 models, only 16 are shown to satisfy all these constraints. Additional, more microscopic, constraints on the density dependence of the neutron and proton effective mass β-equilibrium matter, Landau parameters of symmetric and pure neutron nuclear matter, and observational data on high- and low-mass cold neutron stars further reduce this number to 5, a very small group of recommended Skyrme parametrizations to be used in future applications of the Skyrme interaction of nuclear-matter-related observables. Full information on partial fulfillment of individual constraints by all Skyrme models considered is given. The results are discussed in terms of the physical interpretation of the Skyrme interaction and the validity of its use in mean-field models. Future work on application of the Skyrme forces, selected on the basis of variables of nuclear matter, in the Hartree-Fock calculation of properties of finite nuclei, is outlined.

• . (2010) 'Discovery of W-157 and Os-161'. PHYSICS LETTERS B, 690 (1), pp. 15-18.
• . (2010) 'The effect of the tensor force on the predicted stability of superheavy nuclei'. EPL, 90 (1) Article number ARTN 12001
• . (2008) 'Mass dispersions from giant dipole resonances using the Balian-Veneroni variational approach'. JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS, 35 (9) Article number ARTN 095102

### Journal articles

• . (2016) 'Excited states and reduced transition probabilities in 168Os'. Physical Review C: Nuclear Physics, 94 (4)

#### Abstract

The level scheme of the neutron-deficient nuclide 168Os has been extended and mean lifetimes of excited states have been measured by the recoil distance Doppler-shift method using the JUROGAM \gamma-ray spectrometer in conjunction with the IKP K\"oln plunger device. The 168Os \gamma rays were measured in delayed coincidence with recoiling fusion-evaporation residues detected at the focal plane of the RITU gas-filled separator. The ratio of reduced transition probabilities B(E2;4_1^+ \rightarrow 2_1^+)/B(E2;2_1^+ \rightarrow 0_1^+) is measured to be 0.34(18), which is very unusual for collective band structures and cannot be reproduced by IBM-2 model calculations based on the SkM* energy-density functional.

• . (2016) 'Skyrme tensor force in heavy ion collisions'. PHYSICAL REVIEW C, 93 (5) Article number ARTN 054617
• . (2016) 'Sensitivity of the fusion cross section to the density dependence of the symmetry energy'. PHYSICAL REVIEW C, 93 (4) Article number ARTN 044618
• . (2016) 'Fission dynamics within time-dependent Hartree-Fock. II. Boost-induced fission'. PHYSICAL REVIEW C, 93 (1) Article number ARTN 014620

#### Abstract

Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus and the daughter products. Purpose: We explore the ability of dynamic mean-field methods to describe induced fission processes, using quadrupole boosts in the nuclide 240Pu as an example. Methods: Following upon the work presented in Goddard et al. [Phys. Rev. C 92, 054610 (2015)], quadrupoleconstrained Hartree-Fock calculations are used to create a potential energy surface. An isomeric state and a state beyond the second barrier peak are excited by means of instantaneous as well as temporally extended gauge boosts with quadrupole shapes. The subsequent deexcitation is studied in a time-dependent Hartree-Fock simulation, with emphasis on fissioned final states. The corresponding fission fragment mass numbers are studied. Results: In general, the energy deposited by the quadrupole boost is quickly absorbed by the nucleus. In instantaneous boosts, this leads to fast shape rearrangements and violent dynamics that can ultimately lead to fission. This is a qualitatively different process than the deformation-induced fission. Boosts induced within a finite time window excite the system in a relatively gentler way and do induce fission but with a smaller energy deposition. Conclusions: The fission products obtained using boost-induced fission in time-dependent Hartree-Fock are more asymmetric than the fragments obtained in deformation-induced fission or the corresponding adiabatic approaches.

• . (2015) 'Shapes and Dynamics from the Time-Dependent Mean Field'. Bulgarian Journal of Physics, 42 (4), pp. 354-361.

#### Abstract

Explaining observed properties in terms of underlying shape degrees of freedom is a well–established prism with which to understand atomic nuclei. Self–consistent mean–field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time–dependent extension of the mean–field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of 28Si in the first case, and 240Pu in the latter case.

• . (2015) 'Fission dynamics within time-dependent Hartree-Fock: Deformation-induced fission'. PHYSICAL REVIEW C, 92 (5) Article number ARTN 054610
• . (2015) 'Modelling proton tunnelling in the adenine-thymine base pair.'. Phys Chem Chem Phys, England: 17 (19), pp. 13034-13044.

#### Abstract

The energies of the canonical (standard, amino-keto) and tautomeric (non-standard, imino-enol) charge-neutral forms of the adenine-thymine base pair (A-T and A*-T*, respectively) are calculated using density functional theory. The reaction pathway is then computed using a transition state search to provide the asymmetric double-well potential minima along with the barrier height and shape, which are combined to create the potential energy surface using a polynomial fit. The influence of quantum tunnelling on proton transfer within a base pair H-bond (modelled as the DFT deduced double-well potential) is then investigated by solving the time-dependent master equation for the density matrix. The effect on a quantum system by its surrounding water molecules is explored via the inclusion of a dissipative Lindblad term in the master equation, in which the environment is modelled as a heat bath of harmonic oscillators. It is found that quantum tunnelling, due to transitions to higher energy eigenstates with significant amplitudes in the shallow (tautomeric) side of the potential, is unlikely to be a significant mechanism for the creation of adenine-thymine tautomers within DNA, with thermally assisted coupling of the environment only able to boost the tunnelling probability to a maximum of 2 × 10(-9). This is barely increased for different choices of the starting wave function or when the geometry of the potential energy surface is varied.

