arXiv subjects

Ting-Yun Shi

Publications and source records attributed to Ting-Yun Shi.

At least 19 recordsLinked to original sources

arXiv2026

Nuclear-size correction to the one-loop self-energy in hydrogenlike ions

The nuclear-size effect on both diagonal and off-diagonal one-loop self-energy matrix elements is considered for hydrogenlike ions with $Z=60$, $82$, $90$, and $92$. Specifically, the $1s$, $2s$, $3s$, $2p_{1/2}$, and $2p_{3/2}$ states, as well as the off-diagonal $1s-2s$, $1s-3s$, and $2s-3s$ matrix elements are considered. The calculations are performed within the rigorous quantum-electrodynamics framework, nonperturbatively in the nuclear-strength parameter $\alpha Z$. Excellent agreement is found with results reported in the literature. Simple and useful approximate formulas to treat the nuclear-size correction are obtained, which, in particular, can be used to study the self-energy contributions to the field-shift factors.

physics.atom-ph↗

arXiv2026

Low-energy positron scattering from metastable helium

Low-energy positron scattering from singlet and triplet metastable He($1s2s$) is investigated using the $R$-matrix propagation method in hyperspherical coordinates. Elastic and positronium-formation cross sections are reported, and near-threshold resonance structures are analyzed in terms of eigenphase sums and the time-delay matrix. For the triplet target, the calculated cross sections are in agreement with available convergent-close-coupling results and display the expected threshold behavior. Beyond the known $S$-wave features, Feshbach resonance series in higher partial waves extending up to highly excited atomic thresholds are systematically identified. The time-delay matrix further uncovers hidden resonances that produce obvious structures in the positronium-formation cross sections.

physics.atom-ph↗

arXiv2026

Ionization energies for Rydberg $^4 \mathrm{He}$ ($1snp\,^{1,3}P$) states using the correlated B-spline basis function method

We extend the correlated B-spline basis function (C-BSBF) method to high-precision calculations of the ionization energies of helium Rydberg $n^{1,3}P$ states ($n=24$--$35$). Using a unified basis set, we evaluate nonrelativistic energies, relativistic corrections of order $mα^4$ (including finite-mass recoil), QED contributions of order $mα^5$, and partial $mα^6$ terms (singlet-triplet mixing, one- and two-loop radiative corrections). The remaining higher-order contributions are estimated via $1/n^3$ scaling. The resulting ionization energies achieve kHz-level accuracy and are in excellent agreement with independent Hylleraas calculations, thereby providing cross-validation between two distinct theoretical approaches. From these data, the quantum-defect parameters are determined and used to extrapolate the ionization energies up to $n=102$. Combining our Rydberg ionization energies with high-precision experimental $2S \rightarrow nP$ transition frequencies yields the ionization energies for the metastable $2^{1}S$ and $2^{3}S$ states as \num{960332040.533(10)}$_\mathrm{stat}(20)_ \mathrm{sys}$ MHz and \num{1152842742.7274(53)}$_\mathrm{stat}(25)_ \mathrm{sys}$ MHz, respectively. The C-BSBF result for the $2 \, ^1 S$ state is consistent with the experimental ionization energy obtained from Rydberg-series extrapolation, while for the $2 \, ^3 S$ state the difference is 0.019(10) MHz.

physics.atom-ph↗

arXiv2026

QED corrections of orders $m\alpha^6$ and $m\alpha^6(m/M)$ for HD$^+$ rovibrational transitions beyond Born-Oppenheimer approximation

The effective Hamiltonian of $m\alpha^6$ and $m\alpha^6(m/M)$ order corrections for hydrogen molecular ions has been derived in [ Z.-X. Zhong, \emph{et al.}, Phys. Rev. A {\bf98}, 032502(2018).], in this work we express the energy correction in the form of finite-value effective operators. The cut-off regularization scheme is used to determine finite part of divergent operators of the leading-order recoil corrections. Numerical calculations of first-order contributions are performed in the Hylleraas basis set. Combining the second-order terms calculated in recent work [V. I. Korobov, \emph{et al.}, Mol. Phys. e2563023 (2025).], the $m\alpha^6$-order corrections for the fundamental rovibrational transition are obtained with an uncertainty three times smaller than in previous calculations.

