Light-particle emission in the reactions of 16O with Ti

Inclusive energy spectra and angular distributions for heavy ions $\text{(Z ≧ 3)}$ produced in the reactions of 227 MeV and 310 MeV ¹⁶O with Ti were measured. Also measured at the projectile energy of 310 MeV were energy and angular correlations between light charged particles (Z ≦ 2) and heavy ions. From comparisons with statistical model calculations upper limits to the complete fusion cross sections of 647 mb and 265 mb were derived for projectile energies of 227 MeV and 310 MeV, respectively. At 310 MeV the cross section of incomplete fusion processes was estimated to be over 505 mb. Emission of fast, high-energy α-particles and protons was observed to be a characteristic feature of quasi-elastic, deep-inelastic and fusion-like reactions. Average multiplicities of fast light particles in coincidence with heavy ions at +20° and +40° were estimated to be of the order of 1. The prompt emission of light appears to be the principal mechanism which limits complete fusion. A second component of α-particles observed in coincidence with deep-inelastic projectile-like fragments and having an energy comparable to Coulomb energies of particles emitted from target-like and projectile-like fragments appears as an excess yield in the direction of the recoiling target-like fragments. This component cannot be accounted for in terms of sequential emission processes and may result from a mechanism other than the one which leads to fast particle emission.     

Possible contribution of low-l waves to the deep inelastic collisions of 32S with 27Al

The deep inelastic reactions of ³²S with ²⁷A1 have been studied at incident energies of 152.6 and 175 MeV by measuring inclusive fragment distributions, fragment-fragment and fragment-light particle coincidences. The observed Q-value distributions of the primary deep inelastic process range down to large negative Q-values as predicted by time-dependent Hartree-Fock calculations in the presence of low partial waves. No distinct low-l window for deep inelastic reactions can, however, be inferred from the data.     

Reaction mechanisms of 10 to 43 MeV/u heavy ions

Measurements of particle emission, linear momentum transfer and angular momentum transfer have been used to explore reaction mechanisms in the intermediate energy range where qualitatively different nuclear processes may be observable. The current status of our understanding of heavy ion reaction mechanisms with projectiles having velocities comparable to the velocity of sound and the Fermi velocity is summarized.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.