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K. Hagino

Publications and source records attributed to K. Hagino.

At least 37 records · Page 2Linked to original sources
arXiv2024

Microscopic derivation of transition-state theory for complex quantum systems

The decay of quantum complex systems through a potential barrier is often described with transition-state theory, also known as RRKM theory in chemistry. Here we derive the basic formula for transition-state theory based on a generic Hamiltonian as might be constructed in a configuration-interaction basis. Two reservoirs of random Hamiltonians from Gaussian orthogonal ensembles are coupled to intermediate states representing the transition states at a barrier. Under the condition that the decay of the reservoirs to open channels is large, an analytic formula for reaction rates is derived. The transition states act as independent Breit-Wigner resonances which contribute additively to the total transition probability, as is well known for electronic conductance through resonant tunneling states. It is also found that the transition probability is independent of the decay properties of the states in the second reservoir over a wide range of decay widths.

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arXiv2024

Barrier penetration in a discrete basis formalism

A standard way to solve a Schrödinger equation is to discreteize the radial coordinates and apply a numerical method for a differential equation, such as the Runge-Kutta method or the Numerov method. Here I employ a discrete basis formalism based on a finite mesh method as a simpler alternative, with which the numerical computation can be easily implemented by ordinary linear algebra operations. I compare the numerical convergence of the Numerov integration method to the finite mesh method for calculating penetrabilities of a one-dimensional potential barrier, and show that the latter approach has better convergence properties.

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arXiv2024

Barrier penetration in a discrete-basis formalism

The dynamics of a many-particle system are often modeled by mapping the Hamiltonian onto a Schrödinger equation. An alternative approach is to solve the Hamiltonian equations directly in a model space of many-body configurations. In a previous paper the numerical convergence of the two approaches was compared with a simplified treatment of the Hamiltonian representation. Here we extend the comparison to the nonorthogonal model spaces that would be obtained by the generator-coordinate method. With a suitable choice of the collective-variable grid, a configuration-interaction Hamiltonian can reproduce the Schrödinger dynamics very well. However, the method as implemented here requires that the barrier height is not much larger than the zero-point energy in the collective coordinates of the configurations.

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arXiv2023

Non-empirical shape dynamics of heavy nuclei with multi-task deep learning

A microscopic description of nuclear fission represents one of the most challenging problems in nuclear theory. While phenomenological coordinates, such as multipole moments, have often been employed to describe fission, it is not obvious whether these parameters fully reflect the shape dynamics of interest. We here propose a novel method to extract collective coordinates, which are free from phenomenology, based on multi-task deep learning in conjunction with a density functional theory (DFT). To this end, we first introduce randomly generated external fields to a Skyrme-EDF and construct a set of nuclear number densities and binding energies for deformed states of ${}^{236}$U around the ground state. By training a neural network on such dataset with a combination of an autoencoder and supervised learning, we successfully identify a two-dimensional latent variables that accurately reproduce both the energies and the densities of the original Skyrme-EDF calculations, within a mean absolute error of 113 keV for the energies. In contrast, when multipole moments are used as latent variables for training in constructing the decoders, we find that the training data for the binding energies are reproduced only within 2 MeV. This implies that conventional multipole moments do not provide fully adequate variables for a shape dynamics of heavy nuclei.

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arXiv2023

Visualizing quantum coherence and decoherence in nuclear reactions

Differential cross sections of nuclear reactions often exhibit characteristic oscillations in the angular distribution originated from an interference of two indistinguishable processes. Here we propose a novel method to visualize origins of such oscillations. This is achieved by taking Fourier transform of scattering amplitudes, following the idea in wave optics. We apply this method to elastic scattering of $^{16}$O+$^{16}$O and $^{18}$O+$^{18}$O at energies above the Coulomb barrier. The former system shows strong oscillations in the angular distribution due to the nearside-farside interferences, while the oscillations are largely suppressed in the latter system due to a stronger absorption. We show that the image of the former and the latter systems corresponds to a double-slit and a single-slit problems in quantum mechanics, respectively.

