An experiment was performed to study excited states in neutron-deficient nuclei around Ca. After a first fragmentation of the primary beam, the one-neutron knockout reaction was used to produce ³⁶Ca ions from the ³⁷Ca secondary beam and in-beam \gamma rays were measured. The energy of the first excited 2⁺ state in ³⁶Ca and the cross section for the 1-neutron knock-out reaction from ³⁷Ca at \approx 45 A MeV were obtained. The 2⁺ energy in ³⁶Ca is compared to the mirror nucleus ³⁶S to deduce information on the isospin dependence of the nuclear force near the proton drip line. Furthermore, for two other T_z=-2 nuclei, ²⁸S and ³²Ar, the deexcitation of the first 2⁺ states has been observed.

PACS numbers: 21.10.--k, 23.20.Lv, 27.30.+t