Zeeman Effect

In most Atom s, there exist several Electronic Configuration s that have the same Energy , so that transitions between different pairs of configurations correspond to a single line. The presence of a magnetic field breaks the degeneracy, since it interacts in a different way with Electron s with different Quantum Numbers , slightly modifying their energies. The result is that, where there were several configurations with the same energy, now there are different energies, which give rise to several very close spectral lines. Without a magnetic field, configurations a, b and c have the same energy, as do d, e and f. The presence of a magnetic field splits the energy levels. A line produced by a transition from a, b or c to d, e or f now will be several lines between different combinations of a, b, c and d, e, f. Not all transitions will be possible -- see Transition Rule s. Since the distance between the Zeeman sub-levels is proportional with the magnetic field, this effect was used by astronomers to measure the magnetic field of the Sun and other stars. There is also an "anomalous Zeeman" effect that appears on transitions where the net Spin of the Electrons is not 0, the number of Zeeman sub-levels being even instead of odd if there's an uneven number of Electrons involved. It was called "anomalous" because the electron spin was not yet discovered and so there was no good explanation for it when Zeeman discovered the effect. If the magnetic field strength is too high, the effect is no longer linear; at even higher field strength, electron coupling is disturbed and the spectral lines rearrange. This is called Paschen-Back Effect . The Zeeman effect is named after the Dutch physicist Pieter Zeeman . THEORETICAL PRESENTATION The total Hamiltonian of an atom in a magnetic field is: : $H = H_0 + H_1 = H_0 + \sum_\alpha \xi(ec{r_\alpha}) ec{L} \cdot ec{S} -\sum_\alpha ec{\mu_{\alpha}} \cdot ec{B}$ where $H_0$ is the unperturbed Hamiltonian of the atom, and the sums over α are sums over the electrons in the atom. The term : $\xi(ec{r_\alpha}) ec{L} \cdot ec{S}$ is the LS-coupling for each electron (indexed by α) in the atom. The sum vanishes if there is only one electron. The magnetic coupling : $ec{\mu_{\alpha}} \cdot ec{B} = rac{\mu_{B}}{\hbar}(g_L ec{L} + g_S ec{S}) \cdot ec{B}$ is the energy due to the magnetic moment μ of the α-th electron. It can be written as sum of contributions of the Orbital Angular Momentum and of Spin Angular Momentum , with each multiplied by the gyroscopic or Landé G-factor . By projecting the vector quantities onto the z-axis, the Hamiltonian may be written as : $H = H_0 + \xi(r) ec{L}\cdot ec{S} + \mu_B (g_L L_z+ g_s S_z) B_z \approx H_{at} + rac{\mu_B}{\hbar}(J_z + S_z) B_z$ where the approximation results from taking the g-factors are $g_L=1$ and $g_S \approx 2$ . The summation over the electrons was omitted for readability. Here, $J_z=L_z+S_z$ is the total angular momentum, and the LS-coupling term has been folded into $H_0$ . The size of the interaction term ''H'' ' is not always small, and can induce large effects on the system. In the Paschen-Back Effect , described below, ''H'' ' cannot be treated as a perturbation, as its magnitude is comparable to or larger than the unperturbed system $H_{at}$ . The ''H'' ' term does not commute with $H_{at}$ . In particular, $S_z$ doesn't commute with the Spin-orbit Interaction in $H_{at}$ . STRONG FIELD (PASCHEN-BACK EFFECT)
	:<math> \left( H {at} + Rac{B {z}\mu B}{\hbar}(L {z}+2S Z) Ight) A Angle	(E_{at} + B_z\mu_B (m_l + 2m_s)A angle </math>

	CATEGORIES ABOUT ZEEMAN EFFECT

	atomic physics

	magnetism

	foundational quantum physics

	physical phenomena

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Zeeman Effect