It is shown that the proton formation probability, extracted from experimental data corresponding to one-proton radioactivity, is divided into two regions when plotted as a function of an universal parameter. This parameter is derived from a microscopic description of the decay process. In this way we explain the systematics of proton emission half-lives. At the same time the formation probability is shown to be a useful quantity to determine the deformation property of the mother nucleus.

We present a systematic configuration-interaction shell-model calculation on the structure of light tin isotopes with a global optimized effective interaction. The starting point of the calculation is the realistic CD-Bonn nucleon-nucleon potential. The unknown single-particle energies of the 1d3/2, 2s1/2, and 0h11/2 orbitals and the T=1 monopole interactions are determined by fitting to the binding energies of 157 low-lying yrast states in 102$-${}132Sn. We apply the Hamiltonian to analyze the origin of the spin inversion between 101Sn and 103Sn that was observed recently and to explore the possible contribution from interaction terms beyond the normal pairing.

Shell-model calculations using realistic interactions reveal that the ground and low-lying yrast states of the $N=Z$ nucleus ${}_{46}^{92}$Pd are mainly built upon isoscalar neutron-proton pairs, each carrying the maximum angular momentum $J=9$ allowed by the shell $0g_{9/2}$, which is dominant in this nuclear region. This structure is different from that found in the ground and low-lying yrast states of all other even-even nuclei studied so far. The low-lying spectrum of excited states generated by such correlated neutron-proton pairs has two distinctive features: (i) the levels are almost equidistant at low energies and (ii) the transition probability $I\to I-2$ is approximately constant and strongly selective. This unique mode is shown to replace normal isovector pairing as the dominant coupling scheme in $N=Z$ nuclei approaching the doubly magic nucleus ${}^{100}$Sn.

The Geiger-Nuttall (GN) law relates the partial $\alpha$-decay half-life with the energy of the escaping $\alpha$ particle and contains for every isotopic chain two experimentally determined coefficients. The expression is supported by several phenomenological approaches, however its coefficients lack a fully microscopic basis. In this paper we will show that: 1) the empirical coefficients that appear in the GN law have a deep physical meaning and 2) the GN law is successful within the restricted experimental data sets available so far, but is not valid in general. We will show that, when the dependence of logarithm values of the $\alpha$ formation probability on the neutron number is not linear or constant, the GN law is broken. For the $\alpha$ decay of neutron-deficient nucleus $^{186}$Po, the difference between the experimental half-life and that predicted by the GN Law is as large as one order of magnitude.Comment: 4 pages, 5 figures, to appear in Phys. Lett.