Weak Decay Rates Research Articles

The nuclear structure and associated electron capture rates on odd-Z nucleus 51V in stellar matter

The Gamow-Teller strength distribution function, B(GT), for the odd Z parent $^{51}$V, $N-Z$ =5, up to 30 MeV of excitation energy in the daughter $^{51}$Ti is calculated in the domain of proton-neutron Quasiparticle Random Phase Approximation (pn-QRPA) theory. The pn-QRPA results are compared against other theoretical calculations, (n, p) and high resolution (d, $^{2}$He) reaction experiments. For the case of (d, $^{2}$He) reaction the calibration was performed for $0\leq E_{j} \leq 5.0$ MeV, where the authors stressed that within this excitation energy range the $\Delta L = 0$ transition strength can be extracted with high accuracy for $^{51}$V. Within this energy range the current pn-QRPA total B(GT) strength 0.75 is in good agreement with the (d, $^{2}$He) experiment's total strength of 0.9 $\pm$ 0.1. The pn-QRPA calculated Gamow-Teller centroid at 4.20 MeV in daughter $^{51}$Ti is also in good agreement with high resolution (d, $^{2}$He) experiment which placed the Gamow-Teller centroid at 4.1 $\pm$ 0.4 MeV in daughter $^{51}$Ti. The low energy detailed Gamow-Teller structure and Gamow-Teller centroid play a sumptuous role in associated weak decay rates and consequently affect the stellar dynamics. The stellar weak rates are sensitive to the location and structure of these low-lying states in daughter $^{51}$Ti. The calculated electron capture rates on $^{51}$V in stellar matter are also in good agreement with the large scale shell model rates.

Nuclear uncertainties in the s-process simulation

The heavy elements in the Universe are formed during the s- and r-processes mainly in AGB stars and supernovae, respectively. Simulation of s- and r-nucleosynthesis critically depends on the neutron capture and weak decay rates for all the nuclei on the reaction chain. The present work analyzes systematically the neutron capture rates (cross sections) for the s-process nuclei, including ∼3000 rates on ∼200 nuclei. The network calculations for the constant temperature s-process have been performed using the different data sets selected as the nuclear inputs to investigate the uncertainties in the predicted s-abundances. We show that the available cross sections of neutron capture on many s-process nuclei still carry large uncertainties, which lead to low accuracy in the determination of s-process isotope abundances. We analyze the neutron capture cross section data for the same unique isobar nucleus accorded by year from previous work. Such an analysis indicates that the s-process has been studied for more than fifty years and there exist two research stages around 1976 and 2002, respectively. The needs and opportunities for future experiments and theoretical tools are highlighted to remove the existing shortcomings in the neutron capture rates.

Optimal number of stimulation contacts for coordinated reset neuromodulation

In this computational study we investigate coordinated reset (CR) neuromodulation designed for an effective control of synchronization by multi-site stimulation of neuronal target populations. This method was suggested to effectively counteract pathological neuronal synchrony characteristic for several neurological disorders. We study how many stimulation sites are required for optimal CR-induced desynchronization. We found that a moderate increase of the number of stimulation sites may significantly prolong the post-stimulation desynchronized transient after the stimulation is completely switched off. This can, in turn, reduce the amount of the administered stimulation current for the intermittent ON–OFF CR stimulation protocol, where time intervals with stimulation ON are recurrently followed by time intervals with stimulation OFF. In addition, we found that the optimal number of stimulation sites essentially depends on how strongly the administered current decays within the neuronal tissue with increasing distance from the stimulation site. In particular, for a broad spatial stimulation profile, i.e., for a weak spatial decay rate of the stimulation current, CR stimulation can optimally be delivered via a small number of stimulation sites. Our findings may contribute to an optimization of therapeutic applications of CR neuromodulation.

On the effect of the [formula omitted] in hypernuclear non-mesonic weak decay: A microscopic approach

The non-mesonic weak decay of Λ-hypernuclei is studied within a microscopic diagrammatic approach which includes, for the first time, the effect or the Δ-baryon resonance. We adopt a nuclear matter formalism extended to finite nuclei via the local density approximation, a one-meson exchange weak transition potential, a Bonn nucleon–nucleon strong potential and a ΔN→NN strong potential based on the Landau–Migdal theory. Ground state correlations and final state interactions (FSI), at second order in the baryon–baryon strong interaction, are introduced on the same footing for all the isospin channels of one- and two-nucleon induced decays. Weak decay rates and single and double-coincidence nucleon spectra are predicted for CΛ12 and compared with recent KEK and FINUDA data. The Δ(1232) introduces new FSI-induced decay mechanisms which lead to an improvement when comparing the obtained nucleon spectra with data, while it turns out to have a negligible effect on the decay rates. Discrepancies with experiment remain only for emission spectra involving protons, but are mostly restricted to double-nucleon correlations in the non-back-to-back kinematics.

