Searcharxiv⌕ Search

arXiv subjects

F. R. Xu

Publications and source records attributed to F. R. Xu.

At least 19 recordsLinked to original sources
arXiv2026

First \textit{ab initio} calculations of first-forbidden $\beta$ transitions in the reactor antineutrino anomaly

Forbidden $\beta$ transitions are important for understanding the reactor antineutrino anomaly. Starting from chiral two- plus three-nucleon forces, we have derived the valence-space effective Hamiltonian and effective operators of first-forbidden transitions using the many-body perturbation theory. 20 dominant first-forbidden transitions have been investigated, which provide important contributors to the reactor antineutrino spectrum anomaly. Calculated $\log ft$ values are in reasonable agreement with experimental data. Obtained shape factors exhibit significant deviations from the values approximated with forbidden transitions treated as allowed transitions. The ``5 MeV bump'' observed in the experimental ${}^{235}$U-fission antineutrino spectrum was discussed with self-consistent shape factors obtained in the present \textit{ab initio} calculations. Unlike phenomenological models that require empirical quenching factors to reproduce $\beta$-decay data, the present \textit{ab initio} calculations do not need to introduce quenching factors for calculations of the first-forbidden transitions.

nucl-th↗
arXiv2025

$Z=14$ Magicity Revealed by the Mass of the Proton Dripline Nucleus $^{22}$Si

Using the $Bρ$-defined isochronous mass spectrometry technique, we conducted the first mass measurement of the proton dripline nucleus $^{22}$Si. We confirm that $^{22}$Si is bound against particle emission with $S_p/S_{2p}=+1412(114)/+229(54)$ keV, fixing the proton dripline location for the Si element. By analyzing the mass differences of the neighboring $sd$-shell nuclei, we find that $^{22}$Si exhibits a doubly-magic character similar to its mirror partner $^{22}$O, and that the mirror energy difference of $^{22}$Si-$^{22}$O deviates from the predictions assuming mirror symmetry. Gamow shell-model calculations reveal that the average occupations of valence protons in $^{22}$Si are nearly identical to those of valence neutrons in $^{22}$O, supporting the $Z=14$ magicity in $^{22}$Si. The observed mirror-symmetry breaking is attributed to the extended proton distribution in $^{22}$Si arising from a small contribution of the unbound $\pi2s_{1/2}$ orbital.

nucl-ex↗
arXiv2025

Direct observation of $β$ and $γ$ decay from a high-spin long-lived isomer in $^{187}$Ta

$^{187}$Ta ($Z=73$, $N=114$) is located in the neutron-rich $A \approx 190$ region where a prolate-to-oblate shape transition via triaxial softness is predicted to take place. A preceding work on the $K^π = (25/2^-)$ isomer and a rotational band to which the isomer decays carried out by the same collaboration revealed that axial symmetry is slightly violated in this nucleus. This paper focuses on a higher-lying isomer, which was previously identified at 2933(14) keV by mass measurements with the Experimental Storage Ring at GSI. The isomer of interest has been populated by a multi-nucleon transfer reaction with a $^{136}$Xe primary beam incident on a natural tungsten target, using the KEK Isotope Separation System at RIKEN. New experimental findings obtained in the present paper include the internal and external $β$-decay branches from the high-spin isomer and a revised half-life of 136(24) s. The evaluated hindrances for $K$-forbidden transitions put constraints on the spin-parity assignment, which can be interpreted as being ascribed to a prolate shape with a five-quasiparticle configuration by model calculations.

nucl-ex↗
arXiv2024

Nuclear structure of dripline nuclei elucidated through precision mass measurements of $^{23}$Si, $^{26}$P, $^{27,28}$S, and $^{31}$Ar

Using the B$ρ$-defined isochronous mass spectrometry technique, we report the first determination of the $^{23}$Si, $^{26}$P, $^{27}$S, and $^{31}$Ar masses and improve the precision of the $^{28}$S mass by a factor of 11. Our measurements confirm that these isotopes are bound and fix the location of the proton dripline in P, S, and Ar. We find that the mirror energy differences of the mirror-nuclei pairs $^{26}$P-$^{26}$Na, $^{27}$P-$^{27}$Mg, $^{27}$S-$^{27}$Na, $^{28}$S-$^{28}$Mg, and $^{31}$Ar-$^{31}$Al deviate significantly from the values predicted assuming mirror symmetry. In addition, we observe similar anomalies in the excited states, but not in the ground states, of the mirror-nuclei pairs $^{22}$Al-$^{22}$F and $^{23}$Al-$^{23}$Ne. Using $ab~ initio$ VS-IMSRG and mean field calculations, we show that such a mirror-symmetry breaking phenomeon can be explained by the extended charge distributions of weakly-bound, proton-rich nuclei. When observed, this phenomenon serves as a unique signature that can be valuable for identifying proton-halo candidates.

