(π⁺,K⁺) Reaction Spectroscopy of Heavy Hypernuclei

Abstract

For the last few decades the (π + , K + ) reaction has played an important role in heavy hypernuclear spectroscopy where the Λ spin-orbit splitting should be one of the most interesting subjects. In this article, first, various stages of calculational frameworks for hypernuclear production cross sections are discussed. Then, focusing on the 89 Y(π + , K + ) 89 Λ Y experimental data, new DWIA analysis has been carried out by taking full account of the core nuclear excitation effects. As a result we found that one of the doublet peaks comes from the nuclear core excitation and that the Λ spin-orbit splitting is small in consistent with the finding in the p-shell hypernuclei. §1. IntroductionFor the last few decades the (π + , K + ) reaction has played a special role in hypernuclear reaction spectroscopy. It excites Λ-particle, neutron-hole states of stretched angular momentum quite selectively, so that it has revealed a series of almost all the bound Λ single-particle states inside some nuclei. The reaction mechanism and the theoretical demonstrations were discussed first by Dover et al. 1) and by Bandō and one of the present authors (T.M.). 2) In fact, the first (π + , K + ) experiment on a 12 C target, carried out at Brookhaven National Laboratory, showed promising results. 3) Sophisticated calculations using the Kapur-Peierls framework were performed in order to include quasi-free continuum strengths in addition to the wellseparated bound-state peaks. 4) On the experimental side, the BNL group extended the (π + , K + ) studies up to medium-mass systems with A 28 − 89, 6), 7) while at KEK better energy resolution was ¡achieved using the SKS spectrometer up to a heaviest target of 208 Pb. 8)-11) See Ref. 13) for review of the (π + , K + ) experiments.One of the purposes of the (π + , K + ) experiments on heavy nuclear targets was to extract the Λ spin-orbit splittings over a wide range of hypernuclear species. 4), 5) The 89 Y(π + , K + ) 89 Λ Y experiment 11) among others provides us with the most typical spectrum with good energy resolution (1.65 MeV) in which four (five) well-separated major peaks are understood to correspond basically to the s Λ , p Λ , d Λ , and f Λ (g Λ ) orbits. In addition, according to the experimental analysis, each peak (labeled p Λ , d Λ , f Λ in Fig. 5 of Ref. 11)) consists of two subpeaks, which are denoted as (1L,1R), (2L,2R), and (3L,3R), respectively. 11) If this double-peak structure is attributed to the spin-orbit partners, the splittings are ΔE exp 1 = 1.37 MeV (p Λ ), ΔE exp 2 = 1.63 MeV (d Λ ), and ΔE exp 3 = 1.70 MeV (f Λ ), respectively, 11) but, as shown later, these values are two or three times larger than the spin-orbit splittings estimated using the

Low-lying level structure of Λ hypernuclei and spin dependence of the ΛN interaction with antisymmetrized molecular dynamics

“…It is found that the present calculation with Gogny D1S reproduces the level ordering except for the 1/2 − state in 9 Be and 9 B. However, the excitation energies are slightly lower than the experimental data in 8 Be, 9 Be and 9 B. Since they have the well-developed 2α cluster structure, it is considered that the difference of the excitation energies shows the overestimation of the momentum of inertia of the the 2α clustering.…”

“…We perform the antisymmetrized molecular dynamics (AMD) calculation for 6 Li, 8 Li, 8 Be, 9 Be, 9 B, 10 B, 11 C, 12 C, 14 N, and 15 O using the original parameter set of Gogny D1S given in Refs. [29,30].…”

“…First, we discuss the excitation spectra of the nuclei other than 8 Be, 9 Be and 9 B, namely 6 Li, 8 Li, 9 B, 10 B, 11 C, 12 C, 14 N, and 15 O, which are shown in Fig. 1.…”

“…In Fig. 2, we show the excitation spectra of 8 Be, 9 Be and 9 B, which are characterized by having the 2α, 2α + n and 2α + p cluster structure, respectively. It is found that the present calculation with Gogny D1S reproduces the level ordering except for the 1/2 − state in 9 Be and 9 B.…”

“…Especially, structure of light Λ hypernuclei is of interest because ordinary nuclei in p-shell and sd-shell mass regions have various structures such as cluster and deformed mean-field like structures near the ground states. For example, in 7 Λ Li [9][10][11][12], it was predicted that the addition of a Λ particle reduces the intercluster distance between α and d of the core nucleus 6 Li, which was confirmed through the observations of the B(E2) values by the γ-ray spectroscopy experiment. In the other Λ hypernuclei such as 13 Λ C, several theoretical calculations showed that a Λ particle reduces the nuclear quadrupole deformation of the ground states [13][14][15][16][17][18][19][20].…”