physics.atom-ph↗

arXiv2025

Characterizing resonances in positron-sodium scattering

We investigate resonances in positron-sodium scattering using the $R$-matrix propagation method formulated in hyperspherical coordinates. The interaction between the sodium core and the valence electron is described by analytical model potentials. High partial-wave resonances are calculated for collision energies up to the Na($4f$) threshold. Several resonant states of debated character are identified, and their behavior is analyzed through phase-variation studies, the associated structures in the calculated cross sections, and the characteristic patterns observed in the stability plots. The calculated dipole series of resonances, supported by the ion-dipole interaction between Na$^{\scriptscriptstyle+}$ and Ps($n=2$), shows good agreement with recent complex-scaling calculations. In addition, a sequence of quasi-dipole resonances is found to arise from the near degeneracy of the Na($4d$) and Na($4f$) states in the e$^{+}$-Na system, which accumulate geometrically toward the Na($4d$) threshold.

physics.atom-ph↗

arXiv2025

Precise ab initio calculations of $^4$He($1snp \, ^3P_J$) fine structure of high Rydberg states

High-precision measurements of the fine-structure splittings in helium high Rydberg states have been reported, yet corresponding ab initio benchmarks for direct comparison remain unavailable. In this work, we extend the correlated B-spline basis function (C-BSBF) method to calculate the fine-structure splittings of high Rydberg states in $^4$He. The calculations include the $mα^4$- and $mα^5$-order contributions, the singlet-triplet mixing effect, and estimated spin-dependent $mα^6$-order corrections obtained using a $1/n^3$ scaling approximation. High-precision ab initio results are obtained for principal quantum numbers $n=24$-37 with kilohertz-level accuracy and further extended to $n=45$-51 by extrapolation and fitting. The theoretical results show excellent agreement with quantum-defect theory (QDT) predictions and allow direct comparison with experimental measurements. Additionally, the discrepancy observed at $n=34$ is expected to be clarified with improved experimental precision.

physics.atom-ph↗

arXiv2025

Positronium formation and threshold behavior in positron-sodium collisions at low energies

We investigate the elastic and inelastic scattering of positrons by sodium atoms in both the ground state, Na($3s$), and excited states, Na*($3p$, $4s$, $3d$), using the hyperspherical coordinate method with a model potential to represent the atomic core. The threshold behavior of positronium (Ps) formation cross sections is analyzed as the positron impact energy $E$ approaches zero. Within this framework, we derive a generalized expression for partial-wave Ps-formation cross sections at low positron energies, which applies to both ground-state and excited-state sodium targets. Our results confirm that the total threshold behavior follows the expected power-law dependence: $ σ_{\text{Ps}} \propto E^{-1/2} $ for exothermic reactions and $ σ_{\text{Ps}} \propto E^{a} $ for endothermic reactions, where $ a > 0 $. Furthermore, we find that Ps-formation cross sections for positron scattering from excited Na states are significantly larger than those from the ground state in the low-energy region. A notable enhancement of Gailitis-Damburg oscillations is observed above the Ps($n=2$) threshold, which may account for the increase observed in experimental data. Incorporating contributions from excited sodium targets improves agreement with experimental results and may help resolve discrepancies between theoretical predictions and measurements.

physics.atom-ph↗

arXiv2025

Direct Extraction of Nuclear Structure Information Using Precision Lithium-Ion Spectroscopy

