https://dictionary.iucr.org/index.php?title=Selection_rules&feed=atom&action=historySelection rules - Revision history2024-03-29T09:21:02ZRevision history for this page on the wikiMediaWiki 1.30.0https://dictionary.iucr.org/index.php?title=Selection_rules&diff=4879&oldid=prevBrianMcMahon: Language (Fe -> Fr!)2021-07-14T16:15:49Z<p>Language (Fe -> Fr!)</p>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><font color="blue">Règles de sélection</font> (''<del class="diffchange diffchange-inline">Fe</del>'').  <font color="red">Auswahlregeln</font> (''Ge'').  <font color="black">Regole di selezione</font> (''It'').  <font color="purple">選択則</font> (''Ja''). <font color="green">Reglas de selección</font> (''Sp'').</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><font color="blue">Règles de sélection</font> (''<ins class="diffchange diffchange-inline">Fr</ins>'').  <font color="red">Auswahlregeln</font> (''Ge'').  <font color="black">Regole di selezione</font> (''It'').  <font color="purple">選択則</font> (''Ja''). <font color="green">Reglas de selección</font> (''Sp'').</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Definition ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Definition ==</div></td></tr>
</table>BrianMcMahonhttps://dictionary.iucr.org/index.php?title=Selection_rules&diff=4850&oldid=prevMassimoNespolo: lang2021-02-19T13:35:41Z<p>lang</p>
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<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><font color="red">Auswahlregeln</font> (''Ge'').  <font color="purple">選択則</font> (''Ja''). <del class="diffchange diffchange-inline"> </del><font color="green">Reglas de selección</font> (''Sp'').</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><font color="blue">Règles de sélection</font> (''Fe'').  </ins><font color="red">Auswahlregeln</font> (''Ge<ins class="diffchange diffchange-inline">'').  <font color="black">Regole di selezione</font> (''It</ins>'').  <font color="purple">選択則</font> (''Ja''). <font color="green">Reglas de selección</font> (''Sp'').</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Definition ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Definition ==</div></td></tr>
</table>MassimoNespolohttps://dictionary.iucr.org/index.php?title=Selection_rules&diff=4790&oldid=prevShigeruOhba at 13:30, 26 March 20192019-03-26T13:30:37Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Definition ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Definition ==</div></td></tr>
</table>ShigeruOhbahttps://dictionary.iucr.org/index.php?title=Selection_rules&diff=4593&oldid=prevBrianMcMahon: Added German and Spanish translations (U. Mueller)2017-11-20T08:40:25Z<p>Added German and Spanish translations (U. Mueller)</p>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><font color="red">Auswahlregeln</font> (''Ge''). <font color="green">Reglas de selección</font> (''Sp'').</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Definition ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Definition ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Selection rules refer to the conditions under which the quantum mechanical transition matrix elements for a process are different from zero (and hence the process is allowed), due to constraints derived from the symmetry properties of the states involved and those of the transition operator. Since the set of symmetries for a quantum system form a group, one can classify the transformation properties of the states (eigenfunctions) and the transition operator according to the irreducible representations of the group itself. In such a case the Wigner&ndash;Eckart theorem dictates the conditions for the process to occur (see any standard text on group theory).</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Selection rules refer to the conditions under which the quantum mechanical transition matrix elements for a process are different from zero (and hence the process is allowed), due to constraints derived from the symmetry properties of the states involved and those of the transition operator. Since the set of symmetries for a quantum system form a group, one can classify the transformation properties of the states (eigenfunctions) and the transition operator according to the irreducible representations of the group itself. In such a case the Wigner&ndash;Eckart theorem dictates the conditions for the process to occur (see any standard text on group theory).</div></td></tr>
</table>BrianMcMahonhttps://dictionary.iucr.org/index.php?title=Selection_rules&diff=4219&oldid=prevBrianMcMahon at 10:10, 20 May 20172017-05-20T10:10:09Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In the most common example for transition theory, if we classify the system states (eigenfunctions) according to the full rotation group and expand the transition operator in multipoles as</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>In the most common example for transition theory, if we classify the system states (eigenfunctions) according to the full rotation group and expand the transition operator in multipoles as</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\mathbf{p}e^{i\mathbf{k \cdot r}} = \sum\limits_l f_l(r)\mathbf{Y}_l(\hat\mathbf{r})</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\mathbf{p}e^{i\mathbf{k \cdot r}} = \sum\limits_l f_l(r)\mathbf{Y}_l(\hat<ins class="diffchange diffchange-inline">{</ins>\mathbf{r<ins class="diffchange diffchange-inline">}</ins>})</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>then the angular part of the matrix element will be proportional to <math>\langle J_f|Y_l|J_i\rangle</math> where <math>J=L+S \quad (j=l+s)</math> in a Russell&ndash;Saunders coupling scheme. Therefore, from</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>then the angular part of the matrix element will be proportional to <math>\langle J_f|Y_l|J_i\rangle</math> where <math>J=L+S \quad (j=l+s)</math> in a Russell&ndash;Saunders coupling scheme. Therefore, from</div></td></tr>
