The isoscalar giant dipole resonance in [sup 208]Pb and the nuclear incompressibility

Abstract

Abstract. The isoscalar giant dipole resonnace (ISGDR) has been investigated in 208 Pb using inelastic scattering of 400 MeV α particles at extremely forward angles, including 0 • . Using the superior capabilities of the Grand Raiden spectrometer, it has been possible to obtain inelastic spectra devoid of any "instrumental" background. The ISGDR strength distribution has been extracted from a multipole-decomposition of the observed spectra. The implications of these results on the experimental value of nuclear incompressibility are discussed.Nuclear Incompressibility is a crucial component of the nuclear equation of state and, as such, has very important bearing on diverse nuclear and astrophysical phenomena: for example, strength of supernova collapse, the emission of neutrinos in supernova explosions, and collective flow in medium-and high-energy heavy-ion collisions. The only direct experimental measurement of nuclear incompressibility is possible via the compressional-mode giant resonances in nuclei. Of the two important comprssional modes, the isoscalar giant monopole resonance (GMR) is the better known and has been studied now for more than 20 years. The other mode, the isoscalar giant dipole resonance (ISGDR), is an exotic oscillation-to first order, isoscalar dipole mode represents simply the motion of the centerof-mass which, in itself, cannot lead to any nuclear excitation-which has remained somewhat elusive, even though initial (although inconclusive) evidence for the mode was reported as long ago as the early 80's.The ISGDR can be thought of a hydrodynamic density oscillation in which the volume of the nucleus remains constant and a compressional wave-akin to a sound wave-traverses back and forth through the nucleus. The mode has generally been referred to as the "squeezing mode" in analogy with the mnemonic "breathing mode" for the GMR. A general description of this mode, along with the relevant transition densities and sum-rules, has been provided in Refs. [1,2]. The energy of this resonance is related to the nuclear incompressibilty via the scaling relation:where K A is the incompressibility of the nucleus, m is the nucleon mass, and ε F is the Fermi energy [3]. As mentioned above, indications of the ISGDR were reported as early as the beginning of the 1980's. However, the first conclusive evidence for this mode, based on the differences in angular distribution of the ISGDR from that of the nearby high-energy octupole resonance (HEOR), was provided by Davis et al. [4], who demonstrated that in inelastic scattering of 200 MeV α's at angles near 0 • , the giant resonance "bump" at 3hω excitation energy could be separated into two components, with the higher-energy component corresponding to the ISGDR. Further evidence for

Nuclear equation of state from ground and collective excited state properties of nuclei

“…[47] it was derived theoretically that the relation between the ISGMR and ISGDR excitation energies should roughly scale by a constant factor E ISGDR x E ISGMR x ≈ 15 7 ≈ 1.46 (very close to the HO prediction) meaning that the information content of both observables is, in first approximation, redundant. In the right panel of Fig.7, the rate between these energies for available experimental data in 208 Pb [54] and Sn isotopes [55] 13 are shown. A fit to a constant value is also depicted being the result equal to 1.67 (4).…”

“…In the right panel of Fig. 7, the rate between these energies for available experimental data in 208 Pb [54] and Sn isotopes [55] 13 are shown. A fit to a constant value is also depicted being the result equal to 1.67 (4).…”

Isoscalar giant resonances in the Sn nuclei and implications for the asymmetry term in the nuclear-matter incompressibility

“…In the last decade, the Texas A&M (TAMU) group has carried out (α, α ′ ) studies of many nuclei at a bombarding energy of 240 MeV and extracted the strength distributions of various isoscalar giant resonances in a number of nuclei [14][15][16][17][18][19][20][21][22][23][24] using a multipole decomposition analysis (MDA) [25]. Contemporaneously, we have carried out giant resonance measurements using inelastic scattering of 386 MeV α particles at extremely small angles, including 0 • [26][27][28][29][30][31][32][33][34][35]. An especially useful feature of our measurements has been the elimination of all instrumental background events from the inelastic scattering spectra which was rendered possible by the optical properties of the Grand Raiden spectrometer [36].…”