Construction of Symmetric Balanced Squares with Blocksize More than One

In this paper we study a generalization of symmetric latin squares. A symmetric balanced square of order v, side s and blocksize k is an s×s symmetric array of k-element subsets of {1,2,..., v} such that every element occurs in ks/v or ks/v cells of each row and column. every element occurs in ks²/v or ks ² v cells of the array. Depending on the values s, k and v, the problem naturally divides into three subproblems: (1) vks (2) s < v < ks (3) v s. We completely solve the first problem and we recursively reduce the third problem to the first two. For s 4 we provide direct constructions for the second problem. Moreover, we provide a general construction method for the second problem utilizing flows in a network. We have been able to show the correctness of this construction for k 3. For k4, the problem remains open.     

The probability of prompt and delayed fission of muonic237Np

Fission fragments from the reaction²³⁷Np(μ ^?,γ,f) have been measured in coincidence with muonic X-rays. The efficiency of the fission fragment detector is determined from (μ ^?,γ,f)-data of the same experiment. The total fission probability perμ-stopP _t has been measured as well as the fission probabilities P_f of the non-radiative muonic (3d→1s)- and (2p→1s)-transitions; the latter has been divided into two parts leading to different mean excitation energiesE:P _t =(54±17)%,P _f (3d→1s)=(41±21)%,P _f (2p→1s,E=6.218 MeV)=(61±19)%, andP _f (2p→1s,E=6.525 MeV)=(57±18)%. The influence of the muon on the fission barrier is discussed. The fission probability after muon capture is compared with a calculated value using a distribution of nuclear excitation energies following muon capture and the fission probability as measured in a²³⁸U(³He,αf)-reaction.