Accurately describing nuclear interactions within atomic nuclei remains a challenge, which hinders our exploration of new physics beyond the Standard Model. However, these nuclear interactions can be characterized by nuclear parameters such as the Zemach radius and the electric quadrupole moment, which are reflected in atomic spectra. Our work has achieved high-precision measurements of lithium ion hyperfine splittings at the level of $10$~kHz, and directly extracted these important nuclear structure parameters. We observed significant discrepancies between our results and both nuclear theory and molecular spectra regarding the electric quadrupole moment. The result for $^7$Li deviated by $2.3σ$ from the currently recommended value, whereas the result for $^6$Li deviated by up to $6.2σ$ from the recommended value determined by molecular spectroscopy. These discrepancies motivated us to conduct independent calculations based on nuclear structure theory, which provided support for the results obtained from ion spectroscopy. Our results provide valuable information for characterizing nuclear forces, serve as sensitive benchmarks for testing nuclear structure theories, and enable critical comparisons with both electron-nuclear scattering and molecular spectroscopy.

physics.atom-ph↗

arXiv2025

Investigation of Efimov Features and Universality in $^{87}$Rb-$^{40}$K Mixtures with finite-range interaction

The study of Efimov features and their relationships in $^{40}$K-$^{87}$Rb Mixtures has generated extensive discussion, yet the discrepancy between Efimov universality predictions based on the zero-range approximation and experimental observations remains unresolved. In this study, we investigate the three-body collision properties with $J=0$ symmetry for a $^{87}$Rb-$^{87}$Rb-$^{40}$K system on both sides of Rb-K scattering length to understand the mechanisms underlying this discrepancy. Our approach employs the R-matrix propagation method within a hyperspherical coordinate frame, utilizing the Lennard-Jones model potential to describe atom interactions. We predicts the existence of three-body shape resonances at large negative Rb-K scattering lengths, which leads to the enhancement of three-body recombination rates. On the positive Rb-K scattering length side, we find an Efimov recombination minimum beyond the range of previous measurements. These Efimov features, combined with experimental observations of the atom-dimer Efimov resonance, offer an opportunity to test the universality of Efimov features. Our study demonstrates the influence of finite-range effects and non-resonant intraspecies scattering length in $^{40}$K-$^{87}$Rb mixtures, providing valuable insights into the universal relations between Efimov features in heteronuclear systems.

physics.atom-ph↗

arXiv2025

Effects of $p$-wave Interactions on Borromean Efimov Trimers in Heavy-Light Fermi Systems

We investigate the effects of $p$-wave interactions on Efimov trimers in systems comprising two identical heavy fermions and a light particle, with mass ratios larger than $13.6$. Our focus lies on the borromean regime where the ground-state trimer exists in the absence of dimers. Using pair-wise Lennard-Jones potentials and concentrating on the $L^π = 1^{-}$ symmetry, we explore the critical value of the interspecies $s$-wave scattering length $a_{c}$ at which the borromean state appears in several two-component particle systems. Our exploration encompasses the universal properties of $a_{c}$ and the influence of $p$-wave fermion-fermion interactions on its value. We find that, in the absence of $p$-wave fermion-fermion interactions, $a_{c}$ is determined universally by the van der Waals radius and mass ratio. However, the introduction of $p$-wave fermion-fermion interactions unveiled a departure from this universality. Our calculations show that the critical interspecies scattering length $a_{c}$ now depends on the details of the fermion-fermion $p$-wave interaction. And, the presence of $p$-wave fermion-fermion interactions favors the formation of the borromean state. Additionally, our investigation reveals that Efimov effect in the $1^{-}$ symmetry persist even when the fermion-fermion interaction reaches the $p$-wave unitary limit.