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arXiv2023

Schematic model for induced fission in a configuration-interaction approach

We model fission at barrier-top energies in a simplified model space that permits comparison of different components of the residual nucleon-nucleon interaction. The model space is built on particle-hole excitations of reference configurations. These are Slater determinants of uniformly spaced orbitals characterized only by their quantum numbers and orbital energies. The residual interaction in the Hamiltonian includes the diabatic interaction connecting similar orbitals at different deformations, the pairing interaction between like nucleons, and a schematic off-diagonal neutron-proton interaction. We find that the fission reaction probability is sensitive to the off-diagonal neutron-proton interaction much more than to the pairing and the diabatic interactions. In particular, the transmission coefficients become insensitive to th e strength of the pairing interaction when the neutron-proton interaction is large. We also find that the branching ratio is insensitive to the final-state scission dynamics, as is assumed in the well-known Bohr-Wheeler theory.

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arXiv2023

Analysis of a Skyrme energy density functional with deep learning

Over the past decade, machine learning has been successfully applied in various fields of science. In this study, we employ a deep learning method to analyze a Skyrme energy density functional (Skyrme-EDF), that is a Kohn-Sham type functional commonly used in nuclear physics. Our goal is to construct an orbital-free functional that reproduces the results of the Skyrme-EDF. To this end, we first compute energies and densities of a nucleus with the Skyrme Kohn-Sham + Bardeen-Cooper-Schrieffer method by introducing a set of external fields. Those are then used as training data for deep learning to construct a functional which depends only on the density distribution. Applying this scheme to the $^{24}$Mg nucleus with two distinct random external fields, we successfully obtain a new functional which reproduces the binding energy of the original Skyrme-EDF with an accuracy of about 0.04 MeV. The rate at which the neural network outputs the energy for a given density is about $10^5$--$10^6$ times faster than the Kohn-Sham scheme, demonstrating a promising potential for applications to heavy and superheavy nuclei, including the dynamics of fission.

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arXiv2023

Precise determination of quadrupole and hexadecapole deformation parameters of the $sd$-shell nucleus, $^{28}$Si

Quasi-elastic (QEL) scattering measurements have been performed using $^{28}$Si projectile off a $^{90}$Zr target at energies around the Coulomb barrier. A Bayesian analysis within the framework of coupled channels (CC) calculations is performed in a large parameter space of quadrupole and hexadecapole deformations ($β_{2}$ and $β_{4}$) of $^{28}$Si. Our results clearly show that $^{28}$Si is an oblate shaped nucleus with $β_{2}$=-$0.38 \pm 0.01$ which is in excellent agreement with electromagnetic probes. A precise value of hexadecapole deformation for $^{28}$Si, $β_{4}$=+$0.03 \pm 0.01$, along with a consistent value of quadrupole deformation has now been determined for the first time using QEL scattering. A remarkable agreement between the experimental $β_{4}$ value of $^{28}$Si and Skyrme-Hartree-Fock based calculations is obtained. The QEL results obtained previously for $^{24}$Mg (prolate) and the present result for $^{28}$Si (oblate) hereby affirm the strong sensitivity of the quasi-elastic scattering to ground state deformations, thus reinforcing its suitability as a potential probe for rare exotic nuclei.

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arXiv2023

Modeling barrier-top fission dynamics in a discrete-basis formalism

A configuration-interaction model is presented for the barrier region of induced fission. The configuration space is composed of seniority-zero configurations constructed from self-consistent mean-field wave functions. The Hamiltonian matrix elements between configurations include diabatic and pairing interactions between particles. Other aspects of the Hamiltonian are treated statistically, guided by phenomenological input of compound-nucleus transmission coefficients. In this exploratory study the configuration space is restricted to neutron excitations only. A key observable calculated in the model is the fission-to-capture branching ratio. We find that both pairing and diabatic interactions are important for achieving large branching to the fission channels. In accordance with the transition-state theory of fission, the calculated branching ratio is found to be quite insensitive to the fission decay widths of the pre-scission configurations. However, the barrier-top dynamics appear to be quite different from transition-state theory in that the transport is distributed over many excited configurations at the barrier top.