nucl-ex↗
arXiv2024

Ground-state mass of $^{22}$Al and test of state-of-the-art \textit{ab initio} calculations

The ground-state mass excess of the $T_{z}=-2$ drip-line nucleus $^{22}$Al is measured for the first time to be $18103(10)$ keV using the newly-developed B$ρ$-defined isochronous mass spectrometry method at the cooler storage ring in Lanzhou. The new mass excess value allowed us to determine the excitation energies of the two low-lying $1^+$ states in $^{22}$Al with significantly reduced uncertainties of 51 keV. Comparing to the analogue states in its mirror nucleus $^{22}$F, the mirror energy differences of the two $1^+$ states in the $^{22}$Al-$^{22}$F mirror pair are determined to be $-625(51)$ keV and $-330(51)$ keV, respectively. The excitation energies and the mirror energy differences are used to test the state-of-the-art \textit{ab initio} valence-space in-medium similarity renormalization group calculations with four sets of interactions derived from the chiral effective field theory. The mechanism leading to the large mirror energy differences is investigated and attributed to the occupation of the $πs_{1/2}$ orbital.

nucl-ex↗
arXiv2023

Ab initio descriptions of $A=16$ mirror nuclei with resonance and continuum coupling

We have used an {\it ab initio} Gamow shell model to study the isospin symmetry breaking in the $A=16$ mirror nuclei of $^{16}$F, $^{16}$N, $^{16}$Ne and $^{16}$C. Starting from a chiral interaction with two-nucleon force (2NF) at N$^3$LO and three-nucleon force (3NF) at N$^2$LO, a complex-momentum ${\it psd}$-shell Hamiltonian was constructed by employing the many-body perturbation theory in the Gamow Hartree-Fock basis which includes bound, resonant and continuum states self-consistently. Such an elaborated {\it ab initio} Gamow shell model with both continuum coupling and 3NF included can properly treat the many-body correlations of weakly bound and unbound nuclei. The mirror partners of $^{16}$F and $^{16}$N exhibit different level orders in their excitation spectra, which can be well explained by the inclusion of 3NF in the calculation. The isospin asymmetry between the mirror partners $^{16}$Ne and $^{16}$C was studied in detail by insight into their configuration structures. The interplay between 3NF and the continuum coupling is discussed in the weakly bound and unbound nuclear states.

nucl-th↗
arXiv2023

The renormalization of the shell-model GT operator starting from effective field theory for nuclear systems

For the first time, we approach in this work the problem of the renormalization of the Gamow-Teller decay operator for nuclear shell-model calculations by way of many-body perturbation theory, starting from a nuclear Hamiltonian and electroweak currents derived consistently by way of the chiral perturbation theory. These are the inputs we need to construct microscopically the effective shell-model Hamiltonians and decay operators. The goal is to assess the role of both electroweak currents and many-body correlations as the origins of the well-known problem of the quenching of the axial coupling constant gA. To this end, the calculation of observables related to the Gamow-Teller transitions has been performed for several nuclear systems outside the 40Ca and 56Ni closed cores and compared with the available data.

nucl-th↗
arXiv2023

Complex valence-space effective operators for observables: the Gamow-Teller transition

Nuclei in the vicinity of driplines have been receiving a lot of attention in nuclear structure studies. In the nuclei, the continuum coupling is crucial in reproducing weakly-bound and unbound phenomena. To calculate observables of the nuclei as open quantum systems, we have developed valence-space effective operators in the complex-energy Berggren basis using many-body perturbation theory. We focus on the Gamow-Teller $β$ decay in the {\it sd} shell. The two- plus three-nucleon force from the chiral effective field theory (EFT), named EM1.8/2.0, has been used. The Gamow shell model which takes the continuum coupling into account can properly reproduce experimental observations of weakly-bound and unbound states. The $β$-decay isospin asymmetry between the dripline nucleus $^{22}\rm Si$ and its mirror partner $^{22}\rm O$ is reproduced, in which the $s_{1/2}$ continuum plays a key role. Significant Thomas-Ehrman shift is seen through mirror energy differences between the mirror daughters $^{22}\rm Al$ and $^{22}\rm F$, in which the continuum effect plays an important role.

