Shell Hypernuclei Research Articles

Deformation and hyperon halo in hypernuclei

The effects of deformation and the change of the nuclear core on the hyperon binding and halo structure in single-$\mathrm{\ensuremath{\Lambda}}$ $p$-shell hypernuclei are studied for the C hyperisotopes and $N=6$ hyperisotones in the framework of the deformed Skyrme-Hartree-Fock approach with combinations of the $NN$ interactions SIII, SGII, SkI4 and the $\mathrm{\ensuremath{\Lambda}}N$ interactions LY1 and SLL4, respectively. Deformation causes more deeply bound states with smaller extension of the density distributions and radii. The possibility of deformed halo structures of $\mathrm{\ensuremath{\Lambda}}$ $1p$ states in hypernuclei up to a mass number $A=15$ is found.

Induced Hyperon-Nucleon-Nucleon Interactions and the Hyperon Puzzle.

We present the first abinitio calculations for p-shell hypernuclei including hyperon-nucleon-nucleon (YNN) contributions induced by a similarity renormalization group transformation of the initial hyperon-nucleon interaction. The transformation including the YNN terms conserves the spectrum of the Hamiltonian while drastically improving model-space convergence of the importance-truncated no-core model, allowing a precise extraction of binding and excitation energies. Results using a hyperon-nucleon interaction at leading order in chiral effective field theory for lower- to mid-p-shell hypernuclei show a good reproduction of experimental excitation energies while hyperon separation energies are typically overestimated. The induced YNN contributions are strongly repulsive and we show that they are related to a decoupling of the Σ hyperons from the hypernuclear system, i.e., a suppression of the Λ-Σ conversion terms in the Hamiltonian. This is linked to the so-called hyperon puzzle in neutron-star physics and provides a basic mechanism for the explanation of strong ΛNN three-baryon forces.

Ab initio description of p-shell hypernuclei.

We present the first ab initio calculations for p-shell single-Λ hypernuclei. For the solution of the many-baryon problem, we develop two variants of the no-core shell model with explicit Λ and Σ(+),Σ(0),Σ(-) hyperons including Λ-Σ conversion, optionally supplemented by a similarity renormalization group transformation to accelerate model-space convergence. In addition to state-of-the-art chiral two- and three-nucleon interactions, we use leading-order chiral hyperon-nucleon interactions and a recent meson-exchange hyperon-nucleon interaction. We validate the approach for s-shell hypernuclei and apply it to p-shell hypernuclei, in particular to (Λ)(7)Li, (Λ)(9)Be, and (Λ)(13)C. We show that the chiral hyperon-nucleon interactions provide ground-state and excitation energies that generally agree with experiment within the cutoff dependence. At the same time we demonstrate that hypernuclear spectroscopy provides tight constraints on the hyperon-nucleon interactions.

Hypernuclear weak decay studies with FINUDA

The FINUDA experiment has recently completed an extensive study of the weak decay of p -shell Λ -hypernuclei including both mesonic and non-mesonic modes. Charged mesonic decay rates have been determined based on the analysis of π − kinetic energy spectra, never measured before. The study of proton spectra from non-mesonic weak decay for p -shell hypernuclei, both single and in coincidence with a neutron, has triggered the investigation of the two-nucleon induced Λ N N → n N N decay channel: its weight has been evaluated to be Γ 2 / Γ N M = 0.21 ± 0.07 stat − 0.02 sys + 0.03 sys . Finally, a direct experimental evidence of the occurrence of the weak reaction Λ n p → n n p in nuclei is presented for the first time. Three events have been found which can be attributed to Li Λ 7 and Be Λ 9 two-nucleon induced non-mesonic weak decay; the kinematical analysis is discussed here.

