Nuclear Collective Motion Research Articles

Symmetric Electron Transfer Coordinates are Intrinsic to Bridged Systems: An ab Initio Treatment of the Creutz-Taube Ion.

A long-standing question in electron transfer research concerns the number and identity of collective nuclear motions that drive electron transfer or localisation. It is well established that these nuclear motions are commonly gathered into a so-called electron transfer coordinate. In this theoretical study, we demonstrate that both anti-symmetric and symmetric vibrational motions are intrinsic to bridged systems, and that both are required to explain the characteristic shape of their intervalence charge transfer bands. Using the properties of a two-state Marcus-Hush model, we identify and quantify these two coordinates as linear combinations of normal modes from ab initio calculations. This quantification gives access to the potential coupling, reorganization energy and curvature of the potential energy surfaces involved in electron transfer, independent of any prior assumptions about the system of interest. We showcase these claims with the Creutz-Taube ion, a prototypical Class III mixed valence complex. We find that the symmetric dimension is responsible for the asymmetric band shape, and trace this back to the offset of the ground and excited state potentials in this dimension. The significance of the symmetric dimension originates from geometry dependent coupling, which in turn is a natural consequence of the well-established superexchange mechanism. The conceptual connection between the symmetric and anti-symmetric motions and the superexchange mechanism appears as a general result for bridged systems.

Symmetric Electron Transfer Coordinates are Intrinsic to Bridged Systems: An ab Initio Treatment of the Creutz–Taube Ion

AbstractA long‐standing question in electron transfer research concerns the number and identity of collective nuclear motions that drive electron transfer or localisation. It is well established that these nuclear motions are commonly gathered into a so‐called electron transfer coordinate. In this theoretical study, we demonstrate that both anti‐symmetric and symmetric vibrational motions are intrinsic to bridged systems, and that both are required to explain the characteristic shape of their intervalence charge transfer bands. Using the properties of a two‐state Marcus–Hush model, we identify and quantify these two coordinates as linear combinations of normal modes from ab initio calculations. This quantification gives access to the potential coupling, reorganization energy and curvature of the potential energy surfaces involved in electron transfer, independent of any prior assumptions about the system of interest. We showcase these claims with the Creutz–Taube ion, a prototypical Class III mixed valence complex. We find that the symmetric dimension is responsible for the asymmetric band shape, and trace this back to the offset of the ground and excited state potentials in this dimension. The significance of the symmetric dimension originates from geometry dependent coupling, which in turn is a natural consequence of the well‐established superexchange mechanism. The conceptual connection between the symmetric and anti‐symmetric motions and the superexchange mechanism appears as a general result for bridged systems.

Non-empirical description of nuclear collective motion with optimized basis for multi-reference density functional theory

The generator coordinate method (GCM) has been a well-known method to describe nuclear collective motions. In this method, one a priori specifies collective degrees of freedom as inputs of the method based on empirical and/or phenomenological assumptions. We here present an extension of the GCM, in which both the basis Slater determinants and weight factors are optimized in a non-empirical manner. The result for 16O nucleus with the Skyrme functional suggests that a collective coordinate should be determined in a more complex way than what has been assumed so far.

Generator coordinate method for nuclear octupole excitations: Status and perspectives

Strong octupole correlations have been observed in the low-lying states of atomic nuclei across various mass regions. In this paper, we provide an overview of Beyond Mean-Field (BMF) studies of nuclear octupole collective motions with Generator Coordinate Method (GCM) in combination with quantum-number projections that are implemented to restore the broken symmetries in nuclear mean-field states. We highlight recent developments within this framework and their applications to excitation spectra and electromagnetic transition rates in octupole-shaped nuclei and hypernuclei. We discuss the novel phenomena of nucleon clustering in light nuclei. Additionally, we explore the phase transition from octupole vibrations to rotational motions as spin increases in heavy nuclei. Lastly, we examine the status and future prospects of studies on octupole deformation effects in nuclear Schiff moments. These studies, along with the upper limits of atomic Electric Dipole Moment (EDM), impose stringent constraints on beyond-standard-model time-reversal-violating nucleon–nucleon interactions.