• . (2014) 'Environment-induced dephasing versus von Neumann measurements in proton tunneling'. Physical Review A - Atomic, Molecular, and Optical Physics, 90 (1)

#### Abstract

In this work we compare two theoretical approaches to modeling the action of the environment on an open quantum system. It is often assumed that as the temperature of the environment surrounding a quantum system increases, so does the speed of environment-induced dephasing, or decoherence (dynamical noise), and so the efficacy of processes such as quantum tunneling drops. An alternative way of viewing the action of the environment is to consider it as carrying out von Neumann-type measurements that, in the limit of continuous observation, lead to the so-called quantum Zeno effect, whereby the system is never allowed to evolve because its wave function is collapsed to its initial state with overwhelming likelihood. However, it has been established in recent years that under certain conditions quantum processes such as tunneling can actually be enhanced (thermally assisted) when the system couples to its environment, as this allows transitions to higher-energy eigenstates closer to the top of the potential barrier. Here we show that, over a specific temperature range, increasing the temperature of the heat bath to encourage such thermally induced tunneling is equivalent to increasing the frequency of a von Neumann-type measurement on the system by the environment (an anti-Zeno effect). However, this correspondence between these two independent pictures of quantum measurement breaks down above a certain limit: Increasing the frequency of measurement above this limit leads to a reversal from an anti-Zeno to a Zeno effect and the tunneling rate decreases again, whereas raising the temperature further leads to a leveling off in the tunneling probability. © 2014 American Physical Society.

• . (2014) 'The TDHF code Sky3D'. Computer Physics Communications, 185 (7), pp. 2195-2216.

#### Abstract

The nuclear mean-field model based on Skyrme forces or related density functionals has found widespread application to the description of nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The code Sky3D solves the static or dynamic equations on a three-dimensional Cartesian mesh with isolated or periodic boundary conditions and no further symmetry assumptions. Pairing can be included in the BCS approximation for the static case. The code is implemented with a view to allow easy modifications for including additional physics or special analysis of the results. © 2014 Elsevier B.V. All rights reserved.

• . (2014) 'Isoscalar and isovector giant monopole resonances from a continuum Hartree-Fock method'. EPJ Web of Conferences, 66

#### Abstract

We motivate and summarise some recent results in the application of formally exact boundary conditions in nuclear time-dependent Hartree-Fock calculations, making use of Laplace transformations to calculate the values of the wave functions at the boundaries. We have realised the method in the case of giant monopole resonances of spherically-symmetric nuclei, and present strength functions of 16O and 40Ca using a simplified version of the Skyrme force, showing that no artefacts from discretisation occur as contaminatnts © Owned by the authors, published by EDP Sciences, 2014.

• . (2014) 'Cause of the charge radius isotope shift at the N =126 shell gap'. EPJ Web of Conferences, 66

#### Abstract

We discuss the mechanism causing the 'kink' in the charge radius isotope shift at the N = 126 shell closure. The occupation of the 1i11/2 neutron orbital is the decisive factor for reproducing the experimentally observed kink. We investigate whether this orbital is occupied or not by different Skyrme effective interactions as neutrons are added above the shell closure. Our results demonstrate that several factors can cause an appreciable occupation of the 1i11/2 neutron orbital, including the magnitude of the spin-orbit field, and the isoscalar effective mass of the Skyrme interaction. The symmetry energy of the effective interaction has little influence upon its ability to reproduce the kink. © Owned by the authors, published by EDP Sciences, 2014.

• . (2014) 'The TDHF code Sky3D'. Computer Physics Communications,

#### Abstract

The nuclear mean-field model based on Skyrme forces or related density functionals has found widespread application to the description of nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The code Sky3D solves the static or dynamic equations on a three-dimensional Cartesian mesh with isolated or periodic boundary conditions and no further symmetry assumptions. Pairing can be included in the BCS approximation for the static case. The code is implemented with a view to allow easy modifications for including additional physics or special analysis of the results. Program summary: Program title: Sky3D. Catalogue identifier: AESW_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AESW_v1_0.html. Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html. No. of lines in distributed program, including test data, etc.: 43 187. No. of bytes in distributed program, including test data, etc.: 1 423 973. Distribution format: tar.gz. Programming language: Fortran 90. The OpenMP version requires a relatively recent compiler; it was found to work using gfortran 4.6.2 or later and the Intel compiler version 12 or later. Computer: All computers with a Fortran compiler supporting at least Fortran 90. Operating system: All operating systems with such a compiler. Some of the Makefiles and scripts depend on a Unix-like system and need modification under Windows. Has the code been vectorized or parallelized?: Yes, Runs under OpenMP and MPI, unlimited number of processors can be used. RAM: 1 GB. Classification: 17.16, 17.22, 17.23. External routines: LAPACK, FFTW3. Nature of problem:. The time-dependent Hartree-Fock equations can be used to simulate nuclear vibrations and collisions between nuclei for low energies. This code implements the equations based on a Skyrme energy functional and also allows the determination of the ground-state structure of nuclei through the static version of the equations. For the case of vibrations the principal aim is to calculate the excitation spectra by Fourier-analyzing the time dependence of suitable observables. In collisions, the formation of a neck between nuclei, the dissipation of energy from collective motion, processes like charge transfer and the approach to fusion are of principal interest. Solution method:. The nucleonic wave function spinors are represented on a three-dimen

• . (2013) 'Dipole response of $^76$Se above 4 MeV'. Phys. Rev. C, 88 (6), pp. 064308-064308.

