The hypernucleus has been analyzed by use of a four-body model which allows for distortion of the core by the particles. In particular, the dependence of the internal energy of the core on the rms separation of the particles is required. This was obtained from three-body calculations for . Several types of potentials, whose -wave phase shifts had been previously obtained, were considered. Calculations for were made for a singlet Yukawa potential (I) of intrinsic range F, appropriate to the exchange of two pions, and for a hard-core Yukawa potential (II) with a hard-core radius F and F, appropriate to a range corresponding to two pion masses for the attractive Yukawa part. Results are also given for a hard-core meson-theory potential (III) which has F and F. Calculations for III were made for , and the results were adapted to . For potentials which give -wave phase shifts consistent with experiment, it is found that (almost independently of the details of the potential) the effects of core distortion account for rather more than a third of the experimental additional binding energy of 4.5±0.5 MeV which is obtained after the separation energy of has been allowed for. Slightly more than half the contribution due to core distortion comes from the core energy of . The remainder is due to the further distortion of the core by the second , which causes approximately a 10% decrease in the rms separation relative to the value for . The effects of core distortion weaken the resulting potential quite appreciably. For F, one obtains the scattering length F and the effective range F, approximately independent of the shape of the potential. For II, one gets F and F. The well-depth parameters are 0.45±0.08, 0.675±0.065, and 0.77±0.04 for I, II, and III, respectively. These values are about 35%, 20%, and 12%, respectively, less than the values obtained for a rigid core with a three-body model. The coupling constant, obtained with III, is close to the value obtained from the singlet interaction for the same hard-core radius.
- Received 28 December 1964
- Published in the issue dated May 1965
© 1965 The American Physical Society