Multiple-channel generalization of Lellouch-Lüscher formula

We generalize the Lellouch-L\"uscher formula, relating weak matrix elements in finite and infinite volumes, to the case of multiple strongly coupled decay channels into two scalar particles. This is a necessary first step on the way to a lattice quantum chromodynamics calculation of weak decay rates for processes such as $D\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $D\ensuremath{\rightarrow}K\overline{K}$. We also present a field theoretic derivation of the generalization of L\"uscher's finite-volume quantization condition to multiple two-particle channels. We give fully explicit results for the case of two channels, including a form of the generalized Lellouch-L\"uscher formula expressed in terms of derivatives of the energies of finite-volume states with respect to the box size. Our results hold for arbitrary total momentum and for degenerate or nondegenerate particles.

Weak decay rates for waiting-point nuclei involved in the rp-process

We study weak interaction rates under the stellar density and temperature conditions encountered in the rp process. Special attention is paid to neutron-deficient waiting-point nuclei. The nuclear structure part of the problem is described within a deformed Skyrme Hartree-Fock + BCS + QRPA approach, which reproduces not only the beta-decay half-lives but also the available Gamow-Teller strength distributions, measured under terrestrial conditions. The various sensitivities of the decay rates to both density and temperature are discussed. In particular, we study the contributions coming from excited states in the parent nucleus, which are thermally populated, and the competition between beta-decays and continuum electron captures.

Stellar weak decay rates in neutron-deficient medium-mass nuclei

Weak decay rates under stellar density and temperature conditions holding at the rapid proton capture process are studied in neutron-deficient medium-mass waiting point nuclei extending from Ni up to Sn. Neighboring isotopes to these waiting point nuclei are also included in the analysis. The nuclear structure part of the problem is described within a deformed Skyrme Hartree-Fock + BCS + QRPA approach, which reproduces not only the beta-decay half-lives but also the available Gamow-Teller strength distributions, measured under terrestrial conditions. The various sensitivities of the decay rates to both density and temperature are discussed. In particular, we study the impact of contributions coming from thermally populated excited states in the parent nucleus, as well as the competition between beta decays and continuum electron captures.

Gamow-Teller strength distribution in proton-rich nucleus 57Zn and its implications in astrophysics

Gamow-Teller (GT) transitions play a preeminent role in the collapse of stellar core in the stages leading to a Type-II supernova. The microscopically calculated GT strength distributions from ground and excited states are used for the calculation of weak decay rates for the core-collapse supernova dynamics and for probing the concomitant nucleosynthesis problem. The B(GT) strength for 57Zn is calculated in the domain of proton-neutron Quasiparticle Random Phase Approximation (pn-QRPA) theory. No experimental insertions were made (as usually made in other pn-QRPA calculations of B(GT) strength function) to check the performance of the model for proton-rich nuclei. The calculated B(GT) strength distribution is in good agreement with measurements and shows differences with the earlier reported shell model calculation. The pn-QRPA model reproduced the measured low-lying strength for 57Zn better in comparison to the KB3G interaction used in the large-scale shell model calculation. The stellar weak rates are sensitive to the location and structure of these low-lying states in daughter 57Cu. The structure of 57Cu plays a sumptuous role in the nucleosynthesis of proton-rich nuclei. The primary mechanism for producing such nuclei is the rp-process and is believed to be important in the dynamics of the collapsing supermassive stars. Small changes in the binding and excitation energies can lead to significant modifications of the predictions for the synthesis of proton rich isotopes. The β +-decay and electron capture (EC) rates on 57Zn are compared to the seminal work of Fuller, Fowler and Newman (FFN). The pn-QRPA calculated β +-decay rates are generally in good agreement with the FFN calculation. However at high stellar temperatures the calculated β +-decay rates are almost half of FFN rates. On the other hand, for rp-process conditions, the calculated electron capture (β +-decay) rates are bigger than FFN rates by more than a factor 2 (1.5) and may have interesting astrophysical consequences.