#### Abstract

The dipole response of 76 34 Se in the energy range from 4 to 9 MeV has been analyzed using a (γ ⃗ ,γ ′ ) polarized photon scattering technique, performed at the High Intensity γ -Ray Source facility at Triangle Universities Nuclear Laboratory, to complement previous work performed using unpolarized photons. The results of this work offer both an enhanced sensitivity scan of the dipole response and an unambiguous determination of the parities of the observed J=1 states. The dipole response is found to be dominated by E1 excitations, and can reasonably be attributed to a pygmy dipole resonance. Evidence is presented to suggest that a significant amount of directly unobserved excitation strength is present in the region, due to unobserved branching transitions in the decays of resonantly excited states. The dipole response of the region is underestimated when considering only ground state decay branches. We investigate the electric dipole response theoretically, performing calculations in a three-dimensional (3D) Cartesian-basis time-dependent Skyrme-Hartree-Fock framework.

• . (2013) 'Half-life of the yrast 2(+) state in W-188: Evolution of deformation and collectivity in neutron-rich tungsten isotopes'. PHYSICAL REVIEW C, 88 (4) Article number ARTN 044301
• . (2013) 'Extension of continuum time-dependent Hartree-Fock method to proton states'.

#### Abstract

This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region yields an artificial boundary, which is not present physically. The question of how to ensure the boundary does not interfere with the internal solution, while keeping the overall calculation time low is studied. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. An inverse Laplace transform required by the absorbing boundaries is calculated using a method of non-linear least squares. The accuracy and efficiency of the scheme is tested and results presented to support the case that they are a effective way of handling the artificial boundary.

• . (2013) 'Continuum time-dependent Hartree-Fock method for giant resonances in spherical nuclei'. Physical Review C - Nuclear Physics, 87 (1)

#### Abstract

This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied in the case of nuclear giant monopole resonances in the small and large amplitude regimes. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region results in a difficulty with the spatial boundary conditions. Here we propose an absorbing boundary condition scheme to handle the conflict. The derivation, via a Laplace transform method, and implementation is described. The accuracy and efficiency of the scheme is tested and the results presented to support the case that they are a effective way of handling the artificial boundary. © 2013 American Physical Society.

• . (2013) 'Charge radius isotope shift across the N=126 shell gap'. Physical Review Letters, 110 (3)

#### Abstract

We revisit the problem of the kink in the charge radius shift of neutron-rich even isotopes near the N=126 shell closure. We show that the ability of a Skyrme force to reproduce the isotope shift is determined by the occupation of the neutron 1i orbital beyond N=126 and the corresponding change it causes to deeply-bound protons orbitals with a principal quantum number of 1. Given the observed position of the single-particle energies, one must either ensure occupation is allowed through correlations, or not demand that the single-particle energies agree with experimental values at the mean-field level. © 2013 American Physical Society.

• . (2012) 'The tensor-kinetic field in nuclear collisions'. Journal of Physics: Conference Series, 381 Article number 1 , pp. 012105-012105.

#### Abstract

The role of the tensor terms in the Skyrme interaction is studied for their effect in dynamic calculations where non-zero contributions to the mean-field may arise, even when the starting nucleus, or nuclei are even-even and have no active time-odd potentials in the ground state. We study collisions in the test-bed 16 O- 16 O system, and give a qualitative analysis of the behaviour of the time-odd tensor-kinetic density, which only appears in the mean field Hamiltonian in the presence of the tensor force. We find an axial excitation of this density is induced by a collision.

• . (2012) 'Single-particle dissipation in a time-dependent Hartree-Fock approach studied from a phase-space perspective'. PHYSICAL REVIEW C, 86 (2) Article number ARTN 024608
• . (2012) 'Unrestricted Skyrme-tensor time-dependent Hartree-Fock model and its application to the nuclear response from spherical to triaxial nuclei'. Physical Review C - Nuclear Physics, 86 (4)

#### Abstract

The nuclear time-dependent Hartree-Fock model formulated in three-dimensional space, based on the full standard Skyrme energy density functional complemented with the tensor force, is presented. Full self-consistency is achieved by the model. The application to the isovector giant dipole resonance is discussed in the linear limit, ranging from spherical nuclei (16O and 120Sn) to systems displaying axial or triaxial deformation (24Mg, 28Si, 178Os, 190W and 238U). Particular attention is paid to the spin-dependent terms from the central sector of the functional, recently included together with the tensor. They turn out to be capable of producing a qualitative change on the strength distribution in this channel. The effect on the deformation properties is also discussed. The quantitative effects on the linear response are small and, overall, the giant dipole energy remains unaffected. Calculations are compared to predictions from the (quasi)-particle random-phase approximation and experimental data where available, finding good agreement. © 2012 American Physical Society.

