Interaction of 12- to 13-Mev Neutrons with Deuterons

Abstract

443With the quantities of material available at the time has been able to characterize the isotope as decaying of these experiments, attempts to isolate the Tl 209 with a 2.2-min. half-life by emission of a 1.8-Mev betaactivity were unsuccessful. Since then one of us 30 particle. Gamma-rays if present constitute a maximum 30 French Hagemann, Phys. Rev. 79, 534 (1950).of one percent of the Geiger activity.By use of a CD 4 -filled high pressure cloud chamber, the angular distribution of recoils from 12-to 13-Mev neutrons has been studied. The angular range 0° to 140° in the center-of-mass system was covered by these measurements. The distribution indicates a rather large asymmetry in the forward and backward directions with a minimum at about 60° in the center-of-mass system. The existence of a D(w, 2n)p reaction was evident by the presence of tracks between 60° and 90° in the laboratory system which were too long to be accounted for by either deuteron or proton elastic recoils. * This report is part of a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the University of Illinois, 1950. A preliminary report of these data was given in Phys. Rev. 77, 748 (1950).t Assisted by a joint program of the ONR and the AEC.

Fock coordinate function method for separation of spin variables in transition density matrices

“…The obtained results are in complete agreement with the spin-Hamiltonian theory for the transition-metal ions developed by Griffith [16] vanish as a result of @r' antisymmetry: &:' (12; 34)= -@? '(34; 12).…”

“…Unlike Ref. 16 the results obtained by the Fock method permit one to calculate the spin-Hamiltonian parameters by means of only RDM components. The interest of such a possibility for the second-order perturbation theory has been expressed by McWeeny and Sutcliffe [ll].…”

NMR chemical shift as analytical derivative of the Helmholtz free energy

“…(4)) within the true wave functions of the Kramers doublet are the same as the matrix elements of H S within the fictitious spin doublet. 16,17 For example, if we denote the basis states of the Kramers doublet by |0 a and |0 b and let |0 a correspond to the fictitious spin state | 1 2 and |0 b to |− 1 2 , then we have…”

“…An expansion of this kind is an application of a general theorem to the effect that any n × n matrix can be reproduced by a unique spin operator, polynomial in the spin components S i . 16 Mathematical details about the construction and properties of this spin operator are given in Appendix . The main result is that the matrix of an operator X in a basis {ψ i } i=1...n can be reproduced by a spin operator X S in a fictitious spin multiplet {|S M } whose dimension equals n, i.e., 2S + 1 = n. Specifically, 16…”

“…In the second part of the paper, we show that this expression lends itself easily to a reformulation of the paramagnetic shielding in a degenerate state in terms of the spin Hamiltonian g and A parameters (Eq. (16)), which provides a general solution to point (ii).…”