Lattice-point examples for a question of Erdős

Here we establish a set of eight points in general position in the plane, i.e. no three on a line, no four on a circle, and they determine 7 distinct distances, so that, thei-th distance occursi times,i = 1, 2, , 7. The points are embedded in a triangular net, and the distances are not ordered by size or in any other way. We shall show that some known and unknown examples forn < 8 with the above properties may also be lattice points of a similar net.Research (partially) supported by the Hungarian National Foundation for Scientific Research (OTKA) grant, no. 1808.     

Low-lying levels in103Rh from Coulomb excitation

Five low-lying negative parity states of¹⁰³Rh up to 1277 keV excitation energy were observed to be Coulomb excited with 2·5–4·5 MeV protons. The de-excitation gamma rays from these levels were identified in the singles spectra recorded with a 57 cc Ge(Li) detector. The level energies, branching ratios, reduced transition probabilitiesB(E2) and the multipole mixing ratios () were obtained. The 880, 1106 and 1277 keV levels have been Coulomb excited with protons for the first time. The ambiguity in theJ values for 803 and 1106 keV levels have been resolved using ²-fits, the assigned spin values are 1/2^– and 5/2^–, respectively. The-values for 474·1 and 811·2 keV transitions were obtained for the first time. The results have been discussed in the light of previously reported results.The authors wish to thank Professor I. M. Govil for his active interest at various stages of this work. One of us (DCT) acknowledges the financial support from U.G.C., New Delhi, under Faculty Improvement Programme.