The Ground State of the One-Dimensional Ising Chain

We consider a linear spin 1/2 Ising chain with pair interactions extending up to the nth neighbor. The following general theorem is proved: 'The energy of any arbitrary spin sequence may be written as a linear sum of cluster energies, the upper limit of the number of Ising spins in a cluster being 2n'. The term cluster energy here is used to mean the energy of a group of spins in a certain configuration, evaluated as if the same configuration repeated itself throughout the chain. The structure of the ground state of the system is investigated using the above theorem. It is shown that the ground state is a repetition of a certain cluster, and that the upper limit of the cluster size is 2n, except for some specific combinations of the interaction strengths when the ground state may admit mixing of different clusters. The possible ground state configurations are worked out explicitly for n = 2, 3, and 4 in the absence of the magnetic field using the above theorem. Previous attempts were confined only up to n = 3.

Measurement of the directional correlation of the 1038–605 keV gamma cascade in 134Ba

The directional correlation of the 1038–605 keV gamma-ray cascade in 134Ba has been determined using the well-known 1365–605 keV gamma-ray cascade as a reference. The detection system was a conventional fast–slow coincidence system using a 9 cm3 cylindrical Ge(Li) counter and a 5 cm × 5 cm NaI(Tl) counter. The observed correlation coefficients were A2 = 0.285 ± 0.030, A4 = −0.002 ± 0.050. The most probable spin sequence for the 1038–605 cascade is 3 (1, 2) 2 (2) 0 with a quadrupole content of 35–49% for the 1038-keV transition.

DIRECTIONAL CORRELATIONS IN 127I

Gamma–gamma coincidence measurements on the decay of 9.3-hour 127Te to 127I form the basis of the decay scheme presented, which confirms the accepted decay sequence. Directional correlation measurements have been made on the 215–203 keV and 360–58 keV cascades. The respective correlation functions are:[Formula: see text]The directional correlation results have been interpreted in terms of the accepted spin sequence, and limits of multipole mixtures are presented. A short discussion of the collective properties of the levels is presented.

EXPERIMENTAL EVIDENCE FOR AXIAL VECTOR INTERACTION IN THE DISINTEGRATION OF Pr144

A detailed study of the disintegration scheme of Pr144 has been carried out using lens spectrometers, scintillation spectrometers, and fast coincidence techniques. The 2293 kev β-component (1.3%) studied in coincidence with γ 691 has a predominantly first forbidden unique shape and the β–γ directional correlation is strongly anisotropic. The results indicate a probable spin-sequence 0−(β)2+(γ)0+, but the accuracy is not sufficient to exclude completely a 1− assignment for the Pr144 ground state. The β 803 component (1.0%) observed in coincidence with γ 2181 has an allowed shape and the β–γ directional correlation is isotropic. The shape of the total β-spectrum was studied in a double lens spectrometer having good anti-scattering properties using sources of Ce144 oxide sublimed onto 200 μg/cm2 Al leaf. Subtraction of a unique (Bij) shape 2293 kev 1.3% component and an allowed shape 803 kev 1.0% component yields the ground state β-spectrum. Analyses were made using the electronic functions of Zerianova which assume uniform charge distribution with ρ = 1.2 A1/3 10−13 cm as well as the point charge functions of Rose with ρ = 1.41 A1/3 10−13 cm. The observed spectrum shape can be explained on 0− to 0+ selection rules only by the axial vector interaction. Limits on the permissible tensor or pseudoscalar admixtures with the axial vector are discussed. No acceptable fit is possible with tensor, pseudoscalar, or any TP admixture (interfering or not) using Rose and Osborn's pseudoscalar formalism.