Dịch chuyển trường nguyên tử và sai lệch quang phổ
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| spin–orbit/spɪn ˈɔːbɪt/ | The coupling between an electron’s spin and its orbital motion. |
| Zeeman effect/ˈziːmən ɪˈfekt/ | The splitting of spectral lines in a magnetic field. |
| Stark effect/stɑːk ɪˈfekt/ | The shift and splitting of energy levels in an electric field. |
Same field, different labels
- The same magnetic field splits a level one way when it is weak compared with spin–orbit 自旋–轨道 coupling, and differently when it is strong. Which labels you use depends on that comparison.
- GRE atomic questions test the Zeeman effect 塞曼效应 in both regimes, transition counts and the Stark effect 斯塔克效应.
Strong field: uncoupled labels
- $H_Z = \mu_BB(L_z + 2S_z)/\hbar$, shift $\mu_BB(m_l + 2m_s)$, $\mu_B \approx 5.79\times10^{-5}$ eV/T.
- Valid when $\mu_BB$ exceeds the spin–orbit splitting (Paschen–Back).
Weak field: $g_J$
- $\Delta E = g_J\mu_BBm_J$, $g_J = 1 + \dfrac{J(J+1) + S(S+1) - L(L+1)}{2J(J+1)}$.
- $L = 1$, $S = \tfrac12$: $J = \tfrac32$ has $g_J = \tfrac43$; $J = \tfrac12$ has $g_J = \tfrac23$.
$B = 2$ T, $J = \tfrac32$, $m_J = \tfrac12$: $\Delta E = \tfrac43 \cdot \tfrac12 \cdot 5.788\times10^{-5} \cdot 2 \approx 7.72\times10^{-5}$ eV.
Weak field or strong field?
Choose the Zeeman regime from the energy comparison.
$g_J = 2/3$, $m_J = 1/2$, $B = 3$ T. Zeeman shift in μeV (two decimal places)? Use $\mu_B = 5.788\times10^{-5}$ eV/T.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
$\Delta E = g_J m_J \mu_B B = (2/3)(1/2)(3)\mu_B = \mu_B = 57.88$ μeV.
$g_J$ for the level $L = 1$, $S = 1/2$, $J = 3/2$ is
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
1 + (15/4 + 3/4 − 2)/(15/2).
Counting lines
- Photon shift = upper shift − lower shift. Normal triplet ($L = 1 \to 0$, spin ignored): $\Delta m_l = 0, \pm1$ gives three lines $-\mu_BB, 0, +\mu_BB$.
- Several transitions can share a frequency; count lines, not levels.
How many lines does the normal Zeeman triplet $L = 1 \to 0$ show?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
In the normal Zeeman effect the allowed $\Delta m_l = -1, 0, +1$ give three lines.
Stark effect
- Perturbation $eFz$. A nondegenerate parity eigenstate has $\langle z\rangle = 0$: no linear shift (a quadratic one remains).
- Degenerate opposite-parity pair with dipole matrix $\begin{pmatrix} 0&d\\d&0 \end{pmatrix}$: shifts $\pm dF$, splitting $2|dF|$.
A degenerate pair has $d = 1$ e·nm in a field $F = 2\times10^5$ V/m. Splitting in meV?
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
2dF = 2 × 10⁻⁹ m × 2×10⁵ V/m × e.
A nondegenerate state of definite parity shows a linear Stark shift.
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
A state of definite parity has $\langle z\rangle = 0$, so the first-order (linear) Stark shift vanishes.
Recap
- Strong field: $m_l + 2m_s$. Weak field: $g_Jm_J$.
- Photon shift = upper − lower.
- Linear Stark shifts need degenerate opposite-parity states.
- Spin–orbit refers to the coupling between an electron’s spin and its orbital motion.
- Stark effect: The shift and splitting of energy levels in an electric field.