Since the strong interactions conserve strangeness (
) one must
necessarily make use of particles (essentially mesons) endowed with strangeness
to produce 
hyperons via strong interactions. The following are
the physical processes commonly considered:
i) reactions where a s quark is exchanged, namely
Here the s quark is transferred from a kaon K to a hyperon Y, both
having strangeness S=-1 (in the above N and 
represent a
nucleon and pion, respectively).
In this reaction the momentum transfer can be quite small. Actually if a
with a momentum 
hits a neutron n at rest, then in the reaction
a "magic" momentum exists such that the 
also stays at rest while
the 
moves in the forward direction.
The equation fixing such a momentum is easily found to be
which yields 
MeV/c.
If, instead of a 
, a 
particle is considered one gets
MeV/c.
In Fig.2 the momentum transferred from the kaon to the pion (in the forward
direction) is displayed as a function of the incident kaon momentum.
Note that because of the smallness of the momentum transfer also the
polarization 
of the 
is almost negligible.
On the other hand
for 
and 
GeV/c it is found that 
and
respectively.
Figure 2: Kinematics of the 
reaction (from ref.[2]).
ii) Reactions where a 
pair is created.
In this instance typical processes are 
, 
and 
.
Here a s-quark is transferred to a nucleon
yielding an hyperon, whereas the antiquark 
becomes a constituent
of the final 
.
At variance with the case i) now the momentum transfers are large
(because the final particles, namely the Y and the 
, are heavy):
accordingly the 
will be large as well.
iii) Reactions in which the two processes above described are combined into a single one.
Examples of this case are
and
where the so-called "cascade particles" 
and 
are produced.
The reactions we have referred to above are indeed exploited to obtain
hyperons inside nuclei. A number of 
experiments have been performed at CERN and at Brookhaven (BNL).
With the direct 
mechanism a neutron can be
replaced with a 
inside the nucleus so gently that the wave
function of the nuclear system remains essentially unchanged (hence the name
of "substitutional reaction"
for the process). If the pion is emitted in the forward direction
then the angular momentum change occurring in the reaction is
, otherwise 
and 
transitions become
possible as well.
As an illustration in Fig.3 the spectra of the 
and
hypernuclei, obtained via the 
process, are shown.
In both cases it is clearly apparent that when the
particle and the neutron hole, which together identify the
excited state of the hypernuclear system, are in the same single particle orbit
(and coupled to a state of
zero angular momentum and positive parity, i.e. 
),
then the corresponding
peak in the cross-section is quite pronounced, whereas for the other
configurations a sizable reduction of the cross-section is seen to occur
(the associated peaks are much less evident).
This finding reflects the marked preference of the 
reaction for the 
transitions rather than for those having
. In turn this explains why the 
process is not appropriate for exciting low-lying 
hypernuclear
states in heavy nuclei: indeed here the neutron has in general a high
angular momentum thus entailing large 
reactions when the
sits in low lying orbits.
Figure 3: Production of hypernuclei 
and 
by the
reaction (from ref.[2]).
For exciting high spin hypernuclear states actually the process
is preferable to (7) (actually (7) and (11) are in fact complementary).
This reaction indeed prefers to create the 
in a high angular
momentum state at large excitation energy (quasi-free scattering).
It is, accordingly, well-suited for unfolding the shell
structure of nuclei heavier than those previously considered.
As an example in Fig.4 the
spectrum of the hypernucleus 
thus obtained is shown.
It is indeed impressive to see in the
figure how the 
is probing all the nuclear shells down to the inner
one, namely the 
(remember that in 
the neutron shells are closed and the 
single particle level is
fully occupied).
Figure 4: Production of 
hypernuclear states in 
with the 
reaction (from ref.[2]).
In connection with the reaction (11) it should be observed that the
, being produced in a high angular momentum state and above its
emission threshold (quasi-free region), may
either escape from the hypernucleus ( with a width 
) or be
captured inside the hypernucleus (with a width 
) where it
spreads its energy with the other constituents. In the latter instance
a compound nucleus is formed eventually decaying by the emission of
several nucleons in addition to a number of 
-rays:
at the end of the process a hypernucleus is left
in a variety of quantum states.
In the range of excitation energies from 30 to 120 MeV in 
the following value
has been experimentally found [6]
Now the above energy range is dominated by the quasi-free scattering,
whose cross-section 
is larger by about two orders of
magnitude than the cross section 
for the formation of an
hypernucleus directly in a bound state,
via, e.g., the process (7). Thus, even by taking the lower value for
the ratio (12), we obtain
for the cross section 
, corresponding to the
formation of an hypernucleus through the compound nucleus mechanism
via (11), the estimate
still an order of magnitude larger than 
.
Due to its importance it is appropriate in conclusion to this Section to
shortly return to consider the
polarization of the 
-hypernuclei. It is largely due to the
polarization of the hyperons
produced in the elementary processes like 
, 
,
and 
which occurs, as we have already seen,
if the momenta involved are sufficiently
large and reflects the quite significant spin dependence of the
-N interaction (for example, a notable feature of the latter is that
rather than yielding the strongest attraction
in the triplet state 
, like the N-N force, appears to be preferring
the singlet state 
). However
it is also contributed to by the distortion of the pionic waves
either in the initial or in the final state, which orients the angular
momentum transferred in the reaction.
Estimates of the polarization of the 
hypernuclei, obtained through
the 
process have been performed since this type of
experiments are expected to be performed at CEBAF. On the other hand the
mechanism for obtaining polarized hypernuclei
has been explored by Ejiri [6].
This author considers closed shell nuclei having the lowest
spin--orbit partner filled. As we already know the considered reaction proceeds
primarily through the compound nucleus formation and
the most populated final hypernuclear states, reached at the end of
the statistical decaying process, are those with
a 
neutron hole and a
particle coupled to J=2l.
In other words stretched states with maximum spin are preferentially excited
by the 
reaction.
Large polarizations of the hypernuclei (of the order of 
)
are found. The corresponding polarizations of the spin of the 
turn out to be of the order of 
.
Another interesting case is provided by the elementary 
reaction: indeed the latter yields, for momenta larger than 1 GeV/c,
a 
almost 100
polarized [7]. When applied to
populate natural parity states of the hypernucleus 
this
reaction leads to polarizations very small, large and positive and large
and negative for momenta of the incident 
of 0.7, 1.1 and 1.5 GeV/c,
respectively. This shows how sensitive the polarization of an hypernucleus
can be to the kinematics of the reaction selected for its own production.
Because the produced hypernuclei are polarized, it becomes possible to
measure their magnetic moments. This is an important measurement as it
will test the hypothesis that the hypernucleus consists of a host nucleus
plus a 
. One would learn if the hyperon state consists of just a
or if there is a 
component [14].
