Recent hypernuclear investigation

Although the spectra of many light $\Lambda$ hypernuclei have been studied, there are only a few experiments on hypernuclear systems beyond the $p$-shell. Most of these later data were obtained using the $( \pi ^ + ,{\rm K}^ +)$ reaction, which strongly populates deeply-bound, high-spin states due to the large momentum transfer in this reaction. The BNL-AGS experiments surveyed the single particle nature of $\Lambda$ hypernuclei up to $^{89}_{\Lambda}$Y, and observed peaks corresponding to the major $\Lambda$ shell structure [1]. The KEK E140a experiment made an intensive spectroscopic study using the SKS spectrometer, and observed the major shell structure of the single particle $\Lambda$ orbits up to $^{208}_{\Lambda}$Pb [2,10]. These spectra, shown in Fig. 1 were interpreted in terms of a $\Lambda$ bound in a Woods-Saxon, density-dependent potential. However, the spectra are of poor quality as seen in the spectra, and the peak positions of the various shell structures were not well determined. Resolutions varied from 1.5 to 4 MeV FWHM from the light to heavy systems.

The best hypernuclear spectrum in the medium-heavy mass region was taken for the $^{89}_\Lambda$Y by the $( \pi ^ + ,{\rm K}^ +)$ reaction having an energy resolution of 1.7 MeV (FWHM). This spectrum is shown in Fig. 2 [11]. In addition to the major shell structure, the figure clearly shows the splitting of the higher shell orbitals, e.g. the $f$ orbit. The origin of this splitting is under intensive discussion, and may be related to the hypernuclear $ls$ splitting.

The progress $( \pi ^ + ,{\rm K}^ +)$ reaction spectroscopy has largely been driven by the superconducting kaon spectrometer (SKS), which has momentum resolution of 0.1 %, and a large solid angle of 100 msr [12,13]. Using this spectrometer as a microscope, an intensive spectroscopic study of $\Lambda$ hypernuclei has been undertaken at KEK. Binding energies of a $\Lambda$ within nuclei as heavy as Pb have been extracted from the spectra, and the central part of the $\Lambda$ hyperon potential has been experimentally investigated .

For $p$-shell $\Lambda$ hypernuclei, high quality hypernuclear spectra have been derived again by the $( \pi ^ + ,{\rm K}^ +)$ reaction at KEK PS and the structure information on light $\Lambda$ hypernuclei were obtained [3]. The spectra yielded information on the hypernuclear structure such as core excited states and also on spin-dependent $\Lambda$N interaction. A sample spectrum for the $^{12}$C($\pi ^+$,K$^+$) reaction is shown in Fig. 3.

Other recent progress in hypernuclear spectroscopy involves the observation of $\gamma$ transitions between hypernuclear states which are excited by pion or kaon production reactions. The $\gamma$ rays are observed by Germanium and NaI detectors in coincidence with the production of bound hypernuclear levels. Because the splitting of the hypernuclear states by spin-dependent interactions (spin-spin and spin-orbit) is small, high precision $\gamma$ ray spectroscopy is the only technique available which can directly measure these splittings. Of course identifying hypernuclear as opposed to nuclear gammas is difficulty and is presently limited to states in light $\Lambda$ hypernuclei in the low excitation region. Previously observation of the $^7_{\Lambda}$Li E2 and M1 transition gave crucial information on the spin-spin interaction, and the structure change of the nucleus when a $\Lambda$ is added to the system [15]. The observation of the E1 gamma transition between the p$_{3/2}$ excited and the s$_{1/2}$ ground states of $^{13}_{\Lambda}$C [17] and the determination of the splitting between 5/2$^+$ and 3/2$^+$ spin-orbit partners in $^9_{\Lambda}$Be [16] confirmed the smallness of the $\Lambda$N spin-orbit splitting.

Both reaction and the $\gamma$ ray spectroscopy have greatly advanced in the past few years, but spin splittings are too small to be observed by reaction spectroscopy. The best energy resolution achievable by the $( \pi ^ + ,{\rm K}^ +)$ reaction spectroscopy is 1.5 MeV (FWHM), and is mainly dependent on beam quality and target thickness. Thus until improved kaon and pion beams of much higher intensity become available, this resolution cannot be improved.

In summary, the present issues in hypernuclear spectroscopy are as follows.

• One would like to know the extent to which the single-particle properties of a baryon remain unchanged in deeply bound states. This can be explored by placing a $\Lambda$ hyperon deeply within the nucleus.
• One would like to determination the spin dependent interaction strengths, of the effective $\Lambda$-Nucleus and thus extract the form of the $\Lambda$-N potential.

Although the spin-dependent interaction is best intensively studied in the $p$-shell by the $\gamma$-ray spectroscopy, complementary information from higher mass nuclei and higher excitation energies will be important. However the single particle nature of the $\Lambda$ hyperon embedded in nuclear matter must be studied by the spectroscopy of heavy hypernuclei, and this is the key motivation of this proposal.