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Next: 2 Production of Hypernuclei Up: Chapter 12 Section 1 Previous: Chapter 12 Section 1

1 Hyperons and hypernuclei

Strangeness has been introduced in particle physics to account for lifetimes in the baryon and meson spectrum much longer (by orders of magnitude) than those expected for strongly interacting systems. Indeed in 1953, Gell-Mann [1] interpreted this experimental finding in terms of selection rules associated with a new (at the time) quantum number, namely the strangeness, S, defined as

 

in terms of the charge number Z, isospin (third component of) and baryon number A. Alternatively, instead of the strangeness S, one may as well consider the hypercharge Y = S + A as indicated in formula (1).

Because of the charge and baryon number conservation, (1) entails the equivalence between isospin and strangeness conservation, a requirement indeed respected by the strong and electromagnetic forces, but violated by the weak interactions, which do not conserve neither T nor S.

As is well-known the introduction of this additional quantum number allows to classify in a larger scheme based on the unitary symmetry SU(3), which encompasses both isospin and strangeness, a new generation of baryons, i.e. the hyperons, endowed with the strangeness degree of freedom . Thus in this frame the and particles, in addition to a pair of first generation quarks (namely the u and d) embody as well a strange quark s, whereas the possesses two strange quarks in addition to a first generation one.

The stability of the particles, which moreover interact with the protons and neutrons with a force comparable to, although somewhat weaker than the one acting among the latter, permits the existence of strange nuclei, i.e. hypernuclei. On the other hand nuclei with an additional meson are not bound since the interaction between a and a nucleon is predominantly repulsive.

Our present knowledge on hypernuclei is limited and cannot be compared with the one available on conventional nuclei , yet it has already provided important clues on nuclear structure; most importantly it has much broadened the concept of nuclear structure itself.

Since the particle, with isospin I=0, strangeness S=-1 and mass =1115.6 MeV, is about 80 MeV lighter than the (which also has S=-1), the most "stable" among the S=-1 hypernuclei are those made up of nucleons and a particle. However because

and being the nucleon and the pion mass respectively and

the binding energy of the , the hypernucleus will eventually decay by weak interactions.

 
Figure 1: Chart of observed hypernuclei as of 1988 (from ref.[2]).

Yet it lives long enough to be detected and indeed a number of hypernuclei have been observed: they are shown in Fig.1 and the binding energies of the lighter among them are listed in Table 1.

  
Table 1: The binding energies of some hypernuclei (taken from ref. [3], p.55 and ref.[4], p.4028). In the second and third columns are indicated the isospin and its third component. In the fourth column the binding energy and in last column the ground state spin and parity, when available, are quoted.

In this Table is seen to be indeed comparable with the binding energy of a nucleon in a S=0 nucleus, but the striking difference between and lies in the fact that the former grows with the mass number A whereas, as it is well-known, saturates around a value of about -8 MeV per particle. This outcome reflects the freedom of the to occupy in the host nucleus orbits which are forbidden to a nucleon since it does not have to obey to the Pauli principle. In turn the low energy spectrum of a hypernucleus exhibits new states not present in the normal nuclei.

In this connection Feshbach [2] observes that this might not be exactly true since the u and d quarks in the nucleon and in the have to satisfy the Pauli principle. Actually, to assess the impact on the spectra of the hypernuclei of the Pauli principle, which must be obeyed by the quarks, will represent a challenging theme of investigation for the future hypernuclear physics.

Leaving aside this observation a rough estimate of the potential well binding the in a hypernucleus might be obtained by considering the kinetic energy of a particle in the lowest orbit it can occupy in a "shell model" nucleus, namely the . One gets [3]

R being the nuclear radius.

For example in one has MeV. Hence, since in this nucleus MeV (see Table 1), from the relationship

it follows that MeV to be compared with about 55 MeV [5], which is the depth of the potential well felt by a nucleon in carbon. Of course the above should only be considered as a rough estimate for the depth of the well acting on the particle in a nucleus. More realistic evaluations will be later considered.

Concerning the spin and parity assignments in Table II they were obtained from angular correlations measurements as well as from the determination of branching ratios for different decays modes (note that to the an intrinsic parity +1 is assigned).



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Next: 2 Production of Hypernuclei Up: Chapter 12 Section 1 Previous: Chapter 12 Section 1



Carlos E.Piedrafita