The purpose of this note is to report predictions of the binding energy of the $Λ$ hyperon in nuclear matter using the latest version of the Juelich nucleon-nucleon meson-exchange potential. Results from a conventional Brueckner calculation are compared with previously reported values. A calculation including Dirac effects on the $Λ$ single-particle potential is also presented. Issues encountered in Dirac calculations with nucleon-hyperon potentials are discussed.
Two approximate formulae are given for the binding energies in Lambda-hypernuclei and light nuclei by means of the (reduced) Poeschl-Teller and the Gaussian central potentials. Those easily programmable formulae combine the eigenvalues of the transformed Jacobi eigenequation and an application of the hypervirial theorems.
To understand the difference between the value of the nn and Lambda-Lambda two-body matrix elements, we examine the role of the coupling between the Lambda-Lambda and Xi-N channels, first within the framework of SU(3), and second in the numerical results for the binding energy of Lambda-Lambda 6He. We find that it is essential to include the coupled channel nature of the BB interaction as we proceed from strangeness zero to the strangeness -1 and -2 channels if we are to understand the relative magnitude of the two-body matrix elements in the different strangeness channels.
Configuration space Faddeev calculations are performed for the binding energy of Lambda-Lambda-6He and Lambda-9Be bound states, here considered as alpha-Lambda-Lambda and alpha-alpha-Lambda clusters respectively, in order to study the dependence of the calculated binding energy on the alpha-Lambda potential input. For Lambda-Lambda-6He, using realistic interactions, the uncertainty in extracting the Lambda-Lambda S=L=0 interaction strength does not exceed 0.1 MeV, which is a fraction of the order of magnitude derived for other theoretical uncertainties. For Lambda-9Be, the dependence of the ca…
Recent experiments on production of Lambda-Lambda hypernuclei have renewed interest in extracting the Lambda-Lambda interaction from the few events identified since the inception of this field forty years ago. Few-body calculations relating to this issue are reviewed, particularly with respect to the possibility that A=4 marks the onset of Lambda-Lambda binding in nuclei. The Nijmegen soft-core model potentials NSC97 qualitatively agree with the strength of the Lambda-Lambda interaction deduced from the newly determined binding energy of Lambda-Lambda-6He. Applying the extended NSC97 model to …
We first determine the Lambda-N S-wave phase shifts so as to reproduce the experimental Lambda separation energies of A=3, 4 Lambda-hypernuclei, and then construct three phase-equivalent Lambda-N potentials with different central repulsion. By the stochastic variational method with correlated Gaussian basis we perform an extensive calculation of ab initio type for the hypernuclei of up to A=6. The binding energies and the sizes of the Lambda-hypernuclei are very insensitive to the type of the phase-equivalent Lambda-N potentials. We use two different Lambda-Lambda potentials which both reprodu…
Evidence for particle stability of Lambda-Lambda hydrogen-4 (4LLH) has been suggested by the BNL-AGS E906 experiment. We report on Faddeev-Yakubovsky calculations for the four-body Lambda-Lambda-p-n system using Lambda-N interactions which reproduce the observed binding energy of Lambda hydrogen-3 (3LH) within a Faddeev calculation for the Lambda-p-n subsystem. No 4LLH bound state is found over a wide range of Lambda-Lambda interaction strengths, although the Faddeev equations for a three-body Lambda-Lambda-d model of 4LLH admit a 1+ bound state for as weak a Lambda-Lambda interaction strength…
New Faddeev-Yakubovsky calculations for light Lambda-Lambda hypernuclei are presented in order to assess the self consistency of the Lambda-Lambda hypernuclear binding-energy world data and the implied strength of the Lambda-Lambda interaction, in the wake of recent experimental reports on Lambda-Lambda-4H and Lambda-Lambda-6He. Using Gaussian soft-core simulations of Nijmegen one-boson-exchange model interactions, the Nijmegen soft-core model NSC97 simulations are found close to reproducing the recently reported binding energy of Lambda-Lambda-6He, but not those of other species. For stranger…
We have revisited the possible existence and the binding mechanism of heavy hyperhydrogen 6^H_Lambda. This Lambda hypernucleus is enriched in information about Lambda hypernuclear dynamics which would shed a light on significant role of coherent Lambda-Sigma coupling effect in neutron-rich nuclear medium, discussed by the authors. Recently, reports on an experimental evidence of 6^H_Lambda with theoretical comparison have appeared, wherein the significance of the coherent coupling in 6^H_Lambda has been criticized. In this report, we are revising our previous work and give further theoretical …
Effective lambda-proton and lambda-neutron potentials, restored from theoretical scattering phases through Gel'fand-Levitan-Marchenko theory, are tested on a lambda hypertriton through three-body calculations. The lambda hypertriton is treated as a three-body system consisting of lambda-proton, lambda-neutron and proton-neutron subsystems. Binding energy and root-mean-square radius are computed for the ground state of lambda hypertriton ($J^π=1/2^+$). In coordinate space, the dynamics of the system is described using a set of coupled hyperradial equations obtained from the Differential Faddeev…
We study the properties of hypernuclei containing one lambda hyperon in the framework of the correlated basis function theory with Jastrow correlations. Fermi hypernetted chain integral equations are derived and used to evaluate energies and one-body densities of lambda hypernuclei having a doubly closed shell nucleonic core in the jj coupling scheme, from Carbon to Lead. We also study hypernuclei having the least bound neutron substituted by the lambda particle. The semi-realistic Afnan and Tang nucleon-nucleon potential and Bodmer and Usmani lambda-nucleon potential are adopted. The effect o…
We calculate self-consistent single-nucleon and single-Lambda potentials in hyperonic matter for different Lambda concentrations. The predictions include relativistic Dirac effects as reported previously in a calculation of the Lambda binding energy in symmetric nuclear matter. We discuss the dependence on momentum, density, and Lambda fraction.
