Dr Paul Stevenson

MA (Oxon) MSc (Open) DPhil (Oxon)

Academic and research departments

Department of Physics.


Areas of specialism

Nuclear Physics; Theoretical Physics; Computational Physics

University roles and responsibilities

  • MPhys Research Year Coordinator
  • Head of Nuclear Theory Group

My qualifications

D.Phil, Nuclear Physics
University of Oxford


Research interests

My publications


"Low-Energy Heavy-Ion Reactions and Effective Forces", P. D. Stevenson and M. C. Barton, Prog. Part. Nucl. Phys. 104, 142 (2019) [ open access journal download | arxiv download (1809.05801) | surrey epubs download ]

"Two-body dissipation effect in nuclear fusion reactions", Kai Wen, M. C. Barton, Arnau Rios Huguet, and P. D. Stevenson, Phys. Rev. C 98, 014603 (2018) [ journal download | arxiv download (1805.08152) | surrey epubs download ]

"The Skyrme tensor force in heavy ion collisions", P. D. Stevenson, E. B. Suckling, S. Fracasso, M. C. Barton and A. S. Umar, Phys. Rev. C 93, 054617 (2016) [ journal download | arxiv download (1507.00645) | surrey epubs download ]

"The TDHF Code Sky3D", J. A. Maruhn, P.-G. Reinhard, P. D. Stevenson and A. S. Umar, Comput. Phys. Commun. 185, 2195 (2014) [ open access journal download | arxiv download (1310.5946) | surrey epubs download ]