Hypernuclear Weak Decays

The recent theoretical studies of Λ-hypernuclear weak decays of the nonmesonic and π-mesonic ones are developed with the aim to disclose the link between the experimental decay observables and the underlying basic weak decay interactions and the weak decay mechanisms. The expressions of the nonmesonic decay rates Γnm and the decay asymmetry parameter α1 of protons from the polarized hypernuclei are presented in the shell model framework. We then introduce the meson theoretical ΛN → NN interactions which include the one-meson exchanges, the correlated-2π exchanges, and the chiral-pair-meson exchanges. The features of meson exchange potentials and their roles on the nonmesonic decays are discussed. With the adoption of the π + 2π/ρ + 2π/σ + ω + K + ρπ/a1 + σπ/a1 exchange potentials, we have carried out the systematic calculations of the nonmesonic decay observables for light-to-heavy hypernuclei. The present model can account for the available experimental data of the decay rates, Γn/Γp ratios, and the intrinsic asymmetry parameters αΛ (αΛ is related to α1) of emitted protons well and consistently within the error bars. The hypernuclear lifetimes are evaluated by converting the total weak decay rates Γtot = Γπ+Γnm to τ , which exhibit saturation property for the hypernuclear mass A ≥ 30 and agree grossly well with experimental data for the mass range from light to heavy hypernuclei except for the very light ones. Future extensions of the model and the remaining problems are also mentioned. The π-mesonic weak processes are briefly surveyed, and the calculations and predictions are compared and confirmed by the recent high precision FINUDA π-mesonic decay data. This shows that the theoretical basis seems to be firmly grounded.

Formula omitted] decay rates of p-shell hypernuclei revisited

Explicit expressions for the parity-violating s-wave and the parity-conserving p-wave contributions to π − weak decay rates of Λ hypernuclei in the 1 p shell are given in the weak-coupling limit, to update previous shell-model calculations and to compare with recent π − spectra and total decay rates measured by the FINUDA Collaboration for Li Λ 7 , Be Λ 9 , B Λ 11 and N Λ 15 . A useful sum rule for the summed strength of Λ 1 s → p 1 p hypernuclear π − weak decays is derived. Fair agreement between experiment and calculations is reached, using the primary s-wave amplitude and Cohen–Kurath nuclear wavefunctions. The role of the p-wave amplitude is studied in detail for N Λ 15 and found to be secondary. Previous assignments of ground-state spin-parity values J π ( Li g.s. Λ 7 ) = 1 2 + and J π ( B g.s. Λ 11 ) = 5 2 + are confirmed, and a new assignment J π ( N g.s. Λ 15 ) = 3 2 + is made, based on the substantial suppression calculated here for the N Λ 15 ( 1 2 + ) → π − O g.s. 15 weak decay rate.

Nuclear quantum Monte Carlo: Expanding into the continuum

I discuss calculations of nuclear properties using the variational Monte-Carlo (VMC) and Green’s function Monte-Carlo (GFMC) methods in combination with realistic two- and three-nucleon interactions. Work to date has emphasized energies of bound and narrow states, and the results agree well with measured masses and energies. We are now directing more effort toward other nuclear properties, including weak decay rates and nuclear charge radii. The main new direction is the computation of low-energy scattering and reaction properties. We have incorporated R-matrix-like boundary conditions into GFMC calculations, and our first calculation of this kind has yielded phase shifts for neutron scattering on 4He up to a few MeV. We find strong dependence of the results on the three-nucleon interaction used.

Weak decays of J/ψ: the non-leptonic case

In our previous study, we calculated the transition form factors of J/ψ→D(*) (s) using the QCD sum rules. Based on the factorization approximation, the form factors obtained can be applied to evaluate the weak non-leptonic decay rates of J/ψ→D(*) (s)+M, where M stands for a light pseudoscalar or vector meson. We predict that the branching ratio for inclusive non-leptonic two-body weak decays of J/ψ, which are realized via the spectator mechanism, can be as large as 1.3×10-8; in particular, the branching ratio of J/ψ→D*± s+ρ∓ can reach 5.3×10-9. Such values will be marginally accessed by the ability of BESIII, which will begin running very soon.

