arXiv subjects

San-Jiang Yang

Publications and source records attributed to San-Jiang Yang.

4 recordsLinked to original sources

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↗

arXiv2019

Application of the Hylleraas-$B$-spline basis set: Nonrelativistic Bethe logarithm of helium

In this work, we report an application of Hylleraas-$B$-spline basis set to the nonrelativistic Bethe logarithm calculation of helium. The Bethe logarithm for $n\ ^1S$, $n$ up to 10, states of helium are calculated with a precision of 7-9 significant digits in two gauges, which greatly improves the accuracy of the traditional $B$-spline basis set. In addition, to deal with the numerical linear correlation problem in Bethe logarithm calculation, we developed a multiple-precision generalized symmetric eigenvalue problem solver (MGSEPS). This program may be very useful to precision calculations.

physics.atom-ph↗

arXiv2018

Relativistic full-configuration-interaction calculations of magic wavelengths for the $2\,^3S_1\rightarrow2\,^1S_0$ transition of helium isotopes

A large-scale full-configuration-interaction calculation based on Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2\,^1S_0$ and $2\,^3S_1$ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved n (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states. And a series of magic wavelengths with QED and hyperfine effects included for the $2\,^3S_1\rightarrow2\,^1S_0$ transition of helium are identified. In addition, the high-order Ac Stark shift determined by the dynamic hyperpolarizabilities at the magic wavelengths are also evaluated. Since the most promising magic wavelength for application in experiment is 319.8 nm, the high-accuracy magic wavelength of 319.815 3(6) nm of $^4$He is in good agreement with recent measurement value of 319.815 92(15) nm [Nature Physics (2018)/arXiv:1804.06693], and present magic wavelength of 319.830 2(7) nm for $^3$He would provide theoretical support for experimental designing an optical dipole trap to precisely determine the nuclear charge radius of helium in future.

physics.atom-ph↗

arXiv2017

An application of the Hylleraas-B-splines basis set: High accuracy calculations of the static dipole polarizabilities of helium

The Hylleraas-B-splines basis set is introduced in this paper, which can be used to obtain the eigenvalues and eigenstates of helium-like system's Hamiltonian. Comparing with traditional B-splines basis, the rate of convergence of our results has been significantly improved. Through combine this method and pseudo-states sum over scheme, we obtained the high precision values of static dipole porlarizabilities of the $1{}^1S-5{}^1S$, $2{}^3S-6{}^3S$ states of helium in length and velocity gauges respectively, and the results get good agreements. The final extrapolate results of porlarizabilities in different quantum states arrived eight significant digits at least, which fully illustrates the advantage and convenience of this method in the problems involving continuous states.

physics.atom-ph↗