double-Λ Hypernuclei Research Articles

Experimental Study of Double-Λ Hypernuclei with Nuclear Emulsion

briefly. Latest numerical values of energies are given for Λ-Λ interaction and binding of two Λ hyperons in several nuclei. A double-Λ hypernucleus of 6 ΛΛHe (“Lambpha” / NAGARA event) strongly suggested an weak attractive Λ-Λ interaction with ΔBΛΛ = 0.67±0.16 MeV, and the lower mass limit of the H-dibaryon to be 2223.7 MeV/c (90% C.L.). A probable candidate of 10 ΛΛBe ∗ nucleus was observed with its excitation energy of 2.8 ± 0.4 MeV.

S= -2 Hypernuclear Structure

The structure of light hypernuclei with strangeness S = −2 is investigated with the three-, four-, and five-body cluster model and the Gaussian Expansion method (GEM). Energy levels of the double-Λ hypernuclei ΛΛΛ7He, ΛΛΛ7Li, ΛΛΛ8Li, ΛΛΛ9Li, ΛΛΛ9Be, and ΛΛΛ10Be are predicted with the framework of αxΛΛ four-body model, where x = n, p, d, t, 3He, and α, respectively. Also, energy levels of the double Λ hypernucleus, ΛΛΛ11Be are calculated within the framework of a ααnΛΛ five-body model. The Demachi-Yanagi event, identified as ΛΛΛ10Be, is interpreted as an observation of its 2+ state excited state. The Hida event, recently observed at KEK-E373 experiment, is interpreted as an observation of the ground state of the ΛΛΛ11Be. Detailed structure calculations in Ξ12_Be, Ξ5_H, Ξ9_Li, Ξ7_H and Ξ10_Li are performed within the framework of the microscopic two-, three- and four-body cluster models. Ξ7_H and Ξ10_Li are predicted to have bound states.

Properties of Zr hypernuclei in deformed Skyrme Hartree–Fock approach

Properties of the even-N Zr isotopes and their corresponding single-Λ and double-Λ hypernuclei are studied in the deformed Skyrme–Hartree–Fock approach. Binding energy, the two-neutron separation energies, radii are studied from beta-stable zone to the neutron drip line in this paper. The neutron drip line nuclei predicted with SLy4 and SkI4 interactions are 122Zr and 138Zr, respectively. The neutron drip line of single-Λ and double-Λ hypernuclei are 139ΛZr and 1422ΛZr with SkI4 interaction, respectively. The predicted hyperon drip line hypernuclei with 80Zr and 138Zr cores are 10020ΛZr and 18850ΛZr, respectively.

Double- Hypernuclei in the Relativistic Mean-Field Theory

We study the properties of double-Λ hypernuclei in the relativistic mean-field theory, which has been successfully used for the description of stable and unstable nuclei. With the meson-hyperon couplings determined by the experimental binding energies of single-Λ hypernuclei, we present a self-consistent calculation of double-Λ hypernuclei in the relativistic mean-field theory, and discuss the influence of hyperons on the nuclear core. The contribution of two mesons with dominant strange quark components (scalar σ* and vector φ) to the ΛΛ binding energy of double-Λ hypernuclei is examined.

ANTIPROTON PHYSICS AT GSI WITH PANDA

Detector PANDA was proposed for studies of the interaction of antiprotons with nucleons and nuclei at the future GSI accelerator facility. Selected topics of physics program at PANDA including studies of the interaction of charmed hadrons in matter, production of double Λ-hypernuclei, CP-violation in the [Formula: see text] and [Formula: see text] system as well as studies of electromagnetic form factors of proton are presented.

