# Professor Paul Stevenson

## Academic and research departments

School of Mathematics and Physics, Theoretical Nuclear Physics Group.## About

### Biography

Paul Stevenson studied physics at the University of Oxford, worked for one year at the University of Tennessee in Knoxville, and has been at the University of Surrey since 2000. He works on nuclear structure and reaction theory, quantum computation, mathematical and computational physics, and some quantum biology. Since 2020 he has been an AWE William Penney Fellow

### Areas of specialism

### My qualifications

### Affiliations and memberships

## News

### In the media

## Research

### Research interests

I work on nuclear structure and nuclear reactions using density-functional theory techniques, with a particular interest in time-dependent methods and the kinds of nuclear processes that you can describe with them: Nuclear fusion, fission, giant resonance states, reaction mechanisms, creation of superheavy elements, nuclear size, shape, structure and how all these physical observables and processes are influenced by the assumed nuclear interaction. I am the author of a recent (2019) review on the role of the nuclear interaction in the reactions between nuclei, available as an Open Access publication in Progress in Particle and Nuclear Physics.

## Teaching

Surrey courses I currently teach / coordinate are: PHY3038: Special Relativity, PHY3042: Modern Computational Techniques, PHY3002: Final Year Project, and PHYM051: Research Year Dissertation.

## Publications

### Highlights

"*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 ]

The Sky3D code has been widely used to describe nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The approach is based on Skyrme forces or related energy density functionals. The static and dynamic equations are solved on a three-dimensional grid, and pairing is been implemented in the BCS approximation. This updated version of the code aims to facilitate the calculation of nuclear strength functions in the regime of linear response theory, while retaining all existing functionality and use cases. The strength functions are benchmarked against available RPA codes, and the user has the freedom of choice when selecting the nature of external excitation (from monopole to hexadecapole and more). Some utility programs are also provided that calculate the strength function from the time-dependent output of the dynamic calculations of the Sky3D code.

Nuclear friction causes energy dissipation in heavy-ion collisions. Its understanding and inclusion in quantum mechanical reaction models are crucial for advancing the physics of heavy-ion reactions forming heavy elements. The effects of nuclear friction on heavy-ion fusion reactions are investigated using the coupled-channels density-matrix method. In this open-quantum-system description, a phenomenological nuclear friction form factor is introduced along with coherent coupled-channels effects. The key nucleus was the 92 Zr target, due to its high density of low-lying non-collective excited states, which was recently theorised to be cause of nuclear friction. The calculations using the 16O + 92Zr collision showed that the inclusion of nuclear friction effects increased the fusion probability significantly, and that the agreement between the theoretical and experimental fusion barrier distributions was improved when nuclear friction effects were included.

The isoscalar giant monopole resonance in molybdenum-100 has been measured in recent alpha scattering experiments and its strength function extracted. By performing time-dependent Hartree-Fock calculations with Skyrme effective interactions, we are able to reproduce the gross features of the observed strength. The details of the structure are found to be dependent on the ground state shape. We use a measure of fit to determine which ground state shape correlates with the observed strength and find evidence for triaxiality in this nucleus.

Based on both the time-dependent Hartree–Fock (TDHF) and the time-dependent density matrix (TDDM) methods, we adopt a macroscopic reduction procedure to investigate the dissipation dynamics of nuclear fusion reactions. The TDDM method is an extension of TDHF, in the sense that it goes beyond the mean-field concept and takes into account two-body correlations explicitly. To investigate the effect of correlations on dissipation, the collective trajectories as well as the friction coefficients for the reaction ¹⁶O + ¹⁶O →³²S are extracted. Our results suggest that two-body correlations play a relevant role in the fusion process.

