Fine structure in the hydrogen atom boxed in a spherical impenetrable cavity

Rojas R. A.; Aquino N.; Flores‐Riveros A.

摘要

Abstract > The spectrum of the hydrogen atom confined in a spherical impenetrable box of radius R <sub>c</sub> has been investigated by many authors up to date, but not at the level of relativistic corrections. It is well known that, as R <sub>c</sub> diminishes, all energy levels and the pressure increase very rapidly, whereas the polarizability goes to zero. In this report, we have computed the relativistic corrections that underlie the fine structure of the confined hydrogen atom, as a function of R <sub>c</sub> . Such corrections correspond to relativistic kinetic energy, spin‐orbit coupling and the Darwin term, which are calculated in the frame of time‐independent perturbation theory, for which, use was made of the exact confined hydrogen atom wave functions. We show that for a confinement radius of 0.5 au the relativistic corrections increase up to three orders of magnitude with respect to those corresponding to the free atom. As R <sub>c</sub> decreases, the kinetic energy correction and the spin‐orbit coupling for <mat:math display="inline" altimg="urn:x-wiley:00207608:media:qua25584:qua25584-math-0001" wiley:location="equation/qua25584-math-0001.png"> <mat:mrow> <mat:mi>j</mat:mi> <mat:mo>=</mat:mo> <mat:mn>1</mat:mn> <mat:mo>/</mat:mo> <mat:mn>2</mat:mn> </mat:mrow> </mat:math> become negative whereas their absolute value and the Darwin term, which is positive, increase very rapidly. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><抽象类型= “主”> <标题类型= “主”>抽象</ TITLE> >在半径的球形不可穿透的框限定的氢原子的光谱的 [R </ i>的<子>Ç </子>已由许多作者最新研究，但不能以相对论修正的水平。众所周知，作为<I> - [R </ i>的<子> C </子>减少，所有的能量水平和非常迅速的压力增加，而极化变为零。在本报告中，我们已经计算所依据的密闭氢原子的精细结构的相对论修正，如<I> - [R </ i>的<子> C </子>的功能。这种校正对应于相对论动能，自旋 - 轨道耦合和达尔文术语，这是在时间无关微扰理论的帧计算，为此，使用了的确切局限于氢原子波函数。我们表明，0.5 Au的限制半径相对论修正增加高达三个数量级相对于那些对应于自由原子。如<I> - [R </ i>的<子> C </子>减小，动能校正和用于<垫的自旋 - 轨道耦合：数学显示= “内联” altimg =“瓮：X-威利：00207608：媒体：qua25584：qua25584-数学-0001" 威利：位置= “方程/ qua25584-数学0001.png”> <垫：MROW> <垫：MI>Ĵ</垫：MI> <垫：MO> = < /垫：MO> <垫：MN> 1 </垫：MN> <垫：MO> / </垫：MO> <垫：MN> 2 </垫：MN> </垫：MROW> </垫：数学>变为负值，而它们的绝对值和达尔文来看，这是积极的，增加非常迅速。 </ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-21753/'>《International Journal of Quantum Chemistry》</a> <b style="margin: 0 2px;">|</b><span>2018年第14期</span><b style="margin: 0 2px;">|</b><span>共9页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Rojas R. A.&option=202" target="_blank" rel="nofollow">Rojas R. A.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Aquino N.&option=202" target="_blank" rel="nofollow">Aquino N.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Flores‐Riveros A.&option=202" target="_blank" rel="nofollow">Flores‐Riveros A.;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Departamento de FísicaUniversidad Autónoma Metropolitana‐Iztapalapa Avenida San Rafael Atlixco 186 Col. VicentinaIztapalapa México D. F 09340 México;</p> <p>Departamento de FísicaUniversidad Autónoma Metropolitana‐Iztapalapa Avenida San Rafael Atlixco 186 Col. VicentinaIztapalapa México D. F 09340 México;</p> <p>Instituto de Física Benemérita Universidad Autónoma de Puebla Apartado Postal J‐4872570 Puebla Pue México;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1186.html" title="物理化学（理论化学）、化学物理学">物理化学（理论化学）、化学物理学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=confined hydrogen atom&option=203" rel="nofollow">confined hydrogen atom;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Darwin term&option=203" rel="nofollow">Darwin term;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=fine structure&option=203" rel="nofollow">fine structure;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=kinetic energy correction&option=203" rel="nofollow">kinetic energy correction;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=spin‐orbit coupling&option=203" rel="nofollow">spin‐orbit coupling;</a> </p> <div class="translation"> 机译：限制氢原子;达尔文术语;精细结构;动能校正;旋转轨道耦合; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704019755795.html">Fine structure in the hydrogen atom boxed in a spherical impenetrable cavity</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Rojas R. 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href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=罗俊燕&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,罗俊燕</a> <span> <a href="/journal-cn-8346/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 弹箭与制导学报 </a> </span> <span> . 2004</span><span>,第004期</span> </span> </div> </li> <li> <div> <b>6. </b><a class="enjiyixqcontent" href="/academic-conference-cn_meeting-57989_thesis/020222865565.html">微重状态下容器受迫运动时球形腔内液体晃动的研究</a> <b>[C]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=魏金铎&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 魏金铎</a> <span> <a href="/conference-cn-57989/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 全国第四届一般力学学术会议 </a> <span> <span> . 1987</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020314776092.html">腹部火器伤肠管穿透后肝内NF-κB活性变化及其在肝损伤中的作用研究</a> <b>[A] </b> <span> <a 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</div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：腔谐振器中带有谐振单元的原子频率标准-在足够强的磁场下运行，具有时钟转换的超精细结构 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130405229225.html">SPHERICAL HYDROGEN POLYSILSESQUIOXANE FINE PARTICLE, SPHERICAL SILICON OXIDE FINE PARTICLE, AND METHODS FOR PRODUCING THEM</a> <b>[P]</b> . <span> 外国专利：  JP2019178038A </span> <span> . 2019-10-17</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：球形氢聚倍半硅氧烷细颗粒，球形氧化硅细颗粒及其制备方法 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130489534461.html">Composite atom storage cell and cavity resonator structure for an atomic hydrogen maser</a> <b>[P]</b> . <span> 外国专利：  US3263183A </span> <span> . 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