Simulation and test of the SLEGS TOF spectrometer at SSRF

The Shanghai laser electron gamma source (SLEGS) is a powerful tool for exploring photonuclear physics, such as giant dipole resonance (GDR) and pygmy dipole resonance, which are the main mechanisms of collective nuclear motion. The goal of the SLEGS neutron time-of-flight (TOF) spectrometer is to measure GDR and specific nuclear structures in the energy region above the neutron threshold. The SLEGS TOF spectrometer was designed to hold 20 sets of EJ301 and {hbox {LaBr}_{3}} detectors. Geant4 was used to simulate the efficiency of each detector and the entire spectrometer, which provides a reference for the selection of detectors and layout of the SLEGS TOF spectrometer. Under the events of ^{208}hbox {Pb}, implementations of coincidence and time-of-flight technology for complex experiments are available; thus, gamma and neutron decay events can be separated. The performance of SLEGS TOF spectrometer was systematically evaluated using offline experiments, in which the time resolution reached approximately 0.9 ns.

Collective response in light-matter interactions: The interplay between strong coupling and local dynamics.

A model designed to mimic the implications of the collective optical response of molecular ensembles in optical cavities on molecular vibronic dynamics is investigated. Strong molecule-radiation field coupling is often reached when a large number N of molecules respond collectively to the radiation field. In electronic strong coupling, molecular nuclear dynamics following polariton excitation reflects (a) the timescale separation between the fast electronic and photonic dynamics and the slow nuclear motion on one hand and (b) the interplay between the collective nature of the molecule-field coupling and the local nature of the molecules nuclear response on the other. The first implies that the electronic excitation takes place, in the spirit of the Born approximation, at an approximately fixed nuclear configuration. The second can be rephrased as the intriguing question of whether the collective nature of optical excitation leads to collective nuclear motion following polariton formation resulting in so-called polaron decoupled dynamics. We address this issue by studying the dynamical properties of a simplified Holstein-Tavis-Cummings-type model, in which boson modes representing molecular vibrations are replaced by two-level systems, while the boson frequency and the vibronic coupling are represented by the coupling between these levels (that induces Rabi oscillations between them) and electronic state dependence of this coupling. We investigate the short-time behavior of this model following polariton excitation as well as its response to CW driving and its density of states spectrum. We find that, while some aspects of the dynamical behavior appear to adhere to the polaron decoupling picture, the observed dynamics mostly reflect the local nature of the nuclear configuration of the electronic polariton rather than this picture.

Rotation of proton-neutron scissors-vibration state: A novel mode of nuclear collective motion

Rotation of proton-neutron scissors-vibration state: A novel mode of nuclear collective motion

Nuclear collective motion of heavy nuclei with axial quadrupole and octupole deformation

A quadrupole-octupole axially symmetric model is constructed for the unified description of alternate parity bands corresponding to octupole vibration or a stable deformation. The model depends on two parameters whose clear physical meaning allows a systematic description of the rotation-vibration dynamics of alternate parity bands analyzed for isotopic sequences of Ra, Th, U, and Pu nuclei. A critical point is identified in the $A=224--228$ mass region of the Ra and Th nuclei marking different stages of the transition between static and dynamic octupole deformation. Model predictions are performed for energies of unobserved states of the yrast sequence and of the excited bands as well as for the $E1, E2$, and $E3$ transition rates, which reproduce the available experimental data and exhibit a specific spin dependence for the transitional nuclei.

