Volume 68B, number 2 PHYSICS LETTERS 23 May 1977 zyxwvutsrqpo ELASTIC ELECTRON SCATTERING AS A TEST OF EFFECTIVE INTERACTIONS IN THE Is-Od SHELL* R.P. SINGHAL’, E.A. KNIGHT’, M.W.S. MACAULEY' , D. KELVIN, A. WATT and R.R. WHITEHEAD zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ Department of Natural Philosophy, University of Glasgow, Glasgow, Scotland Received 25 March 1977 Wave functions obtained from untruncated shell-model calculations for various effective interactions have been used to calculate the elastic electron scattering form factors for 24Mg and 32S. Chung-Wildenthal matrix elements best reproduce the form factors and the experimental excitation spectra for these nuclei. It is also shown that the use of harmonic oscillator wave functions and/or Born approximation can lead to a misjudgement of the actual situation. In this letter we wish to point out the possibility of testing shell-model effective interactions by means of elastic electron scattering experiments. As was pointed out by Watt et al. [l] that different effective interactions predict differing occupation numbers for the various valence orbitals. Consequently, the radial dependence of the ground-state charge distribution will be different for different effective interactions. Elastic electron scattering form factors are Fourier- Bessel transforms of the ground-state charge distribu- tion and hence they can be used to investigate this radial distribution. We consider the nuclei 24Mg and 32S for this exer- cise. These nuclei are chosen for their positions in the lower and upper half of the Is-Od shell; the numbers of active particles outside the 160 core are eight and sixteen, respectively. Extensive elastic electron scatter- ing data are available for these nuclei [2]. Untruncated shell-model calculations [3] were performed for these nuclei using the following interactions: Kuo [4], Preedom-Wildenthal (PW) I.51 and Chung-Wildenthal (CW) [6]. The latter two interactions particularly have been more successful than any others in reproducing the spectra and other properties of Is-Od shell nuclei. In shell-model calculations of the present type, the definition of the effective interaction leaves open the choice of the single-particle basis wave functions. The two obvious choices are the Saxon-Woods (SW) and l Work supported by the S.R.C. (UK). ’ Levin Laboratory. 24 Mg io,e) E, - 250 Me’.’ CWC INTERACTION i i -5 \ ’ IO 0.5 07 0.9 I.1 I.3 1.5 I.7 I .9 2.1 q zyxwvutsrqponmlkjihgfedcbaZYXWVUT in zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQP fm-’ Fig. 1. Elastic form factor for 24Mg. The experimental data are from ref. [2]. The curves are calculated using the ground- state wave function for 24Mg as given by CWC interaction. In all cases the radial parameters were chosen to reproduce the form factor up to the minimum. The dashed line is the Born approximation calculation using HO wave functions while HO(PSA) represents the phase-shift calculation. The use of Saxon-Woods wave functions gives the solid curve marked SW(PSA). It is obvious that quite erronous conclusions may be drawn by the use of unrealistic HO wave functions and a Born approximation analysis. 133