H.I. Liou

Recent Experimental Neutron Resonance Spectroscopy Results as a Test of Statistical Theories of Short and Long Range Order for Level Spacings

During 1968 and 1970, we obtained large amounts of high quality neutron resonance spectroscopy data using the Columbia University Nevis Synchrocyclotron. This report emphasizes our experimental results for even-even nuclei having 150 < A < 190. In the oast, attempts to make detailed comparison of experimental resonance energies for nuclei for such “best test” cases as Th232 or U238 with theory gave poor fits for those tests which assumed that a single s level population only was present, and were sensitive to the inclusion of a partial extra p level population. For 150 < A < 190, the s level strength function S0 is sufficiently greater than the p level strength function S1 that all p levels tend to be weaker than all but a very small fraction of the s levels, providing a better separation of the two populations. Our results for Erl66, Erl68, wl82, wl84, Sml52, and Ybl72 were of particularly good quality, and give good agreement with the following statistical tests. Except for Er168, they seem to have only s levels, and for Er168 the p levels can be cleanly separated out on the basis of their strength.

HIGH-RESOLUTION NEUTRON RESONANCE SPECTROSCOPY IN NATURAL FLUORINE, ALUMINUM, CHLORINE, AND POTASSIUM.

In order to understand the features of nuclear reactions, we need to be able to relate the cross sections to the internal properties of the nucleus. The simple Breit Wigner formule(1) has been intensively used with the necessary modifications for Doppler broadening in the analysis of resonances observed in neutron interactions with heavy nuclei. Another important theory is due to Kapur and Peierls(2) which employs two sets of eigenstates and eigenvalues. The boundary conditions required for their definition require the logarithmic derivatives of the interior wave function at each channel entrance to be equal to the logarithmic derivative of the radial outgoing or ingoing wave function, respectively, in that channel. These two sets of eigenstates are mutually, but not separately, orthogonal, and the necessary expansions must be made in terms of both of them. The resulting cross section expressions are very familiar in form to those of S-matrix theory, but the parameters are all energy dependent. The S-matrix formulation of nuclear reaction theory by Humblet and Rosenfeld(3) has the advantage of a physically clear definition of resonance energy and rather simple expressions for the cross sections.