Time-dependent generator coordinate method study of fission: Dissipation effects

Starting from a quantum theory of dissipation for nuclear collective motion introduced by Kerman and Koonin [Phys. Scr. 10, 118 (1974)], the time-dependent generator coordinate method (TDGCM) is extended to allow for dissipation effects in the description of induced fission dynamics. The extension is based on a generalization of the GCM generating functions that includes excited states, and the resulting equation of motion in the collective coordinates and excitation energy. With the assumption of a narrow Hamiltonian kernel, an expansion in a power series in collective momenta leads to a Schr\"odinger-like equation that explicitly includes a dissipation term, proportional to the momentum of the statistical wave function. An illustrative calculation is performed for induced fission of $^{228}\mathrm{Th}$. The three-dimensional model space includes the axially symmetric quadrupole and octupole shape variables, and the nuclear temperature. When compared with data for photoinduced fission of $^{228}\mathrm{Th}$, the calculated fission yields demonstrate the important role of the additional term in the Hamiltonian that explicitly takes into account the dissipation of energy of collective motion into intrinsic degrees of freedom.

Evolution of collectivity and neutron-proton interactions

In this paper we study the correlation between the evolution of nuclear collective motion and neutron-proton interactions. We construct empirical neutron-proton interactions (denoted by ${V}_{\mathrm{NP}}$) for nuclei in the $(28<Z<50,$ $50<N<82)$, $(50<Z<82,$ $50<N<82$), and $(50<Z<82,$ $82<N<126)$ major shells. The ratios between ${V}_{\mathrm{NP}}$ and ${N}_{\mathrm{n}}{N}_{\mathrm{p}}$ (the product of valence proton number and valence neutron number) are found to be different for particle-particle, particle-hole, and hole-hole regions of the same major shell, suggesting different average strengths of neutron-proton interactions for these regions. Very interestingly, collective observables of even-even nuclei, e.g., ${2}^{+}$ and ${4}^{+}$ state energies, which follow different trajectories in the ${N}_{\mathrm{n}}{N}_{\mathrm{p}}$ scheme for particle-particle, particle-hole, and hole-hole regions, are found to form one unified and compact trajectory if those collective observables are plotted in terms of total neutron-proton interactions, ${V}_{\mathrm{NP}}$.

Theoretical description of fission yields: Toward a fast and efficient global model

Background: A quantitative microscopic understanding of the fission-fragment yield distributions represents a major challenge for nuclear theory as it involves the intricate competition between large-amplitude nuclear collective motion and single-particle nucleonic motion. Purpose: A recently proposed approach to global modeling of fission fragment distributions is extended to account for odd-even staggering in charge yields and for neutron evaporation. Method: Fission trajectories are obtained within the density functional theory framework, allowing for a microscopic determination of the most probable fission prefragment configurations. Mass and charge yields distributions are constructed by means of a statistical approach rooted in a microcanonical ensemble. Result: We show that the proposed hybrid model can reproduce experimental mass and charge fragment yields, including the odd-even staggering, for a wide range of fissioning nuclei. Experimental isotopic yields can be described within a simple neutron evaporation scheme. We also explore fission fragment distributions of exotic neutron-rich and superheavy systems, and compare our predictions with other state-of-the art global calculations. Conclusion: Our study suggests that the microscopic rearrangement of nucleons into fission fragments occurs well before the scission, and that the subsequent dynamics is mainly driven by the thermal excitations and bulk features of the nuclear binding. The proposed simple hybrid approach is well suited for large-scale calculations involving hundreds of fissioning nuclei.