The first low-energy Coulomb-excitation measurement of the radioactive, semi-magic, two proton -hole nucleus 206Hg, was performed at CERN's recently-commissioned HIE-ISOLDE facility. Two gamma rays depopulating low-lying states in 206Hg were observed. From the data, a reduced transition strength B(E2; 2+1 -> 0+1 ) = 4.4(6) W.u. was determined, the first such value for an N = 126 nucleus south of 208Pb, which is found to be slightly lower than that predicted by shell-model calculations. In addition, a collective octupole state was identified at an excitation energy of 2705 keV, for which a reduced B(E3) transition probability of 30+10 -13 W.u. was extracted. These results are crucial for understanding both quadrupole and octupole collectivity in the vicinity of the heaviest doubly-magic nucleus 208Pb, and for benchmarking a number of theoretical approaches in this key region. This is of particular importance given the paucity of data on transition strengths in this region, which could be used, in principle, to test calculations relevant to the astrophysical r-process.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

A survey has been conducted of the resonance data available in the major evaluated libraries for a range of mid-mass isotopes. Although many isotopes have data derived from experimental measurements and rigorous analyses, the data for some others, particularly for isotopes that are unstable, are purely theoretically generated, e.g. via the use of the TARES code. A subsequent project has developed a suite of automated tools to rapidly inspect the resonance data available for a specified isotope. These tools calculate a range of values and distributions for the available data (e.g. cumulative number of resonances versus neutron energy) and use a comparison against expected theoretical values (e.g. a Porter-Thomas distribution) to suggest their physical validity or otherwise. The motivation for this study, the tools developed, and results for a number of isotopes, are presented in this paper.

Calculations of nuclear properties and nuclear models are performed using quantum computing algorithms on simulated and real quantum computers. The models are a realistic calculation of deuteron binding based on effective field theory, and a simplified two-level version of the nuclear shell model. A method of reducing the number of qubits needed for practical calculation is presented, the reduction being with respect to that used when the standard Jordan-Wigner encoding is used. Its efficacy is shown in the case of the deuteron binding and shell model. A version of the variational quantum eigensolver in which all eigenstates in a spectrum are targeted on an equal basis is shown. The method involves finding the minima of the variance of the Hamiltonian, and its ability to find the full spectrum of small version of the simplified shell model is presented.

Quantum computing opens up new possibilities for the simulation of many-body nuclear systems. As the number of particles in a many-body system increases, the size of the space if the associated Hamiltonian increases exponentially. This presents a challenge when performing calculations on large systems when using classical computing methods. By using a quantum computer, one may be able to overcome this difficulty thanks to the exponential way the Hilbert space of a quantum computer grows with the number of quantum bits (qubits). Our aim is to develop quantum computing algorithms which can reproduce and predict nuclear structure such as level schemes and level densities. As a sample Hamiltonian, we use the Lipkin-Meshkov-Glick model. We use an efficient encoding of the Hamiltonian onto many-qubit systems, and have developed an algorithm allowing the full excitation spectrum of a nucleus to be determined with a variational algorithm capable of implementation on today’s quantum computers with a limited number of qubits. Our algorithm uses the variance of the Hamiltonian,⟨H⟩2 − ⟨H⟩2, as a cost function for the widely-used variational quantum eigensolver (VQE). In this work we present a variance based method of finding the excited state spectrum of a small nuclear system using a quantum computer, using a reduced-qubit encoding method.

The quantum imaginary time evolution (QITE) algorithm is a direct implementation of the classical imaginary time evolution algorithm on quantum computer. We implement the QITE algorithm for the case of nuclear Hartree-Fock equations in a formalism equivalent to nuclear density functional theory. We demonstrate the algorithm in the case of the helium-4 nucleus with a simplified effective interaction of the Skyrme kind and demonstrate that the QITE, as implemented on simulated quantum computer, gives identical results to the classical algorithm.

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.

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.

This note presents a minor alteration to, and subsequent use of, the Sky3D nuclear time-dependent Hartree-Fock code to calculate ion-ion potentials in the Frozen Hartree-Fock approximation. An example of 16O + 16O is presented.

There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical avenues were the subject of a workshop held at the University of York in October 2019; this report summarises its findings and recommendations.

We review recent research on quantum computing applications for cal-culations and simulation of nuclear physics. As systems of interacting fermions, nuclei and their quantum simulation bear much similarity to the quantum computation of chemical systems, whose studies are rel-atively more advanced. Hence techniques from the quantum chemistry literature may be readily adopted. Some ways in which nuclei differ from other many-body systems, such as the strong non-perturbative interaction, are highlighted, and a selection of existing results are dis-cussed, covering nuclear structure and reactions.