physics.atom-ph↗

arXiv2024

Revised $^3$He nuclear charge radius due to electronic hyperfine mixing

The significant discrepancy in the difference of squared nuclear charge radii $ΔR^2$ of $^{3,4}$He obtained from electronic-atom or muonic-atom energy levels is a puzzle. In this paper, we show that the tension is resolved by including off-diagonal mixing effects due to the hyperfine interaction. Our findings indicate that the hyperfine mixing effect from the $n\,^3\!S$ and $n\,^1\!S$ states ($n>2$) of $^3$He leads to a $-1.37$ kHz adjustment in the isotope shift of the $2\,^1\!S-2\,^3\!S$ transition, surpassing the current uncertainty by a factor of $7$. This results in a change of $-0.0064~\rm{fm}^2$ in $ΔR^2$, shifting from $1.0757(15)~\mathrm{fm}^2$ to $1.0693(15)~\mathrm{fm}^2$ as determined by Werf {\it et al.}, significantly reducing the discrepancy with the value of $1.0636(31)~\mathrm{fm}^2$ determined by $μ\rm{He}^+$, and aligning with the result of $1.069(3)$ $\mathrm{fm}^2$ obtained from the $2\,^3\!S-2\,^3\!P$ transition. This adjustment will result in a noticeable change in the absolute nuclear charge radius of $^{3}$He by $-0.0017~\rm{fm}$, aligning the revised value of $1.9715(11)~\mathrm{fm}$ with the value of $1.97007(94)~\mathrm{fm}$ determined by $μ^3\rm{He}^+$ within $1σ$. Our results offer crucial insights into resolving discrepancy in $ΔR^2$ for $^{3,4}$He and determining the charge radius of $^3$He.

physics.atom-ph↗

arXiv2024

A Simple approach for precision calculation of Bethe logarithm

In this article we propose a simple approach for the precision calculation of Bethe logarithm. The leading contributions are obtained using specific operators, while the remaining terms are eliminated by adjusting the parameter $λ$. Through the use of dimensional regularization, singular divergences are algebraically canceled. Compared to the standard form of Bethe logarithm, our approach significantly reduces the complexity of constructing pseudostates in numerical evaluations. Using this approach we obtain a very highly precise result of Bethe logarithm for the ground state of the hydrogen, achieving 49 significant digits. And for multi-electron systems this approach appears simplicity and efficiency as well.

physics.atom-ph↗

arXiv2023

Role of negative-energy states on the E2-M1 polarizability of optical clocks

The theoretical calculations of the dynamic E2-M1 polarizability at the magic wavelength of the Sr optical clock are inconsistent with experimental results. We investigate role of negative-energy states in the E2 and M1 polarizabilities. Our result for E2-M1 polarizability difference $-$7.74(3.92)$\times$10$^{-5}$ a.u. is dominated by the contribution from negative-energy states to M1 polarizability and has the same sign as and consistent with all the experimental values. In addition, we apply the present calculations to various other optical clocks, further confirming the importance of negative-energy states to the M1 polarizability.

physics.atom-ph↗

arXiv2023

Measurement of hyperfine structure and the Zemach radius in $\rm^6Li^+$ using optical Ramsey technique

We investigate the $2\,^3\!S_1$--$2\,^3\!P_J$ ($J = 0, 1, 2$) transitions in $\rm^6Li^+$ using the optical Ramsey technique and achieve the most precise values of the hyperfine splittings of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states, with smallest uncertainty of about 10~kHz. The present results reduce the uncertainties of previous experiments by a factor of 5 for the $2\,^3\!S_1$ state and a factor of 50 for the $2\,^3\!P_J$ states, and are in better agreement with theoretical values. Combining our measured hyperfine intervals of the $2\,^3\!S_1$ state with the latest quantum electrodynamic (QED) calculations, the improved Zemach radius of the $\rm^6Li$ nucleus is determined to be 2.44(2)~fm, with the uncertainty entirely due to the uncalculated QED effects of order $mα^7$. The result is in sharp disagreement with the value 3.71(16) fm determined from simple models of the nuclear charge and magnetization distribution. We call for a more definitive nuclear physics value of the $\rm^6Li$ Zemach radius.

physics.atom-ph↗

arXiv2023

Contributions of negative-energy states to the E2-M1 polarizability of the Sr clock

