Multipole analysis of (e, e?? 0) angular correlations

Abstract

ABSTRACT:We show by analytical expressions the various solutions for the multipole decomposition of (e,e'cto) angular correlations when longitudinal excitations of three'different multipolarities interfere.The spectroscopy of giant resonances (GRs) meets the challenging problem of how to disentangle the various multipole contributions in the regime of many overlapping resonance structures of unknown centroids and widths. With the feasibility of coincidence (e,e'x) electron scattering the multipole decomposition problem can be much more rigorously attacked since the huge elastic radiative tail background which plagued the analysis of inclusive (e,e') scattering is completely eliminated by the requirement of detecting a nuclear decay product x in coincidence with the inelastically scattered electron. Recent (e,e'x) studies [1][2][3] have been performed at kinematic conditions where longitudinal E0, E1 and E2 excitations dominate; the multipole decomposition was based on (i) a novel multlpole expansion method of the 4r integrated coincidence cross sections measured at various momentum transfers [1,2], and (ii) an analysis of the angular correlation functions (ACFs) obtained at one momentum transfer [3]. While approach (i) yields E1 and E2/E0 form factors and strength distributions model-independently, the similarity of E0 and E2 form factors does not allow one to distinguish between these transitions; moreover the 47r integration eliminates the phase relations of the various multipole excitations which manifest themselves in the ACFs. None of these limitations is present in the ACF approach, which seems, of course, to be the obvious method to analyse coincidence data. Depending on the decay channel x and the number of interfering resonances, the mathematical structure of the theoretical expression for the ACF may, however, prevent an unambiguous multlpole decomposition. We illustrate this problem by the most simple case of the (e,e'c%) reaction, i.e. the decay of an intermediate resonance by emission of a spinless c~ particle to a final state of spin 0 + where the coupling of angular momenta is unique. Compared to previous work [3] our discussion extends the analysis of (e,e'c~0) ACFs to include 3 interfering resonances and shows analytically that for more than 2 overlapping resonances ambiguous results are obtained.The following analysis assumes that only E0, E1 and E2 excitations contribute. We consider the ACF in a chosen interval of excitation energy w at fixed momentum transfer q; the a0 emission angles (0, r are defined in the center-of-mass system of the decaying nucleus in a polar coordinate system where ~" coincides with the z-axis. Neglecting trivial kinematic factors, the ACF = 2~CoC, co~, co46, ~, (2) ~3 = 3 J-~C, C2cos( ~1o -~2o ) 45 C2 a4 = ~-2 and ~10 and ~20 are defined as 61 -~0 and ~ -60, respectively. This expansion may be applied to fit the experimental data yielding a set of the 5 physically relevant entities C0, C1, C2, gl0 and ~20. W(O,w,q) =_ W(O)atSince the powers of cosO form a set of li...