The Nu-SNS proposal - ORNL Physics Division - Oak Ridge ...

neutrons in the 1f 5/2 level. Improved weak interaction rates for electron/positron capture and β
decays on nuclei relevant for stellar evolution (nuclear mass between 45 and 65) have become
available in recent years using shell model diagonalization [27,28]. Heger et al. [29] utilized
these new weak reaction rates to improve upon the stellar evolution simulations of Woosley &
Weaver [30] (WW95). The WW95 models used the electron capture rates of Fuller, Fowler, &
Newman [31] (FFN), which estimated the GT contributions based on an independent particle
model parameterization, and older sets of β decay rates [32,33]. The most noticeable effect of
these improvements is a marked increase in the electron fraction (Y e ) throughout the iron core
before collapse.
It was suggested that the persistence of these initial differences in Y e throughout collapse should
have a discernible (positive) effect on the shock energetics, because the final size of the
homologous core is proportional to the square of the trapped lepton fraction at core bounce [34].
However, the electron/lepton fraction is greatly modified during the collapse of the stellar core.
The increasing density, and concomitant increase in the electron chemical potential, accelerates
the capture of electrons on heavy nuclei and free protons in the core, producing electron
neutrinos that initially escape, thus deleptonizing the core. Thus the location at which the shock
forms in the stellar core at bounce and the initial strength of the shock are largely set by the
amount of deleptonization during collapse. Figure 3.2 summarizes the thermodynamic conditions
throughout the core at bounce and displays the temperature, electron fraction (Y e ), electron
chemical potential (µ e ), and mean electron neutrino energy (E νe ) in MeV as functions of the
matter density. Also shown is the representative nuclear mass (A). The kinks near 3×10 7 g/cm 3
mark the transition to the silicon shell. Deleptonization would be complete (Y e ~0) if electron
capture continued without competition, but at densities of order 10 11-12 g/cm 3 , the electron
neutrinos become “trapped” in the core, and inverse neutrino capture reactions begin to compete
with electron capture until the reactions are in weak equilibrium and the net deleptonization of
the core ceases on the core collapse time scale. The equilibration of electron neutrinos with
matter occurs at densities between 10 12-13 g/cm 3 .
As the densities increase, the characteristic nuclei in the core increase in mass, owing to a
competition between Coulomb contributions to the nuclear free energy and nuclear surface
tension, until heavy nuclei are replaced by nuclear matter for mass densities near that of the
nucleons in the nucleus (~10 14 g/cm 3 ). For densities of order 10 13 g/cm 3 , nuclei with mass ∼100
dominate. Figure 3.3 demonstrates that the nuclear composition during stellar collapse shows a
wide spread in mass (species with significant concentrations have masses that differ by 40 mass
units) and that the abundances of nuclei with mass greater than 100 are significant as early as
10 11 g/cm 3 . Fuller [36] realized that electron capture on heavy nuclei would soon be quenched in
the picture of Bethe et al. [26], as neutron numbers approach 40, filling the neutron 1f 5/2 orbital.
Calculations using the independent particle model (IPM) showed that neither thermal excitations
nor forbidden transitions substantially alleviated this blocking [36,37]. For many years, this
prescription was widely adopted in core collapse simulations (see e.g. [8]), leading to a higher
rate of electron capture on protons than on heavy nuclei during collapse.
ν-SNS Proposal 20 8/4/2005