Structure and decay at rapid proton capture waiting points

We investigate the region of the nuclear chart around $A \simeq 70$ from a three-body perspective, where we compute reaction rates for the radiative capture of two protons. One key quantity is here the photon dissociation cross section for the inverse process where two protons are liberated from the borromean nucleus by photon bombardment. We find a number of peaks at low photon energy in this cross section where each peak is located at the energy corresponding to population of a three-body resonance. Thus, for these energies the decay or capture processes proceed through these resonances. However, the next step in the dissociation process still has the option of following several paths, that is either sequential decay by emission of one proton at a time with an intermediate two-body resonance as stepping stone, or direct decay into the continuum of both protons simultaneously. The astrophysical reaction rate is obtained by folding of the cross section as function of energy with the occupation probability for a Maxwell-Boltzmann temperature distribution. The reaction rate is then a function of temperature, and of course depending on the underlying three-body bound state and resonance structures. We show that a very simple formula at low temperature reproduces the elaborate numerically computed reaction rate.Comment: 4 pages, 3 figures, conference proceedings, publishe

Spin-dependent effective interactions for halo nuclei

We discuss the spin-dependence of the effective two-body interactions appropriate for three-body computations. The only reasonable choice seems to be the fine and hyperfine interactions known for atomic electrons interacting with the nucleus. One exception is the nucleon-nucleon interaction imposing a different type of symmetry. We use the two-neutron halo nucleus 11Li as illustration. We demonstrate that models with the wrong spin-dependence are basically without predictive power. The Pauli forbidden core and valence states must be consistently treated.Comment: TeX file, 6 pages, 3 postscript figure

Three-body Thomas-Ehrman shifts of analog states of 17^{17}Ne and 17^{17}N

The lowest-lying states of the Borromean nucleus $^{17}$Ne ($^{15}$O+$p$ + $p$) and its mirror nucleus $^{17}$N ($^{15}$N+$n$ + $n$) are compared by using the hyperspheric adiabatic expansion. Three-body resonances are computed by use of the complex scaling method. The measured size of $^{15}$O and the low-lying resonances of $^{16}$F ($^{15}$O+$p$) are first used as constraints to determine both central and spin-dependent two-body interactions. The interaction obtained reproduces relatively accurately both experimental three-body spectra. The Thomas-Ehrman shifts, involving excitation energy differences, are computed and found to be less than 3% of the total Coulomb energy shift for all states.Comment: 9 pages, 3 postscript figures, revtex style. To be published in Phys. Rev.

A combined mean-field and three-body model tested on the 26^{26}O-nucleus

We combine few- and many-body degrees of freedom in a model applicable to both bound and continuum states and adaptable to different subfields of physics. We formulate a self-consistent three-body model for a core-nucleus surrounded by two valence nucleons. We treat the core in the mean-field approximation and use the same effective Skyrme interaction between both core and valence nucleons. We apply the model to $^{26}$O where we reproduce the known experimental data as well as phenomenological models with more parameters. The decay of the ground state is found to proceed directly into the continuum without effect of the virtual sequential decay through the well reproduced $d_{3/2}$-resonance of $^{25}$O.Comment: 5 pages, 5 figures, under revie

Combining few-body cluster structures with many-body mean-field methods

Nuclear cluster physics implicitly assumes a distinction between groups of degrees-of-freedom, that is the (frozen) intrinsic and (explicitly treated) relative cluster motion. We formulate a realistic and practical method to describe the coupled motion of these two sets of degrees-of-freedom. We derive a coupled set of differential equations for the system using the phenomenologically adjusted effective in-medium Skyrme type of nucleon-nucleon interaction. We select a two-nucleon plus core system where the mean-field approximation corresponding to the Skyrme interaction is used for the core. A hyperspherical adiabatic expansion of the Faddeev equations is used for the relative cluster motion. We shall specifically compare both the structure and the decay mechanism found from the traditional three-body calculations with the result using the new boundary condition provided by the full microscopic structure at small distance. The extended Hilbert space guaranties an improved wave function compared to both mean-field and three-body solutions. We shall investigate the structures and decay mechanism of $^{22}$C ($^{20}$C+n+n). In conclusion, we have developed a method combining nuclear few- and many-body techniques without losing the descriptive power of each approximation at medium-to-large distances and small distances respectively. The coupled set of equations are solved self-consistently, and both structure and dynamic evolution are studied.Comment: 4 pages, 3 figures, conference proceedings, publishe