Semiclassical approach to the decay of protons in circular motion under the influence of gravitational fields

We investigate the possible decay of protons in geodesic circular motion around neutral compact objects. Weak and strong decay rates and the associated emitted powers are calculated using a semi-classical approach. Our results are discussed with respect to distinct ones in the literature, which consider the decay of accelerated protons in electromagnetic fields. A number of consistency checks are presented along the paper.

An EFT for the weak ΛN interaction

The nonleptonic weak | Δ S | = 1 ΛN 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 ( π and K), while the short-range potential is parametrized in terms of lowest-order contact terms obtained from the most general non-derivative local four-fermion interaction. Fitting to available weak hypernuclear decay rates for 5 Λ He, 11 Λ B and 12 Λ C yields reasonable values for the low-energy constants.

ΛN→NNweak interaction in effective-field theory

The nonleptonic weak $|\Delta S|=1$ $\Lambda N$ 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.

Publisher’s Note: Ground-state scalarq¯qnonet: SU(3) mass splittings and strong, electromagnetic, and weak decay rates [Phys. Rev. D69, 014010 (2004)

By comparing SU(3)-breaking scales of linear mass formulae, it is shown that the lowest vector and scalar mesons all have a $\bar{q}q$ configuration, while the ground-state octet and decuplet baryons are $qqq$. Also, the quark-level linear $\sigma$ model is employed to predict similar $\bar{q}q$ and $qqq$ states. Furthermore, the approximate mass degeneracy of the scalar $a_0$(985) and $f_0$(980) mesons is demonstrated to be accidental. Finally, it is shown that various strong, electromagnetic, and weak mesonic decay rates are successfully explained within the framework of the quark-level linear $\sigma$ model.

Ground-state scalarq¯qnonet: SU(3) mass splittings and strong, electromagnetic, and weak decay rates

By comparing SU(3)-breaking scales of linear mass formulas, it is shown that the lowest vector and scalar mesons all have a $\overline{q}q$ configuration, while the ground-state octet and decuplet baryons are qqq. Also, the quark-level linear $\ensuremath{\sigma}$ model is employed to predict similar $\overline{q}q$ and qqq states. Furthermore, the approximate mass degeneracy of the scalar ${a}_{0}(985)$ and ${f}_{0}(980)$ mesons is demonstrated to be accidental. Finally, it is shown that various strong, electromagnetic, and weak mesonic decay rates are successfully explained within the framework of the quark-level linear $\ensuremath{\sigma}$ model.

NONMESONIC WEAK DECAYS OF SINGLE-Λ AND DOUBLE-Λ HYPERNUCLEI OF LIGHT MASS SYSTEMS

The nucleon-induced and hyperon-induced nonmesonic weak decay rates of the single-Λ and double-Λ hypernuclei are evaluated in the meson-exchange potential model. The roles of K-meson exchange are discussed. The ΛΛ → nΛ decay rate of [Formula: see text] is estimated to be fair and might be detectable in a future experiment.

Effects of quenching and partial quenching on penguin matrix elements

In the calculation of non-leptonic weak decay rates, a "mismatch" arises when the QCD evolution of the relevant weak hamiltonian down to hadronic scales is performed in unquenched QCD, but the hadronic matrix elements are then computed in (partially) quenched lattice QCD. This mismatch arises because the transformation properties of penguin operators under chiral symmetry change in the transition from unquenched to (partially) quenched QCD. Here we discuss QCD-penguin contributions to $\Delta S=1$ matrix elements, and show that new low-energy constants contribute at leading order in chiral perturbation theory in this case. In the partially quenched case (in which sea quarks are present), these low-energy constants are related to electro-magnetic penguins, while in the quenched case (with no sea quarks) no such relation exists. As a simple example, we give explicit results for $K^+\to\pi^+$ and $K^0\to vacuum$ matrix elements, and discuss the implications for lattice determinations of $K\to\pi\pi$ amplitudes from these matrix elements.

Non-spectator Diquark Effects on Lifetimes of and Weak Decay Rates of , **The project supported in part by National Natural Science Foundation of China and the Australian Research Council

The difference of and indicates the role of the light flavors. We calculate the lifetimes of -meson and based on the weak effective Hamiltonian while assuming the heavy baryon is constructed by a heavy -quark and a diquark containing two light quarks. In this scenario, we use the information of the measured ratio as input to predict rates of the inclusive weak decays of and into non-bottom final states. We find that these rates of and are much larger than those of -mesons and . We also give the predictions for the lifetimes of and . Phenomenological implication of our result is discussed.