</table>BrianMcMahonhttps://dictionary.iucr.org/index.php?title=Selection_rules&diff=4218&oldid=prevBrianMcMahon: Style edits to align with printed edition2017-05-20T10:01:41Z<p>Style edits to align with printed edition</p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>|L_f - L_i| \le l \le L_f + L_i</math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math>|L_f - L_i| \le l \le L_f + L_i</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><math>\Delta S=0; \Delta M_S = 0; \Delta M_j = m_i</math></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><math>\Delta S=0; \Delta M_S = 0; \Delta M_j = m_i<ins class="diffchange diffchange-inline">,</ins></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>which provide a set of selection rules in this case. <math>J_f=0</math> to <math>J_i=0</math> transitions are forbidden by the above rule, since the lowest multipole operator (dipole radiation) is a vector (<math>l=1;</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>which provide a set of selection rules in this case. <math>J_f=0</math> to <math>J_i=0</math> transitions are forbidden by the above rule, since the lowest multipole operator (dipole radiation) is a vector (<math>l=1;</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>m_l =\pm 1,0</math>). Conditions on symmetries include those relating to parity, orbital angular momentum quantum number, spin quantum number, (multi-)polarity of the photon field causing the transition, <del class="diffchange diffchange-inline">polarisation </del>of the photon field causing the transition, etc. For summation of angular momenta, such as for molecular levels; hyperfine structure including nuclear angular momenta; or coupling within Russell&ndash;Saunders, ''j&ndash;j'' or mixed schemes, a vector triangle summation must generally be followed as above, which provides most selection rules. Different <del class="diffchange diffchange-inline">polarisations </del>have different selection rules, so an edge or XAFS spectrum using (<del class="diffchange diffchange-inline">polarised</del>) synchrotron radiation will have a different shape and structure depending upon whether the incident X-ray field is <del class="diffchange diffchange-inline">linear polarised</del>, circularly <del class="diffchange diffchange-inline">polarised, </del>partially <del class="diffchange diffchange-inline">polarised</del>.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>m_l =\pm 1,0</math>). Conditions on symmetries include those relating to parity, orbital angular momentum quantum number, spin quantum number, (multi-)polarity of the photon field causing the transition, <ins class="diffchange diffchange-inline">polarization </ins>of the photon field causing the transition, etc. For summation of angular momenta, such as for molecular levels; hyperfine structure including nuclear angular momenta; or coupling within Russell&ndash;Saunders, ''j&ndash;j'' or mixed schemes, a vector triangle summation must generally be followed as above, which provides most selection rules. Different <ins class="diffchange diffchange-inline">polarizations </ins>have different selection rules, so an edge or XAFS spectrum using (<ins class="diffchange diffchange-inline">polarized</ins>) synchrotron radiation will have a different shape and structure depending upon whether the incident X-ray field is <ins class="diffchange diffchange-inline">linearly polarized</ins>, circularly <ins class="diffchange diffchange-inline">polarized or </ins>partially <ins class="diffchange diffchange-inline">polarized</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Electric dipole transition is only the dominant lowest order transition coupling, tending to be dominant for low energies or low-''Z'' elements (even in compounds). However, for such elements as transition metals, higher order terms including electric quadrupole radiation and magnetic dipole radiation become stronger and have complementary selection rules for atomic, molecular and condensed matter quantum systems. Higher order radiation is crucial for the interpretation of <math>K\alpha</math> spectra satellites<del class="diffchange diffchange-inline">; </del>for continuum <del class="diffchange diffchange-inline">photoionisation </del>amplitudes and XAFS and absorption edges and for pre-edge features.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Electric dipole transition is only the dominant lowest<ins class="diffchange diffchange-inline">-</ins>order transition coupling, tending to be dominant for low energies or low-''Z'' elements (even in compounds). However, for such elements as transition metals, higher<ins class="diffchange diffchange-inline">-</ins>order terms including electric quadrupole radiation and magnetic dipole radiation become stronger and have complementary selection rules for atomic, molecular and condensed matter quantum systems. Higher<ins class="diffchange diffchange-inline">-</ins>order radiation is crucial for the interpretation of <math>K\alpha</math> spectra satellites<ins class="diffchange diffchange-inline">, </ins>for continuum <ins class="diffchange diffchange-inline">photoionization </ins>amplitudes and XAFS and absorption edges<ins class="diffchange diffchange-inline">, </ins>and for pre-edge features.