<i>g</i>-matrix calculations in finite hypernuclei

Halderson, Dean

doi:10.1103/physrevc.48.581

Cited by 43 publications

(47 citation statements)

References 15 publications

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“…As in the case of the OPE, in the OMEM, a weak baryon-baryon-meson (BBM) coupling is always combined with a strong BBM coupling. The strong one is determined experimentally with some help from the SU(3) symmetry, and the involving uncertainties have been copiously discussed in the literature [40][41][42][43]. It is the weak BBM couplings which could become the largest source of errors.…”

Section: Introductionmentioning

confidence: 99%

Nuclear structure in nonmesonic weak decay of hypernuclei

Krmpotić¹,

Tadić²

2003

Braz. J. Phys.

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A general shell model formalism for the nonmesonic weak decay of the hypernuclei has been developed. It involves a partial wave expansion of the emitted nucleon waves, preserves naturally the antisymmetrization between the escaping particles and the residual core, and contains as a particular case the weak Λ-core coupling formalism. The hypernuclei are grouped having in view their A − 1 cores, that is in those with even-even, evenodd and odd-odd cores. It is shown that in all three cases the nuclear structure manifests itself basically through Pauli Principle, and very simple expressions are derived for the neutron and proton induced decays rates, Γ n and Γ p , which does not involve the spectroscopic factors. For the strangeness-changing weak ΛN → N N transition potential we use the One-Meson-Exchange Model (OMEM), which comprises the exchange of the complete pseudoscalar and vector meson octets (π, η, K, ρ, ω Λ Si hypernuclei, with commonly used parametrization for the OMEM, and compare the results with the available experimental information. The calculated rates Γ N M = Γ n + Γ p are consistent with the data, but the measurements of Γ n/p = Γn/Γp are not well accounted for by the theory. It is suggested that, unless additional degrees of freedom are incorporated, the OMEM parameters should be radically modified. I IntroductionHypernuclear physics adds another flavor (strangeness) to the traditional nuclear physics, and its goal is to study the behavior of hyperons (Λ, Σ, Ξ, Ω) in the nuclear environments, which are now bound system of neutrons, protons and one or more hyperons. Interesting strange nuclei with strangeness S = −1 are the Λ hypernuclei, in which a Λ hyperon, having a mass of 1116 MeV and zero charge and isospin, replaces one of the nucleons. Same as the free Λ hyperon, they are mostly produced via the strong interactions, i.e., in the reaction processes π, by making use of the pion (π) and kaon (K) beams. They also basically decay through the weak interactions, as the free Λ does. Yet, as it is well known and explained below, there are some very important differences in the corresponding decaying modes. First, it should be remembered that the free Λ hyperon decays nearly 100 % of the time by the Λ → N π weakmesonic mode (Fig. 1): sec). For the decay at rest the energy-momentum conservation impliesTherefore the energy released isand the kinetic energies and momenta in the final state are:

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Section: Introductionmentioning

confidence: 99%

Nuclear structure in nonmesonic weak decay of hypernuclei

Krmpotić¹,

Tadić²

2003

Braz. J. Phys.

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“…In the present calculation, we use a shell model for the initial hypernucleus, where the single-particle ⌳ and N orbits are taken to be solutions of harmonicoscillator mean-field potentials with parameters (b ⌳ and b N ) adjusted to experimental separation energies and charge form factor (respectively) of the hypernucleus under study. For The strong YN interaction at short distances, absent in mean-field models, is accounted for by replacing the mean-field two-particle ⌳N wave function by a correlated [23] one obtained from a microscopic finite-nucleus G-matrix calculation [24] using the soft-core and hard-core Nijmegen models [25]. The NN wave function is obtained from the Lippmann-Schwinger (T-matrix) equation with the input of the Nijmegen soft-core potential model; details of the calculation can be found in the appendix of Ref.…”

