Yield estimation

The expected yields of the hypernuclear states were evaluated based on the E89-009 result for $^{12}_{\Lambda }$B ground state in the $^{12}$C(e,e'K$^+$) $^{12}_{\Lambda }$B reaction, comparing the beam intensity, acceptance ratio of the virtual photons, kaon detection efficiency $etc.$. The E01-011 experiment is expected to gain hypernuclear yield by a factor of 50.

Table 4 shows the cross sections of the hypernuclear states for the targets, $^{12}$C,$^{28}$Si,$^{51}$V which were calculated by Motoba and Sotona. Although the order of magnitude for the cross sections seems to agree with the E89-009 preliminary result, the calculated cross sections might vary by a factor of 2-5 depending on the choice of model parameters for the elementary reaction, hypernuclear potentials, configuration of the states and so on. In the present yield estimate given in Table 3, the expected yield rates were obtained with normalization assuming that the cross section of the $^{12}$C(e,e'K$^+$) $^{12}_{\Lambda }$B reaction for the ground state doublet is 100 nb/sr.

表 4: Cross sections of $^{12}_{\Lambda }$B, $^{28}_{\Lambda }$Al and $^{51}_{\Lambda }$Ti calculated by DWIA (T. Motoba 1997)

Target	Hypernucleus	$\begin{array}{c}{\rm Hypernuclear}\\ {\rm configuration}\end{array}$	$\begin{array}{c}{\rm Cross}\\ {\rm section}\\ {\rm (nb/sr)}\end{array}$
$^{12}$C	$^{12}_{\Lambda }$B	$s_{1/2}$	112
		$p_{3/2}$	79
		$p_{1/2}$	45
$^{28}$Si	$^{28}_{\Lambda }$Al	$s_{1/2}$	56
		$p_{3/2}$	95
		$p_{3/2}$	57
		$d_{5/2}$	131
		$d_{3/2}$	111
$^{51}$V	$^{51}_{\Lambda }$Ti	$s_{1/2}$	18
		$p_{3/2}$	41
		$p_{3/2}$	26
		$d_{5/2}$	52
		$d_{3/2}$	48
		$1s_{1/2}$	16
		$f_{7/2}$	32
		$f_{5/2}$	38