Significance of hypernuclear investigation

A hypernucleus contains a hyperon implanted as an ``impurity'' within the nuclear medium. This introduces a new quantum number, strangeness, into the nucleus, and if the hyperon maintains its identity it will not experience Pauli-blocking, easily interacting with deeply bound nucleons. In this sense, it has been proposed that the hyperon is a good probe of the interior of a nucleus, where information is difficult to obtain.

In the proposed experiment, we intend to extract the characteristics of a $\Lambda$ hyperon embedded in a nucleus by observing the spectroscopy of its states. It is a unique characteristic of $\Lambda$ hypernuclei that deeply bound states, even the ground $s-shell$ states, have very small widths and can be measured as individual peaks in the excitation spectra. These properties have, to some extent, been shown experimentally in recent hypernuclear spectroscopy by the $( \pi ^ + ,{\rm K}^ +)$ reaction[1,2,3].

In hypernuclear production, most of the states are excited as nucleon-hole $\Lambda$-particle states, (N$^{-1}$,$\Lambda$). The spreading widths of these states were calculated to be less than a few 100 keV [4,5]. This occurs because: 1) The $\Lambda$ isospin is 0 and only isoscaler particle-hole modes of the core nucleus are excited; 2) the $\Lambda$N interaction is much weaker than the nucleon-nucleon interaction; 3) the $\Lambda$N spin-spin interaction is weak and therefore the spin vector p$_N$-h$_N$ excitation is suppressed; and 4) There is no exchange term.

As a result, particle-hole $\Lambda$-hypernuclear states are much narrower than nucleon-nuclear states of the same excitation energy. In the case of Ca for example, it was predicted that $\Gamma _{\Lambda}$(1s or 0d)/$\Gamma _{N}$(0s) = 0.03-0.07, resulting in a spreading width narrower than a few hundred keV even for the excited states above the particle emission threshold. This shows that spectroscopic studies of deeply bound $\Lambda$-hypernuclear states can be successfully undertaken. Thus through the widths and excitation energies of the single particle levels, the validity of the mean field description of hypernuclear potentials can be examined.

There is also the fundamental question, ``to what extent does a $\Lambda$ hyperon keep its identity as a baryon inside a nucleus?'' [6]. Spectroscopic data in heavier hypernuclei can help answer this question. Indeed, the relevance of the mean-field approximation in nuclear physics is one of the prime questions related to role that the sub-structure of nucleons plays in the nucleus. It was, for example, suggested that the mass dependence of the binding energy difference between $s$ and $d$ orbitals may provide information on the ``distinguishability'' of a $\Lambda$ hyperon as a baryon in nuclear medium [7].

The effective $\Lambda$-Nucleus interaction can be derived from a $\Lambda$-nucleon interaction such as the YNG or Njimegen potential forms [8]. The Njimegen potentials are obtained from phenomenological OBE fits to the baryon-baryon data using SU(3) with broken symmetry. The fit well represents the N-N and limited Y-N data. The YNG analytical form of the $\Lambda$-N effective interaction [9] is particularly useful in calculating hypernuclear binding energies, level structure, and reaction cross sections and polarizations. Because the Y-N interactions are weaker than N-N, and the Pauli exclusion principle is absent for the $\Lambda$ hyperons in nucleus, hypernuclear properties can be reliably calculated. Therefore, experimental observables can be connected in a straightforward way to YN interactions, and precision spectroscopic data can constrain the elementary $\Lambda$-N interaction. Indeed, because hyperon-nucleon scattering data cannot be easily obtained, the interaction is mainly constrained by hypernuclear structure.