Ortho-state

In very pure hydrogen, there can be hardly any permanent chemical change produced by irradiation. However, the ion-molecule reaction (5.1) does occur in the mass spectrometer, and it is believed to be important in radiolysis. The H2 molecule can exist in the ortho (nuclear spin parallel) or para (antiparallel) states. At ordinary temperatures, equilibrium should favor the ortho state by 3 1. However, the rate of equilibration is slow in the absence of catalysts but can be affected by irradiation. Initially, an H atom is produced either by the reaction (5.1) or by the dissociation of an excited molecule. This is followed by the chain reaction (H. Eyring et al, 1936)... 

ORTHO-STATE. I. In diatomic molecules, such as hydrogen molecules, the ortho-state exists when the spin vectors of the two atomic nuclei are in the same direction (i.e., parallel), whereas the para-state is the one in which the nuclei arc spinning in opposite directions. 

In helium the ortho-state is characterized by a particular mode of coupling of the electron spins. See also Helium. 

The requirement set by the exclusion principle, given in equation (6.235), restricts the nuclear spin states which can combine with a rotational level of a given parity. They can be either symmettic or antisymmettic with respect to Pu. The number of symmetric (ortho) states is always greater than the number of antisymmetric (para) states. For equivalent nuclei with spin I, ... 

The nuclear partition function of any molecule or atom is the degeneracy of the ground state nuclear energy level. The degeneracy of the ortho state is given as... 

The I So) state couples to the symmetric ground para-state to form a singlet manifold and the T ) states couple to the odd ortho-state and forms the triplet manifold. The splitting between these states is described by the quantum mechanical exchange interaction, which was given by Dirac in the form... 

The origins of symmetry induced nuclear polarization can be summarized as follows as mentioned above molecular dihydrogen is composed of two species, para-H2, which is characterized by the product of a symmetric rotational wave-function and an antisymmetric nuclear spin wave function and ortho-H2, which is characterized by an antisymmetric rotational and one of the symmetric nuclear spin wavefunctions. In thermal equilibrium at room temperature each of the three ortho-states and the single para-state have practically all equal probability. In contrast, at temperatures below liquid nitrogen mainly the energetically lower para-state is populated. Therefore, an enrichment of the para-state and even the separation of the two species can be easily achieved at low temperatures as their interconversion is a rather slow process. Pure para-H2 is stable even in liquid solutions and para-H2 enriched hydrogen can be stored and used subsequently for hydrogenation reactions [54]. 

Conversely, since totai bas this character when orbital antisymmetrical (different electronic orbital quantum numbers), the spin combinations must be symmetrical. There are three of them and the triplet ortho states result. 

Deuterium proves to have its ortho states (higher statistical weight, antisymmetrical spin function) associated with even numbers of rotational quanta. Thus its total wave function is symmetrical, and it is said to follow the Bose-Einstein statistics. Moreover, the nuclear spin appears to have the value 1 instead of the value as with hydrogen. 

Vibration-rotation-tuimehng energy levels for the 4- 4 (ortho-ortho) states. The dashed arrows indicate perpendicular bands, whereas solid arrows correspond to parallel bands. The transitions are tentatively assigned to an out of plane vibration with a = 0 state at 89.141305(47), and aK= state at 86.77785 (9) cm [06Lin]. 

A certain fraction of these positrons, however, may enter the bound state of the positronium (Ps), by combining with an electron. Ps can be formed in two ground states either in the triplet or ortho state, with parallel spin orientation and an intrinsic average annihilation lifetime of 1.4 x 10" s, or in the singlet or para state with antiparallel spin orientation, which has an intrinsic average lifetime of 1.25 x 10"l s (Fig. 3). 

In any homonuclear diatomic molecule, with nuclear spin s, the statistical weight of the ortho states is s + 1) 2s + 1) that of the para states is s(2s -b 1). The rotational partition function will thus in general be... 

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