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== History ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== History ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In widespread tabulations of photoeffect for atomic systems (''viz.'' Creagh in ''International Tables for X-ray Crystallography, Volume C'', FFAST in the USA and XCOM/Hubbell), some authors have clarified the significance in the computations of dipole, higher order or 'all-order’ computations.  </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In widespread tabulations of photoeffect for atomic systems (''viz.'' Creagh in ''International Tables for X-ray Crystallography, Volume C'', FFAST in the USA and XCOM/Hubbell), some authors have clarified the significance in the computations of dipole, higher<ins class="diffchange diffchange-inline">-</ins>order or 'all-order’ computations.  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:X-ray absorption spectroscopy]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:X-ray absorption spectroscopy]]</div></td></tr>
</table>BrianMcMahonhttps://dictionary.iucr.org/index.php?title=Selection_rules&diff=3699&oldid=prevBrianMcMahon: Created page with "== Definition == Selection rules refer to the conditions under which the quantum mechanical transition matrix elements for a process are different from zero (and hence the proces..."2016-04-13T15:18:34Z<p>Created page with "== Definition == Selection rules refer to the conditions under which the quantum mechanical transition matrix elements for a process are different from zero (and hence the proces..."</p>
<p><b>New page</b></p><div>== Definition ==<br />
Selection rules refer to the conditions under which the quantum mechanical transition matrix elements for a process are different from zero (and hence the process is allowed), due to constraints derived from the symmetry properties of the states involved and those of the transition operator. Since the set of symmetries for a quantum system form a group, one can classify the transformation properties of the states (eigenfunctions) and the transition operator according to the irreducible representations of the group itself. In such a case the Wigner&ndash;Eckart theorem dictates the conditions for the process to occur (see any standard text on group theory).<br />
<br />
In the most common example for transition theory, if we classify the system states (eigenfunctions) according to the full rotation group and expand the transition operator in multipoles as<br />
<br />
<math>\mathbf{p}e^{i\mathbf{k \cdot r}} = \sum\limits_l f_l(r)\mathbf{Y}_l(\hat\mathbf{r})</math><br />
<br />
then the angular part of the matrix element will be proportional to <math>\langle J_f|Y_l|J_i\rangle</math> where <math>J=L+S \quad (j=l+s)</math> in a Russell&ndash;Saunders coupling scheme. Therefore, from<br />
addition of angular momenta and the fact that the transition operator does not affect the spin, we derive<br />
<br />
<math>|J_f - J_i| \le l \le J_f + J_i</math><br />
<br />
<math>|L_f - L_i| \le l \le L_f + L_i</math><br />
<br />
<math>\Delta S=0; \Delta M_S = 0; \Delta M_j = m_i</math><br />
<br />
which provide a set of selection rules in this case. <math>J_f=0</math> to <math>J_i=0</math> transitions are forbidden by the above rule, since the lowest multipole operator (dipole radiation) is a vector (<math>l=1;<br />
m_l =\pm 1,0</math>). Conditions on symmetries include those relating to parity, orbital angular momentum quantum number, spin quantum number, (multi-)polarity of the photon field causing the transition, polarisation of the photon field causing the transition, etc. For summation of angular momenta, such as for molecular levels; hyperfine structure including nuclear angular momenta; or coupling within Russell&ndash;Saunders, ''j&ndash;j'' or mixed schemes, a vector triangle summation must generally be followed as above, which provides most selection rules. Different polarisations have different selection rules, so an edge or XAFS spectrum using (polarised) synchrotron radiation will have a different shape and structure depending upon whether the incident X-ray field is linear polarised, circularly polarised, partially polarised.<br />
<br />
Electric dipole transition is only the dominant lowest order transition coupling, tending to be dominant for low energies or low-''Z'' elements (even in compounds). However, for such elements as transition metals, higher order terms including electric quadrupole radiation and magnetic dipole radiation become stronger and have complementary selection rules for atomic, molecular and condensed matter quantum systems. Higher order radiation is crucial for the interpretation of <math>K\alpha</math> spectra satellites; for continuum photoionisation amplitudes and XAFS and absorption edges and for pre-edge features.<br />
<br />
== History ==<br />
In widespread tabulations of photoeffect for atomic systems (''viz.'' Creagh in ''International Tables for X-ray Crystallography, Volume C'', FFAST in the USA and XCOM/Hubbell), some authors have clarified the significance in the computations of dipole, higher order or 'all-order’ computations. <br />
<br />
[[Category:X-ray absorption spectroscopy]]</div>BrianMcMahon