P. D. Stevenson and M. C. Barton (2019). Low-Energy Heavy-Ion Reactions and Effective Forces, Prog. Part. Nucl. Phys. 104, 142
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The Skyrme effective interaction, with its multitude of parameterisations, along with its implementation using the static and time-dependent density functional (TDHF) formalism has allowed for a range of microscopic calculations of low-energy heavy-ion collisions. These calculations allow variation of the effective interaction along with an interpretation of the results of this variation informed by a comparison to experimental data. Initial progress in implementing TDHF for heavy-ion collisions necessarily used many approximations in the geometry or the interaction. Over the last decade or so, the implementations have overcome all restrictions, and studies have begun to be made where details of the effective interaction are being probed. This review surveys these studies in low-energy heavy-ion reactions, finding significant effects on observables from the form of the spin–orbit interaction, the use of the tensor force, and the inclusion of time-odd terms in the density functional
Kai Wen, M. C. Barton, Arnau Rios Huguet, and P. D. Stevenson (2018). Two-body dissipation effect in nuclear fusion reactions, Phys. Rev. C 98, 014603
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Friction coefficients for the fusion reaction 16O+16O→32S are extracted based on both the time-dependent Hartree-Fock and the time-dependent density matrix methods. The latter goes beyond the mean-field approximation by taking into account the effect of two-body correlations, but in practical simulations of fusion reactions we find that the total energy is not conserved. We analyze this problem and propose a solution that allows for a clear quantification of dissipative effects in the dynamics. Compared to mean-field simulations, friction coefficients in the density-matrix approach are enhanced by about 20%. An energy dependence of the dissipative mechanism is also demonstrated, indicating that two-body collisions are more efficient at generating friction at low incident energies.
T. Grahn, D. T. Joss, R. D. Page, B. Sayğı, S. Stolze, D. O'Donnell, M. Akmali, K. Andgren, L. Bianco, D. M. Cullen, A. Dewald, P. T. Greenlees, K. Heyde, H. Iwasaki, U. Jakobsson, J. Jolie, P. Jones, D. S. Judson, R. Julin, S. Juutinen, S. Ketelhut, M. L (2016). Excited States and Reduced Transition Probabilities in 168Os, Phys. Rev. C 94, 044327
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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 γ-ray spectrometer in conjunction with the IKP Köln plunger device. The 168Osγ 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→2+1)/B(E2;2+1→0+1) is measured to be 0.34(18), which is very unusual for collective band structures and cannot be reproduced by interacting boson model (IBM-2) calculations based on the SkM* energy-density functional.
P. D. Stevenson, E. B. Suckling, S. Fracasso, M. C. Barton and A. S. Umar (2016). The Skyrme tensor force in heavy ion collisions, Phys. Rev. C 93, 054617
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Background: It is generally acknowledged that the time-dependent Hartree–Fock (TDHF) method provides a useful foundation for a fully microscopic many-body theory of low-energy heavy ion reactions. The TDHF method is also known in nuclear physics in the small-amplitude domain, where it provides a useful description of collective states, and is based on the mean-field formalism, which has been a relatively successful approximation to the nuclear many-body problem. Currently, the TDHF theory is being widely used in the study of fusion excitation functions, fission, and deep-inelastic scattering of heavy mass systems, while providing a natural foundation for many other studies. Purpose: With the advancement of computational power it is now possible to undertake TDHF calculations without any symmetry assumptions and incorporate the major strides made by the nuclear structure community in improving the energy density functionals used in these calculations. In particular, time-odd and tensor terms in these functionals are naturally present during the dynamical evolution, while being absent or minimally important for most static calculations. The parameters of these terms are determined by the requirement of Galilean invariance or local gauge invariance but their significance for the reaction dynamics have not been fully studied. This work addresses this question with emphasis on the tensor force. Method: The full version of the Skyrme force, including terms arising only from the Skyrme tensor force, is applied to the study of collisions within a completely symmetry-unrestricted TDHF implementation. Results: We examine the effect on upper fusion thresholds with and without the tensor force terms and find an effect on the fusion threshold energy of the order several MeV. Details of the distribution of the energy within terms in the energy density functional are also discussed. Conclusions: Terms in the energy density functional linked to the tensor force can play a non-negligible role in dynamic processes in nuclei.
P.-G. Reinhard, A. S. Umar, P. D. Stevenson, J. Piekarewicz, J. A. Maruhn, and V. E. Oberacker (2016). Sensitivity of the fusion cross section to the density dependence of the symmetry energy, Phys. Rev. C 93, 044618
