Narrow Results

We study the nuclear reaction cross-sections for some of the neutron-rich nuclei in the lighter mass region of the periodic chart which are recently measured. The well-known Glauber formalism is used by taking deformed relativistic and nonrelativistic densities as input in the calculations. We find reasonable reaction cross-sections with both the densities. However with a better inspection of the results, it is noticed that the results obtained with relativistic densities are more closure to the experimental data than the nonrelativistic Skyrme densities.

A common procedure for selecting a particular density from a given class of densities is to choose one with maximum entropy. The problem addressed here is this. Let S be a finite set and let B be a belief function on 2^S. Then B induces a density on 2^S, which in turn induces a host of densities on S. Provide an algorithm for choosing from this host of densities one with maximum entropy.

Given positive integers $a_1,\dots ,a_k$, we prove that the set of primes $p$ such that $p\not\equiv 1mod{a}_i$ for $i=1,\dots ,k$ admits asymptotic density relative to the set of all primes which is at least ${\prod }_{i=1}^k(1-\frac{1}{\phi (a_i)})$, where $\phi$ is the Euler totient function. This result is similar to the one of Heilbronn and Rohrbach, which says that the set of positive integer $n$ such that $n\not\equiv 0mod{a}_i$ for $i=1,\dots ,k$ admits asymptotic density which is at least ${\prod }_{i=1}^k(1-\frac{1}{a_i})$.