Quantum three-body Coulomb problem in two dimensions

Hilico, Laurent; Grémaud, Benoît; Jonckheere, Thibaut; Billy, N.; Delande, Dominique

doi:10.1103/physreva.66.022101

Cited by 27 publications

(19 citation statements)

References 30 publications

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“…In all calculations we have assumed that all particle masses and corresponding conversion factors (e.g., the factor Ry mentioned below) are exact. In fact, such assumptions are always made in the papers on highly accurate computations in few-body systems (see, e.g., [12] and [13]). The known experimental uncertainties in particle masses and conversion factors are taken into account at the last step of calculations, when the most accurate computations are simply repeated for a few times with the use of different particle masses and conversion factors.…”

Section: Resultsmentioning

confidence: 99%

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On the bound states in the muonic molecular ions

Frolov

2012

Eur. Phys. J. D

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The mass corrections to the bound state energies of the three-body muonic molecular ions ppµ, pdµ, ptµ, ddµ, dtµ and ttµ are determined numerically from the results of highly accurate computations. The total energies and some other bound state properties of these ions are evaluated to very high accuracy for the bound S(L = 0)−, P (L = 1)− and D(L = 2)−states. In these highly accurate calculations we used the most recent and accurate masses of particles m p , m d , m t and m µ known from high energy experiments. We also investigate some bound state properties of the muonic molecular ions. In particular, we determine the hyperfine structure splittings of the ground states of the pdµ, ptµ and dtµ ions. In these calculations we used our highly accurate expectation values of the interparticle delta-functions obtained in recent computations. The corresponding hyperfine structure splittings, e.g., ∆ 12 = 1.3400149·10 7 M Hz and ∆ 23 = 3.3518984·10 7 M Hz for the ptµ ion, can directly be measured in modern experiments. Analogous hyperfine structure splittings are evaluated to very high accuracy for all five bound S(L = 0)−states in the three symmetric muonic molecular ions: ppµ, ddµ and ttµ.

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Section: Resultsmentioning

confidence: 99%

“…These works were [36], [37]. Around that time another paper was published on highly accurate bound state computations of the three-body muonic molecular ions [38]. In [1] we have used very large basis sets and performed an accurate optimization of the non-llinear parameters of our method.…”

Section: Appendixmentioning

confidence: 99%

On the bound states in the muonic molecular ions

Frolov

2012

Eur. Phys. J. D

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“…A natural and effective way to perform such calculations is to assume that all particle masses and corresponding conversion factors (e.g., the factor Ry below) are exact. Such assumptions are always made in papers on highly accurate computations in few-body systems (see, e.g., [14] and [15]). The known experimental uncertainties in particle masses and conversion factors are taken into account at the last step of calculations, when the most accurate computations are simply repeated for a few times with the use of different particle masses and conversion factors.…”

Section: Variational Energies Of Muonic Molecular Ionsmentioning

confidence: 99%

Bound state spectra of three-body muonic molecular ions

Frolov

Wardlaw

2011

Eur. Phys. J. D

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The results of highly accurate calculations are presented for all twenty-two known bound S(L = 0)−, P (L = 1)−, D(L = 2)− and F (L = 3)−states in the six three-body muonic molecular ions ppµ, pdµ, ptµ, ddµ, dtµ and ttµ. A number of bound state properties of these muonic molecular ions have been determined numerically to high accuracy. The dependence of the total energies of these muonic molecules upon particle masses is considered. We also discuss the current status of muon-catalysis of nuclear fusion reactions. PACS number(s):

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“…Prompt 2p decay is a subset of a more general phenomenon of three-body Coulomb decay (TBCD) which exists in mathematical physics (as a formal solution of the 3 → 3 scattering of charged particles), in atomic physics (as a solution of the e → 3e process), and in molecular physics (as exotic molecules composed from three charged constituents) [3][4][5][6][7][8]. The theoretical treatment of TBCD is one of the oldest and most complicated problems in physics because of the difficulty associated with the boundary conditions due the the infinite range of the Coulomb force.…”

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confidence: 99%

Observation of Long-Range Three-Body Coulomb Effects in the Decay ofNe16

et al. 2014

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The interaction of an E/A=57.6-MeV 17 Ne beam with a Be target was used to populate levels in 16 Ne following neutron knockout reactions. The decay of 16 Ne states into the three-body 14 O+p+p continuum was observed in the High Resolution Array (HiRA). For the first time for a 2p emitter, correlations between the momenta of the three decay products were measured with sufficient resolution and statistics to allow for an unambiguous demonstration of their dependence on the long-range nature of the Coulomb interaction. Contrary to previous measurements, our measured limit Γ < 80 keV for the intrinsic decay width of the ground state is not in contradiction with the small values (of the order of keV) predicted theoretically.PACS numbers: 25.10.+s, 23.50.+z, 21.60.Gx, 27.20.+n Introduction -Two-proton (2p) radioactivity [1] is the most recently discovered type of radioactive decay. It is a facet of a broader three-body decay phenomenon actively investigated within the last decade [2]. In binary decay, the correlations between the momenta of the two decay products are entirely constrained by energy and momentum conservation. In contrast for three-body decay, the corresponding correlations are also sensitive to the internal nuclear structure of the decaying system and the decay dynamics providing, in principle, another way to constrain this information from experiment. In 2p decay, as the separation between the decay products becomes greater than the range of the nuclear interaction, the subsequent modification of the initial correlations is determined solely by the Coulomb interaction between the decay products. As the range of the Coulomb force is infinite, its long-range contribution to the correlations can be substantial, especially, in heavy 2p emitters.

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Quantum three-body Coulomb problem in two dimensions

Cited by 27 publications

References 30 publications

On the bound states in the muonic molecular ions

On the bound states in the muonic molecular ions

Bound state spectra of three-body muonic molecular ions

Observation of Long-Range Three-Body Coulomb Effects in the Decay ofNe16

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