Hiyama et al. [PRL 104 (2010) 212502] have recently reported on a pioneering five-body alpha-alpha-n-Lambda-Lambda cluster-model calculation of Lambda-Lambda-11Be in order to confront a possible interpretation of the KEK-E373 HIDA event. Unfortunately, a six-body alpha-alpha-n-n-Lambda-Lambda calculation of Lambda-Lambda-12Be to confront another possible interpretation is beyond reach at present. Using experimental B-Lambda values with small corrections based on recently determined Lambda-N spin-dependent interaction parameters, we obtain binding-energy shell-model estimates for both Lambda-La…
An OBE potential model for the ^{1}S_0 S = -2 interaction is analyzed with emphasis on the role of coupling between the Lambda Lambda, N Xi, and Sigma Sigma channels. Singlet scalar exchange, an approximation to two-pion exchange, is significant in all channels; surprisingly, the one-pion exchange component is almost negligible. The size of the channel coupling as a function of the overall strength of the OBE model potential is examined. Implications of the analysis for the binding energy of ^{6}_{Lambda Lambda}He are considered; the new experimental datum may suggest a consistency between the…
The binding energies of neutron rich strangeness $S=-1$ hypernuclei are estimated in the chiral soliton approach using the bound state rigid oscillator version of the SU(3) quantization model. Additional binding of strange hypernuclei in comparison with nonstrange neutron rich nuclei takes place at not large values of atomic (baryon) numbers, $A=B\leq\sim 10$. This effect becomes stronger with increasing isospin of nuclides, and for "nuclear variant" of the model with rescaled Skyrme constant $e$. Total binding energies of (Lambda)He-8 and recently discovered (Lambda)H-6 satisfactorily agree w…
Four-body Faddeev-Yakubovsky calculations for Lambda-Lambda-p-n do not produce a bound state for Lambda-Lambda hydrogen 4, although suitably defined three-body Faddeev calculations for Lambda-Lambda-d produce a 1+ bound state for Lambda-Lambda interactions fitted to the Lambda-Lambda helium 6 emulsion event from KEK E373. This is opposite to the normal situation where a four-body Faddeev-Yakubovsky calculation yields stronger binding than that due to a suitably defined three-body Faddeev calculation. For stranger systems, Faddeev calculations using Lambda-Xi interactions which simulate the Nij…
Variational Monte Carlo calculations for ${_Λ^4}H$ (ground and excited states) and ${_Λ^5}He$ are performed to decipher information on $Λ$-nuclear interactions. Appropriate operatorial nuclear and $Λ$-nuclear correlations have been incorporated to minimize the expectation values of the energies. We use the Argonne $\upsilon_{18}$ two-body NN along with the Urbana IX three-body NNN interactions. The study demonstrates that a large part of the splitting energy in ${_Λ^4}H$ ($0^+-1^+$) is due to the three-body $Λ$ NN forces. $_Λ^{17}O$ hypernucleus is analyzed using the {\it s}-shell results. $Λ$…
The energy spectra of light-mass kaonic nuclei were investigated using the theoretical framework of the $0s$-orbital model with zero-range $\bar{K} N$ and $\bar{K}\bar{K}$ interactions of effective single-channel real potentials. The energies of the $\bar{K} NN$, $\bar{K} NNN$, $\bar{K} NNNN$, $\bar{K}\bar{K} N$, and $\bar{K}\bar{K} NN$ systems were calculated in the cases of weak- and deep-binding of the $\bar{K} N$ interaction, which was adjusted to fit the $Λ(1405)$ mass with the energy of the $\bar{K} N$ bound state. The results qualitatively reproduced the energy systematics of kaonic nuc…
Highlights of Lambda-Lambda emulsion events are briefly reviewed. Given three accepted events, shell-model predictions based on p-shell Lambda hypernuclear spectroscopic studies are shown to reproduce the Lambda-Lambda (LL) binding energies of LL10Be and LL13B in terms of the LL binding energy of LL6He. Predictions for other species offer judgement on several alternative assignments of the LL13B KEK-E176 event, and on the assignments LL11Be and LL12Be suggested recently for the KEK-E373 HIDA event. The predictions of the shell model, spanning a wide range of A values, are compared with those o…
We investigate the properties of the single Lambda hypernuclei within a Skyrme-Hartree-Fock (SHF) model. The parameters of the Skyrme type effective lambda-nucleon (Lambda N) interaction are obtained by fitting to the experimental Lambda binding energies of hypernuclei with masses spanning a wide range of the periodic table. Alternative parameter sets are also obtained by omitting nuclei below mass number 16 from the fitting procedure. The SHF calculations are performed for the binding energies of the Lambda single-particle states over a full mass range using the best fit parameter sets obtain…
