Excited-state density distributions in neutron-rich nuclei

Abstract

We calculate densities of excited states in the quasiparticle random-phase approximation (QRPA) with Skyrme interactions and volume pairing. We focus on low-energy peaks/bumps in the strength functions of a range of Ca, Ni, and Sn isotopes for J π = 0 + , 1 − , and 2 + . We define an "emittedneutron number", which we then use to distinguish localized states from scattering-like states. The degree of delocalization either increases as the neutron-drip line is approached or stays high between the stability line and the drip line. In the 2 + channel of Sn, however, the low-lying states, not even counting surface vibrations, are still fairly well localized on average, even at the neutron drip line. The structure of excited states in exotic nuclei has been much studied recently, both in nuclei between Li and O [1,2,3,4] and in heavier Ca [5] and Sn [6] isotopes. Lowenergy strength is often enhanced, and theorists have tried to understand the mechanisms responsible. Besides strength functions, they have examined transition densities, which can be measured and provide information on excited-state structure. Our earlier paper [7] contains an investigation of strength functions and transition densities in a large range of medium-heavy spherical nuclei, from one drip line to the other.Transition densities tell us about where in the nucleus transitions occur; they reflect the spatial distribution of products of single-particle and single-hole wave functions and, as a consequence, are always localized, though they can be very extended near the neutron drip line. In nuclei near stability large transition strength implies collectivity, which in turn tends to cause localization (as we shall see in giant resonances). Near the drip line, however, the familiar connection between strength and collectivity is less systematic at low energies. Reference [7] shows many examples of behavior like that characterizing light halo nuclei and predicted for certain 0 + states in heavy nuclei in Ref. [8]: large strength coming from noncollective transitions to very spatially-extended singleparticle states. Those excited states are usually unbound, and may not even be quasibound, that is they may be completely delocalized scattering states [8].In this letter we suggest a measure of localization and then investigate the extent to which the strong low-lying excited states are localized, independent of their collectivity. To uncover changes in structure near the drip line, we track the degree of localization as N increases in J π = 0 + , 1 − , and 2 + channels. Localization, which we analyze by examining diagonal density distributions of the excited states, has not been systematically studied before and offers a new window into excitations in exotic neutron-rich nuclei.We can adopt ideas from simple one-particle quantum mechanics to distinguish localized states from extended ones. If the energy of a single particle in, e.g., a squarewell potential is negative (Chap. 3 of Ref.[9]) then the tail of its wave function decays exponentially, and if th...

Fine structure of the isoscalar giant quadrupole resonance in 40Ca due to Landau damping?

“…To the best of our knowledge, all existing RPA calculations of the ISGQR in 40 Ca (see Refs. [35][36][37] for some recent examples) except the one discussed below and shown in Fig. 3(b) on the l.h.s.…”

Fine Structure of the Pygmy Dipole Resonance inXe136

“…An enhancement of the integrated strength of the PDR to higher neutron-to-proton ratios N=Z is predicted in many microscopic model calculations [23][24][25][26][27][28][29][30][31]. The low-lying part of the E1 strength arises in most models from excess neutrons forming a neutron skin and oscillating against an isospin saturated core.…”

“…The availability of intense exotic beams allows one to extend the search for low-energy E1 strength to very neutron rich systems in Coulomb breakup experiments in inverse kinematics [20]. Using this method, neutron rich Sn and Sb isotopes have been studied at the FRS/LAND setup at GSI [21,22].An enhancement of the integrated strength of the PDR to higher neutron-to-proton ratios N=Z is predicted in many microscopic model calculations [23][24][25][26][27][28][29][30][31]. The low-lying part of the E1 strength arises in most models from excess neutrons forming a neutron skin and oscillating against an isospin saturated core.…”

Existence problem of proton semi-bubble structure in the 21 + state of 34Si

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