Yield estimate and requested beam time

The expected yield of the hypernuclear states are evaluated based on the E89-009 result for $^{12}_{\Lambda }$B ground state in the $^{12}$C(e,e'K$^+$) $^{12}_{\Lambda }$B reaction. As described in Appendix B, the proposed ``Tilt method'' is expected to realize more than factor of 50 yield gain. It is partly because we can use higher intensity beams and thick targets and partly because the kaon spectrometer has a larger solid angle acceptance.

The cross sections of the hypernuclear states for the targets, $^{12}$C,$^{28}$Si,$^{51}$V have been calculated by Motoba and Sotona [26,22]. They are listed in Table 7.

It is noted, however, 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, the cross sections were normalized 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 7: Cross sections of $^{12}_{\Lambda }$B, $^{28}_{\Lambda }$Al and $^{51}_{\Lambda }$Ti calculated by DWIA [26]

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

表 8: Requested beam time

	Target	Hypernucleus	Number of days	Number of hours
HKS commissioning			7	168
Tuning and calibration			7	168
Data taking
	$^{12}$C	$^{12}_{\Lambda }$B	4	96
	$^{28}$Si	$^{28}_\Lambda$Al	8	192
	$^{51}$V	$^{51}_\Lambda$Ti	14	336
	$^{89}$Y	$^{89}_\Lambda$Sr	4	96
Total			40	960

表 9: Requested beam conditions

Typical beam energy	1.8 GeV
Typical beam current	30 $\mu$A
Beam energy stability	$\le$ 1 $\times$ 10$^{-4}$

For the beam time, we request commissioning beam time for the HKS itself as the spectrometer is newly installed. The performance of the HKS spectrometer, particularly momentum resolution, will be examined using the requested beam time for the commissioning.

It is our request that the commissioning beam time is allocated a few months before the tuning and data taking beam time so that we can analyze the data and understand the performance of the spectrometer in advance.

Tuning the spectrometer system coupled with the tilted Enge spectrometer will be carried out with a CH$_{2}$ target using the $\Lambda$ peak and with the $^{12}$C target.

The requested data taking hours for C, Si and V targets were calculated so that 3000 counts for ground states of $^{12}_{\Lambda }$B, 1000 counts for $^{28}_\Lambda$Al and 400 counts for $^{51}_\Lambda$Ti can be accumulated, assuming 50 % efficiency for data taking and data analysis. For $^{89}_\Lambda$Sr, the requested beam time is only for an exploratory run. The requested beam times are summarized in Table 8. Requested beam conditions are listed in Table 9.