Background: Time-dependent techniques in nuclear theory often rely on mean-field or Hartree-Fock descriptions. Beyond-mean-field dynamical calculations within the time-dependent density matrix (TDDM) theory have often invoked symmetry restrictions and ignored the connection between the mean field and the induced interaction. Purpose: We study the ground states obtained in a TDDM approach for nuclei from A = 12 to A = 24, including examples of even-even and odd-even nuclei with and without intrinsic deformation. We overcome previous limitations using three-dimensional simulations and employ density-independent Skyrme interactions self-consistently. Methods: The correlated ground states are found starting from the Hartree-Fock solution, by adiabatically including the beyond-mean-field terms in real time. Results: We find that, within this approach, correlations are responsible for similar to 4-5% of the total energy. Radii are generally unaffected by the introduction of beyond-mean-field correlations. Large nuclear correlation entropies are associated with large correlation energies. By all measures, C-12 is the most correlated isotope in the mass region considered. Conclusions: Our work is the starting point of a consistent implementation of the TDDM technique for applications into nuclear reactions. Our results indicate that correlation effects in structure are small, but beyond-mean-field dynamical simulations could provide insight into several issues of interest.

The adenine-thymine tautomer (A*-T*) has previously been discounted as a spontaneous mutagenesis mechanism due to the energetic instability of the tautomeric configuration. We study the stability of A*-T* while the nucleobases undergo DNA strand separation. Our calculations indicate an increase in the stability of A*-T* as the DNA strands unzip and the hydrogen bonds between the bases stretch. Molecular Dynamics simulations reveal the time scales and dynamics of DNA strand separation and the statistical ensemble of opening angles present in a biological environment. Our results demonstrate that the unwinding of DNA, an inherently out-of-equilibrium process facilitated by helicase, will change the energy landscape of the adenine-thymine tautomerization reaction. We propose that DNA strand separation allows the stable tautomeriza-tion of adenine-thymine, providing a feasible pathway for genetic point mutations via proton transfer between the A-T bases.

The Skyrme effective interaction, with its multitude of parameterisations, along with its implementation using the static and time-dependent density functional (TDHF) formalism have 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.

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 1 ph states). Results are shown for the chain of Nd isotopes, superdeformed Dy-152, triaxial Os-188, and U-238.

An extended decay scheme for Xe-128 has been constructed by using data from the Sn-124(Be-9, 5n)Xe-128 reaction at a beam energy of 58 MeV. Bands have been identified as being built on several intrinsic states, including a proposed 9/2(-)[514] circle times 1/2(+)[400] two-quasineutron configuration that forms the K-pi=5(-) intrinsic state at 2228 keV, and on a previously assigned K-pi=8(-) intrinsic state at 2786 keV. A half-life of 73(3) ns has been measured for the latter. Theoretical calculations have been performed by using the configuration-constrained blocking method based on a nonaxial Woods-Saxon potential. Large gamma deformation and gamma softness are predicted for the ground state and the K-pi=5(-) intrinsic state, whereas a nearly axially symmetric shape is predicted for the K-pi=8(-) two-quasiparticle configuration. The low value of the hindrance factor for the E1 transition depopulating the K-pi=8(-) intrinsic state is discussed in the context of analogous transitions in neighbouring N=74 isotones.

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 Pb-208. The ground-state deformations, nuclear radii, neutron-skin thicknesses and alpha-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 (292)120 nucleus. Earlier predictions of remarkably low central density are not supported when deformation is allowed for.

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.

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.

A previously unreported isomer has been identified in Mo-99 at an excitation energy of E-x = 3010 keV, decaying with a half-life of T-1/2 = 8(2) ns. The nucleus of interest was produced following fusion-fission reactions between a thick Al-27 target frame and a Hf-178 beam at a laboratory energy of 1150 MeV. This isomeric state is interpreted as an energetically favored, maximally aligned configuration of nu h (11/2) circle times pi(g (9/2))(2).

