Binding energies of hypernuclei and ΛN interaction

A central ΛN potential V _ΛN that describes, in the limits of experimental errors, the binding energies of three-, four-, and five-particle ground and excited states of hypernuclei, as well as energy and angular dependence of Λp scattering cross sections, is found on the basis of a conjoint analysis of binding energies of 1s-shell hypernuclei and Λp scattering. The reliability and accuracy of three-, four-, and five-particle calculations of hypernuclei and related nuclear systems are assured by the estimation of, an upper, as well as a lower bound of energy. In the framework of the model Λ+core, V _ΛN agrees with binding energies of heavy hypernuclei.     

Binding energies of hypernuclei and ΛN interaction

A central ΛN potential V _ΛN is found on the basis of an analysis of the binding energies of 1s-shell hypernuclei and Λp scattering. Within the exprerimental errors, this potential makes it possible to reproduce the binding energies of three-, four-, and five-particle ground and excited states of hypernuclei and the angular and energy dependences of the cross sections for Λp scattering. The accuracy and reliability of the calculation of three-, four-, and five-particle hypernuclear and the respective nuclear systems is ensured by determining both upper and lower bounds on the energy. Within the Λ plus core model, the potential V _ΛN is matched with binding energies of heavy hypernuclei.     

Average Λ-nucleus potentials

A few model Λ-nucleus potentials are proposed which explain the ground state binding energy data of⁵He and thep-shell hypernuclei satisfactorily. Potential-II is capable of distinguishing the hypernuclei of the same mass number but of differentN andZ values. The dependence of this potential on (N ? Z) term indicates that there is a charge symmetry breaking component in ΛN force. Alongwith the earlier density dependent effective Λ-nucleus interaction, these potentials may be used to determine approximately the density distributions of light nuclei. From these potentials an estimate ofD _Λ is also made. It is found to be in conformity with the earlier estimates.     

Production of exotic Λ hypernuclei via mesonic beams

We study the production of neutron-rich hypernuclei _Λ ¹² Be, _Λ ¹⁶ C, and _Λ ¹⁰ Li by the (π^?, K⁺) and (K^?, π⁺) reactions in flight and treat two different mechanisms of production. The first mechanism is a two-step process with meson charge exchange (e.g., π^?p → π⁰n, π⁰p → K⁺Λ). The other mechanism is one-step production (π^?p → K⁺Σ^?) proceeding via a small Σ^? component, arising in Λ hypernuclei due to ΛN–ΣN coupling, as a doorway state. Typically, the two-step mechanism is more productive. The forward differential cross section of the ¹⁰B(π^?,K⁺) reaction is about 70 nb/sr at an incident momentum of 1.05 GeV/c. On the other hand, the one-step process can serve as a direct measurement of the Σ admixture if the two-step contribution is suppressed by a suitable choice of the reaction kinematics.     

Skyrme-Hartree-Fock calculation of Λ-hypernuclear states from (π+,K +) reactions

We present a self consistent Skyrme-Hartree-Fock calculation of the binding energies ofΛ-hypernuclear states experimentally determined by (π⁺,K ⁺) reactions. A Skyrme type parametrization of theΛ-N interaction is derived, including two and three body terms, The importance of each of these terms is discussed. An overall agreement is reached even for deeply boundΛ states. The binding energies of thes- andp-shell hypernuclei are also well reproduced. No signal of quark deconfinement has been found. We conclude that the shell model picture works very well to describe deeply bound states for heavyΛ hypernuclei.     

Excitation and structure of hypernuclear resonances in (K −,π ¯0)-reactions on 1p-shell nuclei

The available experimental data on the excitation functions (EF) of the 1p-shellΛ-hy-pernuclei in (K ^?, π^?) reactions atθ _π = 0^° has been analysed in terms of shell model and weak coupling scheme. It is substantiated by the experimental data on the neutron spectroscopic factors and on the fragmentation of nuclear hole excitations. The pronounced nuclear spectroscopic characteristics in the hypernuclear spectra are indicative of a weak coupling ofΛ-hyperon with nuclear subsystem. The analysis has made it possible to determine the difference is single-particle energies ofΛ-hyperon in the 1p- and 1s-states and to obtain additional evidence for the smallness of theΛ-nucleus spin-orbit interaction. The resonance structure of EF of hypernuclei, which were not studied in (K ^?,π ₀ ^? ) reactions, is predicted. The interrelated aspects of the studies of the (K ^?,π ₀ ^? ), (K ^?,π ₀ ^? β^′), and (K ^?, π⁺) reactions which are of interest to spectroscopy ofΛ-andΣ-hypernuclei are discussed.     