Baryon-baryon bound states in the strangeness S=-2, S=-3, and S=-4 sectors are considered. In particular, the dependence of the corresponding binding energies on the quark mass (or equivalently the pion mass) is explored in the framework of chiral effective field theory, in order to connect with current lattice QCD calculations. For a bound state in the Xi-Xi 1S0 channel, predicted by our leading-order effective field theory interaction, binding energies are inferred that are roughly in line with a recent lattice QCD result at meson and baryon masses that correspond to those in the lattice sim…
Doublet Lambda d scattering and the hypertriton are studied in the framework of an effective field theory for large scattering lengths. As in the triton case, consistent renormalization requires a one-parameter three-body force at leading order whose renormalization group evolution is governed by a limit cycle. Constraining unknown parameters from symmetry considerations and the measured binding energy of the hypertriton, we calculate the low-energy phase shifts for doublet Lambda d scattering. For the low-energy parameters, we find a_{Lambda d}=(16.8^{+4.4}_{-2.4}) fm and r_{Lambda d}=(2.3 +/…
The three-body energy-dependent effective interaction given by the Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator spaces. The results are applied to the test case of the three-body problem (triton and He3), where it is shown that the interaction reproduces the exact binding energy, regardless of the parameterization (number of oscillator quanta or value of the oscillator parameter b) of the low-energy included space. We demonstrate a non-perturbative technique for summing the excluded-space three-body ladder diagrams, but also show that accurate results can be obt…
We report on ab-initio NCSM calculations of the A=4 mirror Lambda hypernuclei Lambda-4H and Lambda-4He, using the Bonn-Juelich LO chiral EFT YN potentials plus a CSB Lambda0--Sigma0 mixing vertex. In addition to reproducing rather well the 0+ (g.s.) and 1+ (exc.) binding energies, these four-body calculations demonstrate for the first time that the observed CSB splitting of mirror levels, reaching hundreds of keV for 0+ (g.s.), can be reproduced using realistic theoretical interaction models, although with a non-negligible momentum cutoff dependence. Our results are discussed in relation to re…
Low-momentum nucleon-nucleon interactions are derived within the framework of a unitary-transformation theory, starting with realistic nucleon-nucleon interactions. A cutoff momentum Lambda is introduced to specify a border between the low- and high-momentum spaces. By the Faddeev-Yakubovsky calculations the low-momentum interactions are investigated with respect to the dependence of ground-state energies of ^3H and ^4He on the parameter Lambda. It is found that we need the momentum cutoff parameter Lambda >= 5 fm^-1 in order to reproduce satisfactorily the exact values of the binding energies…
We extend our Skyrme-Hartree-Fock (SHF) approach, which was used earlier to describe successfully the single-$Λ$ hypernuclei, to investigate the binding and the $ΛΛ$ bond energies of the double-$Λ$ hypernuclei. The nucleon-nucleon ($NN$) and $Λ$-nucleon ($ΛN$) interactions are taken from our previous study. For the $ΛΛ$ force several Skyrme-like potentials available in the literature have been used. We discuss the sensitivity of the calculated $ΛΛ$ binding and bond energies to the $ΛΛ$ and $ΛN$ force parameters. It is found that the existing $ΛΛ$ hypernuclear data do not allow to distinguish b…
The internal structure of the resonant Lambda(1405) state is investigated based on meson-baryon coupled-channels chiral dynamics, by evaluating density distributions obtained from the form factors of the Lambda(1405) state. The form factors are defined as an extension of the ordinary stable particles and are directly evaluated from the meson-baryon scattering amplitude, paying attention to the charge conservation of the probe interaction. For the resonant Lambda(1405) state we calculate the density distributions in two ways. One is on the pole position of the Lambda(1405) in the complex energy…
Recent experimental evidence presented by the FINUDA Collaboration for a particle-stable Lambda-6H has stirred renewed interest in charting domains of particle-stable neutron-rich Lambda hypernuclei, particularly for unbound nuclear cores. We have studied within a shell-model approach several neutron-rich Lambda hypernuclei in the nuclear p shell that could be formed in (pi-,K+) or in (K-,pi+) reactions on stable nuclear targets. Hypernuclear shell-model input is taken from a theoretically inspired successful fit of gamma-ray transitions in p-shell Lambda hypernuclei which includes also Lambda…
