| 83 |
|
|
| 84 |
|
The corresponding field is: |
| 85 |
|
|
| 86 |
< |
\f$ \mathbf{E} = \frac{g}{2} \left( |
| 86 |
> |
\f$ \mathbf{E} = \frac{g}{2} \left( \begin{array}{c} |
| 87 |
|
2\left(a_1 b_1 - \frac{\cos\psi}{3}\right) x + (a_1 b_2 + a_2 b_1) y |
| 88 |
|
+ (a_1 b_3 + a_3 b_1) z \\ |
| 89 |
|
(a_2 b_1 + a_1 b_2) x + 2 \left(a_2 b_2 - \frac{\cos\psi}{3}\right) y |
| 96 |
|
|
| 97 |
|
The corresponding field gradient is: |
| 98 |
|
|
| 99 |
< |
\f$ \nabla \mathbf{E} = \frac{g}{2} \left( \array{ccc} |
| 99 |
> |
\f$ \nabla \mathbf{E} = \frac{g}{2} \left( \begin{array}{ccc} |
| 100 |
|
2\left(a_1 b_1 - \frac{\cos\psi}{3}\right) & |
| 101 |
|
(a_1 b_2 + a_2 b_1) & (a_1 b_3 + a_3 b_1) \\ |
| 102 |
|
(a_2 b_1 + a_1 b_2) & 2 \left(a_2 b_2 - \frac{\cos\psi}{3}\right) & |
| 114 |
|
\f$ \mathbf{\tau} = \mathbf{D} \times \mathbf{E}(\mathbf{r}) \f$. |
| 115 |
|
|
| 116 |
|
For quadrupolar atoms, the uniform field gradient exerts a potential, |
| 117 |
< |
\f$ U = - \mathsf{Q}:\nabla \mathbf{E} $\f, and a torque |
| 117 |
> |
\f$ U = - \mathsf{Q}:\nabla \mathbf{E} \f$, and a torque |
| 118 |
|
\f$ \mathbf{F} = 2 \mathsf{Q} \times \nabla \mathbf{E} \f$ |
| 119 |
|
|
| 120 |
|
*/ |
