Positron Annihilation inγ- andα-Cerium

Abstract

similar correlation has been observed by Pierce and Blann for lighter projectiles. 5 There is not enough evidence to say whether this correlation is more than a useful fortuitous fact since the concept of an effective charge for an energetic ion in a solid is vague at best. If the electronic stopping power does follow the dependence of the mean charge of ions in gases, then differences, similar to the differences in the mean charges between I and U ions in air reported by Betz et a/. 16 (see Fig. 5), should be observable in the electronic slowing down process. Unfortunately, the present data do not cover a large enough range of reduced velocities to be sensitive to such deviations. More accurate data, taken over a wider range of energies of very heavy ions are needed in order to detect any possible dependence of the stopping process on the mass of the projectile.It is worth remarking that if the effective charge deduced from dE/dX measurements is indeed a physically meaningful quantity, then, perhaps, the potential charge experienced by the ions on their passage from 1 W. H. Zachariasen, quoted by A. W. Lawson and T. Tang, Phys. Rev. 76, 301 (1949).The 7 -> a phase transition of cerium has been investigated by measurement of the positron lifetime and angular correlation of positron-annihilation radiation in the two phases. The lifetime in the a phase was observed to be 8% shorter than the lifetime in the 7 phase when the a phase was produced by the application of pressure; and it was observed to be 5% longer when the a phase was produced by lowering the temperature. The angular correlation from a-cerium produced by pressure was observed to be slightly broader than that from 7-cerium, in contrast to the narrowing previously observed when a-cerium was produced by lowering the temperature. Since the observed changes are much smaller than predicted by models which explain the 7 -> a: transition by assuming a transfer, or partial transfer, of the 4/ electron to the conduction band, it is concluded that such electronic promotion does not occur. GUSTAFSON,McNUTT, AND ROELLIG

Quantum charge density fluctuations and the phase transition in Ce

“…Though in agreement with some experimental observations [9,11], the concept of a Mottlike transition for the cerium electronic 4f -subsystem has severe internal difficulties since delocalization of f -orbitals in the α phase would involve huge energy transformations in cerium, of the order of the Coulomb on-site repulsion parameter U ff which by several orders of magnitude exceeds the characteristic energy of 100-200 K. Subsequent photoemission [12][13][14] and bremsstrahlung isochromat spectroscopy (BIS) [15,16], as well as X-ray absorption [17], Compton scattering measurements [11] and positron annihilation [9] confirmed a 4f 1 → 4f 0 + e − peak far away (≈ 2 eV) from E F and suggested a 4f occupation nearly equal to one on both sides of the transition. These results are summarized in Figure 1, where schematically the ground state of metallic cerium is shown.…”

“…In a first interpretation [8] ('promotional' model) the localized 4f electrons are believed to be transferred to the (6s5d) 3 conduction band in α-Ce. In contrast to this model, positron annihilation experiments which probe the electron density have shown that there is no substantial difference in the number of 4f electrons in the two phases [9].…”

Self-interaction-corrected local-spin-density calculations for rare earth materials

“…The promotional model [59] advocates a promotion of the Ce 4f electron to the 5d conduction band state to explain the transition. This model is, however, difficult to reconcile with the cohesive properties of Ce [60] as well as with positron annihilation [61] and photoemission [62] data, neither of which indicate a dramatic change in the f -electron population during the transition. In addition, band structure calculations are not able to reproduce this picture, which would require a very narrow f band in the vicinity of the Fermi level [63,64].…”

The puzzle of the $ \gamma\to\alpha$ and other phase transitions in cerium

“…This conclusion was checked in the positron annihilation experiments [59,60] and in Compton scattering experiments [44]. In both cases nearly equal occupation of the f-states (n f  1) was established and the promotional mechanism was concluded irrelevant.…”