We present high precision benchmark calculations for the triton binding energy using the most recent, phase equivalent realistic nucleon-nucleon (NN) potentials and the Tuscon-Melbourne pi-pi three-nucleon force (3NF). That 3NF is included with partial waves up to a total two-body angular momentum of j_max=6. It is shown that the inclusion of the 3NF slows down the convergence in the partial waves and j_max=5 is needed in order to achieve converged results within a few keV. We adjust the cut-off parameter Lambda in the form factors of the Tuscon-Melbourne 3NF separately for the different NN po…
The recently developed method to solve the Faddeev equations in coordinate space is used to study the weakly bound halo nucleus, the hypertriton (Lambda + n + p). The long distances are treated carefully to achieve convergence and high accuracy. We use several sets of two-body interactions which reproduce the deuteron properties and provide the low-energy Lambda-nucleon scattering data close to that of two of Nijmegen potentials. We show that the details of the potentials are unimportant unless the accuracy of the hypertriton binding energy is required to be better than 50 keV. We find that th…
Interactions between the octet-baryons (B8) in the spin-flavor SU6 quark model are investigated in a unified coupled-channels framework of the resonating-group method (RGM). The interaction Hamiltonian for quarks consists of the phenomenological confinement potential, the color Fermi-Breit interaction with explicit flavor-symmetry breaking (FSB), and effective-meson exchange potentials of scalar-, pseudoscalar- and vector-meson types. The model parameters are determined to reproduce the properties of the nucleon-nucleon (NN) system and the low-energy cross section data for the hyperon-nucleon …
The properties of the Lambda(1405) resonance are key ingredients for determining the antikaon-nucleon interaction in strangeness nuclear physics, and the novel internal structure of the Lambda(1405) is of great interest in hadron physics, as a prototype case of a baryon that does not fit into the simple three-quark picture. We show that a quantitative description of the antikaon-nucleon interaction with the Lambda(1405) is achieved in the framework of chiral SU(3) dynamics, with the help of recent experimental progress. Further constraints on the Kbar N subthreshold interaction are provided by…
The $S$-wave $ΛK$ and $ΣK$ states with isospin $I=1/2$ are dynamically investigated within the framework of the chiral SU(3) quark model by solving a resonating group method (RGM) equation. The model parameters are taken from our previous work, which gave a good description of the energies of the baryon ground states, the binding energy of the deuteron, and the experimental data of the nucleon-nucleon ($NN$) and nucleon-hyperon ($NY$) scattering. Assumed not to give important contributions in the scattering processes, the s-channel quark-antiquark ($q\bar q$) annihilation interactions are not …
Big Bang Nucleosynthesis (BBN) has increasingly become the tool of choice for investigating the permitted variation of fundamental constants during the earliest epochs of the Universe. Here we present a BBN calculation that has been modified to permit changes in the QCD scale, Lambda_QCD. The primary effects of changing the QCD scale upon BBN are through the deuteron binding energy, B_D, and the neutron-proton mass difference, delta-m_np, which both play crucial roles in determining the primordial abundances. In this paper, we show how a simplified BBN calculation allows us to restrict the nuc…
We study the binding energies, radii, single-particle energies, spin-orbit potential and density profile for multi-strange hypernuclei in the range of light mass to superheavy region within the relativistic mean field (RMF) theory. The stability of multi-strange hypernuclei as a function of introduced hyperons ($Λ$ and $Σ$) is investigated. The neutron, lambda and sigma mean potentials are presented for light to superheavy hypernuclei. The inclusion of hyperons affects the nucleon, lambda and sigma spin-orbit potentials significantly. The bubble structure of nuclei and corresponding hypernucle…