Few-body aspects of light hypernuclei

Three- and four-body structure calculations of single Λ hypernuclei such as Λ7He, Λ9Be and Λ13C and double Λ hypernuclei such as ΛΛ4H, ΛΛ7He, ΛΛ7Li, ΛΛ8Li, ΛΛ9Li, ΛΛ9Be and ΛΛ10Be are discussed. The energy levels of Λ7He whose core is a famous halo nucleus, Λ6He, are predicted based on Λ5He + 2N three-body model. In the microscopic 2α + Λ(3α + Λ) model for Λ9Be(Λ13C), we predict the spin-orbit splittings of 5/21+−3/21+ in Λ9Be and 3/21−−1/21− in Λ13C to be 0.08–0.16 MeV and 0.39–0.78 MeV, respectively, with the use of OBE-model NSC97a ∼f. On the other hand quark-model ΛN spin-orbit force gives rise to half of the splittings of the smallest OBE-model prediction. The experimental data were reported to be 31.4−3.6+2.5 keV for Λ9Be and to be 152 ± 54 ± 36 keV for Λ13C. By performing four-body calculation of ΛΛ4H with both NNΛΛ and NNNΞ channels, we show that the ΛΛ − ΞN coupling potential plays an important role in making ΛΛ4H. Energy levels of the double-Λ hypernuclei, ΛΛ7He, ΛΛ7Li, ΛΛ8Li, ΛΛ9Li, ΛΛ9Be and ΛΛ10Be are predicted on the basis of an α + x + Λ + Λ four-body model, where x = n,p,d,t 3He and α, respectively.

Few-body aspects of light hypernuclei

Three- and four-body structure calculations of single Λ hypernuclei such as Λ 7He, Λ 9Be and Λ 13C and double Λ hypernuclei such as ΛΛ 4H, ΛΛ 7He, ΛΛ 7Li, ΛΛ 8Li, ΛΛ 9Li, ΛΛ 9Be and ΛΛ 10Be are discussed. The energy levels of Λ 7He whose core is a famous halo nucleus, Λ 6He, are predicted based on Λ 5He + 2 N three-body model. In the microscopic 2α + Λ(3α + Λ) model for Λ 9Be( Λ 13C), we predict the spin-orbit splittings of 5/2 1 +−3/2 1 + in Λ 9Be and 3/2 1 −−1/2 1 − in Λ 13C to be 0.08–0.16 MeV and 0.39–0.78 MeV, respectively, with the use of OBE-model NSC97a ∼f. On the other hand quark-model Λ N spin-orbit force gives rise to half of the splittings of the smallest OBE-model prediction. The experimental data were reported to be 31.4 −3.6 +2.5 keV for Λ 9Be and to be 152 ± 54 ± 36 keV for Λ 13C. By performing four-body calculation of ΛΛ 4H with both NNΛΛ and NNNΞ channels, we show that the ΛΛ − Ξ N coupling potential plays an important role in making ΛΛ 4H. Energy levels of the double-Λ hypernuclei, ΛΛ 7He, ΛΛ 7Li, ΛΛ 8Li, ΛΛ 9Li, ΛΛ 9Be and ΛΛ 10Be are predicted on the basis of an α + x + Λ + Λ four-body model, where x = n, p, d, t 3He and α, respectively.

Ground state structure of some double-λ hypernuclei by a three-body model using a simple coordinate space approach

New experimental data on the binding energyB λλ ofλλ6He, reported very recently, come up with the valuesB λλ = 725 ±0.14 MeV and ΔBλλ = 101 ±0.2 MeV which are substantially lower than the old dataB λλ = 109 ±0.8 MeV and ΔBλλ = 4.7±10 MeV in use in literature since 1966. In view of the new data we decided to undertake a re-study of the λλ 6 He hypernucleus using the same three-body model (α-λ-λ) with a simple coordinate space variational approach which was employed earlier with the old data onλλ/6He. After fitting different λ-λ potentials to the new data of λλ 6 He we have applied our method to study some double-λ hypernuclei in light, medium and heavy mass regions and have determined the structural quantities like Bλλ, the r.m.s. values of core-λ (〈rcore-λ〉〉) and λ-λ (〈rλ-λ〉〉) distances theoretically. The core-λ interaction considered is of Woods-Saxon type. The strength and the range of the core-A potential have been adjusted to reproduce the λ-binding energy(B λ) . These are in good agreement with the relativistic mean field (RMF) results. Our study shows that the λ-λ bonding energy ΔBλλ decreases with increasing mass number from λλ 10 Be to λλ 210 Pb of a double-A hypernucleus

Nonmesonic decay of Λ and ΛΛ hypernuclei

Nonmesonic weak decays of single- and double-Λ hypernuclei are studied on the basis of two-body baryon-baryon interactions, ΛN → NN and ΛΛ → YN transitions. The two-body weak transition is described by the combination of two processes, i.e., which are meson exchange and direct quark processes. The ΛΛ → YN transition in ΛΛ hypernucleus is complement to the ΛN → NN transition as it occurs only in the J = 0 channel, while the J = 1 transition is dominant in the ΛN → NN case.

