Yield estimation

The expected yield of the hypernuclear states are evaluated based on the E89-009 result for the $^{12}_{\Lambda }$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 and so on. The E01-011 experiment is expected to increase hypernuclear yields by a factor of 50, and to improve the signal to accidental ratio by a factor of 10.

Table 4 shows the cross sections of the hypernuclear states for the targets $^{12}$C,$^{28}$Si, and $^{51}$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 vary by a factor of 2-5 depending on the choice of model parameters for the elementary reaction, hypernuclear potentials and configuration of the states etc. In the present yield estimate given in table 5, the expected yield rates were obtained normalizing assuming 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
		$s_{1/2}$	16
		$f_{7/2}$	32
		$f_{5/2}$	38