arXiv subjects

J. Terasaki

Publications and source records attributed to J. Terasaki.

At least 19 recordsLinked to original sources

arXiv2025

Solution to the uncertainty problem of nuclear matrix element for neutrinoless double-$\beta$ decay

The neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) of nuclei is one of the major research subjects of neutrino physics nowadays because of its influence on particle physics and astrophysics. The predicted nuclear matrix elements (NMEs) for the $0\nu\beta\beta$ decay exhibit large uncertainties depending on the models employed. This problem has affected the development of neutrino physics for many years. We have recently performed the calculation of the NMEs for the $0\nu\beta\beta$ and two-neutrino double-$\beta$ decay ($2\nu\beta\beta$) modes with a perturbed transition operator and found that the effective axial-vector current coupling $g_A^\mathrm{eff}$ is similar for the two decay modes. Based on this finding, we calculate the $0\nu\beta\beta$ NMEs using the phenomenological $g_A^\mathrm{eff}$ that reproduces the measured half-life of the $2\nu\beta\beta$ decay. We apply this method to the NMEs for $^{136}$Xe, $^{130}$Te, and $^{76}$Ge obtained by several groups and show that the uncertainty of the $0\nu\beta\beta$ NME is dramatically reduced. Based on this result, we calculate the effective neutrino mass, consistent with the current experimental lower limit of the half-life for the $0\nu\beta\beta$ decay. The results indicate that the extracted value of the effective neutrino mass does not yet reach the inverted-mass-hierarchy region allowed by neutrino oscillation data when the lightest neutrino mass is assumed to be below 10 meV. We also calculate the perturbed $0\nu\beta\beta$ and $2\nu\beta\beta$ NMEs of $^{110}$Pd.

nucl-th↗

arXiv2025

Half-life of $^{136}$Xe for neutrinoless double-$β$ decay calculated with effective axial-vector current coupling unified for two-neurtino and neutrinoless double-$β$ decay modes

The upper limit on the mass of the Majorana neutrino, extracted from the limits on the nonobservation of the neutrinoless double-$β$ ($0νββ$) decay, is hampered by uncertainties in the matrix elements of the transition operators. Recently, we have shown that the values of the effective axial-vector current coupling constants ($g_A^\textrm{eff}$) for the $0νββ$ and the two-neutrino double-$β$ decays are close. This striking result was obtained for the first time by including vertex corrections and two-body currents in these matrix elements. In this letter, we calculate the half-life for the $0νββ$ decay ($T_{1/2}^{0ν}$) of $^{136}$Xe using this closeness and show the convergence of the half-life with respect to the variation of the method to determine $g_A^\textrm{eff}$. The closeness of the $g_A^\textrm{eff}$ of the two decay modes plays a decisive role in predicting $T_{1/2}^{0ν}$. The appropriate value of $g_A^\textrm{eff}$ depends on the assumptions made for the sectors of the nuclear structure and transition operators of the calculations within the perturbation scheme. The value $g_A^\textrm{eff}\approx 1$ is obtained when the SkM$^\ast$ is used to describe the nuclear structure component, while a smaller value of $g_A^\textrm{eff}$ is obtained by applying a less realistic interaction like the SGII one.

nucl-th↗

arXiv2025

Effects of perturbation for transition operator of double-$β$ decay on nuclear matrix element, effective axial-vector current coupling, and half-life

We calculate the nuclear matrix element (NME), effective axial-vector current coupling $g_A^\mathrm{eff}$, and half-life of the double-$β$ ($ββ$) decay using the transition operator perturbed by the nuclear interaction. The correction terms for the NME are obtained by extending the hadron sector to a higher order in terms of the Rayleigh-Schrödinger perturbation theory. The NME calculations are performed for the neutrinoless $ββ$ ($0νββ$) and the two-neutrino $ββ$ ($2νββ$) decays of $^{136}$Xe. The nuclear wave functions are calculated by the quasiparticle random-phase approximation (QRPA) with the Skyrme, the Coulomb, and the contact pairing interactions. Sufficiently large single-particle valence spaces are used. The correction terms for the NME are comparable with the leading term in absolute value, and the sum of the corrections has the opposite sign to that of the leading term. The $g_A^\mathrm{eff}$'s for the $ββ$ NME are calculated by a few methods depending on the truncation of the NME and the half-life referred to. Similarities are found between some of these $g_A^\mathrm{eff}$'s including those of the $0νββ$ NME. This leads to the conclusion that the value of $g_A^\mathrm{eff}$ can indeed be determined by the perturbed transition operator. It is in a comparable range of the $g_A$ for the $2νββ$ NME. The perturbation effect on the $2νββ$ half-life is discussed by comparing the calculated half-lives with the different $g_A$'s and the NME components.