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confidence: 99%

ΛN→NNweak interaction in effective-field theory

2004

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The nonleptonic weak ͉⌬S͉ =1 ⌳N interaction, responsible for the dominant nonmesonic decay of all but the lightest hypernuclei, is studied in the framework of an effective-field theory. The long-range physics is described through tree-level exchange of the SU(3) Goldstone bosons, while the short-range potential is parametrized in terms of the lowest-order contact terms. We obtain reasonable fits to available weak hypernuclear decay rates and quote the values for the parity-violating asymmetry as predicted by the present effective-field theory. For the past 50 years, ⌳ hypernuclei, systems of one or more ⌳ hyperons bound to a core nucleus, have been used to extend our knowledge of both the strong and the weak baryon-baryon interaction from the NN case into the SU(3) sector. The nonmesonic hypernuclear weak decay, facilitated via the ͉⌬S͉ = 1 four-fermion interaction, thus complements the weak ⌬S =0 NN case, which allows the study of only the parity-violating amplitudes.In analogy to NN phenomenology, the nonmesonic hypernuclear decay has traditionally been modeled using a mesonexchange approach [1]. The long-range part of the interaction is naturally explained by one-pion exchange, which could approximately reproduce the total (one-nucleoninduced) nonmesonic decay rate, ⌳N → NN, but not the partial rates, the proton-induced ⌳p → np rate ⌫ p , and the neutron-induced ⌳n → nn rate ⌫ n [2]. Due to the ⌳N mass difference, the process ⌳N → NN produces nucleons with momenta around Ϸ420 MeV, suggesting that the short-range part of the interaction cannot be neglected. These contributions have been described either through the exchange of vector mesons [3,4], whose production thresholds are too high for the free ⌳ decay, or through direct quark exchange [5].In contrast to previous theoretical studies, we present an exploratory study in order to determine the possible efficacy of the use of effective-field theory (EFT) methods in hypernuclear decay. Studies in this direction have already begun in Ref. [6], where a Fermi ͑V-A͒ interaction was added to the one-pion-exchange (OPE) mechanism to describe the weak ⌳N → NN transition. The present approach is motivated by the remarkable success of EFT techniques based on chiral expansions in the (nonstrange) SU(2) sector [7-10], which suggests its extension to the SU(3) realm, even though stability of the chiral expansion is less clear for the SU(3) sector, due to the significant degree of SU(3) symmetry breaking. A well-known example of the problems facing the SU(3) chiral perturbation theory has been the prediction [11][12][13][14] The EFT approach is based on the existence of wellseparated scales in the physical process under study. Formally, the high-momentum (short-distance) modes in the four-baryon interaction Lagrangian are replaced by contact operators, compatible with the underlying physical symmetries, of increasing dimension. Built in such a way, the Lagrangian will contain an infinite number of terms, and a consistent power-counting scheme is needed in order to trunca...

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“…One can see that the calculations are providing considerably more binding than that observed in the heavier systems. Similar calculations for model D gave underbinding for the light systems and overbinding for the heavier systems [15]. The soft core underbound all systems [15].…”

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confidence: 58%

“…The procedure for these calculations is described in Refs. [6] and [7]. Briefly, the four-component Bethe-Goldstone equation is solved to obtain reference spectrum g-matrix elements.…”

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confidence: 99%

Λ-hypernuclei single-particle energies with the Nijmegen ESC04 baryon-baryon interaction

Halderson

2007

Phys. Rev. C

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hypernuclei single-particle energies are calculated for the new Nijmegen ESC04 baryon-baryon interaction. A Brueckner-Hartree approach is employed. Whereas good agreement with experimental results is obtained for the A = 3, 4, and 5 systems, the heavier systems are considerably overbound. A possible source for some of the overbinding is the spin-orbit odd interaction and its effect on the 3 P 2 channel.

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g-matrix calculations in finite hypernuclei

Cited by 43 publications

References 15 publications

Nuclear structure in nonmesonic weak decay of hypernuclei

Nuclear structure in nonmesonic weak decay of hypernuclei

ΛN→NNweak interaction in effective-field theory

Λ-hypernuclei single-particle energies with the Nijmegen ESC04 baryon-baryon interaction

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