We studied the nuclear shape evolutions in fission process of 240Pu by the time-dependent Hartree- Fock approach with various Skyrme forces. Calculations are performed for the later phase of the fission with large initial deformations towards the scission. We show that calculations with Skyrme forces with large surface energies and large symmetry energies can have extremely long fission evolution time. The symmetry energy plays a role in the evolution of neutron-rich necks. In addition, we also demonstrated the shape oscillations of fission fragments after the fission. We see that particularly the heavy near-spherical fragments have remarkable octupole oscillations.

The visualisation of objects moving at relativistic speeds has been a popular topic of study since Special Relativity’s inception. While the standard exposition of the theory describes certain shapechanging effects, such as the Lorentz-contraction, it makes no mention of how an extended object would appear in a snapshot or how apparent distortions could be used for measurement. Previous work on the subject has derived the apparent form of an object, often making mention of George Gamow’s relativistic cyclist thought experiment. Here, a rigorous reanalysis of the cyclist, this time in 3-dimensions, is undertaken for a binocular observer, accounting for both the distortion in apparent position and the relativistic colour and intensity shifts undergone by a fast moving object. A methodology for analysing binocular relativistic data is then introduced, allowing the fitting of experimental readings of an object’s apparent position to determine the distance to the object and its velocity. This method is then applied to the simulation of Gamow’s cyclist, producing selfconsistent results.

The propagation of non-topological solitons in many-nucleus systems is studied based on timedependent density functional calculations, focusing on mass and energy dependence. The dispersive property and the nonlinearity of the system, which are inherently included in the nuclear density functional, are essential factors to form a non-topological soliton. On the other hand, soliton propagation is prevented by charge equilibration, and competition can appear between soliton formation and disruption. In this article, based on the energy-dependence of the two competitive factors, the concept of conditional recovery of time-reversal symmetry is proposed in many-nucleus systems. It clarifies the possibility of preserving the nuclear medium inside natural or artificial nuclear reactors, at a suitable temperature. From an astrophysical point of view, the existence of the low-temperature solitonic core of compact stars is suggested.

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.

^{99}Mo, In: Physical Review C76(047303)

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.

^{128}Xe, In: Physical Review C74(034318)

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.

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.

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.

*K*negative parity states in

^{184}Os, In: Physical Review C65(064310)

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.

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.

The half-life of the yrast I π = 2+ state in the neutron-rich nucleus 188W has been measured using fast-timing techniques with the HPGe and LaBr3:Ce array at the National Institute of Physics and Nuclear Engineering, Bucharest. The resulting value of t1/2 = 0.87(12) ns is equivalent to a reduced transition probability of B(E2; 2+ 1 → 0+ 1 ) = 85(12) W.u. for this transition. The B(E2; 2+ 1 → 0+ 1 ) is compared to neighboring tungsten isotopes and nuclei in the Hf, Os, and Pt isotopic chains. Woods-Saxon potential energy surface (PES) calculations have been performed for nuclei in the tungsten isotopic chain and predict prolate deformed minima with rapidly increasing γ softness for 184–192W and an oblate minimum for 194W.

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.

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, 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 is 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.

_{66}

^{170}Dy

_{104}, In: Physical Review C65(037302)

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 preferenceforforceswhichdeliveraslopeofsymmetryenergyofL ≈ 50MeVthatcorrespondstoaneutron-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.

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.

Recent experimental data on the low-lying states in W-190 show a change in the E(4(1)(+))/E(2(1)(+)) behavior compared to less neutron-rich neigbors. Self-consistent axially-deformed Hartree-Fock calculations, using a separable monopole interaction, of nuclei in the vicinity of W-190 are performed to systematically examine the evolution of ground state quadrupole deformations. It is found that the neutron number N=116 causes a coexistence of oblate and prolate shapes, with a weak dependence on proton number, thereby hindering the development of these isotones as well-deformed rotors.

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.

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.

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.

We present a code in Python3 which takes a square real symmetric matrix, of arbitrary size, and decomposes it as a tensor product of Pauli spin matrices. The application to the decomposition of a Hamiltonian of relevance to nuclear physics for implementation on quantum computer is given.