In present study, we search the lambda magic number in hypernuclei within the framework of relativistic mean field theory (RMF) with inclusion of hyperon-nucleon and hyperon-hyperon potentials. Based on one- and two-lambda separation energy and two-lambda shell gap, 2, 8, 14, 18, 20, 28, 34, 40, 50, 58, 68, 70 and 82 are suggested to be the $Λ$ magic number within the present approach. The weakening strength of $Λ$ spin-orbit interaction is responsible for emerging the new lambda shell closure other than the model scheme. The predicted $Λ$ magic numbers are in remarkable agreement with earlier…
A simultaneous description of non-strange nuclei and hypernuclei is provided by a single mass formula inspired by the spin-flavour SU(6) symmetry breaking. This formula is used to estimate the hyperon binding energies of Lambda, double Lambda, Sigma, Cascade and Theta hypernuclei. The results are found to be in good agreement with the available experimental data on 'bound' nuclei and relativistic as well as quark mean field calculations. This mass formula is useful to estimate binding energies over a wide range of masses including the light mass nuclei. It is not applicable for repulsive poten…
The role of the isoscalar hyperon Lambda in probing the density dependence of the nuclear symmetry energy is studied in multi-Lambda hypernuclei, hyperon-rich matter and neutron stars in relativistic models. Relationships between the properties of three types of objects and the neutron thickness in 208Pb are established with respect to the isoscalar-isovector coupling that modifies the density dependence of the symmetry energy. The exotic isotopes far from the neutron drip line can be stabilized by filling in considerable Lambda hyperons. The difference of the binding energy of multi-Lambda hy…
A recent successful observation of a dense and deeply bound \bar{K} nuclear system, K^-pp, in the p + p \rightarrow K^+ + K^-pp reaction in a DISTO experiment indicates that the double-\bar{K} dibaryon, K^-K^-pp, which was predicted to be a dense nuclear system, can also be formed in p+p collisions. We find theoretically that the K^- -K^- repulsion plays no significant role in reducing the density and binding energy of K^-K^-pp and that, when two Λ(1405) resonances are produced simultaneously in a short-range p+p collision, they act as doorways to copious formation of K^-K^-pp, if and only if …
The binding energies of a range of nuclei and hypernuclei with atomic number A <= 4 and strangeness |s| <= 2, including the deuteron, di-neutron, H-dibaryon, 3He, Lambda 3He, Lambda 4He, and Lambda Lambda 4He, are calculated in the limit of flavor-SU(3) symmetry at the physical strange quark mass with quantum chromodynamics (without electromagnetic interactions). The nuclear states are extracted from Lattice QCD calculations performed with n_f=3 dynamical light quarks using an isotropic clover discretization of the quark-action in three lattice volumes of spatial extent L ~ 3.4 fm, 4.5 fm and …
Deeply bound KNN, KNNN and KNNNN states are discussed. The effective force exerted by the K meson on the nucleons is calculated with static nucleons. Next the binding energies are obtained by solving the Schrodinger equation or by variational calculations. The dominant attraction comes from the S-wave Lambda(1405) and an additional contribution is due to Sigma(1385). The latter state is formed at the nuclear peripheries and absorbs a sizable piece of the binding energy. It also generates new branches of quasi-bound states. The lowest binding energies based on a phenomenological KN input fall i…
The hyperon-hyperon potentials due to a recent SU(3) Nijmegen soft-core potential model are incorporated within a relativistic mean field calculation of strange hadronic matter. We find considerably higher binding energy in bulk matter compared to several recent calculations which constrain the composition of matter. For small strangeness fractions, matter is dominated by a composition of nucleons, Lambdas, and Xis, and the calculated binding energy closely follows that calculated by using the hyperon potentials of our previous calculations. For larger strangeness fractions, the calculated bin…
Baryon-baryon potentials are obtained from 3-flavor QCD simulations with the lattice volume L ~ 4 fm, the lattice spacing a ~ 0.12 fm, and the pseudo-scalar-meson mass M_ps =469 - 1171 MeV. The NN scattering phase shift and the mass of H-dibaryon in the flavor SU(3) limit are extracted from the resultant potentials by solving the Schrodinger equation. The NN phase shift in the SU(3) limit is shown to have qualitatively similar behavior as the experimental data. A bound H-dibaryon in the SU(3) limit is found to exist in the flavor-singlet J^P=0^+ channel with the binding energy of about 26 MeV …
