Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1109.6575

Model tests of cluster separability in relativistic quantum mechanics

B. D. Keister·W. N. Polyzou
View original source ↗Read source document ↗Export metadata ↓

Abstract

A relativistically invariant quantum theory first advanced by Bakamjian and Thomas has proven very useful in modeling few-body systems. For three particles or more, this approach is known formally to fail the constraint of cluster separability, whereby symmetries and conservation laws that hold for a system of particles also hold for isolated subsystems. Cluster separability can be restored by means of a recursive construction using unitary transformations, but implementation is difficult in practice, and the quantitative extent to which the Bakamjian-Thomas approach violates cluster separability has never been tested. This paper provides such a test by means of a model of a scalar probe in a three-particle system for which (1) it is simple enough that there is a straightforward solution that satisfies Poincaré invariance and cluster separability, and (2) one can also apply the Bakamjian-Thomas approach. The difference between these calculations provides a measure of the size of the corrections from the Sokolov construction that are needed to restore cluster properties. Our estimates suggest that, in models based on nucleon degrees of freedom, the corrections that restore cluster properties are too small to effect calculations of observables.

Explore related subjects

nucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

B. D. Keister, W. N. Polyzou. 2012-07-05. Model tests of cluster separability in relativistic quantum mechanics. https://doi.org/10.1103/physrevc.86.014002

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Application of the Skyrme Hartree-Fock-Bogoliubov Theory to WIMP-Nucleus Interactions in 40Ar

WIMP scattering from 40Ar is investigated using a self-consistent Skyrme Hartree-Fock-Bogoliubov (HFB) approach. Nuclear form factors relevant to dark matter direct detection are calculated from the resulting one-body density matrix elements and compared with shell-model predictions. Good agreement is found for the spin-independent response, while significant differences are observed for the spin-orbit response due to variations in single-particle occupancies. The effects of particle-number projection are shown to be small for 40Ar. These results demonstrate the sensitivity of certain dark matter response channels to the underlying nuclear structure model and establish a framework for extending mean-field calculations to nuclei beyond the reach of large-scale shell-model studies.

nucl-th↗
arXiv2026

Breakdown of the Plane-Wave Trojan Horse Analysis of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ Fusion Reaction: Critical Role of Coulomb Distortions

Recently, a new Trojan Horse Method (THM) measurement of carbon-carbon fusion was reported by Li \textit{et al.} [Phys. Lett. B (2026) 140675]. The purpose of the present work is to demonstrate the breakdown of the plane-wave approximation used in the analysis of these data and the critical role of Coulomb distortions in the initial and final states. The reaction mechanism underlying the THM analysis of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction using the $^{16}\mathrm{O}+{}^{12}\mathrm{C}\to α_s+α+{}^{20}\mathrm{Ne}$ reaction is investigated. Particular attention is paid to the spectator momentum distribution and to the dependence of the THM reaction amplitude on the relative carbon-carbon energy $E$. It is demonstrated that agreement with the measured spectator momentum distribution does not by itself validate the plane-wave approximation. Although the experimental momentum distribution can be reproduced, inclusion of Coulomb distortions in both the initial and final channels leads to an energy dependence of the THM amplitude that is completely different from the plane-wave result. Consequently, the energy dependence of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion cross section extracted from the THM data can be strongly distorted by the plane-wave treatment. It is concluded that the astrophysical factor extracted in the plane-wave analysis cannot be regarded as reliable and may lead to misleading conclusions concerning the low-energy $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction.

nucl-th↗