Fitting for the energy levels of hydrogen

IF 1.5 4区 物理与天体物理 Q3 OPTICS Journal of Physics B: Atomic, Molecular and Optical Physics Pub Date : 2023-08-25 DOI:10.1088/1361-6455/acf428
David M Jacobs, M. Horbatsch
{"title":"Fitting for the energy levels of hydrogen","authors":"David M Jacobs, M. Horbatsch","doi":"10.1088/1361-6455/acf428","DOIUrl":null,"url":null,"abstract":"Atomic hydrogen energy levels calculated to high precision are required to assist experimental researchers working on spectroscopy in the pursuit of testing quantum electrodynamics (QEDs) and probing for physics beyond the Standard Model. There are two important parts to the problem of computing these levels: an accurate evaluation of contributions from QED and using an accurate value for the proton charge radius as an input. Recent progress on QED corrections to the fine structure, as well as increasing evidence that a proton charge radius in the range of 0.84 fm is favored over the previously adopted larger value in the 0.88 fm range, has advanced the field, yet several state-of-the-art measurements remain in contradiction with this smaller value. Motivated by on-going and future work in this area, we present here a simple parameterization for the energy levels of hydrogen at the level of hyperfine structure using the so-called relativistic Ritz approach. The fitting of a finite sample of QED-generated levels at low to intermediate principal quantum number, n, gives a generally applicable formula for all values of n for each distinct angular momentum channel, given in this work up to orbital angular momentum number ℓ=30 . We also provide a simple linear parameterization for the shift in hydrogen energy levels as a function of the proton radius, providing a useful cross check for extant and future measured energy intervals.","PeriodicalId":16826,"journal":{"name":"Journal of Physics B: Atomic, Molecular and Optical Physics","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics B: Atomic, Molecular and Optical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1361-6455/acf428","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0

Abstract

Atomic hydrogen energy levels calculated to high precision are required to assist experimental researchers working on spectroscopy in the pursuit of testing quantum electrodynamics (QEDs) and probing for physics beyond the Standard Model. There are two important parts to the problem of computing these levels: an accurate evaluation of contributions from QED and using an accurate value for the proton charge radius as an input. Recent progress on QED corrections to the fine structure, as well as increasing evidence that a proton charge radius in the range of 0.84 fm is favored over the previously adopted larger value in the 0.88 fm range, has advanced the field, yet several state-of-the-art measurements remain in contradiction with this smaller value. Motivated by on-going and future work in this area, we present here a simple parameterization for the energy levels of hydrogen at the level of hyperfine structure using the so-called relativistic Ritz approach. The fitting of a finite sample of QED-generated levels at low to intermediate principal quantum number, n, gives a generally applicable formula for all values of n for each distinct angular momentum channel, given in this work up to orbital angular momentum number ℓ=30 . We also provide a simple linear parameterization for the shift in hydrogen energy levels as a function of the proton radius, providing a useful cross check for extant and future measured energy intervals.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
符合氢的能级
需要高精度计算氢原子能级,以帮助从事光谱学研究的实验研究人员测试量子电动力学(QED),并探索标准模型之外的物理。计算这些水平的问题有两个重要部分:对QED贡献的准确评估和使用质子电荷半径的准确值作为输入。最近在精细结构的QED校正方面取得的进展,以及越来越多的证据表明,0.84fm范围内的质子电荷半径比之前采用的0.88fm范围内更大的值更受欢迎,推动了该领域的发展,但一些最先进的测量结果仍与这个较小的值相矛盾。受该领域正在进行和未来工作的启发,我们在这里使用所谓的相对论Ritz方法,对超精细结构水平下的氢能级进行了简单的参数化。对低到中等主量子数n下QED产生能级的有限样本的拟合,给出了一个适用于每个不同角动量通道的所有n值的通用公式,在本工作中给出,直到轨道角动量数ℓ=30。我们还为氢能级随质子半径的变化提供了一个简单的线性参数化,为现有和未来测量的能量间隔提供了有用的交叉检查。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
3.60
自引率
6.20%
发文量
182
审稿时长
2.8 months
期刊介绍: Published twice-monthly (24 issues per year), Journal of Physics B: Atomic, Molecular and Optical Physics covers the study of atoms, ions, molecules and clusters, and their structure and interactions with particles, photons or fields. The journal also publishes articles dealing with those aspects of spectroscopy, quantum optics and non-linear optics, laser physics, astrophysics, plasma physics, chemical physics, optical cooling and trapping and other investigations where the objects of study are the elementary atomic, ionic or molecular properties of processes.
期刊最新文献
X-ray circular dichroism measured by cross-polarization x-ray transient grating Toward a Mølmer Sørensen gate with .9999 fidelity Quantum states and spectra of small cylindrical and toroidal lattices Addendum: Multichannel quantum defect theory of strontium bound Rydberg states (2014 J. Phys. B: At. Mol. Opt. Phys. 47 155001) Absolute nuclear charge radius by Na-like spectral line separation in high-Z elements
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1