Investigation of the Giant Monopole Resonance in the Cd and Pb Isotopes: The Asymmetry Term in Nuclear Incompressibility and the MEM Effect

Abstract

The giant monopole resonance (GMR) has been investigated in the even-A Cd and Pb isotopes 112−124 Cd, and 204−208 Pb, with the aim of obtaining a confirmatory value for the asymmetry term in nuclear incompressibility, Kτ , and to test the Mutual Enhancement Magicity (MEM) effect in nuclear incompressibilities. The latter was advanced as a possible explanation of the puzzling softness of the Sn and Cd nuclei, as evidenced by their low GMR energies as compared to theoretical predictions. The GMR results in the Cd isotopes give a value Kτ = �490± 100 MeV, in close agreement with the value obtained previously from the Sn isotopes. Our results rule out the MEM effect as an explanation of the aforementioned softness observed for the Sn and Cd nuclei. The asymmetry term of nuclear incompressibility, Kτ , associated with the neutron-excess (NZ), is crucial in obtaining the radii of neutron stars in the equation of state (EOS) calculations. 1)-4) It has been suggested that the radius of a neutron star whose mass is between about 1.0 and 1.5 solar masses (M� )i s mostly determined by the density dependence of the symmetry-energy term. 5),6) In recent measurements on the giant monopole resonance (GMR) in the even- A Sn isotopes (A = 112 � 124), we had obtained an value for this term, Kτ = �550 ± 100 MeV. 7),8) This number is in agreement with the value Kτ = �500 +125100 MeV, obtained by Centelles et al. 9) from constraints put by neutron- skin data from anti-protonic atoms across the mass table; Kτ = �500 ± 50 MeV obtained by Sagawa et al. 10) by comparing our Sn GMR data with calculations using different Skyrme Hamiltonians and RMF Lagrangians; and, Kτ = �370 ± 120 MeV obtained from an analysis of the isotopic transport ratios in medium- energy heavy-ion reactions. 11) Combined with the value of K∞ = 240 ± 10 MeV extracted from data on GMR and the other compression-mode, the isoscalar giant dipole resonance (ISGDR), 12),13) this value for Kτ may provide a means of selecting the most appropriate of the interactions commonly used in nuclear structure and EOS calculations. To confirm the value of Kτ obtained from the GMR in the Sn isotopes, we have investigated the GMR in the another series of isotopes, viz. 106,110,112,114,116 Cd using inelastic scattering of 400-MeV α particles at extremely forward angles, including 0 ◦ . The measurements were performed at the Research Center for Nuclear Physics (RCNP) at Osaka University, Japan, using the Grand Raiden spectrometer. The experimental techniques and data analysis procedures were identical to those in the measurements described previously for the Sn isotopes. 7),8)