• . (2012) 'Skyrme interaction and nuclear matter constraints'. PHYSICAL REVIEW C, 85 (3) Article number 035201

#### Abstract

This paper presents a detailed assessment of the ability of the 240 Skyrme interaction parameter sets in the literature to satisfy a series of criteria derived from macroscopic properties of nuclear matter in the vicinity of nuclear saturation density at zero temperature and their density dependence, derived by the liquid-drop model, in experiments with giant resonances and heavy-ion collisions. The objective is to identify those parametrizations which best satisfy the current understanding of the physics of nuclear matter over a wide range of applications. Out of the 240 models, only 16 are shown to satisfy all these constraints. Additional, more microscopic, constraints on the density dependence of the neutron and proton effective mass β-equilibrium matter, Landau parameters of symmetric and pure neutron nuclear matter, and observational data on high- and low-mass cold neutron stars further reduce this number to 5, a very small group of recommended Skyrme parametrizations to be used in future applications of the Skyrme interaction of nuclear-matter-related observables. Full information on partial fulfillment of individual constraints by all Skyrme models considered is given. The results are discussed in terms of the physical interpretation of the Skyrme interaction and the validity of its use in mean-field models. Future work on application of the Skyrme forces, selected on the basis of variables of nuclear matter, in the Hartree-Fock calculation of properties of finite nuclei, is outlined.

• . (2012) 'Multiple β - Decaying states in 194Re: Shape evolution in neutron-rich osmium isotopes'. Physical Review C - Nuclear Physics, 85 (3)

#### Abstract

β decays from heavy, neutron-rich nuclei with A∼190 have been investigated following their production via the relativistic projectile fragmentation of an E/A=1 GeV 208Pb primary beam on a ∼2.5 g/cm2 9Be target. The reaction products were separated and identified using the GSI FRagment Separator (FRS) and stopped in the RISING active stopper. γ decays were observed and correlated with these secondary ions on an event-by-event basis such that γ-ray transitions following from both internal (isomeric) and β decays were recorded. A number of discrete, β-delayed γ-ray transitions associated with β decays from 194Re to excited states in 194Os have been observed, including previously reported decays from the yrast Iπ=(6 +) state. Three previously unreported γ-ray transitions with energies 194, 349, and 554 keV are also identified; these transitions are associated with decays from higher spin states in 194Os. The results of these investigations are compared with theoretical predictions from Nilsson multi-quasiparticle (MQP) calculations. Based on lifetime measurements and the observed feeding pattern to states in 194Os, it is concluded that there are three β --decaying states in 194Re. © 2012 American Physical Society.

• . (2012) 'Multiple β - Decaying states in 194Re: Shape evolution in neutron-rich osmium isotopes'. Physical Review C - Nuclear Physics, 85 (3) Article number 034301

#### Abstract

decays from heavy, neutron-rich nuclei with A∼190 have been investigated following their production via the relativistic projectile fragmentation of an E/A=1 GeV 208Pb primary beam on a ∼2.5 g/cm2 9Be target. The reaction products were separated and identified using the GSI FRagment Separator (FRS) and stopped in the RISING active stopper. γ decays were observed and correlated with these secondary ions on an event-by-event basis such that γ-ray transitions following from both internal (isomeric) and β decays were recorded. A number of discrete, β-delayed γ-ray transitions associated with β decays from 194Re to excited states in 194Os have been observed, including previously reported decays from the yrast Iπ=(6+) state. Three previously unreported γ-ray transitions with energies 194, 349, and 554 keV are also identified; these transitions are associated with decays from higher spin states in 194Os. The results of these investigations are compared with theoretical predictions from Nilsson multi-quasiparticle (MQP) calculations. Based on lifetime measurements and the observed feeding pattern to states in 194Os, it is concluded that there are three β−-decaying states in 194Re.

• . (2011) 'Spectroscopic calculations of the low-lying structure in exotic Os and W isotopes'. PHYSICAL REVIEW C, 83 (5) Article number ARTN 054303
• . (2011) 'Nuclear charge radii and electromagnetic moments of radioactive scandium isotopes and isomers'. JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS, 38 (2) Article number ARTN 025104
• . (2011) 'The electronion scattering experiment ELISe at the International Facility for Antiproton and Ion Research (FAIR) - A conceptual design study'. Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 637 (1), pp. 60-76.
• . (2011) 'The electron-ion scattering experiment ELISe at the International Facility for Antiproton and Ion Research (FAIR)- A conceptual design study'. Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 637 (1), pp. 60-76.
• . (2010) 'The influence of the symmetry energy on the giant monopole resonance of neutron-rich nuclei analyzed in Thomas-Fermi theory'. JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS, 37 (7) Article number ARTN 075107
• . (2010) 'Discovery of W-157 and Os-161'. PHYSICS LETTERS B, 690 (1), pp. 15-18.
• . (2010) 'Extracting structure information from TDHF'. J PHYS G NUCL PARTIC, 37 (6) Article number 064030
• . (2010) 'Configuration dependence of K-forbidden transition rates from three-quasiparticle isomers'. PHYSICAL REVIEW C, 81 (4) Article number ARTN 041304
• . (2010) 'The effect of the tensor force on the predicted stability of superheavy nuclei'. EPL, 90 (1) Article number ARTN 12001
• . (2010) 'Discovery of 157W and 161Os'. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 690 (1), pp. 15-18.
• . (2010) 'Testing a Variational Method for Fluctuations'. XVIII INTERNATIONAL SCHOOL ON NUCLEAR PHYSICS, NEUTRON PHYSICS AND APPLICATIONS, Varna, BULGARIA: 205 Article number ARTN 012027
• . (2008) 'Mass dispersions from giant dipole resonances using the Balian-Veneroni variational approach'. JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS, 35 (9) Article number ARTN 095102
• . (2008) 'Fission of hyper-hyperdeformed Ni-56: a clustering analysis within mean-field approaches'. JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS, 35 (7) Article number ARTN 075106
• . (2008) 'Simulating the Quantum Zeno and Anti-Zeno Effects During Position Measurements'. ADVANCED SCIENCE LETTERS, 1 (1), pp. 140-144.
• . (2008) 'First results with the rising active stopper'. International Journal of Modern Physics E, 17 (SUPPL. 1), pp. 8-20.
• . (2007) 'Identification of a high-spin isomer in (99)Mo'. PHYSICAL REVIEW C, 76 (4) Article number ARTN 047303
• . (2007) 'Exotic clustering in heavy and superheavy nuclei within the relativistic and non-relativistic mean field formalisms'. JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS, 34 (9), pp. 2073-2090.
• . (2007) 'A highly neutron-rich cluster and/or a superheavy nucleus in the compound nucleus U-238+U-238: A mean field study'. INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS, 16 (6), pp. 1721-1732.
• . (2007) 'alpha decay of Re-159 and proton emission from Ta-155'. PHYSICAL REVIEW C, 75 (6) Article number ARTN 061302
• . (2007) 'Monopole Giant Resonances and TDHF boundary conditions'. Nuclear Physics A, 788, pp. 343-348.
• . (2007) 'Monopole Giant Resonances and TDHF boundary conditions'. Nuclear Physics A, 788 (1-4), pp. 343-348.