Systematical studies of theE1photon strength functions combining the Skyrme-Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation model and experimental giant dipole resonance properties

Valuable theoretical predictions of nuclear dipole excitations in the whole nuclear chart are of great interest for different applications, including in particular nuclear astrophysics. We present here the systematic study of the electric-dipole $(E1)$ photon strength functions combining the microscopic Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation (HFB $+$ QRPA) model and the parametrizations constrained by the available experimental giant dipole resonance (GDR) data. For about 10 000 nuclei with $8\ensuremath{\le}\mathrm{Z}\ensuremath{\le}124$ lying between the proton and the neutron drip-lines on nuclear chart, the particle-hole (ph) strength distributions are computed using the HFB + QRPA model under the assumption of spherical symmetry and making use of the BSk27 Skyrme effective interaction derived from the most accurate HFB mass model (HFB-27) so far achieved. Large-scale calculations of the BSk27 + QRPA $E1$ photon strength functions are performed in the framework of a specific folding procedure describing the damping of nuclear collective motion empirically. In particular, three phenomenological improvements are considered in this folding procedure. First, two interference factors are introduced and adjusted to reproduce at best the available experimental GDR data. Second, an empirical expression accounting for the deformation effect is applied to describe the peak splitting of the strength function. Third, the width of the strength function is corrected by a temperature-dependent term, which effectively increases the deexcitation photon strength function at low energy. The theoretical $E1$ photon strength functions as well as the extracted GDR peaks and widths are comprehensively compared with available experimental data. A relatively good agreement with data indicates the reliability of the present calculations. Eventually, the astrophysical rates of $(n,\ensuremath{\gamma})$ reactions for all the 10 000 nuclei with $8\ensuremath{\le}Z\ensuremath{\le}124$ lying between the proton and the neutron drip lines are estimated using the present $E1$ photon strength functions. The resulting reaction rates are compared with the previous BSk7 + QRPA results as well as the Gogny-HFB + QRPA predictions based on the D1M interaction.

Finite-amplitude method for collective inertia in spontaneous fission

Background: Microscopic description of spontaneous fission is one of the most challenging subjects in nuclear physics. It is necessary to evaluate the collective potential and the collective inertia along a fission path for a description of quantum tunneling in spontaneous or low-energy fission. In past studies of the fission dynamics based on nuclear energy density functional (EDF) theory, the collective inertia has been evaluated with the cranking approximation, which neglects dynamical residual effects. Purpose: The purpose is to provide a reliable and efficient method to include dynamical residual effects in the collective inertia for fission dynamics. Methods: We use the local quasiparticle random-phase approximation (LQRPA) to evaluate the collective inertia along a fission path obtained by the constrained Hartree-Fock-Bogoliubov method with the Skyrme EDF. The finite-amplitude method (FAM) with a contour integration technique enables us to efficiently compute the collective inertia in a large model space. Results: We evaluate the FAM-QRPA collective inertia along a symmetric fission path in $^{240}$Pu and $^{256}$Fm. The FAM-QRPA inertia is significantly larger than the one of the cranking approximation, and shows pronounced peaks around the ground state and the fission isomer. This is due to dynamical residual effects. Conclusions: To describe the spontaneous or low-energy fission, we provide a reliable and efficient method to construct the collective inertia with dynamical residual effects that have been neglected in most of EDF-based works in the past. We show the importance of dynamical residual effects to the collective inertia. This work will be a starting point for a systematic study of fission dynamics in heavy and superheavy nuclei to microscopically describe the nuclear large-amplitude collective motions.

Anthony Milner Lane. 27 July 1928—9 February 2011

Tony Lane came from humble beginnings to become one of the world's leading theoretical nuclear physicists. His career in the Theoretical Physics Division at the Atomic Energy Research Establishment (AERE) at Harwell was characterized by his outstanding successes in explaining experimental nuclear data. He pioneered the understanding of the important nucleon capture reactions by introducing new mechanisms of direct and semi-direct capture and, together with colleagues, he greatly advanced knowledge of nuclear analogue states, and the role of isospin in nuclear physics. With R. G. Thomas, he wrote a comprehensive review of R-matrix theory, applied to analyse resonances in nuclear reactions, which became one of the most cited papers in physics. His book Nuclear theory gave a good account of the use of pairing force theory in nuclear physics, and its application to nuclear collective motion.

