Hypernuclear production reactions

The (e,e'K$^+$) reaction has a unique characteristics for the hypernuclear spectroscopy among a wide variety of reactions which can be used to produce a strangeness -1 hyperon as listed in Table 1. Each reaction has its own characteristics and will plays its role for hypernuclear spectroscopy. However, only the $( {\rm K}^ -,\pi ^ - )$  and $( \pi ^ + ,{\rm K}^ +)$ reactions have been intensively used for the spectroscopic investigation in these reactions, so far. These reactions supposed to convert a neutron in the target nucleus to a $\Lambda$ hyperon. Although the $( \pi ^ + ,{\rm K}^ +)$ reaction is relatively new compared to the $( {\rm K}^ -,\pi ^ - )$ reaction, it is now considered as one of the best reactions for hypernuclear spectroscopy because it favorably populates deeply bound hypernuclear states [1,14,2]. The smaller cross sections of the ($\pi ^+$,K$^+$) reaction compared to that of the (K$^-$,$\pi ^-$) reaction is easily compensated by intensity of pion beams, which is much higher than that of kaon beams. The ($\pi ^+$,K$^+$) reaction selectively populates angular momentum stretched states because of the large momentum transfer to the recoil hypernuclei [19,20,18]. This is in contrast to the $( {\rm K}^ -,\pi ^ - )$ reaction, which transfers small momentum and thus preferentially excites substitutional states. By high quality $( \pi ^ + ,{\rm K}^ +)$ spectra with resolution better than 2 MeV (FWHM), it becomes possible to qualitatively study the unique structure of $\Lambda$ hypernuclei and characteristics of the $\Lambda$-nucleon interaction.

表 1: Comparison of $\Lambda$ Hypernuclear production reactions

$\Delta Z$ = 0	$\Delta Z$ = -1	comment
neutron to $\Lambda$	proton to $\Lambda$
($\pi^+,K^+$)	($\pi^-,K^0$)	stretched,high spin
in-flight ($K^-,\pi^-$)	in-flight ($K^-,\pi^0$)	substitutional
stopped ($K^-,\pi^-$)	stopped ($K^-,\pi^0$)
($e,e'K^0$)	($e,e'K^+$)	spin-flip,unnatural parity
($\gamma,K^0$)	($\gamma,K^+$)