#### Abstract

Using time-dependent Hartree-Fock, we induce isoscalar and isovector monopole vibrations and follow the subsequent vibrations of both the same and opposite isospin nature in the N ≠ Z nucleus 132Sn. By suitable scaling of the proton and neutron parts of the excitation operators, the coupling between the modes is studied, and the approximate normal modes found. Chaotic dynamics are then analysed in the isoscalar giant monopole resonance by using reflecting boundaries in a large space to build up a large number of 0+ states whose spacings are then analysed. A Wigner-like distribution is found. © 2007 Elsevier B.V. All rights reserved.

• . (2007) 'Discovery of the proton emitting nucleus 159Re'. AIP Conference Proceedings, 961, pp. 28-33.

#### Abstract

The observation of the new nuclide 159Re provides important insights into the evolution of single-particle structure in heavy nuclei beyond the proton drip line. The nuclide 159Re was synthesised in the reaction 106Cd(58Ni, p4n) and identified via its proton radioactivity using the RITU gas-filled separator and the GREAT focal-plane spectrometer. Comparisons of the measured proton energy (Ep = 1805±20 keV) and decay half-life (t1/2 = 21±4 μs) with values calculated using the WKB method indicate that the proton is emitted from an h11/2 state. The implications of these results for future experimental investigations into even more proton unbound Re isotopes using in-flight separation techniques are considered. © 2007 American Institute of Physics.

• . (2006) 'Reaction cross-sections for light nuclei on C-12 using relativistic mean field formalism'. JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS, 32 (11), pp. 2089-2097.
• . (2006) 'Probing the limit of nuclear existence: Proton emission from Re-159'. PHYSICS LETTERS B, 641 (1), pp. 34-37.
• . (2006) 'Shape-driving effects in the triaxial nucleus, Xe-128'. PHYSICAL REVIEW C, 74 (3) Article number ARTN 034318
• . (2006) 'Spin-excitation mechanisms in Skyrme-force time-dependent Hartree-Fock calculations'. PHYSICAL REVIEW C, 74 (2) Article number ARTN 027601
• . (2006) 'Role of boundary conditions in dynamic studies of nuclear giant resonances and collisions'. PHYSICAL REVIEW E, 73 (3) Article number ARTN 036709
• . (2006) 'Deformation effects on the structures of N=7 halo nuclei'. NUCLEAR PHYSICS A, 765 (1-2), pp. 29-38.
• . (2006) 'Clustering in superheavy nuclei within the relativistic mean field approach'. JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS, 32 (1), pp. L1-L9.
• . (2006) 'Deformed halo nuclei in mean-field approach'. AIP Conference Proceedings, 865, pp. 96-100.

#### Abstract

The halo properties of the odd light nuclei have been studied with the deformed Skyrme-Hartree-Fock model, in which the blocking effect of the odd nucleon is taken into account. For nuclei near drip lines, the pairing was treated in the frame of Lipkin-Nogami method, using a volume-surface mixing paring interaction. The 1/2+ state in 11Be was calculated to have a very large soft deformation. The origin of deformed halo structures was discussed. © 2006 American Institute of Physics.

• . (2005) 'Shape evolution in the neutron-rich tungsten region'. PHYSICAL REVIEW C, 72 (4) Article number ARTN 047303
• . (2005) 'Isomers in neutron-rich A approximate to 190 nuclides from Pb-208 fragmentation'. EUROPEAN PHYSICAL JOURNAL A, 23 (2), pp. 201-215.
• . (2005) 'Isomers in neutron-rich A ≈ 190 nuclides from 208Pb fragmentation'. European Physical Journal A, 23 (2), pp. 201-215.