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Background: The study of the nuclear equation of state (EOS) and the behavior of nuclear matter under extreme conditions is crucial to our understanding of many nuclear and astrophysical phenomena. Nuclear reactions serve as one of the means for studying the EOS. Purpose: It is the aim of this paper to discuss the impact of nuclear fusion on the EOS. This is a timely subject given the expected availability of increasingly exotic beams at rare isotope facilities [A. B. Balantekin et al., Mod. Phys. Lett. A 29, 1430010 (2014)]. In practice, we focus on 48Ca+48Ca fusion. Method: We employ three different approaches to calculate fusion cross sections for a set of energy density functionals with systematically varying nuclear matter properties. Fusion calculations are performed using frozen densities, using a dynamic microscopic method based on density-constrained time-dependent Hartree-Fock (DC-TDHF) approach, as well as direct TDHF study of above barrier cross sections. For these studies, we employ a family of Skyrme parametrizations with systematically varied nuclear matter properties. Results: The folding-potential model provides a reasonable first estimate of cross sections. DC-TDHF, which includes dynamical polarization, reduces the fusion barriers and delivers much better cross sections. Full TDHF near the barrier agrees nicely with DC-TDHF. Most of the Skyrme forces which we used deliver, on the average, fusion cross sections in good agreement with the data. Trying to read off a trend in the results, we find a slight preference for forces which deliver a slope of symmetry energy of L≈50 MeV that corresponds to a neutron-skin thickness of 48Ca of Rskin=(0.180–0.210) fm. Conclusions: Fusion reactions in the barrier and sub-barrier region can be a tool to study the EOS and the neutron skin of nuclei. The success of the approach will depend on reduced experimental uncertainties of fusion data as well as the development of fusion theories that closely couple to the microscopic structure and dynamics.
Maninder Kaur, B. R. Behara, Gulzar Singh, Varinderjit Singh, N. Madhavan, S. Muralithar, S. Nath, J. Gehlot, G. Mohanto, Ish Mukul, D. Siwal, M. Thakur, K. Kapoor, P. Sharma, T. Banerjee, A. Jhingan, T. Varughese, Indu Bala, B. K. Nayak, A. Saxena, M. B. (2016). Probing dynamics of fusion reactions through cross-section and spin distribution measurement,
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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.  
P. M. Goddard, P. D. Stevenson, and A. Rios (2016). Fission dynamics within time-dependent Hartree-Fock: boost induced fission, Phys. Rev. C 93, 014620
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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)], quadrupole-constrained 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.
P. D. Stevenson (2016). Resonances and Reactions from Mean-Field Dynamics, EPJ Web of Conferences, 107, 08001
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The time-dependent version of nuclear density functional theory, using functionals derived from Skyrme interactions, is able to approximately describe nuclear dynamics. We present time-dependent results of calculations of dipole resonances, concentrating on excitations of valence neutrons against a proton plus neutron core in the neutron-rich doubly-magic 132Sn nucleus, and results of collision dynamics, highlighting potential routes to ternary fusion, with the example of a collision of 48Ca+48Ca+208Pb resulting in a compound nucleus of element 120 stable against immediate fission.
R. Reifarth, S. Altstadt, K. Göbel, T. Heftrich, M. Heil, A. Koloczek, C. Langer, R. Plag, M. Pohl, K. Sonnabend, M. Weigand, T. Adachi, F. Aksouh, J. Al-Khalili, M. AlGarawi, S. AlGhamdi, G. Alkhazov, N. Alkhomashi, H. Alvarez-Pol, R. et al. (2016). Nuclear astrophysics with radioactive ions at FAIR, J. Phys.: Conf. Ser. 665, 012044
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The nucleosynthesis of elements beyond iron is dominated by neutron captures in the s and r processes. However, 32 stable, proton-rich isotopes cannot be formed during those processes, because they are shielded from the s-process flow and r-process, β-decay chains. These nuclei are attributed to the p and rp process. For all those processes, current research in nuclear astrophysics addresses the need for more precise reaction data involving radioactive isotopes. Depending on the particular reaction, direct or inverse kinematics, forward or time-reversed direction are investigated to determine or at least to constrain the desired reaction cross sections. The Facility for Antiproton and Ion Research (FAIR) will offer unique, unprecedented opportunities to investigate many of the important reactions. The high yield of radioactive isotopes, even far away from the valley of stability, allows the investigation of isotopes involved in processes as exotic as the r or rp processes.
P. D. Stevenson, P. M. Goddard and A. Rios (2015). Shapes and Dynamics from the Time-Dependent Mean Field, Bulg. J. Phys. 42, 354
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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.
P. M. Goddard, P. D. Stevenson and A. Rios (2015). on dynamics within time-dependent Hartree-Fock: deformation-induced fission, Phys. Rev. C 92, 054610
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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 fast fission processes beyond the fission barrier, using the nuclide 240Pu as an example. Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate nonadiabatic fission paths, beginning from static constrained Hartree-Fock calculations. The properties of the dynamic states are interpreted in terms of the nature of their collective motion. Fission product properties are compared to data. Results: Parent nuclei constrained to begin dynamic evolution with a deformation less than the fission barrier exhibit giant-resonance-type behavior. Those beginning just beyond the barrier explore large-amplitude motion but do not fission, whereas those beginning beyond the two-fragment pathway crossing fission to final states which differ according to the exact initial deformation. Conclusions: Time-dependent Hartree-Fock is able to give a good qualitative and quantitative description of fast fission, provided one begins from a sufficiently deformed state.
Maninder Kaur et al. (2015). Investigation of dynamics of fusion reactions through cross-section and spin distribution measurements, proceedings of 60th DAE-BRNS Symposium on Nuclear Physics 60 35
A. D. Godbeer, J. S. Al-Khalili, and P. D. Stevenson (2015). Modelling Proton Tunnelling in the Adenine-Thymine Base Pair, Phys. Chem. Chem. Phys., 17, 13034
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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.