Necessary conditions for accurate computations of three-body partial decay widths

Garrido, E.; Jensen, A. S.; Fedorov, D. V.

doi:10.1103/physrevc.78.034004

Cited by 17 publications

(58 citation statements)

References 53 publications

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“…The necessary structures can be described from Borromean systems to systems with bound two-body states in one or more of the three two-body subsystems. The difficulties are often related to large distances (large ρ) that can be calculated accurately with a specific choice of basis and partial waves [12].…”

Section: A Three-body Formulationmentioning

confidence: 99%

“…Lane and Thomas discuss the validity conditions of R-matrix theory for such decays [1], most notably the requirement is that the lifetime of the intermediate state is sufficiently long to allow a correct description of the outer region in the first decay in terms of two-body asymptotics depending only on Coulomb and angular momentum. 8 Be with a lifetime of the order 10 −16 s (width about 8 eV) the two successive two-body decays seem to be appropriate, i.e., 12 C…”

Section: B R-matrix Formulationmentioning

confidence: 99%

“…The breakup of the 1 + state at 12.71 MeV in 12 C provides a good example of the problems discussed. Parity conservation prevents the state from decaying sequentially by α emission to the narrow 0 + ground state of 8 Be.…”

Section: Introductionmentioning

confidence: 99%

“…The discussion will be based on three unnatural parity states in 12 C. Section II gives the pertinent background for the theoretical description of the three-body model and the method of R-matrix simulation. In Sec.…”

Section: Introductionmentioning

confidence: 99%

“…III we discuss the constraints on the fragment momentum distributions from fermion and boson symmetry and from angular momentum and parity conservation. We give a number of numerical results for 12 C resonances from R-matrix analysis in Sec. IV and from the three-body model in Sec.…”

Section: Introductionmentioning

confidence: 99%

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Three-body decays andR-matrix analyses

et al. 2009

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The R-matrix simulation of three-body decays is investigated as function of available Q value and the energy and width of the intermediate two-body resonance. We use three α-decaying unnatural parity states of 12 C for illustration. The energy distributions are shown to be sensitive to the parameters when the two-body energy is significantly smaller than Q and the width is smaller than about 0.5 MeV. The sequential decay inherent in the R-matrix formalism can then be distinguished from direct decay. We provide conditions for the validity of R-matrix analyses. We compare with full three-body computations of the same energy distributions where we also attempt to distinguish between sequential and direct decays. The results give a good reproduction of available experimental data and are consistent with the conclusions from R-matrix analyses. Nodes in the momentum distributions arise from angular momentum and parity conservation. Combined with symmetry requirements this constrains the momentum distributions significantly in some cases. Effects of interactions and decay mechanisms can only be seen in the remaining behavior as, e.g., additional nodes related to nodes in the coordinate wave function at large distance.

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Section: A Three-body Formulationmentioning

confidence: 99%

Section: B R-matrix Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three-body decays andR-matrix analyses

et al. 2009

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Validity of Quasi-classical Approaches to True Three-Body Decays

Sukhareva

Grigorenko

Kostyleva

et al. 2020

Recent Progress in Few-Body Physics

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Within the hyperspherical harmonics approach the three-body problem is reduced to a motion of one effective particle in a "strongly deformed" field, which is described in coupled-channel formalism. This method is especially suited to studies of phenomena characterized by genuine three-body dynamics, e.g. Borromean haloes and true three-body decays. The reduction of the hyperspherical equations set to a single-channel Schrödinger equation provides the basis for the use of the standard quasiclassical expression for calculations of widths for true three-body decays. We demonstrate that the quasiclassical approach by itself is quite precise in application to typical profiles of the three-body effective potentials. However, the reduction to single-channel formalism leads to significant overestimation of the two-proton width Γ 2p . This is demonstrated by the example of the 17 Ne first excited 3/2 − state decay, questioning, however, the applicability of such an approximation in general.

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Systematic study of two-proton radioactivity within various versions of proximity formalisms

Zhu¹,

Li²,

Xu³

et al. 2022

Phys. Scr.

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In this work, we study the two-proton ($2p$) radioactivity half-lives for nuclei near or beyond the proton drip line within the Coulomb and proximity potential model (CPPM). We investigate the 28 versions of proximity potential formalisms, which were proposed for heavy-ion fusion reactions, heavy-ion elastic scattering, ternary fission and other applications. The results indicate that BW91 and Bass77 are inappropriate for handling $2p$ radioactivity since the classical turning point $r_{in}$ cannot be obtained for the depth of the total interaction potential between the released two protons and daughter nucleus being greater than the $2p$ radioactivity released energy. Among the other 26 proximity potential formalisms, the one proposed by Royer \textit{et al.} in 1984 denoted as Prox.77-8 is the best version with the lowest rms deviations between experimental data and relevant theoretical results. It is worth mentioning that the calculations of Coulomb and Proximity Potential Model for Deformed Nuclei [PRC 104, 064613 (2021)] has least standard deviation ($\sigma$=0.592) compared with present model and other models/formulae. Furthermore, we use CPPM with Prox.77-8 to predict the $2p$ radioactivity half-lives of 35 potential candidates whose $2p$ radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. The predicted results are consistent with previous theoretical models such as the unified fission model (UFM), generalized liquid drop model (GLDM) and effective liquid drop model (ELDM).

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Necessary conditions for accurate computations of three-body partial decay widths

Cited by 17 publications

References 53 publications

Three-body decays andR-matrix analyses

Three-body decays andR-matrix analyses

Validity of Quasi-classical Approaches to True Three-Body Decays

Systematic study of two-proton radioactivity within various versions of proximity formalisms

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