Phys. Rev. C 103, 031304 (2021) Energy dependence of fission observables is a key issue for wide nuclear applications. We studied real-time fission dynamics from low-energy to high excitations in the compound nucleus $^{240}$Pu with the time-dependent Hartree-Fock+BCS approach. It is shown that the evolution time of the later phase of fission towards scission is considerably lengthened at finite temperature. As the role of dynamical pairing is vanishing at high excitations, the random transition between single-particle levels around the Fermi surface to mimic thermal fluctuations is indispensable to drive fission. The obtained fission yields and total kinetic energies with fluctuations can be divided into two asymmetric scission channels, namely S1 and S2, which explain well experimental results, and give microscopic support to the Brosa model. With increasing fluctuations, S2 channel takes over S1 channel and the spreading fission observables are obtained.

Einstenium-254 (Z = 99, N = 155), can be prepared as a target for research into nuclear reaction studies. This work presents structure and reaction calculations of Es-254 and Ca-48 (Z = 20, N = 28), using the Skyrme-(Time-Dependent)-Energy-Density-Functional formalism. The reaction calculations show the initial parts of the heavy-ion reaction between the nuclei which, depending on the interaction parameters, can lead to capture to a compound nucleus of element 119. For collisions with the spherical 48Ca impinging on the tip of the prolate 254Es no fusion events are found. For collisions where the calcium approaches the belly of the einsteinium, capture occurs with the compound nucleus outlasting the lifetime of the calculation, indicating a possible fusion candidate. For a sample center-of-mass collision energy of 220 MeV, slightly non-central collisions, up to an impact parameter of 1 fm, also form long-lived compound nuclei.

Hindrance factors for K-forbidden E2 decays from multiquasiparticle isomers are analyzed in relation to mixing matrix elements that are often associated with chance near degeneracies, and a functional relationship is established. Focusing on effective matrix elements for ΔK=6 decays from three-quasiparticle isomers, significant configuration dependence is demonstrated.

We revisit the studies of the isotopic shift in the charge radii of even-even isotopes of Sn and Pb nuclei at N = 82, and 126, respectively, within the relativistic mean-field and Relativistic-Hartree-Bogoliubov approach. The shell model is also used to estimate isotopic shift in these nuclei, for the first time, to the best of our knowledge. The ground state single-particle energies (spe) are calculated for non-linear NL3 & NL3 * and density-dependent DD-ME2 parameter sets compared with the experimental data, wherever available. We establish a correlation between the filling of single-particle levels and the isotopic shift in occupation probabilities. The obtained spe from the relativistic mean-field and Relativistic-Hartree-Bogoliubov approaches are in line with those used in the shell model and experimental data for both the Sn and Pb isotopic chains. The shell model calculated isotopic shift agrees with relativistic mean-field and Relativistic-Hartree-Bogoliubov approaches that explain the experimental data quite well.

The first low-energy Coulomb-excitation measurement of the radioactive, semi-magic, two proton-hole nucleus 206Hg, was performed at CERN's recently-commissioned HIE-ISOLDE facility. Two γ rays depopulating low-lying states in 206Hg were observed. From the data, a reduced transition strength B(E2;21+→01+)=4.4(6) W.u was determined, the first such value for an N=126 nucleus south of 208Pb, which is found to be slightly lower than that predicted by shell-model calculations. In addition, a collective octupole state was identified at an excitation energy of 2705 keV, for which a reduced B(E3) transition probability of 30−13+10 W.u was extracted. These results are crucial for understanding both quadrupole and octupole collectivity in the vicinity of the heaviest doubly-magic nucleus 208Pb, and for benchmarking a number of theoretical approaches in this key region. This is of particular importance given the paucity of data on transition strengths in this region, which could be used, in principle, to test calculations relevant to the astrophysical r-process.

