Giant monopole resonance in even-A Cd isotopes, the asymmetry term in nuclear incompressibility, and the “softness” of Sn and Cd nuclei

Abstract

The isoscalar giant monopole resonance (ISGMR) in even-A Cd isotopes has been studied by inelastic α-scattering at 100 MeV/u and at extremely forward angles, including 0• . The asymmetry term in the nuclear incompressibility extracted from the ISGMR in Cd isotopes is found to be Kτ = −555±75 MeV, confirming the value previously obtained from the Sn isotopes. ISGMR strength has been computed in relativistic RPA using NL3 and FSUGold effective interactions. Both models significantly overestimate the centroids of the ISGMR strength in the Cd isotopes. Combined with other recent theoretical effort, the question of the "softness" of the open-shell nuclei in the tin region remains open still.The equation of state (EOS) of nuclear matter plays an important role in our understanding of a number of interesting phenomena such as the collective behavior of nucleons in the nuclei, the massive stellar collapse leading to a supernova explosion, nuclear properties including the neutron-skin thickness of heavy nuclei, and the radii of neutron stars [1, 2]. The nuclear incompressibility, K ∞ , is the curvature of EOS of nuclear matter at saturation density [3]. K ∞ is, thus, a measure of nuclear stiffness and thereby imposes significant constraints on theoretical descriptions of the effective nuclear interactions. However, even more stringent constraints emerge as one studies the evolution of the incompressibility coefficient as the system becomes neutron rich. Neutron-rich systems are sensitive to the poorly-known density dependence of the symmetry energy and the experiments reported here are of vital importance in this regard.The study of the isoscalar giant monopole resonance (ISGMR) provides a direct experimental tool to study nuclear incompressibility in finite nuclear systems. The centroid energy of ISGMR, E ISGMR , can be directly related to the nuclear incompressibility of finite nuclear matter, K A , as:where, m is the nucleon mass and < r 2 > is the mean square radius of the nucleus [4,5]. K A may be further

Incompressibility of finite fermionic systems: Stable and exotic atomic nuclei

“…For all nuclei analyzed in the present study we have verified the stability of the results with the variation of the size of the mesh. Pairing correlations are taken into account by a contact volume-pairing interaction, with strength V 0 = −218 (−265) MeV fm 3 for Sn (Pb) isotopes. The pairing strength is adjusted to reproduce the empirical pairing gaps extracted from data on odd-even mass differences (five-point formula).…”

“…Recent advances in experimental and theoretical investigations of nuclear incompressibility have also enabled studies of the evolution of incompressibility in isotopic chains [1][2][3][4][5][6]. As for many other structure phenomena, for instance the evolution of magic numbers [7], a study of the isotopic dependence might provide a more general and deeper understanding of nuclear incompressibility.…”

Microscopic study of the isoscalar giant monopole resonance in Cd, Sn, and Pb isotopes

“…In this space, the pairing strength V 0 is fixed by fitting the pairing gap extracted from experimental data of odd-even mass difference by using the five-point formula. The values of V 0 that we have obtained are displayed in Table I [106][107][108][109][110][111][112][113][114][115][116] Cd are compared with the experimental data obtained at RCNP [7]. The SLy5 (solid line), SkM * (dashed line), and SkP (dotted line) forces are adopted in the calculations whose results are shown here, together with the mixed pairing interaction.…”

“…Cd isotopes are compared with the experimental data obtained from Ref. [7]. The forces (a) SLy5, (b) SkM * , and (c) SkP are adopted in the present calculations together with either the filling approximation, the volume, the surface, or the mixed pairing interactions, respectively.…”

“…Recently, the distribution of ISGMR strength in Cd, Sn, and Pb isotopes has been measured at the Research Center for Nuclear Physics (RCNP) at Osaka University [7][8][9][10]. These data raise a further question on the nuclear matter incompressibility.…”