**Table 2:** Details for the molecular clouds towards the VHE sources in the W 28 field, assuming a distance d.
VHE Source	$V_{\rm LSR}$	d	$^\dagger M$	$^\ddagger n$	$^\S k_{\rm CR}$
	(km s^-1)	(kpc)
HESS J1801-233	0-25	2.0	0.5	1.4	13
HESS J1801-233	0-12	2.0	0.2	2.3	32
HESS J1801-233	13-25	4.0	1.1	0.6	23
HESS J1800-240	0-20	2.0	1.0	1.0	18
HESS J1800-240A	12-20	4.0	1.0	0.7	28
HESS J1800-240B	0-12	2.0	0.4	2.3	18
HESS J1800-240B	12-20	4.0	1.5	1.2	19

$^\dagger$ Cloud mass $\times 10^5~M_\odot$ . $^\ddagger$ Cloud density $\times 10^3$ cm^-3. $^\S$ Cosmic-ray density enhancement, $k_{\rm CR}$ above the local value required to produce the E>1 TeV VHE $\gamma$ -ray emission (using Eq. (10) of Aharonian 1991).

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