nucl-th↗

arXiv2023

Investigation of the cause of the discrepancies between calculated running sums for nuclear matrix elements of two-neutrino double-$β$ decay

A qualitative difference in the running sum for the nuclear matrix element of the two-neutrino double-$β$ decay of $^{136}$Xe was found four years ago between quasiparticle random-phase approximation (QRPA) and shell model calculations. The former result has large increase and decrease with respect to the excitation energy of the intermediate state, and the latter one is an almost monotonically and mildly increasing function. My QRPA calculations independently of the above one do not have a remarkable decrease. This discrepancy is a serious problem affecting the reliability of calculations of the neutrinoless double-$β$ decay, and the cause was unknown. I perform several relevant test calculations and make an analytical consideration to find the cause, which is found to be in the strength of the attractive interactions. The possible major local decrease in the running sum is also explained analytically. The interactions of my QRPA calculation are appropriate in terms of the strength, thus the almost monotonic behavior is reasonable.

nucl-th↗

arXiv2021

Estimation of nuclear matrix elements of double-$β$ decay from shell model and quasiparticle random-phase approximation

The nuclear matrix element (NME) of the neutrinoless double-$β$ ($0νββ$) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. The reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME depending on the calculation method. In this paper, we focus on the shell model and the QRPA. The shell model have a rich amount of the many-particle many-hole correlations, and the QRPA can obtain the convergence of the result of calculation with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the $0νββ$ NME with respect to the valence single-particle space. The many-body correlations of the QRPA are insufficient depending on nuclei. We propose a new method to modify phenomenologically the results of the shell model and the QRPA compensating the insufficient point of each method by using the information of other method complementarily. Extrapolations of the components of the $0νββ$ NME of the shell model are made toward a very large valence single-particle space. We introduce a modification factor to the components of the $0νββ$ NME of the QRPA. Our modification method gives similar values of the $0νββ$ NME of the two methods for $^{48}$Ca. The NME of the two-neutrino double-$β$ decay is also modified in a similar but simpler manner, and the consistency of the two methods is improved.

nucl-th↗

arXiv2020

Physical features of strength of isoscalar pairing interaction determined by relation between double charge change and double pair transfer

A new method has been proposed to determine the strength of the isoscalar proton-neutron pairing interaction applicable to many nuclei. The principle is the equivalence between the double charge change and the double transfer of like-particle pair, and a constraint is derived to the effective interactions used in approximations. This method was applied to the quasiparticle random-phase approximation for determining that interaction strength. In this paper, detail of this method is explained thoroughly, and applications are made to nuclei of several instances of the double-$β$ decays. The systematics of the strengths determined for those nuclei is understood in terms of a midshell effect. The effect of the new interaction strength is examined in two examples of the Gamow-Teller strength function with comparisons with the experimental data. The nuclear matrix elements of the neutrinoless double-$β$ decay are also calculated.

nucl-th↗

arXiv2019

Isoscalar pairing interaction for the quasiparticle random-phase approximation approach to double-$β$ and $β$ decays

We have proposed in a series of previous papers a method to determine the effective axial-vector current coupling and the strength of the isoscalar proton-neutron pairing interaction for calculating the nuclear matrix elements of the neutrinoless double-$β$ decay by the quasiparticle random-phase approximation. The combination of these two parameters have had an uncertainty in this approach, but now this uncertainty is removed. In this paper, we apply our method to the neutrinoless double-$β$ decays of $^{136}$Xe and $^{130}$Te and predict the nuclear matrix elements and reduced half-lives. Our calculation is tested first by a self-check method using the two-neutrino double-$β$ decay, and this test ensures the application of our method to $^{136}$Xe. It turns out, however, that our method is not successful in $^{130}$Te. Further test is made for our calculation of the $β$ decay of $^{138}$Xe, and a satisfactory result is obtained.

