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This work presents a computer program that performs symmetry-unrestricted 3D nuclear time-dependent density function theory (DFT) calculations. The program features the augmented Lagrangian constraint in the static calculation. This allows for the calculation of the potential energy surface. In addition, the code includes the full energy density functionals derived from the Skyrme interaction, meaning that the time-even and time-odd tensor parts are included for the time-dependent calculations. The results of the hit3d code are carefully compared with the Sky3D and Ev8 programs. The testing cases include unconstrained DFT calculations for doubly magic nuclei, the constrained DFT + BCS calculations for medium-heavy nucleus 110Mo, and the dynamic applications for harmonic vibration and nuclear reactions., Comment: 18 pages, 3 figures, 6 tables

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., Comment: 3 pages; proceedings of COMEX7 conference

Model calculations of nuclear properties are peformed 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 known as the Lipkin-Meshkov-Glick model. A method of reducing the number of qubits needed for practical calculation is presented, the reduction being with respect to the number needed 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 targetted on an equal basis is shown. The method involves finding the minima of the variance of the Hamiltonian. The method's ability to find the full spectrum of the simplified shell model is presented., Comment: 6 pages, 3 figures, accepted for SPIE Proceedings for SPIE Quantum Technologies 2022 conference

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., Comment: 8 pages

We revisit the studies of the isotopic shift in the charge radii of {\it 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., Comment: Published in Journal of Physics G: Nuclear and Particle Physics

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 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 $\approx 4-5 \%$ of the total energy. Radii are generally unaffected by the introduction of beyond mean-field correlations. Large nuclear correlation entropies are associated to large correlation energies. By all measures, $^{12}$C 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 new insight into several issues of interest., Comment: 14 pages, 7 figures, 8 tables

The surface energy is one of the fundamental properties nuclei, appearing in the simplest form of the semi-empirical mass formula. The surface enery 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 made for a series of effective interactions in which the surface energy is systematically varied, using $^{40}$Ca + $^{48}$Ca 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, Comment: Submitted to proceedings of HIAS 2019

Time-dependent Hartree-Fock calculations have been performed for fusion reactions of He-4 + He-4 -> Be*-8, followed by He-4 + Be*-8 . 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., Comment: Re-submission to SciPost Proceedings following referee comments

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 shape-changing 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 re-analysis 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 self-consistent results., Comment: 18 pages, 15 figures. Submitted to Proc. Roy. Soc. A

The Skyrme effective interaction, with its multitude of parameterisations, along with its implemen- tation 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., Comment: submitted to Prog. Part. Nucl. Phys

Friction coefficients for the fusion reaction $^{16}$O+$^{16}$O $\rightarrow$ $^{32}$S 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., Comment: 9 pages, 6 figures

The purpose of this paper is to investigate the use of the TDHF method with different Skryme force interactions for the prediction of the M1 strength function associated with $^{52}$Cr, in particular due to the tensor part of the Skyrme force.$^{52}$Cr was chosen due to the recent interest experimentally in this nucleus and the clear data avaliable for comparison. The method used involves applying an instantaneous boost to the wavefunction at the beginning of the dynamical calculations in order to initiate a broadband excitation of the nucleus, following which a Fourier analysis is made. The results of the TDHF simulation found broad agreement with experiment for the range of energies which excite an M1 transition for a variety of forces. The tensor terms appear to be important in qualitatively changing the details of the strength distribution in the main part of the strength function between around 8 and 12 MeV., Comment: 8 pages, 2 figures

Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions. In particular, we can define quantities analogous to molecular structure, thermodynamics, and kinetics, and relate these emergent properties to the structure of the underlying landscape. This Perspective aims to describe these analogies with examples from recent applications, and suggest avenues for new interdisciplinary research., Comment: 41 pages, 25 figures. Accepted for publication in Physical Chemistry Chemical Physics, 2017

Using a novel Se-labelled dimer mixed with DTC5C7 aligned by magnetic field, the twist-bend nematic phase (Ntb) in dimers was studied by hard X-ray resonant scattering and by small and wide angle X-ray scattering (SAXS, WAXS). Resonant diffraction spots indicated a helix with a 9-12 nm pitch in the Ntb phase. Unprecedentedly high helix orien-tation enabled deconvolution of global and local order parameters. This, combined with simultaneous resonant and non-resonant SAXS and WAXS data, allowed us to construct a modified model of the Ntb phase matching twisted molecular conformations and the local heliconical director field., Comment: Main text: 5 pages, 4 figures Supporting information: 27 pages, 9 figures, 5 tables

We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett acceptance-ratio method to compute the dimensionless free-energy difference between a series of equilibrium simulations performed within this object. The method produces results that are in excellent agreement with thermodynamic integration, as well as a direct estimate of the associated statistical uncertainties. The histogram method also allows us to directly obtain an estimate of the interior radial probability density profile, thus yielding useful insight into the structural properties of such a high-dimensional body. We illustrate the method by analyzing the effect of structural disorder on the basins of attraction of mechanically stable packings of soft repulsive spheres., Comment: 5 pages, 2 figures, supplemental material

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\,\cite{balantekin2014}. In practice, we focus on $^{48}$Ca+$^{48}$Ca fusion. 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. We find a slight preference for forces which deliver a slope of symmetry energy of $L\approx 50$\,MeV that corresponds to a neutron-skin thickness of $^{48}$Ca of $R_\mathrm{skin}\!=\!(0.180\!-\!0.210)$\,fm., Comment: 15 pages, 10 figures

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 $^{28}$Si in the first case, and $^{240}$Pu in the latter case., Comment: 9 pages, 5 figures, to appear in proceedings of International Workshop "Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects" (SDANCA-15), 8-10 October 2015, Sofia, Bulgaria

