## Abstract

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 coexist 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. First we test the technique on the neutron dripline nucleus O-26, considered as O-24 surrounded by two neutrons. We choose Skyrme effective interactions between all pairs of nucleons. To ensure correct asymptotic behavior we modify the valence neutron-neutron interaction to fit the experimental scattering length in vacuum. This is an example of necessary considerations both of effective interactions between in-medium and free pairs, and renormalizations due to restrictions in allowed Hilbert space. Second, we investigate the heavier neutron dripline nucleus Ca-72, described as Ca-70 plus two neutrons. We continuously vary the strength of the Skyrme interaction to fine tune the approach to the dripline. Halo structure in the s-wave is observed followed by the tendency to form Efimov states. Occurrence of Efimov states are prevented by the exceedingly unfavorable system of two light and one heavy particle. Specifically the neutron-neutron scattering length is comparable to the spatial extension of a possible Efimov state, and scaling would place the next of the states outside our galaxy. Our third application is on the proton dripline nucleus Kr-70, described as Se-68 plus two protons, which is a prominent waiting point for the astrophysical rapid proton-process. We calculate radiative capture rates and discuss the capture mechanism as being either direct, sequential, virtual sequential or an energy dependent mixture of them. We do not find any 1(-) resonance and therefore no significant E1 transition. This is consistent with the long waiting time, since both E2 and background transitions are very slow. 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.

Original language | English |
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Article number | 073001 |

Journal | Journal of Physics G: Nuclear and Particle Physics |

Volume | 45 |

Issue | 7 |

Pages (from-to) | 1-82 |

Number of pages | 82 |

ISSN | 0954-3899 |

DOIs | |

Publication status | Published - 2018 |

## Keywords

- few-body physics
- many-body physics
- nuclear driplines
- Efimov physics
- halo physics
- ANTISYMMETRIZED MOLECULAR-DYNAMICS
- HARTREE-FOCK CALCULATIONS
- SELF-CONSISTENT CALCULATIONS
- RESONATING-GROUP METHOD
- PROCESS WAITING-POINT
- SHELL-MODEL
- RP-PROCESS
- 3-BODY DECAY
- HALO NUCLEI
- MOMENTUM DISTRIBUTIONS