Electron Spin Resonance in the Study of Radiation Damage 247 



the equally coupling nuclei have the same spin, 7= nl, and the total number 

 N of components of the multiplet will be: 



N = 2nl-\\ (11) 



or 



Thus n equally coupling hydrogens (/ = \) gives n + 1 components. The 

 intensities of the components are proportional to the number of different 

 combinations of the /n/s which give the same sum 2 '"j or same value of M^.. 



i 



Because all the -\-h and —\ orientations of n hydrogens are equally probable 

 and mutually independent, the intensities of a multiplet formed by equally 

 coupling hydrogens will be gaussian. 



The interaction constant A^ of the electron spin with the moment of a 

 particular nucleus may contain both an isotropic and an anisotropic component. 

 The isotropic component, the Fermi term, is independent of the orientation 

 of the sample in the magnetic field and arises from the non- vanishing probability 

 density, ^'q t/'o*? of the electronic wave function at the nucleus in question. 

 Since only the s atomic orbitals are non- vanishing at the nucleus (radius r = 0), 

 the presence of an isotropic coupling tenn for a particular atom in a molecule 

 generally indicates 5 character in the bonding orbitals of that atom. 



For an unpaired electron occupying wholly an s orbital of a particular 

 atom, the coupling to the nucleus of that atom arises entirely from the non- 

 vanishing density ipQ i^)q* at the nucleus and has the value (17): 



A. = y fif^igi Wo n* = 3 ^^3 (13) 



where /9 is the Bohr magneton; /5j, the nuclear magneton; gj, the g factor 

 (/ij//) of the nucleus; /;, Planck's constant; c, the velocity of light; R, the 

 Rydberg constant; a, the fine structure constant; Z, the effective nuclear charge; 

 and «, the total quantum number. For atomic hydrogen in the ground state, 

 A is known to be 1420 Mc/sec. This value with equation (7) gives A/Z^ = 507 

 gauss as the expected splitting for the atomic hydrogen doublet for the strong- 

 field case {H ^ ^H^). The non-isotropic components are zero because of the 

 spherical symmetry of the s orbital. Thus the isotropic coupling to the nucleus 

 of a particular atom gives a good measure of the s orbital contribution of that 

 atom to the molecular wave function of the odd electron in a free radical. 

 An electron at a fixed distance from a nucleus / with non-zero spin will 

 experience a magnetic field component arising from the magnetic moment 

 of the nucleus. If the spin vectors of both the electron and the nucleus precess 

 about the direction of an applied field H (this corresponds to the strong-field, 

 Paschen-Back case), the non-vanishing field component at the electron, A//, 

 caused by the nucleus, will lie along H and will have the value: 



(A//) = {jY^.l^^i^y^O C0S2 - 1) (14) 



