Hilbert polynomials and powers of an ideal

Sunto Nel n1. viene definito il complesso generalizzato di Koszul K(A; E; t) di R-moduli associato ad una matrice A sopra un anello R e un R-modulo E. Si studia poi K(A; E; t) nel caso particolare in cui A sia una matrice della forma B(m, s) data nel n.3. Si dimostra infine che, sotto certe condizioni di finitezza, la lunghezza di ogni modulo d'omologia à una funzione polinomiale in m per m grande, e che per ogni m ≥1 la caratteristica di Euler-Poincaré è il prodotto di un coefficiente binomiale per la caratteristica del complesso di Koszul K(B(1, s); E;0).

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Entrata in Redazione il 18 novemb e 1972.     

Configuration mixing effects on molecular dipole transition moments

The behavior of dipole transition matrix elements between adiabatic eigenstates of diatomic molecules is explored in the region of large configuration mixing. It is demonstrated that the matrix element has a lorentzian shape as a function of internuclear distance. The effect of this shape on the spectrum of LiH is investigated. The strong enhancement of the dipole transition moment in the interaction region is suggested as a source for nonthermal population distributions and laser radiation in alkali diatomics and hydrides.     

Generalized oscillator strengths for two transitions in CO2 at incident electron energies of 300, 400 and 500 eV

Generalized oscillator strengths have been obtained for two transitions in CO₂ from inelastic electron scattering determinations as a function of angle. Excitation energies for the two transitions are 11.04 and 11.38 eV, respectively. This spectral region was studied previously by Lassettre and Shiloff¹ but at a resolution too low to resolve the two transitions. In the present experiments the two are clearly resolved. Results are compared with the previous experiments of Foo et al.². Since substantial discrepancies are found both with the previous results of Lassettre and Shiloff and that of Foo et al., the accuracy of angular trends has been checked by comparing elastic scattering with the accurate determinations of Bromberg.⁶ Agreement is good. Multiple scattering is shown to be absent by varying the pressure. Generalized oscillator strengths are compared with the theoretical calculations of McKoy and collaborators. The change in the shape of the CO₂ spectrum in the region of 7–10 eV excitation energy is also studied.     

Nuclear activation as a current detector for ion beams produced by a high intensity laser

This work aims to demonstrate that nuclear activation of an irradiated metal foil can determine the number of accelerated particles in the initial irradiation beam. Even if this is not a novel technique it can be really useful to find out whether other commonly used techniques fail. Tests of the method have been carried out using the proton beam accelerated by the cyclotron of the University of Birmingham. Different metal targets (Cu, Cd and Ti) were irradiated and a HpGe detector was used to count the decay photons emitted by the radioactive isotopes produced. Agreement between proton intensities determined by foil activation and ionisation chamber measurements were ～16%.