Deformation of hypernuclei studied with antisymmetrized molecular dynamics

An extended version of the antisymmetrized molecular dynamics to study structure of $p$-$sd$ shell hypernuclei is developed. By using an effective $\Lambda N$ interaction, we investigate energy curves of $^9_\Lambda$Be, $^{13}_\Lambda$C and $^{20,21}_\Lambda$Ne as function of nuclear quadrupole deformation. Change of nuclear deformation caused by $\Lambda$ particle is discussed. It is found that the $\Lambda$ in p-wave enhances nuclear deformation, while that in s-wave reduces it. This effect is most prominent in $^{13}_\Lambda$C. The possibility of the parity inversion in $^{20}_\Lambda$Ne is also examined.

EXPERIMENTAL OVERVIEW AND CHALLENGE IN STRANGENESS NUCLEAR PHYSICS — STRANGENESS IN THE PAST AND COMING DECADES

A great progress has been made in strangeness nuclear physics in the past decade. Examples are; 1) The "hyperfine" structure of hypernuclei were measured with the Hyperball, and ΛN spin dependent interactions in p -shell hypernuclei were determined. 2) The "complete measurements" of the weak decay of hypernuclei were made and the np ratio puzzle in the non-mesonic decay was solved. 3) The discovery of a clean event of "Lambpha" and determination of its binding energy concluded that the Λ-Λ interaction is weak attractive. However, we still have important questions to be answered in this field, especially in relation with QCD and nuclear physics. For the future strangeness nuclear physics, we have and will have facilities such as JLab, SPring-8, Daphne, J-PARC, FAIR. We discuss experimental challenges in the strangeness nuclear physics and related fields in the next decade.

ΣHyperons in the Nucleus

A search for {sigma} hypernuclear states in p -shell hypernuclei has been performed with the Moby Dick spectrometer and the low energy separated beam (LESB-2) at the Brookhaven Alternating Gradient Synchrotron (BNL AGS). Unlike some previously published reports, no narrow states have been observed for targets of {sup 6}Li and {sup 9}Be in (K{sup -}, {pi}{sup {+-}}) reactions, either for bound state or continuum regions. Together with the previously reported J=0 , T=1/2 bound state in {sup 4}{sub {sigma}} He , these results demonstrate the crucial role of isospin in {sigma} hypernuclei. (c) 1999 The American Physical Society.

Semi-Empirical Formulae for Λ and Ξ Binding Energy in Hypernuclei

On the basis of very general considerations, a semi-empirical formula for Λ binding energy in hypernuclei has been obtained. The parameters in the formula have been fixed from a χ 2 fit to the B Λ of the heavier p -shell hypernuclei ( A > 8). The Λ binding in 32 Λ S and spallation hypernuclei (60 < A < 100) predicted by the formula are fairly close to their respective experimental values. The empirical value of D Λ turns out to be 31.6 MeV. The analysis further shows that on account of the large uncertainties of the B Ξ data, empirical value of D Ξ can not be uniquely determined. However, the value of D Ξ is definitely smaller than D Λ .

Ground state binding energies of hypernuclei.

We show that the folding model with a density-dependent effective ..lambda.. N interaction satisfactorily explains the available ..lambda.. binding energy data of p shell and heavier hypernuclei.

A shell-model analysis of Λ binding energies for the p-shell hypernuclei III. Further analysis and predictions

A simplified phenomenological analysis of the Λ binding energies for the p-shell hypernuclei is given on the basis of the shell-model configuration [(1 s) N 4(1p) N A−5 (1s) Λ ], using the intermediate-coupling formalism set up in Part I, assuming the ΛNN interaction Q 00 0 of central form (as motivated by the double-OPE mechanism), and taking into account the new data recently available about several p 1 2 -shell hypernuclei. The systematics of the mass matrix for p-shell Λ hypernuclei are discussed in some detail. The fit obtained has only moderate strengths for the (ΛN) spin-orbit and (ΛNN) three-body interactions and requires rather little mixing of different nuclear core states into the hypernuclear wavefunctions, except for the special case Λ 8Li. The implications of this fit are spelled out for the well-known hypernuclear species. A discrepancy between the wavefunction calculated here for Λ 8Li and the characteristics of the decay Λ 8Li → ααπ − is emphasized, as is also the need for Λ hypernuclear γ-ray data.