With the improvement of high-precision optical clock, the higher-order multipolar interaction between atoms and light needs quantitative evaluation. However for the Sr clock, the differential dynamic E2-M1 polarizability at the magic wavelength has contradictions among available theoretical and experimental results. Recently, the new experimental measurement of S. Dörscher {\em et al.} [arXiv: 2210. 14727] is consistent with measurement of Ushijima {\em et al.}, which poses new challenges to theory and urgently calls for theoretical explanations. In present work, we investigate contributions of negative-energy states to the E2 and M1 polarizabilities. We find that for the M1 polarizability, the contribution from negative-energy states is crucial and dominant. Our new theoretical result for E2-M1 polarizability difference is $-7.74(3.92)\times 10^{-5}$ a.u., which is in good agreement with the recent experiment of S. Dörscher et al., so the inconsistency problem of E2-M1 polarizability in the Sr clock between theory and experiment is eliminated.

physics.atom-ph↗

arXiv2023

Application of the correlated B-spline basis functions to the leading relativistic and QED corrections of helium

B-spline functions have been widely used in computational atomic physics. Different from the traditional B-spline basis (a simple product of two B-splines), the recently developed correlated B-spline basis functions(C-BSBF), in which the interelectronic coordinate $r_{12}$ is included explicitly, have greatly improved the computational accuracy of polarizability [S. J. Yang \textit{et al}., Phys. Rev. A \textbf{95}, 062505 (2017)] and bethe logarithm [ S. J. Yang \textit{et al}., Phys. Rev. A \textbf{100}, 042509 (2019)] for singlet states of helium. Here, we report the extension of the C-BSBF to the leading relativistic and QED correction calculations for energy levels of the $1\,^1S$, $2\,^1S$, $2\,^3S$, and $3\,^3S$ states of helium. The relativistic kinetic term $p_{1}^{4}$, contact potential $δ^{3}(r_{1})$, $δ^{3}(r_{12})$ and Araki-Sucher correction $\langle 1/r_{12}^{3} \rangle$ are calculated by using the global operator method, in which $r_{12}^n$ and $r_{12}^n\ln r_{12}$ involved are calculated with the generalization of Laplace's expansions. The obtained values for the ground state are $δE_{rel}/α^{2}=-$1.951 754 7(2) and $δE_{QED}/α^{3}=$57.288 165(2), consistent with previous results, which opens the possibility of calculating higher-order relativistic and QED effects using the C-BSBF.

physics.atom-ph↗

arXiv2022

Hyperspherical approach to atom--dimer collision with the Jacobi boundary condition

In this study, we investigate atom--dimer scattering within the framework of the hyperspherical method. The coupled channel Schrödinger equation is solved using the R-matrix propagation technique combined with the smooth variable discretization method. In the matching procedure, the asymptotic wave functions are expressed in the rotated Jacobi coordinates. We apply this approach to the elastic scattering $^{3}$He(T$\uparrow$) + $^{4}$He$_{2}$ and H$\uparrow$ + H$\uparrow$Li processes. The convergence of the scattering length as a function of the propagation distance is studied. We find that the method is reliable and can provide considerable savings over previous propagators.

physics.atom-ph↗

arXiv2022

Precision calculation of hyperfine structure of $^{7,9}$Be$^{2+}$ ions

The hyperfine structures of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states of the $^7$Be$^{2+}$ and $^9$Be$^{2+}$ ions are investigated within the framework of the nonrelativistic quantum electrodynamics (NRQED). The uncertainties of present hyperfine splitting results of $^9$Be$^{2+}$ are in the order of several tens of ppm, where two orders of magnitude improvement over the previous theory and experiment values has been achieved. The contribution of nuclear electric quadrupole moment to hyperfine splitting of $^7$Be$^{2+}$ has been studied. A scheme for determining the properties of Be nuclei in terms of Zemach radius or the electric quadrupole moment based on precise spectra is proposed, and it opens a new window for the study of Be nuclei.

physics.atom-ph↗