Nuclear Astrophysics Before 1957

I discuss especially my summer with Willy Fowler at Kellogg Radiation in 1951, where I did my "triple-alpha" work. I also go back even earlier to Arthur Eddington and Hans Bethe. I also mention the 1953 summer school in Ann Arbor.Comment: 16 page

The Formation of High-Mass Black Holes in Low Mass X-ray Binaries

In this note we suggest that high-mass black holes; i.e., black holes of several solar masses, can be formed in binaries with low-mass main-sequence companions, provided that the hydrogen envelope of the massive star is removed in common envelope evolution which begins only after the massive star has finished He core burning. That is, the massive star is in the supergiant stage, which lasts only $\sim 10^4$ years, so effects of mass loss by He winds are small. Since the removal of the hydrogen envelope of the massive star occurs so late, it evolves essentially as a single star, rather than one in a binary. Thus, we can use evolutionary calculations of Woosley & Weaver (1995) of single stars. We find that the black holes in transient sources can be formed from stars with ZAMS masses in the interval 20-35\msun. The black hole mass is only slightly smaller than the He core mass, typically \sim 7\msun.Comment: 19 pages, substantial changes, accepted in New Astronom

Evolution and Merging of Binaries with Compact Objects

In the light of recent observations in which short gamma-ray bursts are interpreted as arising from black-hole(BH), neutron-star(NS) or NS-NS mergings we would like to review our research on the evolution of compact binaries, especially those containing NS's. These were carried out with predictions for LIGO in mind, but are directly applicable to short gamma-ray bursts in the interpretation above. Most important in our review is that we show that the standard scenario for evolving NS-NS binaries always ends up with a low-mass BH (LMBH), NS binary. Bethe and Brown (1998) showed that this fate could be avoided if the two giants in the progenitor binary burned He at the same time, and that in this way the binary could avoid the common envelope evolution of the NS with red giant companion which sends the first born NS into a BH in the standard scenario. The burning of He at the same time requires, for the more massive giants such as the progenitors of the Hulse-Taylor binary NS that the two giants be within 4% of each other in ZAMS mass. Applying this criterion to all binaries results in a factor 5 of LMBH-NS binaries as compared with NS-NS binaries. Our scenario of NS-NS binaries as having been preceded by a double He-star binary is collecting observational support in terms of the nearly equal NS masses within a given close binary.Comment: 32 pages, 1 figure, substantial changes from v

The Determination of Nuclear Level Densities from Experimental Information -

A novel Information Theory based method for determining the density of states from prior information is presented. The energy dependence of the density of states is determined from the observed number of states per energy interval and model calculations suggest that the method is sufficiently reliable to calculate the thermal properties of nuclei over a reasonable temperature range.Comment: 7 pages + 6 eps figures, REVTEX 3.

Majorana solutions to the two-electron problem

A review of the known different methods and results devised to study the two-electron atom problem, appeared in the early years of quantum mechanics, is given, with particular reference to the calculations of the ground state energy of helium. This is supplemented by several, unpublished results obtained around the same years by Ettore Majorana, which results did not convey in his published papers on the argument, and thus remained unknown until now. Particularly interesting, even for current research in atomic and nuclear physics, is a general variant of the variational method, developed by Majorana in order to take directly into account, already in the trial wavefunction, the action of the full Hamiltonian operator of a given quantum system. Moreover, notable calculations specialized to the study of the two-electron problem show the introduction of the remarkable concept of an effective nuclear charge different for the two electrons (thus generalizing previous known results), and an application of the perturbative method, where the atomic number Z was treated effectively as a continuous variable, contributions to the ground state energy of an atom with given Z coming also from any other Z. Instead, contributions relevant mainly for pedagogical reasons count simple broad range estimates of the helium ionization potential, obtained by suitable choices for the wavefunction, as well as a simple alternative to Hylleraas' method, which led Majorana to first order calculations comparable in accuracy with well-known order 11 results derived, in turn, by Hylleraas.Comment: amsart, 20 pages, no figure