We perform deformation constraint symmetry-unrestricted 3D time-dependent density functional theory (TDDFT) calculations for the isoscalar monopole (ISM) mode in 100 Mo. Monopole moments as a function of time are obtained by time propagating states based on different deformations. A Fourier transform is then performed on the obtained response functions. The resulted ISM strength functions are compared with experimental data. For the static potential-energy-surface (PES) calculations , the results using SkM* and unedf1 energy-density functionals (EDFs) show spherical ground states and considerable softness in the triaxial deformation. The PES obtained with SLy4 EDF shows a static triaxial deformation. The TDDFT results based on different deformations show that a quadrupole deformation (characterized by β2) value of 0.25-0.30 give a two-peak structure of the strength functions. Increasing triaxial deformation (characterized by γ) from 0 • to 30 • results in the occurrence of an additional peak between the two, making the general shape of the strength functions closer to the data. Our microscopic TDDFT analyses suggest that the 100 Mo is triaxi-ally deformed in the ground state. The calculated isoscalar Q20 and Q22 strength functions show peaks at lower energies. The coupling of these two modes with the ISM mode is the reason for the three-peak/plateau structure in the strengths of 100 Mo.

The adenine-thymine tautomer (A*-T*) has previously been discounted as a spontaneous mutagenesis mechanism due to the energetic instability of the tautomeric configuration. We study the stability of A*-T* while the nucleobases undergo DNA strand separation. Our calculations indicate an increase in the stability of A*-T* as the DNA strands unzip and the hydrogen bonds between the bases stretch. Molecular Dynamics simulations reveal the timescales and dynamics of DNA strand separation and the statistical ensemble of opening angles present in a biological environment. Our results demonstrate that the unwinding of DNA, an inherently out-of-equilibrium process facilitated by helicase, will change the energy landscape of the adenine-thymine tautomerisation reaction. We propose that DNA strand separation allows the stable tautomerisation of adenine-thymine, providing a feasible pathway for genetic point mutations via proton transfer between the A-T bases.

The mass distributions for giant dipole resonances in S-32 and Sn-132 decaying through particle emission and for deep-inelastic collisions between O-16 nuclei have been investigated by implementing the Balian-Vénéroni variational technique based upon a three-dimensional time-dependent Hartree-Fock code with realistic Skyrme interactions. The mass distributions obtained have been sown to be significantly larger than standard TDHF results.

The surface energy is one of the fundamental properties of nuclei, appearing in the simplest form of the semi-empirical mass formula. The surface energy has an influence on e.g. the shape of a nucleus and its ability to deform. This in turn could be expected to have an effect in fusion reactions around the Coulomb barrier where dynamical effects such as the formation of a neck is part of the fusion process. Frozen Hartree-Fock and Time-Dependent Hartree-Fock calculations are performed for a series of effective interactions in which the surface energy is systematically varied, using 40Ca + 48Ca as a test case. The dynamical lowering of the barrier is greatest for the largest surface energy, contrary to naive expectations, and we speculate that this may be due to the variation in other nuclear matter properties for these effective interactions.

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 1i11/2 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.

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

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.

Since its first use in Hartree-Fock calculations in 1972, the Skyrme Force, which includes around ten free parameters to be fitted to data, has un- dergone many such fitting procedures to different sets of data. To date there have been more than 200 parameter sets published. Since the Skyrme force can be thought of as an expansion of an in principle exact density functional, the Skyrme force has sufficient degrees of freedom that the different parameter sets can differ from each other quite extensively in how they reproduce the properties of nuclei. We give a selected history of the fitting of Skyrme forces, then ex- plore some recent work on systematically testing each parameterisation against experimentally-derived nuclear matter properties, and discuss the ability of the (few) parameter sets which pass all constraints to reproduce data in finite nuclei.

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.

Time-dependent Hartree-Fock calculations have been performed for fusion reactions of 4He + 4He → 8Be∗, followed by 4He + 8Be∗. Depending on the orientation of the initial state, a linear chain vibrational state or a triangular vibration is found in 12C, with transitions between these states observed. The vibrations of the linear chain state and the triangular state occur at '9 and 4 MeV respectively

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.

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.

We review recent research on quantum computing applications for calculations and simulation of nuclear physics. As systems of interacting fermions, nuclei and their quantum simulation bears much similarity to the quantum computation of chemical systems , whose studies are relatively more advanced. Hence techniques from the quantum chemistry literature may be readily adopted. Some ways in which nuclei differ from other many-body systems, such as the strong non-perturbative interaction, are highlighted, and a selection of existing results are discussed, covering nuclear structure and reactions.