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: To explore the ability of dynamic mean-field methods to describe induced fission processes, using quadrupole boosts in the nuclide $^{240}$Pu as an example. Methods: 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., Comment: Amended version, accepted for publication in Phys. Rev. C. 22 pages, 20 figures, 3 tables

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 $^{132}$Sn nucleus, and results of collision dynamics, highlighting potential routes to ternary fusion, with the example of a collision of $^{48}$Ca+$^{48}$Ca+$^{208}$Pb resulting in a compound nucleus of element 120 stable against immiedate fission, Comment: 6 pages, 4 figures, submitted to proceedings of NSRT15 conference, Dubna, Russia

We report a numerical calculation of the total number of disordered jammed configurations $\Omega$ of $N$ repulsive, three-dimensional spheres in a fixed volume $V$. To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011)) and Asenjo et al. (Phys. Rev. Lett. 112, 098002 (2014)) and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology and machine learning, that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom., Comment: 18 pages, 7 figures

Background: [elided for arXiv character count] 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 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, including those in which the terms do not affect ground state properties., Comment: 6 pages

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: To explore the ability of dynamic mean-field methods to describe fast fission processes beyond the fission barrier, using the nuclide $^{240}$Pu as an example. Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate non-adiabatic 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 behaviour. 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., Comment: Amended version, accepted for publication in Phys. Rev. C. 22 pages, 20 figures, 7 tables

Numerical studies of fractal curves in the plane often focus on subtle geometrical properties such as their left passage probability. Schramm-Loewner evolution (SLE) is a mathematical framework which makes explicit predictions for such features of curve ensembles. The SLE prediction for the left passage probability contains the Gauss hypergeometric function ${}_2F_1$. To perform computational SLE studies it is therefore necessary to have a method for numerical evaluation of ${}_2F_1$ in the relevant parameter regime. In some instances, commercial software provides suitable tools, but freely available implementations are rare and are usually unable to handle the parameter ranges needed for the left passage probability. We discuss different approaches to overcome this problem and also provide a ready-to-use implementation of one conceptually transparent method.

A description is presented of how to use the Sky3D time-dependent Hartree-Fock code to calculate giant monopole resonances. This requires modification to the code, and a step-by-step guide of how to make the necessary modification is given. An example of how to analyse the output of the code to obtain quantities of physics interest is included. Together, the modifications and the post-processing are intended to serve as a typical example of how the code, which was designed to be extendable to particular users' needs, can be extended., Comment: submitted to Proceedings of the International Workshop on Nuclear Theory 33 (Rila, Bulgaria)

The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods, focusing on large, sparse networks. We show that graph transformation provides a much more robust framework, succeeding when numerical precision issues cause the other methods to fail completely. These are precisely the situations that correspond to rare event dynamics for which the graph transformation was introduced.

The theoretical analysis of many problems in physics, astronomy and applied mathematics requires an efficient numerical exploration of multimodal parameter spaces that exhibit broken ergodicity. Monte Carlo methods are widely used to deal with these classes of problems, but such simulations suffer from a ubiquitous sampling problem: the probability of sampling a particular state is proportional to its entropic weight. Devising an algorithm capable of sampling efficiently the full phase space is a long-standing problem. Here we report a new hybrid method for the exploration of multimodal parameter spaces exhibiting broken ergodicity. Superposition enhanced nested sampling (SENS) combines the strengths of global optimization with the unbiased/athermal sampling of nested sampling, greatly enhancing its efficiency with no additional parameters. We report extensive tests of this new approach for atomic clusters that are known to have energy landscapes for which conventional sampling schemes suffer from broken ergodicity. We also introduce a novel parallelization algorithm for nested sampling.

The nuclear mean-field model based on Skyrme forces or related density functionals has found wide-spread application to the description of nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The code Sky3D solves the static or dynamic equations in a three-dimensional Cartesian mesh with isolated or periodic boundary conditions and no further symmetry assumptions. Pairing can be included in the BCS approximation. The code is implemented with a view to allow easy modifications for including additional physics or special analysis of the results., Comment: 24 pages, submitted to Computer Physics Communications

Despite compelling evidence to the contrary in recent years, the view still persists that quantum effects cannot survive very long within a warm, noisy and complex environment that washes out quantum effects at timescales far too short for any chemically or biochemically interesting processes. It is also assumed that as the temperature of the surrounding environment increases, so the efficiency of processes such as quantum tunnelling drops. One way of viewing this has been to invoke the quantum Zeno effect: that the watched pot never boils. In this work we show that the opposite is true. For a quite general open quantum system, a proton in an asymmetric double-well potential, the action of the environment is to enhance the tunnelling rate (an anti-Zeno effect). We compare two simple mathematical models to show that, over a specific temperature range, thermally enhanced quantum tunnelling is equivalent to increasing the frequency of a von Neumann-type measurement by the environment on the system., Comment: 17 pages, 7 figures

We report a study of the basins of attraction for potential energy minima defined by different minimisation algorithms for an atomic system. We find that whereas some minimisation algorithms produce compact basins, others produce basins with complex boundaries or basins consisting of disconnected parts. Such basins deviate from the "correct" basin of attraction defined by steepest-descent pathways, and the differences can be controlled to some extent by adjustment of the maximum step size. The choice of the most convenient minimisation algorithm depends on the problem in hand. We show that while L-BFGS is the fastest minimiser, the FIRE algorithm is also quite fast, and can lead to less fragmented basins of attraction.

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., Comment: 17 pages, 10 figures

We discuss the mechanism causing the `kink' in the charge radius isotope shift at the N=126 shell closure. The occupation of the 1$i_{11/2}$ 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 1$i_{11/2}$ 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., Comment: 4 pages, 4 figures, to be submitted to proceedings of INPC 2013