ΛBinding Energy for the2s−1d-Shell Hypernuclei. I.18&lt;~A&lt;~21

The $\ensuremath{\Lambda}$ binding energies of the $2s\ensuremath{-}1d$-shell hypernuclei with mass number between 18 and 21 are calculated, using the results of a shell-model calculation for the $1p$-shell hypernuclei previously carried out by the authors.

Binding Energies of thep-ShellΛΛHypernuclei

Using the results of a shell-model analysis of the $p$-shell hypernuclei by the authors, the binding energies of the two $\ensuremath{\Lambda}$ particles in the $p$-shell $\ensuremath{\Lambda}\ensuremath{\Lambda}$ hypernuclei are calculated. A consistent account of the binding energies of the two known $\ensuremath{\Lambda}\ensuremath{\Lambda}$ hypernuclei, $_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{ 6}\mathrm{He}$ and $_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{10}\mathrm{Be}$ (or $_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{11}\mathrm{Be}$) is obtained. Close agreement with the results of other investigators who used different methods is also pointed out. The effects of the noncentral potentials in the effective two-body $\ensuremath{\Lambda}\ensuremath{-}N$ interaction are discussed.

Shell-Model Structure of thep-Shell Hypernuclei

A systematic study of the effective two-body $\ensuremath{\Lambda}\ensuremath{-}N$ interaction is made in an exact manner from the binding-energy data of the $p$-shell hypernuclei within the framework of the intermediate-coupling shell model. The binding energy is expressed in terms of the five independent potential integrals of the two-body $\ensuremath{\Lambda}\ensuremath{-}N$ interaction, and the latter are determined by a least-squares fit to the experimental data. The energy levels and the $\ensuremath{\gamma}$ transitions are calculated, and the structures of the $p$-shell hypernuclei are discussed. The potential integrals are then analyzed in terms of phenomenological potentials. A large contribution to the binding energy by noncentral forces, especially the tensor forces, is found. The effect of the existence of a three-body $\ensuremath{\Lambda}\mathrm{NN}$ force is also discussed.

Self-Consistent Calculation ofp-Shell Hypernuclear Binding Energies

Calculations of the binding energies of $p$-shell hypernuclei have been carried out treating all the nucleons and the $\ensuremath{\Lambda}$ self-consistently. The Tabakin potential is used for the $\mathrm{NN}$ interaction and a simple central force which fits $\ensuremath{\Lambda}N$ scattering is used for the $\ensuremath{\Lambda}\ensuremath{-}N$ system. The binding energies obtained exceed those observed. The dynamical aspects of the hypernuclear system are also discussed, as well as various correction terms. Finally, a comparison is made with other hypernuclear calculations.

1p shell hypernuclei deformation and Majorana exchange binding energy effects

The Λ binding energy is reduced in 1p shell hypernuclei by taking deformation into account. The binding also can be reduced by increasing the Majorana exchange component of the ΛN force but this reduces the deformation effect.

Hartree-Fock Calculation of Helium Hypernuclear Binding Energies

The binding energies of the $s$-shell hypernuclei ($_{\ensuremath{\Lambda}}\mathrm{H}^{4}$, $_{\ensuremath{\Lambda}}\mathrm{He}^{5}$, and $_{\ensuremath{\Lambda}\ensuremath{\Lambda}}\mathrm{He}^{6}$) have been calculated in the Hartree-Fock model, using Gaussian particle-particle potentials. Parameters of the $\ensuremath{\Lambda}\ensuremath{-}N$ interaction were determined from the experimental binding energies. These numerical results agree qualitatively with those of other calculations and also with the experimental $\ensuremath{\Lambda}\ensuremath{-}N$ scattering data, if short-range repulsions are included. Equality of the $\ensuremath{\Lambda}\ensuremath{-}N$ and $\ensuremath{\Lambda}\ensuremath{-}\ensuremath{\Lambda}$ potentials is consistent with these calculations.

