arXiv subjects

Hui-Li Han

Publications and source records attributed to Hui-Li Han.

9 recordsLinked to original sources

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↗

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

On some conjectural supercongruences involving the sequence $t_n(x)$

In this paper, we study some supercongruences involving the sequence $$ t_n(x)=\sum_{k=0}^n\binom{n}{k}\binom{x}{k}\binom{x+k}{k}2^k $$ and solve some open problems. For any odd prime $p$ and $p$-adic integer $x$, we determine $\sum_{n=0}^{p-1}t_n(x)^2$ and $\sum_{n=0}^{p-1}(n+1)t_n(x)^2$ modulo $p^2$; for example, we establish that \begin{align*} \sum_{n=0}^{p-1}t_n(x)^2\equiv\begin{cases} \left(\dfrac{-1}{p}\right)\pmod{p^2},&\text{if }2x\equiv-1\pmod{p},\\[8pt] (-1)^{\langle x\rangle_p}\dfrac{p+2(x-\langle x\rangle_p)}{2x+1}\pmod{p^2},&\text{otherwise,} \end{cases} \end{align*} where $\langle x\rangle_p$ denotes the least nonnegative residue of $x$ modulo $p$. This confirms a conjecture of Z.-W. Sun.

math.NT↗

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: $ \sigma_{\text{Ps}} \propto E^{-1/2} $ for exothermic reactions and $ \sigma_{\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↗

arXiv2024

Supercongruences involving binomial coefficients and Euler polynomials

Let $p$ be an odd prime and let $x$ be a $p$-adic integer. In this paper, we establish supercongruences for $$ \sum_{k=0}^{p-1}\frac{\binom{x}{k}\binom{x+k}{k}(-4)^k}{(dk+1)\binom{2k}{k}}\pmod{p^2} $$ and $$ \sum_{k=0}^{p-1}\frac{\binom{x}{k}\binom{x+k}{k}(-2)^k}{(dk+1)\binom{2k}{k}}\pmod{p^2}, $$ where $d\in\{0,1,2\}$. As consequences, we extend some known results. For example, for $p>3$ we show $$ \sum_{k=0}^{p-1}\binom{3k}{k}\left(\frac{4}{27}\right)^k\equiv\frac19+\frac89p+\frac{4}{27}pE_{p-2}\left(\frac13\right)\pmod{p^2}, $$ where $E_n(x)$ denotes the Euler polynomial of degree $n$. This generalizes a known congruence of Z.-W. Sun.

math.NT↗

arXiv2023

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 $L^{\pi} = 1^{-}$ 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↗

arXiv2023

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↗

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 Schr\"odinger 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↗

arXiv2021

Three-body recombination near the d-wave resonance in ultracold $^{85}$Rb\,-$^{87}$Rb mixtures

We have studied the three-body recombination rates on both sides of the interspecies d-wave Feshbach resonance in the $^{85}$Rb\,-$^{87}$Rb-$^{87}$Rb system using the $R$-matrix propagation method in the hyperspherical coordinate frame. Two different mechanisms of recombination rate enhancement for positive and negative $^{85}$Rb\,-$^{87}$Rb d-wave scattering lengths are analyzed. On the positive scattering length side, the recombination rate enhancement occurs due to the existence of three-body shape resonance, while on the negative scattering length side, the coupling between the lowest entrance channel and the highest recombination channel is crucial to the appearance of the enhancement. In addition, our study shows that the intraspecies interaction plays a significant role in determining the emergence of recombination rate enhancements. Compared to the case in which the three pairwise interactions are all in d-wave resonance, when the $^{87}$Rb-$^{87}$Rb interaction is near the d-wave resonance, the values of the interspecies scattering length that produce the recombination enhancement shift. In particular, when the $^{87}$Rb-$^{87}$Rb interaction is away from the d-wave resonance, the enhancement disappears on the negative interspecies scattering length side.

cond-mat.quant-gas↗