#### Abstract

Relativistic projectile fragmentation of 208Pb has been used to produce isomers in neutron-rich, A ≈ 190 nuclides. A forward-focusing spectrometer provided ion-by-ion mass and charge identification. The detection of γ-rays emitted by stopped ions has led to the assignment of isomers in 188Ta, 190W, 192Re, 193Re, 195Os, 197Ir, 198Ir, 200Pt, 201Pt, 202Pt and 203Au, with half-lives ranging from approximately 10 ns to 1 ms. Tentative isomer information has been found also for 174Er, 175Er, 185Hf, 191Re, 194Re and 199Ir. In most cases, time-correlated, singles γ-ray events provided the first spectroscopic data on excited states for each nuclide. In 200Pt and 201Pt, the assignments are supported by γ-γ coincidences. Isomeric ratios provide additional information, such as half-life and transition energy constraints in particular cases. The level structures of the platinum isotopes are discussed, and comparisons are made with isomer systematics. © Società, Italiana, di Fisica/Springer-Verlag 2004.

• . (2005) 'Densities of superheavy nuclei at closed shells'. Journal of Physics G: Nuclear and Particle Physics, 31 (10)

#### Abstract

We employed the Skyrme-Hartree-Fock + BCS model to investigate the density distributions of even-even superheavy nuclei around the predicted magic numbers of Z ≤ 114, 120, 126 and N ≤ 172, 184. The central depressions in densities are shown in the heaviest nuclei with Z ≤ 120 and N ≤ 178, which is due to high-j orbits occupied. However, densities become flatter when deformations occur. The superheavy nuclei with N ≤ 180-188 and Z ≤ 126 have no central depressions, due to that low-j orbits become occupied. Shell closures in the superheavy mass region are isospin dependent. © 2005 IOP Publishing Ltd.

• . (2005) 'Density distributions of superheavy nuclei'. Physical Review C - Nuclear Physics, 71 (3)

#### Abstract

We employed the Skyrme-Hartree-Fock model to investigate the density distributions and their dependence on nuclear shapes and isospins in the superheavy mass region. Different Skyrme forces were used for the calculations with a special comparison to the experimental data in 208Pb. The ground-state deformations, nuclear radii, neutron-skin thicknesses and α-decay energies were also calculated. Density distributions were discussed with the calculations of single-particle wave functions and shell fillings. Calculations show that deformations have considerable effects on the density distributions, with a detailed discussion on the 292120 nucleus. Earlier predictions of remarkably low central density are not supported when deformation is allowed for. © 2005 The American Physical Society.

• . (2005) 'Isovector giant monopole resonances in spherical nuclei'. Journal of Physics G: Nuclear and Particle Physics, 31 (10)

#### Abstract

We study isovector giant monopole resonances in spherical nuclei using the time-dependent Hartree-Fock method with different Skyrme forces. The aim of the investigation is to study how, for example, mass number and neutron excess influence the isovector giant monopole resonances and their mixing with isoscalar modes. We also study how nuclear matter properties, such as the asymmetry energy, of different Skyrme forces affect the behaviour of giant resonances. We find isovector and isoscalar modes to be strongly mixed and that there is little correlation between asymmetry energy and isovector resonance energy. © 2005 IOP Publishing Ltd.

• . (2005) 'Dipole giant resonances in deformed heavy nuclei'. Physical Review C - Nuclear Physics, 71 (6)

#### Abstract

The spectral distribution of isovector dipole strength is computed using the time-dependent Skyrme-Hartree-Fock method with subsequent spectral analysis. The calculations are done without any imposed symmetry restriction, allowing any nuclear shape to be dealt with. The scheme is used to study the deformation dependence of giant resonances and its interplay with Landau fragmentation (owing to 1ph states). Results are shown for the chain of Nd isotopes, superdeformed Dy152, triaxial Os188, and U238. © 2005 The American Physical Society.

• . (2004) 'Giant resonances from TDHF'. International Journal of Modern Physics E, 13 (1), pp. 181-185.

#### Abstract

A method of calculating giant resonance strength functions using Time-Dependent Hartree-Fock techniques is described. An application to isoscalar giant monopole resonances in spherical nuclei is made, thus allowing a comparison between independent 1-, 2- and 3-Dimensional computer codes.

• . (2003) 'Self-consistent description of dysprosium isotopes in the doubly midshell region'. PHYSICAL REVIEW C, 68 (4) Article number ARTN 044315
• . (2003) 'Nuclear matter and neutron star properties calculated with the Skyrme interaction'. Phys. Rev. C, 68 Article number 034324

#### Abstract

The effective Skyrme interaction has been used extensively in mean-field models for several decades and many different parametrizations of the interaction have been proposed. All of these give similar agreement with the experimental observables of nuclear ground states as well as with the properties of infinite symmetric nuclear matter at the saturation density n0. However, when applied over a wider range of densities (up to ∼3n0) they predict widely varying behavior for the observables of both symmetric and asymmetric nuclear matter. A particularly relevant example of naturally occurring asymmetric nuclear matter is the material of which neutron stars are composed. At around nuclear matter density, this can be well represented as a mixture of neutrons, protons, electrons, and muons (n+p+e+μ matter) in β-equilibrium, and these densities turn out to be the key ones for determining the properties of neutron-star models with masses near to the widely used “canonical” value of 1.4M⊙. By constructing equations of state for neutron-star matter using the different Skyrme parametrizations, calculating corresponding neutron-star models and then comparing these with observational data, an additional constraint can be obtained for the values of the Skyrme parameters. Such a constraint is particularly relevant because the parametrizations are initially determined by fitting to the properties of doubly closed-shell nuclei and it is an open question how suitable they then are for nuclei with high values of isospin, such as those at the neutron drip-line and beyond. The neutron-star environment provides an invaluable testing ground for this. We have carried out an investigation of 87 different Skyrme parametrizations in order to examine how successful they are in predicting the expected properties of infinite nuclear matter and generating plausible neutron-star models. This is the first systematic study of the predictions of the various Skyrme parametrizations for the density dependence of the characteristic observables of nuclear matter; the density dependence of the symmetry energy for β-equilibrium matter turns out to be a crucial property for indicating which Skyrme parameter sets will apply equally well for finite nuclei and for neutron-star matter. Only 27 of the 87 parametrizations investigated pass the test of giving satisfactory neutron-star models and we present a list of these.

