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Register a new userUnitary correlation in nuclear reaction theory
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We prove that the amplitudes for the (d,p), (d,pn) and (e,ep) reactions determining the asymptotic behavior of the exact scattering wave functions in the corresponding channels are invariant under unitary correlation operators while the spectroscopic factors are not. Moreover, the exact reaction amplitudes are not parametrized in terms of the spectroscopic factors and cannot provide a tool to determine the spectroscopic factors.
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Nuclear reaction rate ($lambda$) is a significant factor in the process of nucleosynthesis. A multi-layer directed-weighted nuclear reaction network in which the reaction rate as the weight, and neutron, proton, $^4$He and the remainder nuclei as the criterion for different reaction-layers is for the first time built based on all thermonuclear reactions in the JINA REACLIB database. Our results show that with the increase of the stellar temperature ($T_{9}$), the distribution of nuclear reaction rates on the $R$-layer network demonstrates a transition from unimodal to bimodal distributions. Nuclei on the $R$-layer in the region of $lambda = [1,2.5times10^{1}]$ have a more complicated out-going degree distribution than the one in the region of $lambda = [10^{11},10^{13}]$, and the number of involved nuclei at $T_{9} = 1$ is very different from the one at $T_{9} = 3$. The redundant nuclei in the region of $lambda = [1, 2.5times10^{1}]$ at $T_{9} = 3$ prefer $(gamma,p)$ and $({gamma,alpha})$ reactions to the ones at $T_{9}=1$, which produce nuclei around the $beta$ stable line. This work offers a novel way to the big-data analysis on nuclear reaction network at stellar temperatures.
We propose a new variational method for describing nuclear matter from nucleon-nucleon interaction. We use the unitary correlation operator method (UCOM) for central correlation to treat the short-range repulsion and further include the two-particle two-hole (2p2h) excitations of nucleon pair involving a large relative momentum, which is called high-momentum pair(HM). We describe nuclear matter in finite size with finite particle number on periodic boundary condition and increase the 2p2h configurations until we get the convergence of the total energy per particle. We demonstrate the validity of this UCOM+HM framework by applying it to the symmetric nuclear and neutron matters with the Argonne V4$^prime$ potential having short-range repulsion. The nuclear equations of state obtained in UCOM+HM are fairly consistent to those of other calculations such as Brueckner-Hartree-Fock and auxiliary field diffusion Monte Carlo in the overall density region.
The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. The three-nucleon system shows a discrete scale invariance that can be observed by correlations of the triton binding energy with other observables as the doublet nucleon-deuteron scattering length or the alpha-particle binding energy. The low-energy dynamics of these systems is universal; it does not depend on the details of the particular way in which the nucleons interact. Instead, it depends on a few control parameters, the large values of the scattering lengths and the triton binding energy. Using a potential model with variable strength set to give values to the control parameters, we study the spectrum of $A=2,3,4,6$ nuclei in the region between the unitary limit and their physical values. In particular, we analyze how the binding energies emerge from the unitary limit forming the observed levels.
We derive a simple formula relating the cross section for light cluster production (defined via a coalescence factor) to the two-proton correlation function measured in heavy-ion collisions. The formula generalises earlier coalescence-correlation relations found by Scheibl & Heinz and by Mrowczynski for Gaussian source models. It motivates joint experimental analyses of Hanbury Brown-Twiss (HBT) and cluster yield measurements in existing and future data sets.
The goal of nuclear structure theory is to build a comprehensive microscopic framework in which properties of nuclei and extended nuclear matter, and nuclear reactions and decays can all be consistently described. Due to novel theoretical concepts, breakthroughs in the experimentation with rare isotopes, increased exchange of ideas across different research areas, and the progress in computer technologies and numerical algorithms, nuclear theorists have been quite successful in solving various bits and pieces of the nuclear many-body puzzle and the prospects are exciting. This article contains a brief, personal perspective on the status of the field.
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