Λ- and ΛΛ-hypernuclear decay predictions in a OME model

We present the results of the Meson-Exchange model of Refs. [1,2] for the nonmesonic weak decay of single- and double-Λ hypernuclei. The results shown here include the total nonmesonic ( π NM) decay rate, partial decay rates ( i. e. decays induced separately by neutrons, π Λn , protons, π Λp , and Λs, π ΛΛ), the kinetic energy correlation of np coincidence pairs emitted in the decay of Λ 5He, and A, the longitudinal asymmetry in the distribution of final protons coming from the decay of polarized hypernuclei.

ΛΛ− ζN coupling effects in light double-Λ hypernuclei

The suppression and enhancement effects of ΛΛ- ζN coupling are investigated in s-shell double-Λ hypernuclei. The Pauli suppression due to this coupling in ΛΛ 6He is found to be be 0.43 MeV for the coupling strength of the NSC97e potential. This indicates that the free-space ΛΛ interaction is stronger by about 5° phase shift than that deduced from the empirical data of ΛΛ 6He without including the Pauli suppression effect. In ΛΛ 5He and ΛΛ 5H, an attractive term arising from ΛΛ- ζN conversion is enhanced by the formation of an alpha particle in intermediate ζ states. According to this enhancement, ΔB ΛΛ of ΛΛ 5He is about 0.27 MeV larger than that of ΛΛ 6He.

Study of doubly strangeness nuclei at BNL

An experiment searching for double-Λ hypernuclei in (K −, K +) reactions on 9Be was carried out at the D6 line in the BNL-AGS. The technique was the observation of two pions produced in sequential mesonic weak decay. The results indicate production of a significant number of the double hypernucleus ΛΛ 4H.

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.

ΛΛ-Ξ N coupling effects in light hypernuclei

The significance of ΛΛ-Ξ N coupling in double-Λ hypernuclei has been studied. The Pauli suppression effect due to this coupling in 6 ΛΛ He has been found to be 0.43MeV for the coupling strength of the NSC97e potential. This indicates that the free-space ΛΛ interaction is stronger by an about 5° phase shift than that deduced from the empirical data of 6 ΛΛ He without including the Pauli suppression effect. In 5 ΛΛ He and 5 ΛΛ H, an attractive term arising from the ΛΛ-Ξ N conversion is enhanced by the formation of an alpha-particle in the intermediate Ξ states. According to this enhancement, we have found that the ΛΛ binding energy ( ΔB ΛΛ) of 5 ΛΛ He is about 0.27MeV larger than that of 6 ΛΛ He for the NSC97e coupling strength. This finding deviates from the general picture that the heavier is the core nucleus, the larger is ΔB ΛΛ.-1

A simple coordinate space approach to three-body problems — Examples: Halo nucleus and double-λ hypernucleus

We show how to treat the dynamics of an asymmetric three-body system consisting of one heavy and two identical light particles in simple coordinate space variational approach. The method is constructive and gives an efficient way of resolving a three-body system to an effective two-body system. It is illustrated by explaining the structural properties of some nuclei of current interest, namely halo nuclei and double-λ hypernuclei. The ansatz used here may be of value in a number of three particle problems of similar nature.

