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The continuum and the alpha-particle formation

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Abstract

The absolute α-decay width of 212Po is calculated within a harmonic oscillator representation. Clustering features induced by the nuclear interaction appear by considering a large configuration space. The role of the neutronproton interaction is analysed and a reasonable account of the experimental alpha-decay width is given.
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This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program ‘From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory’. One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections.
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Phenomenological Description of Emission Processes.- Binary Emission Processes.- Core-Angular Harmonics.- Coupled Channels Methods.- Semiclassical Approach.- Fine Structure of Emission Processes.- Ternary Emission Processes.- Microscopic Description of Emission Processes.- Microscopic Emission Theories.- Preformation Amplitude.- Selfconsistent Emission Theory.- QRPA Description of the ?-Decay to Excited States.- Heavy Cluster Decays.- Conclusions.- Appendices.
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In a selfconsistent emission theory, the product between the reduced width and penetrability in the decay width should not depend upon the matching radius. This condition is not a trivial one in the microscopic theory and this point is extensively discussed in this chapter. We show that the standard shell model approach is not able to satisfy this property along neutron chains. Only the inclusion of an α-cluster part, depending exponentially upon the Somerfeld parameter, is able to cure this deficiency
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Alpha emission from a nucleus is a fundamental decay process in which the alpha particle formed inside the nucleus tunnels out through the potential barrier. We describe alpha decay of $^{212}$Po and $^{104}$Te by means of the configuration interaction approach. To compute the preformation factor and penetrability, we use the complex-energy shell model with a separable T=1 interaction. The single-particle space is expanded in a Woods-Saxon basis that consists of bound and unbound resonant states. Special attention is paid to the treatment of the norm kernel appearing in the definition of the formation amplitude that guarantees the normalization of the channel function. Without explicitly considering the alpha-cluster component in the wave function of the parent nucleus, we reproduce the experimental alpha-decay width of $^{212}$Po and predict an upper limit of T_{1/2}=5.5x10^{-7} sec for the half-life of $^{104}$Te. The complex-energy shell model in a large valence configuration space is capable of providing a microscopic description of the alpha decay of heavy nuclei having two valence protons and two valence neutrons outside the doubly magic core. The inclusion of proton-neutron interaction between the valence nucleons is likely to shorten the predicted half-live of $^{104}$Te.
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The absolute α-decay in212Po is calculated using a shell-model description of the α-particle formation. It is found that high-lying shell-model configurations greatly enhance both the α-clustering features and the calculated α-decay width. The interaction among the nucleons that form the α-particle is included through correlated two-particle states.
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A brief review of the development of α-decay-rate theory is given. Then in this paper are presented relative αdecay-rate theoretical calculations for doubly odd spherical nuclei for 212At and 212Atm α decay to excited states of 208Bi using mixed-configuration-shell-model parent and daughter wave functions and α particle approximations. Results are presented for no mixing and for Kim and Rasmussen, Ma and True, and Kuo and Herling wave functions for both the parent and daughter nucleus. The results are compared with the experimental data. There is a great sensitivity to configuration mixing, and no set of wave functions is wholly satisfactory. Stripping and pickup experiments testing the wave functions are reviewed and difficulties noted. It is concluded that α-decay rates provide a stringent test for the effective shell-model neutron-proton interaction in the lead region. Further theoretical and experimental work is needed. NUCLEAR STRUCTURE α-decay-rate theory, 212At and 212Atm. Calculation of rates for odd-odd spherical nuclei in modified zero-size approximation with shell-model configuration mixing.
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