nucl-th↗

arXiv2019

Consistency Examinations of Calculations of Nuclear Matrix Elements of Double-$β$ Decay by QRPA

The neutrinoless double-$β$ decay is a hypothetical rare nuclear decay, which can be used for determining the neutrino-mass scale. The scheme to use this decay for determining the neutrino-mass scale is one of few limited methods possible to determine that. Nuclear matrix element of this decay is an important input to this method, and this matrix element cannot be determined by experiment. I examine the validity of the transition density used for calculating the nuclear matrix element by comparing the experimental data and my calculated result of the charge-change strength functions of $^{48}$Ca and $^{48}$Ti. The nuclear wave functions are obtained by the quasiparticle random-phase approximation. A new idea is proposed on the transition operator for this strength function, and the data of those nuclei are reproduced well consistently. Reduced half-life of a few nuclei to the neutrinoless double-$β$ decay are shown.

nucl-th↗

arXiv2019

Determination of Strength of Isoscalar Pairing Interaction by a Mathematical Identity in QRPA

I propose a new method to determine the strength of the isoscalar proton-neutron pairing interaction by a mathematical identity derived in the quasiparticle random-phase approximation. This method is applied for a few nuclei possibly having the neutrinoless double-$β$ decay. Reduced half-life, the theoretical quantity necessary for determining the effective neutrino mass, is calculated for $^{48}$Ca.

nucl-th↗

arXiv2018

Examinations of the consistency of the quasiparticle random-phase approximation approach to double-$β$ decay of $^{48}$Ca

The nuclear matrix elements (NMEs) of the neutrinoless and two-neutrino double-$β$ decays of $^{48}$Ca are calculated by the quasiparticle random-phase approximation (QRPA) with emphasis on the consistency examinations of this calculation method. The main new examination points are the consistency of two ways to treat the intermediate-state energies in the two-neutrino double-$β$ NME and comparison with the experimental charge-exchange strength functions obtained from $^{48}$Ca$(p,n)$ and $^{48}$Ti$(n,p)$ reactions. No decisive problem preventing the QRPA approach is found. The obtained neutrinoless double-$β$ NME adjusted by the ratio of the effective and bare axial-vector current couplings is lowest in those calculated by several groups and close to one of the QRPA values obtained by another group.

nucl-th↗

arXiv2017

Reproduction of exact solutions of Lipkin model by nonlinear random-phase approximation

It is shown that the random-phase approximation (RPA) method with its nonlinear generalization, which was previously considered as approximation, reproduces the exact solutions of the Lipkin model. The nonlinear RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number $N$ = 2 and, numerically, for $N$ = 20. This finding indicates that the nonlinear RPA is equivalent to the exact Schrödinger equation, which opens up new possibilities for realistic calculations in many-body problems.

nucl-th↗

arXiv2015

Many-body correlations of quasiparticle random-phase approximation in nuclear matrix element of neutrinoless double-beta decay

We show that the correlations of the quasiparticle random-phase approximation (QRPA) significantly reduce the nuclear matrix element (NME) of neutrinoless double-beta decay by a new mechanism in the calculation for $^{150}$Nd $\rightarrow$ $^{150}$Sm. This effect is due mainly to the normalization factors of the QRPA ground states included in the overlap of intermediate states, to which the QRPA states based on the initial and final ground states are applied. These normalization factors arise according to the definition of the QRPA ground state as the vacuum of quasibosons. Our NME is close to those of other groups in spite of this new reduction effect because we do not use the proton-neutron pairing interaction usually used for reproducing the experimental NME of the two-neutrino double-beta ($2νββ$) decay. Our method can repeoduce the experimental $2νββ$ NME for $^{150}$Nd $\rightarrow$ $^{150}$Sm with the quenching axial-vector current coupling without approacing the breaking point of the QRPA. The consistency of QRPA approaches taking different virtual paths under the closure approximation is also discussed, and an extension of the QRPA ground state is proposed.

nucl-th↗

arXiv2012

Overlap of QRPA states based on ground states of different nuclei --mathematical properties and test calculations--

The overlap of the excited states in quasiparticle random-phase approximation (QRPA) is calculated in order to simulate the overlap of the intermediate nuclear states of the double-beta decay. Our basic idea is to use the like-particle QRPA with the aid of the closure approximation and calculate the overlap as rigorously as possible by making use of the explicit equation of the QRPA ground state. The formulation is shown in detail, and the mathematical properties of the overlap matrix are investigated. Two test calculations are performed for relatively light nuclei with the Skyrme and volume delta-pairing energy functionals. The validity of the truncations used in the calculation is examined and confirmed.

