page_title: Hyperpolarization (physics)
section_title: Theory
hierarchical_section_title: Hyperpolarization (physics) / Spin-exchange optical pumping / Theory
caption_attribution_description: English: Transitions that occur when circularly polarized light interacts with the alkali metal atoms. The red arrow represents the first transition that occurs when the alkali metal electrons are excited by the laser light.
context_page_description: Hyperpolarization is the nuclear spin polarization of a material in a magnetic field far beyond thermal equilibrium conditions determined by the Boltzmann distribution. It can be applied to gases such as ¹²⁹Xe and ³He, and small molecules where the polarization levels can be enhanced by a factor of 10⁴-10⁵ above thermal equilibrium levels. Hyperpolarized noble gases are typically used in magnetic resonance imaging of the lungs.
  Hyperpolarized small molecules are typically used for in vivo metabolic imaging. For example, a hyperpolarized metabolite can be injected into animals or patients and the metabolic conversion can be tracked in real-time. Other applications include determining the function of the neutron spin-structures by scattering polarized electrons from a very polarized target, surface interaction studies, and neutron polarizing experiments.
context_section_description: To explain the processes of excitation, optical pumping, and spin exchange easier, the most common alkali metal used for this process, rubidium, will be used as an example. Rubidium has an odd number of electrons, with only one in the outermost shell that can be excited under the right conditions. There are two transitions that can occur, one referred to as the D₁ line where the transition occurs from the 5²S1/2 state to the 5²P3/2 state and another referred to the D₂ line where the transition occurs from the 5²S1/2 to the 5²P1/2 state. The D₁ and D₂ transitions can occur if the rubidium atoms are illuminated with light at a wavelength of 794.7 nm and 780 nm, respectively (Figure 1). While it is possible to cause either excitation, laser technology is well-developed for causing the D₁ transition to occur. Those lasers are said to be tuned to the D₁ wavelength (794.7 nm) of rubidium.
  In order to increase the polarization level above thermal equilibrium, the populations of the spin states must be altered. In the absence of magnetic field, the two spin states of a spin I = ½ nuclei are in the same energy level, but in the presence of a magnetic field, the energy levels split into mₛ = ±1/2 energy levels (Figure 2). Here, mₛ is the spin angular momentum with possible values of +1/2 (spin up) or -1/2 (spin down), often drawn as vectors pointing up or down, respectively. The difference in population between these two energy levels is what produces an NMR signal. For example, the two electrons in the spin down state cancel two of the electrons in the spin up state, leaving only one spin up nucleus to be detected with NMR. However, the populations of these states can be altered via hyperpolarization, allowing the spin up energy level to be more populated and therefore increase the NMR signal. This is done by first optically pumping alkali metal, then transferring the polarization to a noble gas nucleus to increase the population of the spin up state.
  The absorption of laser light by the alkali metal is the first process in SEOP. Left-circularly polarized light tuned to the D₁ wavelength of the alkali metal excites the electrons from the spin down ²S1/2 (mₛ=-1/2) state into the spin up ²P1/2 (mₛ=+1/2) state, where collisional mixing then occurs as the noble gas atoms collide with the alkali metal atoms and the mₛ=-1/2 state is partially populated (Figure 3). Circularly polarized light is necessary at low magnetic fields because it allows only one type of angular momentum to be absorbed, allowing the spins to be polarized. Relaxation then occurs from the excited states (mₛ=±1/2) to the ground states (mₛ=±1/2) as the atoms collide with nitrogen, thus quenching any chance of fluorescence and causing the electrons to return to the two ground states in equal populations. Once the spins are depolarized (return to the mₛ=-1/2 state), they are excited again by the continuous wave laser light and the process repeats itself. In this way, a larger population of electron spins in the mₛ=+1/2 state accumulates. The polarization of the rubidium, PRb, can be calculated by using the formula below:
  Where n↑ and n↓ and   are the number of atoms in the spin up (mS=+1/2) and spin down (mS=-1/2) ²S1/2 states.
  Next, the optically pumped alkali metal collides with the noble gas, allowing for spin exchange to occur where the alkali metal electron polarization is transferred to the noble gas nuclei (Figure 4). There are two mechanisms in which this can occur. The angular momentum can be transferred via binary collisions (Figure 4A, also called two-body collisions) or while the noble gas, N₂ buffer gas, and vapor phase alkali metal are held in close proximity via van der Waals forces (Figure 4B, also called three body collisions). In cases where van der Waals forces are very small compared to binary collisions (such is the case for ³He), the noble gas and alkali metal collide and polarization is transferred from the AM to the noble gas. Binary collisions are also possible for ¹²⁹Xe. At high pressures, van der Waals forces dominate, but at low pressures bi
caption: Figure 3. Transitions that occur when circularly polarized light interacts with the alkali metal atoms.
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