A Note on the least squarefree number in an arithmetic progression

We prove an asymptotic formula for squarefree in arithmetic progressions with squarefree moduli, improving previous results by Prachar. The main tool is an estimate for counting solutions of a congruence inside a box that goes beyond what can be obtained by using the Weil bound.Comment: 6 pages, no figure

Sensitivity of 8B breakup cross section to projectile structure in CDCC calculations

Given the Astrophysical interest of $^7$Be$(p,\gamma)^8$B, there have been several experiments applying the Coulomb dissociation method for extracting the capture rate. Measurements at Michigan State are dominated by $E1$ contributions but have a small $E2$ component. On the other hand, a lower energy measurement at Notre Dame has a much stronger $E2$ contribution. The expectation was that the two measurements would tie down the $E2$ and thus allow for an accurate extraction of the $E1$ relevant for the capture process. The aim of this brief report is to show that the $E2$ factor in breakup reactions does not translate into a scaling of the $E2$ contribution in the corresponding capture reaction. We show that changes to the $^8$B single particle parameters, which are directly related to the $E2$ component in the capture reaction, do not effect the corresponding breakup reactions, using the present reaction theory.Comment: 4 pages, 6 figures, revtex