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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| documentation:language_reference:functions:shellaverage [2026/11/12 18:03] – Maurits W. Haverkort | documentation:language_reference:functions:shellaverage [2026/11/12 18:05] (current) – Maurits W. Haverkort | ||
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| $$ | $$ | ||
| - | \begin{eqnarray} \nonumber | + | U_{\mathrm{av}}(p) = F^0 - \frac{2}{25} F^2 |
| - | U_{\mathrm{av}}(p) | + | $$ |
| - | U_{\mathrm{av}}(d) | + | $$ |
| - | U_{\mathrm{av}}(f) | + | U_{\mathrm{av}}(d) = F^0 - \frac{2}{63} \left( F^2 + F^4 \right) |
| - | \end{eqnarray} | + | $$ |
| + | $$ | ||
| + | U_{\mathrm{av}}(f) = F^0 - \frac{4}{195} F^2 - \frac{2}{143} F^4 - \frac{100}{5577} F^6, | ||
| $$ | $$ | ||
| Line 120: | Line 122: | ||
| $$ | $$ | ||
| - | \begin{equation} \nonumber | ||
| U_{\mathrm{av}}(pd) = F^0_{pd} - \frac{1}{15} G^1_{pd} - \frac{3}{70} G^3_{pd} . | U_{\mathrm{av}}(pd) = F^0_{pd} - \frac{1}{15} G^1_{pd} - \frac{3}{70} G^3_{pd} . | ||
| - | \end{equation} | ||
| $$ | $$ | ||
| Line 153: | Line 153: | ||
| $$ | $$ | ||
| - | \begin{equation} \nonumber | ||
| \epsilon_{\uparrow} \hat{N}_{\uparrow} + \epsilon_{\downarrow} \hat{N}_{\downarrow} | \epsilon_{\uparrow} \hat{N}_{\uparrow} + \epsilon_{\downarrow} \hat{N}_{\downarrow} | ||
| + \tfrac{1}{2} U_{\uparrow\uparrow} \hat{N}_{\uparrow} (\hat{N}_{\uparrow}-1) | + \tfrac{1}{2} U_{\uparrow\uparrow} \hat{N}_{\uparrow} (\hat{N}_{\uparrow}-1) | ||
| + \tfrac{1}{2} U_{\downarrow\downarrow} \hat{N}_{\downarrow} (\hat{N}_{\downarrow}-1) | + \tfrac{1}{2} U_{\downarrow\downarrow} \hat{N}_{\downarrow} (\hat{N}_{\downarrow}-1) | ||
| + U_{\uparrow\downarrow} \hat{N}_{\uparrow} \hat{N}_{\downarrow} . | + U_{\uparrow\downarrow} \hat{N}_{\uparrow} \hat{N}_{\downarrow} . | ||
| - | \end{equation} | ||
| $$ | $$ | ||