STUDY OF THE EXCITED STATE OF DOUBLE-Λ HYPERNUCLEI BY HYPERSPHERICAL SUPERSYMMETRIC APPROACH

Hyperspherical harmonics expansion (HHE) method has been applied to study the structure and ΛΛ dynamics for the ground and first excited states of low and medium mass double-Λ hypernuclei in the framework of core+Λ+Λ three-body model. The ΛΛ potential is chosen phenomenologically while core-Λ potential is obtained by folding the phenomenological Λ N interaction into the density distribution of the core. The parameters of this effective Λ N potential is obtained by the condition that they reproduce the experimental (or empirical) data for core-Λ subsystem. The three-body (core+Λ+Λ) Schrödinger equation is solved by hyperspherical adiabatic approximation (HAA) to get the ground state energy and wave function. This ground state energy and wave function are used to construct a partner potential. The three-body Schrödinger equation is solved once again for this partner potential. According to supersymmetric quantum mechanics, the ground state energy of this potential is exactly the same as that of the first excited state of the potential used in the first step. In addition to the two-Λ separation energy for the ground and first excited state, some geometrical quantities for the ground state of double-Λ hypernuclei [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are computed. These include the ΛΛ bond energy and various r.m.s. radii.

Study of ΛΛ dynamics and ground state structure of low and medium mass double Λ hypernuclei

We critically review the ΛΛ dynamics by examining Λ - Λ and Λ-nucleon phenomenological potentials in the study of the bound state properties of double-Λ hypernuclei ΛΛ6He, ΛΛ10Be, ΛΛ14C, ΛΛ18O, ΛΛ22Ne, ΛΛ26Mg, ΛΛ30Si, ΛΛ34S, ΛΛ38Ar, ΛΛ42Ca, ΛΛ46Ti, ΛΛ50Cr, ΛΛ54Fe, ΛΛ58Ni, ΛΛ62Zn, ΛΛ66Ge, ΛΛ70Se, ΛΛ74Kr, ΛΛ78Sr, ΛΛ82Zr, ΛΛ86Mo, ΛΛ90Ru, ΛΛ94Pd, ΛΛ98Cd, ΛΛ102Sn in the frame work of (core+Λ+Λ) three body model. An effective ΛN potential is obtained by folding the phenomenological ΛN potential into the density distribution of the core nuclei. The former two cases (i.e. ΛΛ6He and ΛΛ10Be) are revisited to justify the correctness of the present potential model. Assuming the same potential model we predicted some of the structural properties of heavier doubly Λ-hypernuclei. The hyperspherical harmonics expansion method, which is an essentially exact method has been employed for the three body system. A convergence in binding energy up to 0.15% for Kmax=20 has been achieved. In our calculation we have made no approximation in restricting the allowed l-values of the interacting pairs.

Double-Λ hypernuclei and the nuclear medium effective ΛΛ interaction

We fit the 1 S 0 ΛΛ interaction in the nuclear medium to the masses of the experimentally known double-Λ hypernuclei: ΛΛ 6He, ΛΛ 10Be and ΛΛ 13B. We derive this effective interaction from OBE Jülich ΛΛ-type potentials and using both Hartree-Fock and variational approaches. We find that the inclusion of ΛΛ correlations in the variational scheme leads to significant differences and a better understanding of the dynamical features of the system. We investigate the sensitivity of the binding energies and the mesonic decay widths of the above double-Λ hypernuclei to the ωΛΛ coupling and the form factor at the σΛΛ vertex. We also use this effective interaction to predict binding energies and pionic decay widths of heavier double-Λ hypernuclei, not discovered yet. Finally, we discard the existence of 1S 0 ΛΛ bound states provided the ΛΛ-Ξ N coupling can be neglected.

Double-Λ hypernuclei and the ΛΛ interaction

The $\Lambda$-$\Lambda$ effective interaction, in the channel $L=S=0$, in the nuclear medium is fitted to the available binding energies, $B_{\Lambda\Lambda}$, of double $\Lambda$ hypernuclei: $^{6}_{\Lambda\Lambda}$He, $^{10}_{\Lambda\Lambda}$Be and $^{13}_{\Lambda\Lambda}$B. The mesonic decay of these hypernuclei is also investigated. Finally, this effective interaction is used to predict the binding energies and mesonic decays widths of heavier double $\Lambda$ hypernuclei.

Production of double-Λ hypernuclei at (K −,K +) reaction points

Production of double-Λ hypernuclei at (K −,K +) reaction points