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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.

Content uploaded by Gordana Dodig Crnkovic

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All content in this area was uploaded by Gordana Dodig Crnkovic on Jan 20, 2016

Content may be subject to copyright.

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.

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.

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

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.

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.

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.

Recently some important results have been obtained in calculating absolute alpha-decay widths, the calculations having been performed in the zero range alpha-particle approximation. In this paper the effects of the finite size of the alpha-particle are considered. Two important effects have been found: (i) for the finite size calculation, the absolute alpha-decay widths decrease by 2-3 orders of magnitude, and (ii) the finite size effects are strongly dependent on the shell model configuration of the initial nucleus. In the framework of the superfluid model the absolute probabilities of finite size alpha-particle emission have been calculated for the favored alpha-transitions of more than 200 spherical nuclei. The theoretical alpha-widths turn out to be smaller than the experimental ones by a factor of 10, which is approximately constant for all the nuclei studied.

The importance of higher configuration mixing is shown to increase the amplitude of a reducedwidth amplitudes YL in the nuclear surface area. This surface alpha-clustering effect produces a tremendous enhancement of the alpha-decay widths of 212Po. The overlap kernels 1-K and their eigenvalues and eigenstates are also studied. They are used to obtain new functions OmegaL ≡ YL/sqrt(1-K), which are also used to calculate the alpha-decay widths.

A possible way to remove the discrepancy between calculated and measured alpha-widths is discussed. The decay rates of 212Po and 210Po are computed with the help of shell-model wave functions for parent and daughter nucleus.

The derivation of the width for ..cap alpha..-decay is examined with particular emphasis on methods which do not involve arbitrary channel radii. A new method of treating the initial decaying states is introduced and the use of ambiguous phenomenological potentials is avoided. This method yields consistent and acceptable quantitative results for the g.s. to g.s. (ground state) transitions in even polonium isotopes and for the branching ratio for the decay of the isomeric state Â²Â¹Â²/sup m/Po.

Absolute α-decay widths in Po isotopes are studied in terms of a correlated basis consisting of two-particle (physical) states. It is found that the neutron-neutron, proton-proton and neutron-proton pairing interactions play a fundamental role in clustering the neutrons and protons that eventually constitute the α-particle. As a result, the calculated α-decay widths are enhanced by several orders of magnitude by properly including the pairing interaction. Reasonable agreement with available experimental data is obtained.

Absolute alpha-decay widths for the alpha-decays of 212, 214, 216Po are calculated within the framework of the nuclear field theory. A tremendous enhancement factor produced by configuration mixing is found.

The numerical results of a recent paper on nn and pp clustering are explained in terms of a simple schematic model which emphasizes the role of positive and negative parity single particles.

Dependence of α-cluster and pp- and nn-cluster formation on
high-lying configurations (continuum) in nuclei is studied. Its
importance for α-decay calculations is discussed. RADIOACTIVITY
α-decay, α-transfer reactions, high-lying configurations
(continuum).