• . (2003) 'Nuclear matter and neutron-star properties calculated with the Skyrme interaction'. PHYSICAL REVIEW C, 68 (3) Article number ARTN 034324
• . (2003) 'Automatic generation of vacuum amplitude many-body perturbation series'. International Journal of Modern Physics C, 14 (8), pp. 1135-1141.

#### Abstract

An algorithm and a computer program in Fortran 95 are presented which enumerate the Hugenholtz diagram representation of the many-body perturbation series for the ground state energy with a two-body interaction. The output is in a form suitable for post-processing such as automatic code generation. The result of a particular application, generation of LATEX code to draw the diagrams, is shown.

• . (2002) 'At the N=Z line and beyond: HF+BCS mean-field calculations with the separable monopole interaction.'. ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY, 224, pp. U92-U92.
• . (2002) 'High-K negative parity states in Os-184'. PHYSICAL REVIEW C, 65 (6) Article number ARTN 064310
• . (2002) 'Structure of the doubly midshell nucleus Dy-170(66)104'. PHYSICAL REVIEW C, 65 (3) Article number ARTN 037302
• . (2002) 'Analytic angular momentum coupling coefficient calculators'. Computer Physics Communications, 147 (3), pp. 853-858.

#### Abstract

A Java implementation of a suite of programs was described to calculate the angular momentum coupling coefficients analytically. The angular momentum coupling coefficients were found in problems involving quantum mechanical theory of angular momentum. The operating systems under which the program was tested included Netscape 4.75 on Solaris 7 and Internet Explorer 5.5 on Windows NT4.

• . (2002) 'Mean field calculation of Ne, Mg and Si nuclei at N = 20 with the separable monopole interaction'. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 545 (3-4), pp. 291-297.

#### Abstract

A new model has been developed to study nuclei using many-body perturbation theory with a density dependent separable monopole nucleon-nucleon interaction (SMO) [Phys. Rev. C 63 (2001) 054309; P.D. Stevenson, D.Ph. Thesis, Oxford 1999; Phys. Rev. C 65 (2002) 064312]. The model is in the zeroth order an alternative to mean-field models based on more conventional effective nucleon-nucleon interactions (e.g., Skyrme, Gogny). Results on shapes and related ground state observables are reported for even-even Ne, Mg, and Si nuclei with N ∼ 20. The model predicts the weakening of the expected N = 20 shell closure in Ne isotopes and its disappearance in Mg nuclei in full agreement with experimental results. © 2002 Elsevier Science B.V. All rights reserved.

### Conference papers

• . (2016) 'Probing dynamics of fusion reactions through cross-section and spin distribution measurement'. EDP Sciences EPJ Web of Conferences, Catania, Italy: 12th International Conference on Nucleus-Nucleus Collisions 2015 117

#### Abstract

Present work aims to explicate the effect of entrance channel mass asymmetry on fusion dynamics for the Compound Nucleus 80Sr populated through two different channels, 16O+64Zn and 32S+48Ti, using cross-section and spin distribution measurements as probes. The evaporation spectra studies for these systems, reported earlier indicate the presence of dynamical effects for mass symmetric 32S+48Ti system. The CCDEF and TDHF calculations have been performed for both the systems and an attempt has been made to explain the reported deviations in the α-particle spectrum for the mass symmetric system.

• . (2016) 'Resonances and reactions from mean-field dynamics'. E D P SCIENCES INTERNATIONAL CONFERENCE ON NUCLEAR STRUCTURE AND RELATED TOPICS (NSRT15), Joint Inst Nucl Res, Bogoliubov Lab Theoret Phys, Dubna, RUSSIA: 7th International Conference on Nuclear Structure and Related Topics (NSRT) 107
• . (2015) 'Role of the Skyrme tensor force in heavy-ion fusion'. E D P SCIENCES VI INTERNATIONAL CONFERENCE FUSION14, New Delhi, INDIA: 6th International Conference on FUSION 86

#### Abstract

We make use of the Skyrme e ff ective nuclear interaction within the time-dependent Hartree-Fock framework to assess the e ff ect of inclusion of the tensor terms of the Skyrme interaction on the fusion window of the 16 O– 16 O reaction. We find that the lower fusion threshold, around the barrier, is quite insensitive to these details of the force, but the higher threshold, above which the nuclei pass through each other, changes by several MeV between di ff erent tensor parametrisations. The results suggest that eventually fusion properties may become part of the evaluation or fitting process for e ff ective nuclear interactions