Alpha particles accompanying the weak decay of Λ 10 Be and Λ 10 B hypernuclei

The possibility of a detailed investigation of weak ΛN interaction in the _Λ ¹⁰ Be and _Λ/10B hypernuclei, which stand out owing to their ααNΛ cluster structure, is discussed. The detection of a few groups of correlated αα pairs will furnish information about decays to specific states of product nuclei (⁸Be*, ⁸Li, ⁸B), thereby paving the way to a phenomenological analysis of the weak decays of p-shell hypernuclei. The ratios of the intensities of individual alpha-particle groups to be measured in experiments at the nuclotron of the Joint Institute for Nuclear Research (JINR, Dubna) will provide a useful criterion for choosing an appropriate model of weak ΛN interaction. The current state of hypernuclear physics is briefly reviewed.     

Hypernuclear binding energies in the α-particle model

The binding energies B_Λ for the hypernuclei with baryon number A = 4N + 1 up to_Λ²⁵Mg have been calculated by the variational method in the framework of Brink's α-particle model. The central ΛN potential is adjusted to the binding energy of_Λ⁵He. Due to their strong dependence on the nuclear density, the B_Λ energies are very sensitive to the choice of the effective nuclear interaction and have reasonable values for large A with the potential B1 of Brink and Boeker. The comparison with the B_Λ values obtained in the limiting shell model and the consideration of two different Λ-particle wave functions both indicate that the effect of nuclear clustering on B_Λ is significant only for_Λ⁹Be and_Λ¹³C. The nuclear distortion due to the Λ-particle binding is also evaluated in this calculation.     

The formation of hypernuclei by K− capture

K^? capture leading to the formation of hypernuclei takes place with the kaon either in a Bohr orbit (capture at rest), or in flight. We analyze both situations in the framework of the distorted-wave impulse approximation (DWIA), derive cross sections and formation rates, and compare the results with experimental data on the reaction ¹²C(K^?, π^?)¹²_ΛC¹. Corrections to the DWIA which arise from rescattering, from binding energy effects and from the intermediate formation of a ∑-hyperon, are estimated and found not to be negligible.     

The non-mesonic to π− mesonic decay ratio and Λ-neutron stimulation fraction for p-shell hypernuclei

Kinematic analysis of simple hypernuclear production reactions has produced a sample of hypernuclei of _ΛB, _ΛC and _ΛN with negligible background, and a much smaller sample of _ΛBe. The values of the non-mesonic to π^? mesonic ratio Q^? for the above samples are 5.5 ± 0.5 and 4.3 ± 1.1, respectively. A sub-sample of ¹¹_ΛB hypernuclei was separated on the basis of production via an excited state of _Λ¹²C, giving Q^? = 4.8 ± 1.1 for _Λ¹¹B. Assuming the Fermi gas model is applicable to nuclei of mass A ≈ 11, two independent means of analysis of the non-mesonic decays give values for the Λ-neutron stimulation fraction n of 0.41 ± 0.09 and 0.34 ± 0.07 for hypernuclei of charge 5 ≦ Z ≦ 7.     

OnΛ-hyperon(s) in the nuclear medium

Relativistic mean field theory is tested in reproducing the novel experimentalΛ single particle (π⁺, K⁺) spectra of Λ=12/90 hypernuclei (and extended to _Λ ²⁰⁹ Pb). The adjusted model is then applied to multistrange systems \({}_{n_\Lambda \Lambda }^{16 + n_\Lambda } O,_{n_\Lambda \Lambda }^{40 + n_\Lambda } Ca\) ; no anomalous behaviour of radii and densities in those multi-Λ hypernuclei is encountered.     

Λ(1520) → Λγ radiative-decay width

The radiative decay Λ(1520) → Λγ was recorded in the exclusive reaction p + N → Λ(1520)K ⁺ + N at the SPHINX facility. The branching ratio for this decay and the corresponding partial width were found to be, respectively, Br[Λ(1520) → Λγ] = (1.02 ± 0.21) × 10^?2 and Γ[Λ(1520) → Λγ] = 159 ± 35 keV (the quoted errors are purely statistical, the systematic errors being within 15%).     

The formation of,and the γ-radiation from,the p-shell hypernuclei

The physical factors relevant for the production of various low-lying Λ-hypernuclear states ${}_{\mathrm{\Lambda }}{}^{\mathrm{A}}\text{Z}{}^1$ through the K^? → π^? and K^? → π⁰ reactions, in flight or from rest, on the corresponding target nuclei ^AZ and ^A(Z + 1) are discussed, on the basis of the shell model for these nuclei and hypernuclei, together with the characteristics of the dominant γ-transitions resulting from the excited states thus produced. Detailed consideration is given for a number of hypernuclei of specific interest, including the cases of _Λ⁷He, _ΛLi for A = 7, 9 and 10, _ΛBe for A = 9 and 10, _ΛB for A = 10, 11, and 12, _ΛC for A = 12, 13, 14, and 15, _ΛN for A = 14 and 15, and _Λ¹⁶O. The importance of (γ, π^?) correlation studies for the determination of hypernuclear spin values is stressed, with the discussion of several examples.     