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arXiv2022

Spatial correlation of a particle-hole pair with a repulsive isovector interaction

We study the spatial correlation of a particle-hole pair in the isovector channel in $^{56}$Co and $^{40}$K nuclei. To this end, we employ the Hartree-Fock+Tamm-Dancoff approximation with the Skyrme interaction. We find a large concentration of the two-body density at positions where the neutron particle and the proton hole states locate on the opposite side to each other with respect to the core nucleus. This feature originates from a repulsive nature of the isovector residual interaction, which is in stark contrast to the dineutron correlation with an attractive pairing interaction between the valence neutrons discussed e.g., in $^{11}$Li and $^6$He. A possible experimental implication of the repulsive correlation is also discussed.

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arXiv2022

Applications of the dynamical generator coordinate method to quadrupole excitations

We apply the dynamical generator coordinate method (DGCM) with a conjugate momentum to a nuclear collective excitation. To this end, we first discuss how to construct a numerically workable scheme of the DGCM for a general one-body operator. We then apply the DGCM to the quadrupole vibration of $^{16}$O using the Gogny D1S interaction. We show that both the ground state energy and the excitation energies are lowered as compared to the conventional GCM with the same number of basis functions. We also compute the sum rule values for the quadrupole and monopole operators, and show that the DGCM yields more consistent results than the conventional GCM to the values from the double commutator. These results imply that the conjugate momentum is an important and relevant degree of freedom in collective motions.

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arXiv2022

Diabatic Hamiltonian matrix elements made simple

With a view to applying the Generator Coordinate Method to large configuration spaces, we propose a simple approximate formula to compute diabatic many-body matrix elements without having to evaluate two-body interaction matrix elements. The method is illustrated with two analytically solvable Hamiltonians based on the harmonic oscillator.

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arXiv2022

Coupled-channels calculations for nuclear reactions: from exotic nuclei to superheavy elements

Atomic nuclei are composite systems, and they may be dynamically excited during nuclear reactions. Such excitations are not only relevant to inelastic scattering but they also affect other reaction processes such as elastic scattering and fusion. The coupled-channels approach is a framework which can describe these reaction processes in a unified manner. It expands the total wave function of the system in terms of the ground and excited states of the colliding nuclei, and solves the coupled Shrödinger equations to obtain the $S$-matrix, from which several cross sections can be constructed. This approach has been a standard tool to analyze experimental data for nuclear reactions. In this paper, we review the present status and the recent developments of the coupled-channels approach. This includes the microscopic coupled-channels method and its application to cluster physics, the continuum discretized coupled-channels (CDCC) method for breakup reactions, the semi-microscopic approach to heavy-ion subbarrier fusion reactions, the channel coupling effects on nuclear astrophysics and syntheses of superheavy elements, and inclusive breakup and incomplete fusion reactions of weakly-bound nuclei.

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arXiv2022

Microscopic description of cluster decays based on the generator coordinate method