• . (2013) 'Do Skyrme forces that fit nuclear matter work well in finite nuclei?'. AMER INST PHYSICS XXXV BRAZILIAN WORKSHOP ON NUCLEAR PHYSICS, Sao Sebastiao, BRAZIL: 35th Brazilian Workshop on Nuclear Physics 1529, pp. 262-268.
• . (2012) 'Li-7-Induced Reactions for Fast-Timing With LaBr3:Ce Detectors'. AMER INST PHYSICS NUCLEAR STRUCTURE AND DYNAMICS '12, Opatija, CROATIA: 2nd International Conference on Nuclear Structure and Dynamics 1491, pp. 93-96.
• . (2012) 'The tensor-kinetic field in nuclear collisions'. IOP PUBLISHING LTD RUTHERFORD CENTENNIAL CONFERENCE ON NUCLEAR PHYSICS, 2011, Univ Manchester, Manchester, ENGLAND: Rutherford Centennial Conference on Nuclear Physics 381
• . (2009) 'Mass distributions in a variational model'. SOC MEXICANA FISICA REVISTA MEXICANA DE FISICA, Cocoyoc, MEXICO: 32nd Symposium on Nuclear Physics 55 (2), pp. 114-118.
• . (2009) 'Mass Distributions Beyond TDHF'. AMER INST PHYSICS FUSION 08, Chicago, IL: International Conference on New Aspects of Heavy Ion Collisions Near the Coulomb Barrier 1098, pp. 133-138.
• . (2009) 'New Insights into the Structure of Exotic Nuclei Using the RISING Active Stopper'. AMER INST PHYSICS CAPTURE GAMMA-RAY SPECTROSCOPY AND RELATED TOPICS, Univ Cologne, Inst Nucl Phys, Cologne, GERMANY: 13th International Symposium on Capture Gamma-Ray Spectroscopy and Related Topics 1090, pp. 122-129.
• . (2009) 'A Variational Approach to Mass Fluctuations'. AMER INST PHYSICS NUCLEAR STRUCTURE AND DYNAMICS '09, Dubrovnik, CROATIA: International Conference on Nuclear structure and Dynamics 1165, pp. 177-180.
• . (2007) 'Monopole giant resonances and TDHF boundary conditions'. ELSEVIER SCIENCE BV NUCLEAR PHYSICS A, St Goar, GERMANY: 2nd International Conference on Collective Motion in Nuclei Under Extreme Conditions 788, pp. 343C-348C.
• . (2007) 'Probing single-particle structures beyond the proton drip line'. AMER INST PHYSICS PROTON EMITTING NUCLEI AND RELATED TOPICS, Lisbon, PORTUGAL: International Conference on Proton Emitting Nuclei and Related Topics 961, pp. 137-142.
• . (2007) 'The two-potential approach to one-proton emission'. AMER INST PHYSICS PROTON EMITTING NUCLEI AND RELATED TOPICS, Lisbon, PORTUGAL: International Conference on Proton Emitting Nuclei and Related Topics 961, pp. 66-71.
• . (2006) 'Dipole response in neutron-rich magnesium'. WORLD SCIENTIFIC PUBL CO PTE LTD INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS, Shanghai, PEOPLES R CHINA: International Conference on Nuclear Structure Physics 15 (7), pp. 1417-1423.
• . (2005) 'Isoscalar and isovector giant monopole resonances using TDHF'. AMER INST PHYSICS EXOTIC NUCLEAR SYSTEMS, Debrecen, HUNGARY: International Symposium on Exotic Nuclear Systems 802, pp. 305-308.
• . (2003) 'Interplay between K-isomerism and gamma-softness in Xe-128'. ACTA PHYSICA POLONICA B, JAGELLONIAN UNIV, INST PHYSICS ACTA PHYSICA POLONICA B, ZAKOPANE, POLAND: 37th Zakopane Meeting of Physics on Trends in Nuclear Physics 34 (4), pp. 2253-2256.
• . (2002) 'Cranked-Hartree-Fock-Bogoliubov analysis at the valence maximum: Yrast behaviour of Dy-170(66)104'. PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, KYOTO UNIV, YUKAWA INST THEORET PHYS, KYOTO, JAPAN: 10th Yukawa International Seminar on Physics of Unstable Nuclei (146), pp. 609-610.

### Book chapters

• . (2015) 'Numerical Calculations of TDHF'. in Iwata Y (ed.) Progress of time-dependent nuclear reaction theory Bentham Science Publishers
[ Status: Accepted ]

#### Abstract

We discuss some aspects of implementing the time-dependent Hartree-Fock method in the case of nuclear physics. Topics discussed include implementation of the time-stepping algorithm, considerations involving the ef- fective interaction, and the use (or not) of particular optional terms in the energy density functional, and boundary conditions. Examples of application of the technique to giant resonances and reactions are given, concentrating on issues to do with numerical and conceptual interpretation.

## Teaching

Level 1: Computational Laboratory (in 1EM)
Level 2: Modelling Complex Systems (2MCS)
Level 3: Final Year Project Supervision
Level 3: High Energy Physics (3HEP)
Postgraduate: MSc project supervision (REP and Medical Physics degrees)

## Departmental Duties

Board of Studies Chairman
Institute of Physics Contact
Faculty Representative on Widening Participation and Outreach Subcommittee

## Public Engagement Activities

Paul is involved in public engagement activities and has given public lectures at the Royal Institution, the Cheltenham Festival, the British Science Association Festival, schools, Intitute of Physics Branches, science outreach centres and Cafe Scientifique branches.  He has served as chair of the IoP South Central Branch, and Recorder of the British Science Association Physics and Astronomy section

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