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 [(1s)_N⁴(1p)_N^A?5(1s)_Λ], using the intermediate-coupling formalism set up in Part I, assuming the ΛNN interaction Q₀₀⁰ of central form (as motivated by the double-OPE mechanism), and taking into account the new data recently available about several $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-shell}$ 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 _Λ⁸Li. The implications of this fit are spelled out for the well-known hypernuclear species. A discrepancy between the wavefunction calculated here for _Λ⁸Li and the characteristics of the decay _Λ⁸Li → ααπ^? is emphasized, as is also the need for Λ hypernuclear γ-ray data.     

Λ production in K−p interactions at 32 GeV/c

Lambda production is studied in K^?p interactions at 32 GeV/c. The total Λ cross section is 2.31±0.03 mb. Using the measured Λγ combinations we find that (31±4)% of all Λ's are produced via the Σ⁰→Λγ decay. About 60% of the Λ's are associated with either a $\text{N}\text{N}\text{or K}\text{K}$ pair; about 40% of the Λ's are produced through the hypercharge annihiltion reaction K^?p→Λ+π'a. The two-peak structure of the invariant x distribution can be related to fragmentation processes. The Λ is found to be unpolarized in the target fragmentation region, whereas a transverse polarization is observed for forward produced Λ's. As a function of p⊥, a polarization effect is measured at medium p⊥.     

CP violation with beautiful baryons

CP violation can be studied in modes of charmed or bottom baryons when a decay process is compared with its charge-conjugated partner. It can show up as a rate asymmetry and in a study of other decay parameters. Neither tagging nor time-dependences are required to observeCP violation with modes of baryons, in contrast to the conventionalB ⁰ modes. Numerous modes of bottom baryons have the potential to show largeCP-violating effects within the Standard Model. Those effects can be substantial for modes with aD ⁰, which is seen in a final state that can also be fed from a \(\bar D^0 \) . For instance, a comparison of theΛ _b→Λ _CP ⁰ with the \(\bar \Lambda _b \to \bar \Lambda D_{CP}^0 \) process can show sizeableCP violation. HereD _CP ^o denotesCP eigenstates ofD ⁰, which occur at a few percent. Six related processes, such asΛ _b→ΛD ⁰, \(\Lambda _b \to \Lambda \bar D^0 \) ,Λ _b→Λ _CP ⁰ , and their charge-conjugated counterparts, can extract ?, which is the most problematic angle of the unitarity triangle and which is conventionally probed with theB _s→ρ⁰ K _S asymmetry. HereD ⁰ andD ^?0 are identified by their charged kaon or lepton. We predictB(Λ _b→ΛD ⁰)～10^?5, thusB(Λ _b→Λ _CP ⁰ )～10^?7. Under favourable circumstances,CP violation can occur at the few tens of percent level. Thus 10²–10³ Λ _b→Λ _CP ⁰ decays start probing ?. Tables list many additional modes with typical branching ratios at the 10^?5–10^?6 level, with large detection efficiencies (in contrast to theD _CP ⁰ ), and with potentially largeCP-violating effects, such as Ξ _b ⁰ →ΛΨ, Λ?, ΛK^*0; Ξ _b ^? →ΛK^(*)?, Ξ^?K_s, Ξ^?K^*0, Ω _b ^? →Ξ^?φ, Ξ^?ρ⁰, ΛK^(*)?, ΩK_s, Ω^?K^*0.     

Production of charmed particles at the CERN intersecting storage rings in events triggered by an electron

Production of charmed particles has been investigated at √s = 63 GeV usi ng the Lampshade Magnet detector triggered by electrons and positrons emitted at 30% from the ISR beam axis. The results of a search for Λ_c and $\text{Λ}$_c signals in the K^?pπ⁺ and K⁺$\text{p}$π^? channels are presented. Cross sections for the reactions pp → $\text{D}$Λ_cX and pp → Λ_c$\text{Λ}$_cX, and upper limits. for pp → D$\text{D}$X, are evaluated under various models and compared with other values obtained at the ISR.     

Λc5He and Λc9Be charmed nuclei versus Λ5He and Λ9Be hypernuclei

A comparative study is made for _Λc⁵He and _Λc⁹Be charmed nuclei versus _Λ⁵He and _Λ⁹Be hypernuclei. The Λ_c(Λ)+α and Λ_c(Λ)+α+α systems are treated in a microscopic way. Within certain range of the Λ_cN interaction strength, the energy properties of Λ_c+α and Λ_c+α+α are calculated and discussed. Similarity between the energy spectra of the noted charmed nuclei and hypernuclei is suggested.