nucl-th↗
arXiv2023

The role of three-nucleon potentials within the shell model: past and present

We survey the impact of nuclear three-body forces on structure properties of nuclei within the shell model. It has long been acknowledged, since the seminal works of Zuker and coworkers, that three-body forces play a fundamental role in making the monopole component of shell-model Hamiltonians, derived from realistic nucleon-nucleon potentials, able to reproduce the observed evolution of the shell structure. In the vast majority of calculations, however, their effects have been taken into account by shell-model practitioners by introducing ad hoc modifications of the monopole matrix elements. During last twenty years, a new theoretical approach, framed within the chiral perturbation theory, has progressed in developing nuclear potentials, where two- and many-body components are naturally and consistently built in. This new class of nuclear forces allows to carry out nuclear structure studies that are improving our ability to understand nuclear phenomena in a microscopic approach. We provide in this work an update on the status of the nuclear shell model based on realistic Hamiltonians that are derived from two- and three-nucleon chiral potentials, focusing on the role of the three-body component to provide the observed shell evolution and closure properties, as well as the location of driplines. To this end, we present the results of shell-model calculations and their comparison with recent experimental measurements, which enlighten the relevance of the inclusion of three-nucleon forces to master our knowledge of the physics of atomic nuclei.

nucl-th↗
arXiv2023

Investigation of isospin-symmetry-breaking in mirror energy difference and nuclear mass with ab initio calculations

Isospin-symmetry breaking is responsible for the energy difference of excited states in mirror nuclei. It also influences the coefficient of the isobaric multiplet mass equation. In the present work, we extensively investigate isospin-symmetry breaking in medium mass nuclei within ab initio frameworks. For this, we employ the ab initio valence-space in-medium similarity renormalization group approach, in which charge-symmetry and charge-independence breakings are included in the adopted nuclear force. The mirror energies of sd- and pf- shell nuclei are computed for that matter. The effects of single-particle states on weakly bound and unbound nuclear states, especially those of the s-wave, are discussed. Predictions are also made concerning proton drip-line nuclei bearing large mirror energy difference. Finally, the coefficient of the isobaric multiplet mass equation in T = 1/2 and T = 1 isospin multiplets for A = 18 to A = 76 is calculated.

nucl-th↗
arXiv2022

Deformed in-medium similarity renormalization group

We have developed an {\it ab initio} deformed in-medium similarity renormalization group (IMSRG) for open-shell nuclei. This is a single-reference IMSRG in deformed Hartree-Fock (HF) basis. Deformed wave functions are more efficient in describing deformed nuclei. The broken spherical symmetry needs to be restored by angular momentum projection, which is computational expensive. The angular momentum mainly capture the static correlations and can be estimated by the projection of the HF state. In this work, we do deformed IMSRG calculation and add the correlation energy from projected HF as a leading order approximation. As the test ground, we have calculated the deformed $^{8,10}\rm Be$ isotopes with the optimized chiral interaction NNLO$_{\rm opt}$. The results are benchmarked with the no-core shell model and valence space IMSRG calculations. Then we systematically investigated the ground-state energies and charge radii of even-even isotopes from light beryllium to medium-mass magnesium. The calculated energies are extrapolated to infinite basis space by an exponential form, and compared with the extrapolated valence-space IMSRG results and experimental data available.

nucl-th↗
arXiv2022

The roles of three-nucleon force and continuum coupling in mirror symmetry breaking of oxygen mass region

With both three-nucleon force and continuum coupling included, we have developed a self-consistent {\it ab initio} Gamow shell model within the Gamow Hartree-Fock (GHF) basis obtained by the realistic interaction itself. With the chiral two-nucleon N$^3$LO and three-nucleon N$^2$LO interactions, the Gamow shell model has been applied to the mirror systems of $Z=8$ neutron-rich isotopes and $N=8$ proton-rich isotones, giving good agreements with data in binding energies, dripline positions and excitation spectra. The GHF calculated that the $0d_{3/2}$, $1s_{1/2}$ and $1p_{3/2}$ orbitals are resonances. The resonance states and their interplay with nonresonant continua play a crucial role in the descriptions of nuclei around driplines. Excitation spectra and Thomas-Ehrman shifts observed can be better described when both three-nucleon force and continuum coupling are considered in calculations. The three-nucleon force and continuum coupling produce a combined effect on the Thomas-Ehrman shift, e.g., for the ${1/2}^+$ resonance level of $^{19}$Na. The calculations help the understandings of related nuclear astrophysical processes.

nucl-th↗
arXiv2021

Bayesian Data Fusion of Imperfect Fission Yields for Augmented Evaluations

We demonstrate that Bayesian machine learning can be used to treat the vast amount of experimental fission data which are noisy, incomplete, discrepant, and correlated. As an example, the two-dimensional cumulative fission yields (CFY) of neutron-induced fission of $^{238}$U are evaluated with energy dependencies and uncertainty qualifications. For independent fission yields (IFY) with very few experimental data, the heterogeneous data fusion of CFY and IFY is employed to interpolate the energy dependence. This work shows that Bayesian data fusion can facilitate the further utilization of imperfect raw nuclear data.

