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The development of a new direction of research on the production and application of spin-polarized isotopes of noble gases, 3He and 129Xe, is overviewed. Methods of laser hyperpolarization, problems of enhancing the efficiency of laser energy input, and methods of storing hyperpolarized (HP) isotopes are described. Examples and advantages of using HP isotopes in fundamental physics, engineering, medicine, and biology, as well as the progress in the creation of biosensors on hyperpolarized noble gases, are discussed. It has been shown that the study of protein structures and host-guest molecular complexes can prove useful in searching for means of the targeted delivery of radioactive isotopes (radiopharmaceuticals) in nuclear medicine. It is concluded that the progress in modern technologies for producing miniature electronic devices is suggestive of an imminent emergence of small-size scanners for human brain research. At the same time, a high sensitivity of the method is expected to provide the possibility of studying not only the structure of tissues and bloodstream, but also the response of the brain to various stimuli, and even cognitive functions. [ABSTRACT FROM AUTHOR]

The spin structure of the first order reduced density matrix (RDM-1) for an arbitrary many-electron state with zero z-projection of the total spin is examined. It is well known that for the state ΨS0(r1σ1,...,rN σN), which is an eigenstate of operators ${\widehat {S^2}}$ and ${\widehat S}_z$ with quantum numbers S and M = 0, the matrix elements for spins α and β are equal for any r and r′: ρS0α(r|r′) = ρS0β(r|r′). In the present article, it is shown that the same is true for any state ΦM = 0(r1σ1,...,rN,σN) with indefinite total spin if in the expansion ΦM = 0 = ∑SDS ΨS0 only spins S with the same parity are present. To prove the statement, it is shown that the wave function ΨS0 acquires the phase factor (-1)N/2-S when all spin functions α(σi) are changed for β(σi) and vice versa. In the developed proof, the Hamiltonian was not used at all and it was not even assumed that the wave function ΨS0 is an eigenfunction of some Hamiltonian. Therefore the obtained result is valid for the stationary and non-stationary states, ground and excited states, with and without homogeneous magnetic field imposed, exact and approximate wave functions. From the result obtained it follows, in particular, that for the stationary state to be spin-polarized (ρ0α(r|r) ≠ ρ0β(r|r)) it is necessary for the Hamiltonian to mix states with different parity spins. The consequences from the proved statement for the antiferromagnetic state are discussed. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [ABSTRACT FROM AUTHOR]