Interaction In Nuclear Matter Research Articles

Isobaric analogue states and the shell model

It is pointed out that the calculation of the energy of the isobaric analogue state using the nuclear shell model provides a test of the consistency of the two-body interaction used and the empirical single-body energies. It is suggested that such calculations would provide information of the effective two-body interaction in nuclear matter. The model of Ikeda, Fujii and Fujita is used to illustrate these ideas and is generalized to include neutron pairing correlations.

The interactions of π−-mesons with complex nuclei in the energy range (100–800) MeV. III. The interaction lengths and elastic scattering of 300 MeV π−-mesons in G5 emulsion

Abstract A stack of pellicles has been exposed to the 300 MeV πminus;-meson beam of the 660 MeV proton synchrotron at C.E.R.N., Geneva. The interaction lengths for the production of inelastic interactions and elastic scatterings through projected angles greater than 5°, found by scanning along 140 m of track, are (37.9 ± 2.0) cm and (77.4 ± 5.8) cm respectively compared to the geometrical interaction length of 29.3 cm. By comparison with the optical model the absorption coefficient and change in wave number are (1.53 ± 0.15) 1012 cm−1 and ± (1.35 ± 0.12)1012 cm−1, corresponding to a nuclear potential with a real component of (25 ± 1) MeV (of which the sign is not known), an imaginary component, −(14.1 ± 1.4) MeV and a mean free path for interaction in nuclear matter of (6.5 ± 0.7) 10−13 cm. The differences from the expected values are consistent with a considerable reduction within the nucleus of the cross section for elastic scattering of π-mesons by nucleons.

Nuclear forces and the properties of nuclear matter

The application of the Brueckner theory to the nuclear many-body problem can be greatly simplified if one separates the two-nucleon interaction (for any given state and relative momentum) into a short range part v s and a long range part v l . The cut is made such that v s alone gives no phase shift for free particle scattering. If the separation is made in this way, then the presence of nuclear matter, as manifested by the Pauli principle, has only a small effect on the two-particle wave function at short distances. On the other hand, the Pauli principle drastically reduces the induced correlations due to v l . In fact, v l is the first approximation to the effective interaction in nuclear matter. This procedure permits one to systematically expand the effective interaction in terms of t s , the reaction operator for free particles caused by v s alone. The contribution of all first- and second-order terms to the binding energy of extended nuclear matter has been calculated numerically. Most of the work was done using a central spin-independent two-body interaction containing a hard core of radius 0.4 fermi followed by an attractive exponential well with parameters chosen to give infinite scattering length and intrinsic range 2.5 fermis. If the potential is assumed to act only in S-states, we obtain a minimum energy of −12 Mev per particle at a density corresponding to a nuclear radius 1.0 A 1 3 fermis. The largest of the second-order terms contributes only 5.4 Mev to the energy per particle at this density (as compared to −42 Mev for the first-order term) and the other second-order terms much less. Thus our expansion appears to converge fairly rapidly. The effect of changes in the well parameters has been investigated. Also, our method was applied to interactions used by Gomes et al., Brueckner and Gammel, and Tagami, and our results compared with some of those obtained by the above authors.