arXiv subjects

K. Uzawa

Publications and source records attributed to K. Uzawa.

13 recordsLinked to original sources

arXiv2026

Microscopic description of $^{12}$C+$^{12,13}$C fusion reactions at nuclear astrophysical energies

The $^{12}$C + $^{12}$C fusion reaction plays a key role in several astrophysical phenomena. However, it is difficult to determine its cross sections in the relevant energy region because of both low cross sections and strong resonant structures. On the other hand, the $^{12}$C + $^{13}$C system shows a much smoother energy dependence of fusion cross sections. To simultaneously analyze the $^{12}$C + $^{12,13}$C systems, we here develop a reaction model that explicitly treats the entrance channel and the compound nucleus states. For this purpose, we combine the discrete basis model for the entrance channel and the shell model for the compound nuclei. The coupling strengths between the entrance channel and the compound nucleus states are determined so that the fusion cross sections for these systems match with each other at the resonance energies for the $^{12}$C + $^{12}$C system, as has been observed experimentally. The model successfully reproduces the significantly different behaviors of fusion cross sections in these systems.

nucl-th↗

arXiv2026

A microscopic analysis of sub-barrier photo-induced fission in $^{236}$U$(\gamma,f)$ based on the non-equilibrium Green function method

Sub-barrier photo-induced fission in $^{236}$U$(\gamma,f)$ is investigated within the non-equilibrium Green function (NEGF) method. A model space for the fission process is constructed by superposing Skyrme-Hartree-Fock wave functions along the fission path allowing the particle-hole excitation. Then, the transition from the photo-absorption channel to the fission channel is described by the non-equilibrium Green-function formalism. The calculated fission cross section in the incident gamma-ray energy range $5 ~ {\rm MeV} \leq E_\gamma \leq 6 ~ {\rm MeV}$ reproduces the overall behavior of the experimental data, including the suppression below the fission barrier. An eigenchannel analysis of the wave propagation in the present fission model space is also performed, and the first eigenchannel is found to dominate the fission probability. This result supports the Bohr-Wheeler transition-state picture from a microscopic viewpoint.

nucl-th↗

arXiv2025

Determination of nuclear deformations with an emulator for sub-barrier fusion reactions

Based on the eigenvector continuation, which is mathematically an instance of the reduced basis method (RBM), we construct an emulator for coupled-channels calculations for heavy-ion fusion reactions at energies around the Coulomb barrier. We apply this to the $^{16}$O+$^{144,154}$Sm, $^{186}$W reactions and examine whether the emulator can be used to extract the deformation parameters of the target nuclei. We show that the emulator not only accelerates the calculations but also has an ability to accurately extract the nuclear shapes. This indicates that the emulator provides a powerful tool to systematically explore intrinsic shapes of atomic nuclei, enhancing our understanding of the fundamental properties of nuclear systems.

nucl-th↗

arXiv2025

Emulating multi-channel scattering based on the eigenvector continuation in the discrete basis formalism

We construct an emulator for a multi-channel scattering problem based on the eigenvector continuation. To this end, we employ the Kohn variational principle formulated in the discrete basis formalism. We apply this to one-dimensional scattering problems with a Gaussian barrier. Both for a single-channel and two-channel problems, we demonstrate that the penetration probability as well as the wave functions are well reproduced by the emulator. In particular, the energy dependence of the penetrability in a wider range of energy from well below the barrier to well above the barrier is successfully reproduced.

nucl-th↗

arXiv2025

A microscopic calculation of fission cross sections with the non-equilibrium Green function method

We apply the non-equilibrium Green function (NEGF) method to microscopically evaluate fission cross sections for the neutron induced $^{235}$U$(n,f)$ reaction. While the model space was restricted only to seniority zero configurations in the previous applications of the NEGF method, we remove this restriction and include seniority non-zero configurations as well. In such model space, a proton-neutron interaction is active, for which we introduce a random interaction. We find that the seniority non-zero configurations significantly increase the fission cross sections, and thus the fission-to-capture branching ratios, even though they are still underestimated by about one order of magnitude as compared to the experimental data. In addition, we also find that the fission dynamics is governed by only a small number of eigenstates of the model Hamiltonian.

nucl-th↗

arXiv2024

Application of the shift-invert Lanczos algorithm to a non-equilibrium Green function for transport problems

Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method can dramatically reduce the computational effort. We apply the method to two test problems, namely a simple model Hamiltonian and to a more realistic Hamiltonian for nuclear fission. For a Hamiltonian of dimension 66103 we find that the computation time is reduced by a factor of 33 compared to the direct calculation of the Green's function.

nucl-th↗

arXiv2024

Non-equilibrium Green's function approach to low-energy fission dynamics: fluctuations in fission reactions

We present a microscopic modeling for a decay of a heavy compound nucleus, starting from a nucleonic degree of freedom. To this end, we develop an approach based on a non-equilibrium Green's function, which is combined with a configuration interaction (CI) approach based on a constrained density-functional theory (DFT). We apply this approach to a barrier-top fission of $^{236}$U, restricting the model space to seniority zero configurations of neutrons and protons. We particularly focus on the distribution of the fission probability. We find that it approximately follows the chi-squared distribution with the number of degrees of freedom $ν$ of the order of 1, which is consistent with the experimental finding. We also show that $ν$ corresponds to the number of eigenstates of the many-body Hamiltonian whose energy is close to the excitation energy of the system and at the same time which have significant components on both sides of a fission barrier.

nucl-th↗

arXiv2024

Generator coordinate method with proton--neutron pairing fluctuations and magnetic properties of $N=Z$ odd--odd nuclei

Pairing correlations play an important role in a variety of nuclear phenomena. However, a quantitative understanding of proton--neutron $(pn)$ pairing, especially isoscalar $pn$ pairing $(S=1, T=0)$ remains elusive. To clarify the property of $pn$ pairing, we investigate the roles of $pn$ pairing in the $M1$ transition of $N=Z$ odd--odd nuclei. We develop a theoretical model based on the generator coordinate method (GCM) in which the isoscalar and isovector $pn$-pair amplitudes are used as the generator coordinates. Using the particle and the angular-momentum projections, the $pn$-pair GCM well reproduces the $M1$ transition of odd--odd nuclei for the exactly solvable SO(8) model. We apply the method to $N=Z$ odd--odd nuclei and find that the experimental values of $B(M1)$ are well reproduced. We also study the sensitivity of $B(M1)$ to the strength of the isoscalar pairing interaction.

nucl-th↗

arXiv2024

Microscopic description of induced fission in a configuration interaction approach

Even though more than 80 years have passed since the discovery of fission, its microscopic understanding has still been unclear. To clarify the underlying mechanics of induced fission, we analyze the distribution of a fission width using a miscropic framework based on a configuration-interaction approach. The distribution is known to follow a chi-squared distribution, which is characterized by the effective number of decay channels, $ν$. We introduce an effective Hamitonian for the space of compound nucleus states and estimate $ν$ from the rank of the imaginary part of the effective Hamiltonian. Applying the model to $^{235}$U(n,f), we succesfully reproduce the empirical value of $ν=2.3\pm1.1$. We also find that $ν$ is insensitve to the number of fission channels, which is consistent with an experimental finding.

nucl-th↗

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.

nucl-th↗

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.

nucl-th↗

arXiv2021

Role of triaxiality in deformed halo nuclei

It is known that nuclear deformation plays an important role in inducing the halo structure in neutron-rich nuclei by mixing several angular momentum components. While previous theoretical studies on this problem in the literature assume axially symmetric deformation, we here consider non-axially symmetric deformations. With triaxial deformation, the $Ω$ quantum number is admixed in a single-particle wave function, where $Ω$ is the projection of the single-particle angular momentum on the symmetric axis, and the halo structure may arise even when it is absent with the axially symmetric deformation. In this way, the area of halo nuclei may be extended when triaxial deformation is considered. We demonstrate this idea using a deformed Woods-Saxon potential for nuclei with neutron number N=13 and 43.

nucl-th↗

arXiv2000

Self-Tuning Dark Energy in Brane World Cosmology

Recently, the self-tuning mechanism of cancellation of vacuum energy has been proposed in which our universe is a flat 3-brane in a 5-dimensional spacetime. In this letter, the self-tuning mechanism of dark energy is proposed by considering the cosmological matter in the brane world. In our model, the bulk scalar field takes the role of the dark energy and its value is slowly varying in time. The claim is that even if the enormous amount of vacuum energy exists on the brane we can adjust the present value of the dark energy to be consistent with the current observations. In this self-tuning mechanism, the existence of the constant of integration associated with the bulk scalar is crucial.

hep-th↗