nucl-th↗

arXiv2012

Overlap of quasiparticle random-phase approximation states for nuclear matrix elements of the neutrino-less double beta decay

Quasiparticle random-phase approximation (QRPA) is applied to two nuclei, and overlap of the QRPA excited states based on the different nuclei is calculated. The aim is to calculate the overlap of intermediate nuclear states of the double-beta decay. We use the like-particle QRPA after the closure approximation is applied to the nuclear matrix elements. The overlap is calculated rigorously by making use of the explicit equation of the QRPA ground state. The formulation of the overlap is shown, and a test calculation is performed. The effectiveness of the truncations used is shown.

nucl-th↗

arXiv2011

Towards a Microscopic Reaction Description Based on Energy-Density-Functional Structure Models

A microscopic calculation of reaction cross sections for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all particle-hole excitations in the target and one-nucleon pickup channels. The particle-hole states may be regarded as doorway states through which the flux flows to more complicated configurations, and subsequently to long-lived compound nucleus resonances. Target excitations for $^{40,48}$Ca, $^{58}$Ni, $^{90}$Zr and $^{144}$Sm were described in a random-phase framework using a Skyrme functional. Reaction cross sections obtained agree very well with experimental data and predictions of a state-of-the-art fitted optical potential. Couplings between inelastic states were found to be negligible, while the pickup channels contribute significantly. The effect of resonances from higher-order channels was assessed. Elastic angular distributions were also calculated within the same method, achieving good agreement with experimental data. For the first time observed absorptions are completely accounted for by explicit channel coupling, for incident energies between 10 and 70 MeV, with consistent angular distribution results.

nucl-th↗

arXiv2011

Testing Skyrme energy-density functionals with the QRPA in low-lying vibrational states of rare-earth nuclei

Although nuclear energy density functionals are determined primarily by fitting to ground state properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle random phase approximation (QRPA). Here we test the Skyrme functionals SkM* and SLy4 along with the self-consistent QRPA by calculating properties of low-lying vibrational states in a large number of well-deformed even-even rare-earth nuclei. We reproduce trends in energies and transition probabilities associated with gamma-vibrational states, but our results are not perfect and indicate the presences of multi-particle-hole correlations that are not included in the QRPA. The Skyrme functional SkM* performs noticeably better than SLy4. In a few nuclei, changes in the treatment of the pairing energy functional have a significant effect. The QRPA is less successful with "beta-vibrational" states than with the gamma-vibrational states.

nucl-th↗

arXiv2010

Coupled-channels calculations of nonelastic cross sections using a density-functional structure model

A microscopic calculation of the reaction cross-section for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all particle-hole (p-h) excitation states in the target and to all one-nucleon pickup channels. The p-h states may be regarded as doorway states through which the flux flows to more complicated configurations, and subsequently to long-lived compound nucleus resonances. Target excitations for 40,48Ca, 58Ni, 90Zr and 144Sm were described in a QRPA framework using a Skyrme functional. Reaction cross sections calculated in this approach were compared to predictions of a fitted optical potential and to experimental data, reaching very good agreement. Couplings between inelastic states were found to be negligible, while the couplings to pickup channels contribute significantly. For the first time observed reaction cross-sections are completely accounted for by explicit channel coupling, for incident energies between 10 and 40 MeV.

nucl-th↗

arXiv2010

Self-consistent Skyrme QRPA for use in axially-symmetric nuclei of arbitrary mass

We describe a new implementation of the quasiparticle random phase approximation (QRPA) in axially-symmetric deformed nuclei with Skyrme and volume-pairing energy-density functionals. After using a variety of tests to demonstrate the accuracy of the code in ^{24,26}Mg and ^{16}O, we report the first fully self-consistent application of the Skyrme QRPA to a heavy deformed nucleus, calculating strength distributions for several K^pi in ^{172}Yb. We present energy-weighted sums, properties of gamma-vibrational and low-energy K^pi=0^+ states, and the complete isovector E1 strength function. The QRPA calculation reproduces the properties of the low-lying 2^+ states as well or better than it typically does in spherical nuclei.

nucl-th↗