SUSYQM in nuclear structure: Bohr Hamiltonian with mass depending on the deformation

A well known problem of the Bohr Hamiltonian for the description of nuclear collective motion is that the nuclear moment of inertia increases with deformation too fast. We show that this can be avoided by allowing the nuclear mass to depend on the deformation. The resulting Hamiltonian is solved exactly, using techniques of Supersymmetric Quantum Mechanics

Molecular Vibrational Frequencies with Multiple Quantum Protons within the Nuclear-Electronic Orbital Framework.

The nuclear-electronic orbital (NEO) approach treats all electrons and specified nuclei, typically protons, on the same quantum mechanical level. Proton vibrational excitations can be calculated using multicomponent time-dependent density functional theory (NEO-TDDFT) for fixed classical nuclei. Recently the NEO-DFT(V) approach was developed to enable the calculation of molecular vibrational frequencies for modes composed of both classical and quantum nuclei. This approach uses input from NEO-TDDFT to construct an extended NEO Hessian that depends on the expectation values of the quantum protons as well as the classical nuclear coordinates. Herein strategies are devised for extending these approaches to molecules with multiple quantum protons in a self-contained, effective, and computationally practical manner. The NEO-TDDFT method is shown to describe vibrational excitations corresponding to collective nuclear motions, such as linear combinations of proton vibrational excitations. The NEO-DFT(V) approach is shown to incorporate the most significant anharmonic effects in the molecular vibrations, particularly for the hydrogen stretching modes. These theoretical strategies pave the way for a wide range of multicomponent quantum chemistry applications.

New approach to the adiabaticity concepts in the collective nuclear motion: Impact for the collective-inertia tensor and comparisons with experiment

We propose a new derivation of the cranking-model expression for the nuclear collective inertia tensor, introducing explicitly the slow- and fast-motion timescales together with a parameter controlling the interplay between the two modes. The new cranking formula is free from the mass tensor divergencies originating from the nucleon-level crossings in the denominators of the first-order perturbation theory expressions and allows the exploration of the unrestricted deformation space without spurious mass tensor contributions caused by those divergencies. We apply the new formalism without extra parameter adjustments to the collective vibrations in $^{208}\mathrm{Pb}$.

The Nuclear Spin Scissors Mode --- Theory and Experiment

A new type of nuclear collective motion—the spin scissors mode—was predicted seven years ago. Promising signs of its existence in 232Th were found. We perform a systematic analysis of experimental data on M1 excitations in rare earth nuclei to find traces of the spin scissors mode in this area. Obvious signs of its existence will be demonstrated. We propose new criteria to attribute the observed 1+ states to the scissors mode, entailing that the agreement of the experimental data with the results of our calculations and with the sum rules is improved substantially.

Heavy nuclei: Introduction to density functional theory and variations on the theme⋆

Density Functional Theory (DFT) is based on the rigorous Hohenberg-Kohn (HK) theorem, that has been first introduced for electronic systems but holds for all fermionic systems including atomic nuclei. Currently, DFT has reached a high level of sophistication, and represents a suitable tool for a self-consistent, quantitative description of bulk nuclear properties (like masses, radii and deformations) of all nuclei except, perhaps, the lightest ones. Furthermore, time-dependent calculations within the same framework account for the observed properties of several different types of nuclear collective motion. In this paper, we introduce these topics by assuming only a previous knowledge of general quantum mechanics and of basic nuclear phenomenology (we actually review some parts of it).

The Nuclear Spin Scissors Mode—Theory and Experiment

A new type of nuclear collective motion—the spin scissors mode—was predicted seven years ago. Promising signs of its existence in 232Th were found. We perform a systematic analysis of experimental data on M1 excitations in rare earth nuclei to find traces of the spin scissors mode in this area. Obvious signs of its existence will be demonstrated. We propose new criteria to attribute the observed 1+ states to the scissors mode, entailing that the agreement of the experimental data with the results of our calculations and with the sum rules is improved substantially.