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xml:space="preserve">π</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>4</ml:real> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">q</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="346" left="6" top="283.5" width="171.75" height="14.25" align-x="47.25" align-y="294" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">θ_</ml:id> <ml:boundVars> <ml:id xml:space="preserve">q</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:real>5</ml:real> <ml:apply> <ml:id xml:space="preserve">η_</ml:id> <ml:sequence> <ml:id xml:space="preserve">q</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:id xml:space="preserve">η_</ml:id> <ml:sequence> <ml:id xml:space="preserve">q</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="19052" left="6" top="306.75" width="195" height="36.75" align-x="26.25" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="DE4F4675-C558-4C6F-B29C-9E4C448865C7" version-id="1574A3E4-98D2-4E34-9F6B-DDC4B42BD94D" branch-id="00000000-0000-0000-0000-000000000000" revision-num="488218844" is-modified="false" region-id="0" href="D:\BURKHARD HEIM\Heim 4\Heim1989a.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="DE4F4675-C558-4C6F-B29C-9E4C448865C7" version-id="1574A3E4-98D2-4E34-9F6B-DDC4B42BD94D" branch-id="00000000-0000-0000-0000-000000000000" revision-num="488213324" is-modified="false" region-id="0" href="D:\BURKHARD HEIM\Heim 4\Heim1989a.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">d295491a49f3f19ddc1c144f0efb29e1</contentHash> <ml:define> <ml:id xml:space="preserve">Kα</ml:id> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">η_</ml:id> <ml:sequence> <ml:real>2</ml:real> <ml:real>2</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">η_</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="13"> <element-image-map> <box left="1.5" top="0.75" width="193.5" height="35.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="2266" left="6" top="350.25" width="58.5" height="33.75" align-x="24" align-y="372" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">dd</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:parens> <ml:real>5</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>9</ml:real> <ml:id xml:space="preserve">θ</ml:id> </ml:apply> <ml:id xml:space="preserve">Kα</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="19059" left="6" top="402.75" width="162" height="13.5" align-x="6" align-y="414" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12"> <c val="#f00">fine structure constant</c> </f> </p> </text> </region> <region region-id="19053" left="6" top="422.25" width="46.5" height="24" align-x="6" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">From Heim</p> </text> </region> <region region-id="19269" left="6" top="450.75" width="119.25" height="51.75" align-x="19.5" align-y="468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">dd</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">dd</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="19272" left="402" top="464.25" width="107.25" height="27.75" align-x="417" align-y="480" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0f0" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">α</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>137.03601894486013</ml:real> </result> </ml:eval> </math> <rendering item-idref="16"/> </region> <region region-id="19055" left="6" top="512.25" width="249.75" height="24" align-x="15.75" align-y="522" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">From the usual definition using calculated elementary charge</p> </text> </region> <region region-id="19268" left="6" top="542.25" width="93.75" height="33.75" align-x="24.75" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">αd</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">eq</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">c</ml:id> </ml:apply> <ml:real>4</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-7</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">hb</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="19273" left="402" top="548.25" width="108" height="27.75" align-x="422.25" align-y="564" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0f0" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:real font="0">1</ml:real> <ml:id xml:space="preserve">αd</ml:id> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>137.0360125330794</ml:real> </result> </ml:eval> </math> <rendering item-idref="18"/> </region> <region region-id="18968" left="6" top="732.75" width="147.75" height="13.5" align-x="6" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="12"> <c val="#f00">giromagnetic factors</c> </f> </p> </text> </region> <region region-id="18969" left="6" top="758.25" width="115.5" height="12" align-x="15.75" align-y="768" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">From Mr. Florian C. Rieger</p> </text> </region> <region region-id="18970" left="6" top="780.75" width="185.25" height="36.75" align-x="23.25" align-y="804" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="#0f0" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Ve</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">θ</ml:id> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:id xml:space="preserve">θ</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="19229" left="402" top="801" width="108" height="12.75" align-x="417.75" align-y="810" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0f0" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Ve</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.0011596196168608</ml:real> </result> </ml:eval> </math> <rendering item-idref="20"/> </region> <region region-id="18972" left="6" top="830.25" width="116.25" height="12" align-x="15.75" align-y="840" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">From 1989 paper version A</p> </text> </region> <region region-id="18973" left="6" top="858.75" width="210.75" height="51.75" align-x="23.25" align-y="882" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Ve</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">θ</ml:id> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">η_</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:id xml:space="preserve">θ</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="19230" left="402" top="879" width="108" height="12.75" align-x="417.75" align-y="888" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#0f0" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Ve</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.0011595388353454</ml:real> </result> </ml:eval> </math> <rendering item-idref="22"/> </region> <region region-id="18975" left="6" top="924.75" width="152.25" height="35.25" align-x="25.5" align-y="948" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Vμ</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Ve</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:id xml:space="preserve">η_</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> 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