PhenomenologicalΛ-Nucleon Potentials fromS-Shell Hypernuclei. III. Dependence on Potential Shape

The binding-energy data of the $s$-shell hypernuclei and the $\ensuremath{\Lambda}$-proton scattering data are analyzed with $\ensuremath{\Lambda}$-nucleon potentials which have a hard core and an attractive part of Yukawa shape. By comparing the results with those obtained in a previous investigation where the attractive part was assumed to be of exponential shape, it is concluded that to analyze these experimental data, the choice of the spatial form for the attractive part is not a critical one.

PhenomenologicalΛ-Nucleon Potentials froms-Shell Hypernuclei. II. Dependence on Intrinsic Range

By examining the binding-energy data of the $s$-shell hypernuclei and the $\ensuremath{\Lambda}$-proton scattering data with a number of effective central $\ensuremath{\Lambda}$-nucleon potentials of various hard-core radii (0-0.6 F) and intrinsic ranges (1.5-2.5 F), a $\ensuremath{\Lambda}$-nucleon potential has been found which yields a very good fit to these experimental data. This potential has an intrinsic range of 2.1 F, a hard-core radius of 0.6 F, and an odd-parity-state strength which is equal to 60% of the even-parity-state strength. Also, it has a rather small degree of spin dependence in the $\ensuremath{\Lambda}$-proton case, with the consequence that the predicted $J=1$ excited state in $_{\ensuremath{\Lambda}}\mathrm{H}^{4}$ has a small excitation energy of only about 0.1 MeV. The $\ensuremath{\Lambda}$-proton effective-range parameters have the following values: ${{a}_{t}}^{p}=\ensuremath{-}2.08$ F, ${{r}_{0t}}^{p}=3.40$ F, ${{a}_{s}}^{p}=\ensuremath{-}2.25$ F, and ${{r}_{0s}}^{p}=3.29$ F. The case of $\ensuremath{\Lambda}$-neutron scattering has also been considered. Here it is found that the total cross sections differ appreciably from those of the corresponding $\ensuremath{\Lambda}$-proton case only when the c.m. energy is less than about 4 MeV.

Evidence forΛNNRepulsive Forces fromp-Shell Hypernuclei

A strongly repulsive three-body $\ensuremath{\Lambda}\mathrm{NN}$ force is proposed for the explanation of some exceptionally large binding-energy differences in the $p$-shell hypernuclei. It is argued that heavy hypernuclei maintain their stability.

The p-shell hypernuclei and the Λ-N interaction

The p shell hypernuclei have been studied in detail using two and three-body central Yukawa Λ-N interactions. Intermediate coupled wave functions and a range of density distributions are considered for the core nuclei. The Λ wave function and volume integrals are obtained by numerical solution of the appropriate two-body (Λ-core nucleus) eigenvalue problems, the results being most conveniently represented by the corresponding numerical spin-dependent and charge-independent two-body interaction turns out to be adequate to account for all the known B Λ. In particular, the values of the spin-averaged volume integral of the two-body interaction, which are obtained from ΛHe 5, ΛBe 9 and ΛC 13, agree very well in the absence of three-body forces. Further, quite small upper limits on the permissible strength of the latter are obtained. Almost nothing can be deduced about the range of the two-body forces or about their interactions in relative p states. The implications of our results for the well depth in nuclear matter are discussed. The spin-dependent interaction energy is found to be completely masked by quite small uncertainties in the core sizes, to a lesser extent, by uncertainties in the re-arrangement energies. Effectively nothing can at present be deduced from the p shell hypernuclei about the spin dependence which most plausible assumptions about the core sizes and re-arrangement energies can be made to agree with the values obtained from the s shell hypernuclei. Conversely assuming such values for the spin dependence can make the Λ into a quite sensitive probe into small size differences.