Further evidence for the presence of an anomaly in binding energies for the ‘‘island of inversion’’ centered at Z=11, N=21 is obtained by comparison of shell-model calculations to experiment. The calculations were done with a shell-model interaction that is applicable to nuclei with active valence nucleons in both the (1s,0d) and (0f,1p) major shells. This interaction is described in detail as are its predictions for binding energies and energy spectra of Z=8–20, N=18–25 nuclei. These calculations provide the background for the exploration of the ‘‘island of inversion.’’ The extent of the ‘‘island’’ and the magnitude of the anomaly is explored by calculating the binding energies of 2ħω excitations of neutrons from the (1s,0d) shell to the (0f,1p) shell relative to the 0ħω ground state. The reason why mixed (0+2)ħω calculations are not considered reliable is addressed. Truncation schemes and a weak-coupling approximation are used to extend the range of the calculations. It is found that for Z=10–12, N=20–22 (and possibly N>22) nuclei the lowest 2ħω state is more bound than the 0ħω ground state. The role of odd n nħω excitations is considered and it is found that the 1ħω ground state always lies below that of 3ħω, and for N=19, 21, and 23, the lowest 1ħω state is in close competition with 2ħω for the lowest binding energy. Collectivity is considered via E2 observables and energy spectra for the 2ħω ground-state bands. The reason for the existence of the ‘‘island’’ is discussed.

Shell-model interactions are constructed in the cross-shell model space connecting the 0p and 1s0d shells with due regard for the perturbative effects of the neighboring 0s and 0f1p shells. The interactions have three distinctive 0p-shell, cross-shell, and 1s0d-shell parts. The latter is taken to be the previously determined W interaction. The 0p-shell interaction is represented by two-body matrix elements and the cross-shell by either a potential or by two-body matrix elements. The interactions are determined by least-squares fits to 51 0p-shell and 165 cross-shell binding energies. It is found that the addition of monopole terms to a potential that is otherwise similar to that of the Millener-Kurath interaction results in a great improvement in the fit. In the fit to two-body matrix elements, 45 of 97 possible linear combinations of parameters are varied and the root-mean-square deviation for the 165 cross-shell energies is 330 keV. Examples of the application of the interactions are given for the prediction of neutron-rich binding energies, Gamow-Teller decays, and 0ħω, 1ħω, and 2ħω energy spectra.

Multizone models of Type I X-ray bursts are presented that use an adaptive nuclear reaction network of unprecedented size, up to 1300 isotopes, for energy generation and include the most recent measurements and estimates of critical nuclear physics. Convection and radiation transport are included in calculations that carefully follow the changing composition in the accreted layer, both during the bursts themselves and in their ashes. Sequences of bursts, up to 15 in one case, are followed for two choices of accretion rate and metallicity, up to the point at which a limit cycle equilibrium is established. For = 1.75 × 10-9 M⊙ yr-1 (and = 3.5 × 10-10 M⊙ yr-1, for low metallicity), combined hydrogen-helium flashes occur. These bursts have light curves with slow rise times (seconds) and long tails. The rise times, shapes, and tails of these light curves are sensitive to the efficiency of nuclear burning at various waiting points along the rp-process path, and these sensitivities are explored. Each displays compositional inertia in that its properties are sensitive to the fact that accretion occurs onto the ashes of previous bursts that contain leftover hydrogen, helium, and CNO nuclei. This acts to reduce the sensitivity of burst properties to metallicity. Only the first anomalous burst in one model produces nuclei as heavy as A = 100. For the present choice of nuclear physics and accretion rates, other bursts and models make chiefly nuclei with A ≈ 64. The amount of carbon remaining after hydrogen-helium bursts is typically 1% by mass and decreases further as the ashes are periodically heated by subsequent bursts. For = 3.5 × 10-10 M⊙ yr-1 and solar metallicity, bursts are ignited in a hydrogen-free helium layer. At the base of this layer, up to 90% of the helium has already burned to carbon prior to the unstable ignition of the helium shell. These helium-ignited bursts have (1) briefer, brighter light curves with shorter tails, (2) very rapid rise times (<0.1 s), and (3) ashes lighter than the iron group.

The experimental values of ${\log }_{10}$ ${\mathit{T}}_{1/2}$(sec) plotted vs ${\mathit{Z}}_{\mathit{d}}^{0.6}$/ √${\mathit{Q}}_{\mathrm{\alpha }}$ are shown to fall on a nearly universal straight line with ${\log }_{10}$ ${\mathit{T}}_{1/2}$(sec)=(9.54${\mathit{Z}}_{\mathit{d}}^{0.6}$/ √${\mathit{Q}}_{\mathrm{\alpha }}$)-51.37, where ${\mathit{Z}}_{\mathit{d}}$ is the charge number of the daughter nucleus and ${\mathit{Q}}_{\mathrm{\alpha }}$ is expressed in units of MeV. This behavior also numerically comes out of the semiclassical WKB calculation of the barrier penetration factor. The fine structure in the ratio of experiment over theory is briefly discussed.