Magnetizabilities of relativistic hydrogenlike atoms in some arbitrary discrete energy eigenstates

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作者：Patrycja Stefańska ^{pstefanska@mif.pg.gda.pl" class="auth_mail" title="E-mail the corresponding author}
关键词：Hydrogenlike atom ; Magnetizability ; Electromagnetic moments ; Dipole moment ; Magnetic field ; Green function
刊名：Atomic Data and Nuclear Data Tables
出版年：2016
出版时间：March 2016
年：2016
卷：108
期：Complete
页码：193-210
全文大小：379 K

文摘

We present the results of numerical calculations of magnetizability (mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si1.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=c306b5b04d2ef13958ca1bddf62e8df2" title="Click to view the MathML source">χmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mi>χmi>math>) of the relativistic one-electron atoms with a pointlike, spinless and motionless nuclei of charge Ze. Exploiting the analytical formula for mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si1.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=c306b5b04d2ef13958ca1bddf62e8df2" title="Click to view the MathML source">χmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mi>χmi>math> recently derived by us Stefańska (2015), valid for an arbitrary discrete energy eigenstate, we have found the values of the magnetizability for the ground state and for the first and the second set of excited states (i.e.: mmlsi13" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si13.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=36b46c9614652e265abb52b8ed6a2c2b">mg class="imgLazyJSB inlineImage" height="16" width="33" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si13.gif">

mg height="16" border="0" style="vertical-align:bottom" width="33" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0092640X15000388-si13.gif">

mathContainer hidden">mathCode"><math altimg="si13.gif" overflow="scroll"><mn>2mn><msub><mrow><mstyle mathvariant="normal"><mi>smi>mstyle>mrow><mrow><mn>1mn><mo>/mo><mn>2mn>mrow>msub>math>, mmlsi23" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si23.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=e45119b2f8b1595d43554cb92364ec2e">mg class="imgLazyJSB inlineImage" height="16" width="36" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si23.gif">

mg height="16" border="0" style="vertical-align:bottom" width="36" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0092640X15000388-si23.gif">

mathContainer hidden">mathCode"><math altimg="si23.gif" overflow="scroll"><mn>2mn><msub><mrow><mstyle mathvariant="normal"><mi>pmi>mstyle>mrow><mrow><mn>1mn><mo>/mo><mn>2mn>mrow>msub>math>, mmlsi33" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si33.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=94b8022b8d528efc0715b694f7b6fdf4">mg class="imgLazyJSB inlineImage" height="16" width="36" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si33.gif">

mathContainer hidden">mathCode"><math altimg="si33.gif" overflow="scroll"><mn>2mn><msub><mrow><mstyle mathvariant="normal"><mi>pmi>mstyle>mrow><mrow><mn>3mn><mo>/mo><mn>2mn>mrow>msub>math>, mmlsi55" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si55.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=959adde79ea3df18c639245dd1c80189">mg class="imgLazyJSB inlineImage" height="16" width="33" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si55.gif">

mathContainer hidden">mathCode"><math altimg="si55.gif" overflow="scroll"><mn>3mn><msub><mrow><mstyle mathvariant="normal"><mi>smi>mstyle>mrow><mrow><mn>1mn><mo>/mo><mn>2mn>mrow>msub>math>, mmlsi65" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si65.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=6c03fdf1120145266ca4519f1eb0ca24">mg class="imgLazyJSB inlineImage" height="16" width="36" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si65.gif">

mathContainer hidden">mathCode"><math altimg="si65.gif" overflow="scroll"><mn>3mn><msub><mrow><mstyle mathvariant="normal"><mi>pmi>mstyle>mrow><mrow><mn>1mn><mo>/mo><mn>2mn>mrow>msub>math>, mmlsi75" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si75.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=9e12ac544aa3f237aaf67f3d6877fbbc">mg class="imgLazyJSB inlineImage" height="16" width="36" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si75.gif">

mathContainer hidden">mathCode"><math altimg="si75.gif" overflow="scroll"><mn>3mn><msub><mrow><mstyle mathvariant="normal"><mi>pmi>mstyle>mrow><mrow><mn>3mn><mo>/mo><mn>2mn>mrow>msub>math>, mmlsi97" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si97.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=e18d1fa7023295c9ee60a42d49953810">mg class="imgLazyJSB inlineImage" height="17" width="36" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si97.gif">

mg height="17" border="0" style="vertical-align:bottom" width="36" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0092640X15000388-si97.gif">

mathContainer hidden">mathCode"><math altimg="si97.gif" overflow="scroll"><mn>3mn><msub><mrow><mstyle mathvariant="normal"><mi>dmi>mstyle>mrow><mrow><mn>3mn><mo>/mo><mn>2mn>mrow>msub>math>, and mmlsi119" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si119.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=bfdd80d7aa501b8223bb62bc19c89631">mg class="imgLazyJSB inlineImage" height="17" width="36" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si119.gif">

mathContainer hidden">mathCode"><math altimg="si119.gif" overflow="scroll"><mn>3mn><msub><mrow><mstyle mathvariant="normal"><mi>dmi>mstyle>mrow><mrow><mn>5mn><mo>/mo><mn>2mn>mrow>msub>math>) of the Dirac one-electron atom. The results for ions with the atomic number mmlsi176" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si176.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=9f4e1216ee5b6f8e2dfbbce645471611" title="Click to view the MathML source">1⩽Z⩽137mathContainer hidden">mathCode"><math altimg="si176.gif" overflow="scroll"><mn>1mn><mo>⩽mo><mi>Zmi><mo>⩽mo><mn>137mn>math> are given in 14 tables. The comparison of the numerical values of magnetizabilities for the ground state and for each state belonging to the first set of excited states of selected hydrogenlike ions, obtained with the use of two different values of the fine-structure constant, i.e.: mmlsi4" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si4.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=47ca772225daa95dfaa19dd241ebf5d5">mg class="imgLazyJSB inlineImage" height="14" width="159" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si4.gif">

mg height="14" border="0" style="vertical-align:bottom" width="159" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0092640X15000388-si4.gif">

mathContainer hidden">mathCode"><math altimg="si4.gif" overflow="scroll"><msup><mrow><mi>αmi>mrow><mrow><mo>−mo><mn>1mn>mrow>msup><mo>=mo><mn>137.035mn><mspace width="0.16667em">mspace><mn>999mn><mspace width="0.16667em">mspace><mn>139mn>math> (CODATA 2014) and mmlsi157" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0092640X15000388&_mathId=si157.gif&_user=111111111&_pii=S0092640X15000388&_rdoc=1&_issn=0092640X&md5=3a52b689be1009c918280d7b3e25ff55">mg class="imgLazyJSB inlineImage" height="14" width="159" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0092640X15000388-si157.gif">

mathContainer hidden">mathCode"><math altimg="si157.gif" overflow="scroll"><msup><mrow><mi>αmi>mrow><mrow><mo>−mo><mn>1mn>mrow>msup><mo>=mo><mn>137.035mn><mspace width="0.16667em">mspace><mn>999mn><mspace width="0.16667em">mspace><mn>074mn>math> (CODATA 2010), is also presented.

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