Emergence of clusters: Halos, Efimov states, and experimental signals

We investigate emergence of halos and Efimov states in nuclei by use of a newly designed model which combines self-consistent mean-field and three-body descriptions. Recent interest in neutron heavy calcium isotopes makes $^{72}$Ca ($^{70}$Ca+n+n) an ideal realistic candidate on the neutron dripline, and we use it as a representative example that illustrates our broadly applicable conclusions. By smooth variation of the interactions we simulate the crossover from well-bound systems to structures beyond the threshold of binding, and find that halo-configurations emerge from the mean-field structure for three-body binding energy less than $\sim 100$keV. Strong evidence is provided that Efimov states cannot exist in nuclei. The structure that bears the most resemblance to an Efimov state is a giant halo extending beyond the neutron-core scattering length. We show that the observable large-distance decay properties of the wave function can differ substantially from the bulk part at short distances, and that this evolution can be traced with our combination of few- and many-body formalisms. This connection is vital for interpretation of measurements such as those where an initial state is populated in a reaction or by a beta-decay.Comment: 5 pages, 5 figures, under revie

Combined few-body and mean-field model for nuclei

The challenging nuclear many-body problem is discussed along with classifications and qualitative descriptions of existing methods and models. We present detailed derivations of a new method where cluster correlations co-exist with an underlying mean-field described core-structure. The variation of an antisymmetrized product of cluster and core wave functions and a given nuclear interaction, provide sets of self-consistent equations of motion. After the applications on dripline nuclei we discuss perspectives with improvements and applications. In the conclusion we summarize while emphasizing the merits of consistently treating both short- and large-distance properties, few- and many-body correlations, ordinary nuclear structure, and concepts of halos and Efimov states

Two-proton capture on the 68^{68}Se nucleus with a new self-consistent cluster model

We investigate the two-proton capture reaction of the prominent rapid proton capture waiting point nucleus, $^{68}$Se, that produces the borromean nucleus $^{70}$Kr ($^{68}$Se$+p+p$). We apply a recently formulated general model where the core nucleus, $^{68}$Se, is treated in the mean-field approximation and the three-body problem of the two valence protons and the core is solved exactly. The same Skyrme interaction is used to find core-nucleon and core valence-proton interactions. We calculate $E2$ electromagnetic two-proton dissociation and capture cross sections, and derive the temperature dependent capture rates. We vary the unknown $2^+$ resonance energy without changing any of the structures computed self-consistently for both core and valence particles. We find rates increasing quickly with temperature below $2-4$~GK after which we find rates varying by less than a factor of two independent of $2^+$ resonance energy. The capture mechanism is sequential through the $f_{5/2}$ proton-core resonance, but the continuum background contributes significantly.Comment: 7 pages, 4 figure

Three-body structure of low-lying 12Be states

We investigate to what extent a description of 12Be as a three-body system made of an inert 10Be-core and two neutrons is able to reproduce the experimental 12Be data. Three-body wave functions are obtained with the hyperspherical adiabatic expansion method. We study the discrete spectrum of 12Be, the structure of the different states, the predominant transition strengths, and the continuum energy spectrum after high energy fragmentation on a light target. Two 0+, one 2+, one 1- and one 0- bound states are found where the first four are known experimentally whereas the 0- is predicted as an isomeric state. An effective neutron charge, reproducing the measured B(E1) transition and the charge rms radius in 11Be, leads to a computed B(E1) transition strength for 12Be in agreement with the experimental value. For the E0 and E2 transitions the contributions from core excitations could be more significant. The experimental 10Be-neutron continuum energy spectrum is also well reproduced except in the energy region corresponding to the 3/2- resonance in 11Be where core excitations contribute.Comment: 16 pages, 9 figures. Accepted for publication in Physical Review