Spin polarization of atomic nuclei beyond thermal equilibrium
Hyperpolarization is the spin polarization of the atomic nuclei 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 and , 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 (MRI) 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 (3He), surface interaction studies, and neutron polarizing experiments.
Spin-exchange optical pumping.
Introduction.
Spin exchange optical pumping (SEOP) is one of several hyperpolarization techniques discussed on this page. This technique specializes in creating hyperpolarized (HP) noble gases, such as 3He, 129Xe, and quadrupolar 131Xe, 83Kr, and 21Ne. Noble gases are required because SEOP is performed in the gas phase, they are chemically inert, non-reactive, chemically stable with respect to alkali metals, and their T1 is long enough to build up polarization. Spin 1/2 noble gases meet all these requirements, and spin 3/2 noble gases do to an extent, although some spin 3/2 do not have a sufficient T1. Each of these noble gases has their own specific application, such as characterizing lung space and tissue via "in vivo" molecular imaging and functional imaging of lungs, to study changes in metabolism of healthy versus cancer cells, or use as targets for nuclear physics experiments. During this process, circularly polarized infrared laser light, tuned to the appropriate wavelength, is used to excite electrons in an alkali metal, such as caesium or rubidium inside a sealed glass vessel. Infrared light is necessary because it contains the wavelengths necessary to excite the alkali metal electrons, although the wavelength necessary to excite sodium electrons is below this region (Table 1).
The angular momentum is transferred from the alkali metal electrons to the noble gas nuclei through collisions. Nitrogen is used as a quenching gas, which prevents the fluorescence of the polarized alkali metal, which would lead to de-polarization of the noble gas. If fluorescence was not quenched, the light emitted during relaxation would be randomly polarized, working against the circularly polarized laser light. While different sizes of glass vessels (also called cells), and therefore different pressures, are used depending on the application, one amagat of total pressure of noble gas and nitrogen is sufficient for SEOP and 0.1 amagat of nitrogen density is needed to quench fluorescence. Great improvements in 129Xe hyperpolarization technology have achieved ; 50% level at flow rates of 1–2 L/min, which enables human clinical applications.
History.
The discovery of SEOP took decades for all the pieces to fall into place to create a complete technique. First, in 1897, Zeeman's studies of sodium vapor led to the first result of "optical pumping". The next piece was found in 1950 when Kastler determined a method to electronically spin-polarize rubidium alkali metal vapor using an applied magnetic field and illuminating the vapor with resonant circularly polarized light. Ten years later, Marie-Anne Bouchiat, T. M. Carver, and C. M. Varnum performed "spin exchange", in which the electronic spin polarization was transferred to nuclear spins of a noble gas (3He and 129Xe) through gas-phased collisions. Since then, this method has been greatly improved and expanded to use with other noble gases and alkali metals.
Theory.
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 52P1/2 state and another referred to the D2 line where the transition occurs from the 52S1/2 to the 52P3/2 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 = 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:
formula_1
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 binary collisions dominate.
Buildup of polarization.
This cycle of excitation, polarization, depolarization, and re-polarization, etc. takes time before a net polarization is achieved. The buildup of nuclear polarization, PN(t), is given by:
formula_2
Where ⟨PA⟩ is the alkali metal polarization, γSE is the spin exchange rate, and Γ is the longitudinal relaxation rate of the noble gas. Relaxation of the nuclear polarization can occur via several mechanisms and is written as a sum of these contributions:
formula_3
Where Γt, Γp, Γg, and Γw represent the relaxation from the transient Xe2 dimer, the persistent Xe2 dimer, diffusion through gradients in the applied magnetic field, and wall relaxation, respectively. In most cases, the largest contributors to the total relaxation are persistent dimers and wall relaxations. A Xe2 dimer can occur when two Xe atoms collide and are held together via van der Waals forces, and it can be broken when a third atom collides with it. It is similar to Xe-Rb during spin exchange (spin transfer) where they are held in close proximity to each other via van der Waals forces. Wall relaxation is when the hyperpolarized Xe collides with the walls of the cell and is de-polarized due to paramagnetic impurities in the glass.
The buildup time constant, ΓB, can be measured by collecting NMR spectra at time intervals falling within the time it takes to reach steady-state polarization (i.e. the maximum polarization that can be achieved, seen by the maximum signal output). The signal integrals are then plotted over time and can be fit to obtain the buildup time constant. Collecting a buildup curve at several different temperatures and plotting the values as a function of alkali metal vapor density (since vapor density increases with an increase in cell temperature) can be used to determine the spin destruction rate and the per-atom spin exchange rate using:
formula_4
Where γ' is the per-atom spin exchange rate, [AM] is the alkali metal vapor density, and ΓSD is the spin destruction rate. This plot should be linear, where γ' is the slope and ΓSD is the y-intercept.
Relaxation: T1.
Spin exchange optical pumping can continue indefinitely with continuous illumination, but there are several factors that cause relaxation of polarization and thus a return to the thermal equilibrium populations when illumination is stopped. In order to use hyperpolarized noble gases in applications such as lung imaging, the gas must be transferred from the experimental setup to a patient. As soon as the gas is no longer actively being optically pumped, the degree of hyperpolarization begins to decrease until thermal equilibrium is reached. However, the hyperpolarization must last long enough to transfer the gas to the patient and obtain an image. The longitudinal spin relaxation time, denoted as T1, can be measured easily by collecting NMR spectra as the polarization decreases over time once illumination is stopped. This relaxation rate is governed by several depolarization mechanisms and is written as:
formula_5
Where the three contributing terms are for collisional relaxation (CR), magnetic field inhomogeneity (MFI) relaxation, and relaxation caused by the presence of paramagnetic oxygen (O2). The T1 duration could be anywhere from minutes to several hours, depending on how much care is put into lessening the effects of CR, MFI, and O2. The last term has been quantified to be 0.360 s−1 amagat−1, but the first and second terms are hard to quantify since the degree of their contribution to the overall T1 is dependent on how well the experimental setup and cell are optimized and prepared.
Experimental setup in SEOP.
In order to perform SEOP, it is first necessary to prepare the optical cell. Optical cells (Figure 5) are designed for the particular system in mind and glass blown using a transparent material, typically pyrex glass (borosilicate). This cell must then be cleaned to eliminate all contaminants, particularly paramagnetic materials which decrease polarization and the T1. The inner surface of the cell is then coated to (a) serve as a protective layer for the glass in order to lessen the chance of corrosion by the alkali metal, and (b) minimize depolarization caused by the collisions of polarized gas molecules with the walls of the cell. Decreasing wall relaxation leads to longer and higher polarization of the noble gas. 
While several coatings have been tested over the years, SurfaSil (Figure 6, now referred to as hydrocarbon soluble siliconizing fluid) is the most common coating used in a ratio of 1:10 SurfaSil: hexane because it provides long T1 values. The thickness of the SurfaSil layer is about 0.3-0.4 μm. Once evenly coated and dried, the cell is then placed in an inert environment and a droplet of alkali metal (≈200 mg) is placed in the cell, which is then dispersed to create an even