nucl-th↗
arXiv2021

Shell-model study of titanium isotopic chain with chiral two- and three-body forces

The even-even Ti isotopic chain, from A = 42 to 70, has been studied within the nuclear shell-model framework by employing an effective Hamiltonian which is derived by way of many-body perturbation theory from a chiral potential with two- and three-body forces, and includes three-body contributions which account for Pauli principle violations in nuclei with more than two valence particles. We consider 40Ca as a closed core and a model space spanned by the neutron and proton 0f1p orbitals with the addition of the 0g9/2 orbital for neutrons. Calculated two-neutron separation energies and excitation energies of the yrast 2+ states are reported and compared with the experimental data, which are available up to 62Ti. The present study intends to investigate the effects of the adopted effective interactions on the evolution of the shell structure.

nucl-th↗
arXiv2021

Tensor force role in $β$ decays analyzed within the Gogny-interaction shell model

Background: The half-life of the famous $^{14}$C $β$ decay is anomalously long, with different mechanisms: the tensor force, cross-shell mixing, and three-body forces, proposed to explain the cancellations that lead to a small transition matrix element. Purpose: We revisit and analyze the role of the tensor force for the $β$ decay of $^{14}$C as well as of neighboring isotopes. Methods: We add a tensor force to the Gogny interaction, and derive an effective Hamiltonian for shell-model calculations. The calculations were carried out in a $p$-$sd$ model space to investigate cross-shell effects. Furthermore, we decompose the wave functions according to the total orbital angular momentum $L$ in order to analyze the effects of the tensor force and cross-shell mixing. Results: The inclusion of the tensor force significantly improves the shell-model calculations of the $β$-decay properties of carbon isotopes. In particular, the anomalously slow $β$ decay of $^{14}$C can be explained by the isospin $T=0$ part of the tensor force, which changes the components of $^{14}$N with the orbital angular momentum $L=0,1$, and results in a dramatic suppression of the Gamow-Teller transition strength. At the same time, the description of other nearby $β$ decays are improved. Conclusions: Decomposition of wave function into $L$ components illuminates how the tensor force modifies nuclear wave functions, in particular suppression of $β$-decay matrix elements. Cross-shell mixing also has a visible impact on the $β$-decay strength. Inclusion of the tensor force does not seem to significantly change, however, binding energies of the nuclei within the phenomenological interaction.

nucl-th↗
arXiv2021

Resonances of $A=4$ $T=1$ isospin triplet states within the \textit{ab initio} no-core Gamow shell model

The $A=4$ nuclei, i.e., $^4$H, $^4$He and $^4$Li, establish an interesting isospin $T=1$ isobaric system. $^4$H and $^4$Li are unbound broad resonances, whereas $^4$He is deeply bound in its ground state but unbound in all its excited states. The present situation is that experiments so far have not given consistent data on the resonances. Few-body calculations have well studied the scatterings of the $4N$ systems. In the present work, we provide many-body calculations of the broad resonance structures, in an \textit{ab initio} framework with modern realistic interactions. It occurs that, indeed, $^4$H, $^4$Li and excited $^4$He are broad resonances, which is in accordance with experimental observations. The calculations also show that the first $1^-$ excited state almost degenerates with the $2^-$ ground state in the pair of mirror isobars of $^4$H and $^4$Li, which may suggest that the experimental data on energy and width are the mixture of the ground state and the first excited state. The $T = 1$ isospin triplet formed with an excited state of $^4$He and ground states of $^4$H and $^4$Li is studied, focusing on the effect of isospin symmetry breaking.

nucl-th↗
arXiv2021

Revisiting the variational two-particle reduced density matrix for nuclear systems

In most nuclear many-body methods, observables are calculated using many-body wave functions explicitly. The variational two-particle reduced density matrix method is one of the few exceptions to the rule. Ground-state energies of both closed-shell and open-shell nuclear systems can indeed be evaluated by minimizing a constrained linear functional of the two-particle reduced density matrix. However, it has virtually never been used in nuclear theory, because nuclear ground states were found to be well overbound, contrary to those of atoms and molecules. Consequently, we introduced new constraints in the nuclear variational two-particle reduced density matrix method, developed recently for atomic and molecular systems. Our calculations then show that this approach can provide a proper description of nuclear systems where only valence neutrons are included. For the nuclear systems where both neutrons and protons are active, however, the energies obtained with the variational two-particle reduced density matrix method are still overbound. The possible reasons for the noticed discrepancies and solutions to this problem will be discussed.

nucl-th↗