\noindent\textbf{Background:} While many phenomenological models for nuclear fission have been developed, a microscopic understanding of fission has remained one of the most challenging problems in nuclear physics. \noindent\textbf{Purpose:} We investigate an applicability of the generator coordinate method (GCM) as a microscopic theory for cluster radioactivities of heavy nuclei, which can be regarded as a fission with large mass asymmetry, that is, a phenomenon in between fission and $α$-decays. \noindent\textbf{Methods:} Based on the Gamow theory, we evaluate the preformation probability of a cluster with GCM while the penetrability of the Coulomb barrier is estimated with a potential model. To this end, we employ Skyrme interactions and solve the one-dimensional Hill-Wheeler equation with the mass octupole field. We also take into account the dynamical effects of the pairing correlation using BCS wavefunctions constructed with an increased strength of the pairing interaction. \noindent\textbf{Results:} We apply this scheme to the cluster decay of $^{222}$Ra, i.e., $^{222}$Ra$\to^{14}$C+$^{208}$Pb, to show that the experimental decay rate can be reproduced within about two order of magnitude. We also briefly discuss the cluster radioactivities of the $^{228}$Th and $^{232}$U nuclei. For these actinide nuclei, we find that the present calculations reproduce the decay rates with the same order of magnitude and within two or three order of magnitude, respectively. \noindent\textbf{Conclusions:} The method presented in this paper provides a promising way to describe microscopically cluster decays of heavy nuclei.

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arXiv2022

Generator coordinate method for transition-state dynamics in nuclear fission

Since its beginnings, fission theory has asumed that low-energy induced fission takes place through transition-state channels at the barrier tops. Neverthess, up to now there is no microscopic theory applicable to those conditions. We suggest that modern reaction theory is suitable for this purpose, and propose a methodology based on a configuration-interaction framework using the Generator Coordinate Method (GCM). Simple reaction-theoretic models are constructed with the Gaussian Overlap Approximation (GOA) to parameterize both the dynamics within the channels and their incoherent couplings to states outside the barrier. The physical characteristics of the channels examined here are their effective bandwidths and the quality of the coupling to compound-nucleus states as measured by the transmission factor $T$. We also investigate the spacing of GCM states with respect to their degree of overlap. We find that a rather coarse mesh provides an acceptable accuracy for estimating the bandwidths and transmission factors. The common numerical stability problem in using the GCM is avoided due to the choice of meshes and the finite bandwidths of the channels. The bandwidths of the channels are largely controlled by the zero-point energy with respect to the collective coordinate in the GCM configurations.

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arXiv2022

Sub-barrier fusion reactions

The concept of compound nucleus was proposed by Niels Bohr in 1936 to explain narrow resonances observed in scattering of a slow neutron off atomic nuclei. A compound nucleus is a metastable state with a long lifetime, in which all the degrees of freedom are in a sort of thermal equilibrium. Fusion reactions are defined as reactions to form such compound nucleus by merging two atomic nuclei. Here a short description of heavy-ion fusion reactions at energies close the Coulomb barrier is presented. This includes: (i) an overview of a fusion process, (ii) a strong interplay between nuclear structure and fusion, (iii) fusion and multi-dimensional/multi-particle quantum tunneling, and (iv) fusion for superheavy elements.

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arXiv2021

Porter-Thomas fluctuations in complex quantum systems

The Gaussian Orthogonal Ensemble (GOE) of random matrices has been widely employed to describe diverse phenomena in strongly coupled quantum systems. An important prediction is that the decay rates of the GOE eigenstates fluctuate according to the distribution for one degree of freedom, as derived by Brink and by Porter and Thomas. However, we find that the coupling to the decay channels can change the effective number of degrees of freedom from $ν= 1$ to $ν= 2$. Our conclusions are based on a configuration-interaction Hamiltonian originally constructed to test the validity of transition-state theory, also known as Rice-Ramsperger-Kassel-Marcus (RRKM) theory in chemistry. The internal Hamiltonian consists of two sets of GOE reservoirs connected by an internal channel. We find that the effective number of degrees of freedom $ν$ can vary from one to two depending on the control parameter $ρΓ$, where $ρ$ is the level density in the first reservoir and $Γ$ is the level decay width. The $ν= 2$ distribution is a well-known property of the Gaussian Unitary ensemble (GUE); our model demonstrates that the GUE fluctuations can be present under much milder conditions. Our treatment of the model permits an analytic derivation for $ρΓ\gtrsim 1$.

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