The electric quadrupole interaction frequencies eQV zz The study of nuclear properties in long isotopic and isotonic chains has been the subject of many investigations, both experimental and theoretical [1], the main source of information on nuclear ground state properties being optical spectroscopy [2]. Such investigations revealed that the nuclear shape may change drastically between two nuclei which differ only by one or two nucleons. It was first observed with 80 Hg, for which a drastic change in the mean square charge radius was found between 187 Hg and 185 Hg [3]. This phenomenon was explained by nearly degenerate nuclear states of different shape and is now usually denoted as "shape coexistence." As N changes for a given Z or vice versa strong competition can occur between the different forces which separately drive the nucleus towards prolate, oblate, triaxial, and spherical shapes. For 80 Hg, 79 Au, and 78 Pt-these elements are just below the Z 82 shell closure-, the neutron-rich nuclei are weakly deformed with oblate shapes, whereas the neutron-deficient isotopes are strongly deformed with prolate shapes [4][5][6]. For Hg and Au the shape transition is sharp [4,7], whereas it is smooth for Pt [6]. Meanwhile it is generally adopted that the phenomenon of shape coexistence exists in many regions of the nuclear chart [1]. One of these is the region just below the Z 40 shell closure, which has been studied extensively meanwhile [8]. In the isotopic chains of 38 Sr, 37 Rb, and 36 Kr the nuclear shape changes from nearly spherical around N 50 ( 88 Sr 50 , 87 Rb 50 , 86 Kr 50 ) to strong prolate deformation (b 2 ϳ 0.4) at N ϳ 40 and N ϳ 60 [9-13]. For the light isotopes of Sr, Rb, and Kr the deformation develops gradually from N ϳ 46 to N ϳ 40. For several even-even nuclei b 2 can be determined also from lifetime measurements available in the literature [14,15]. In this context the nuclear shapes of 35 Br would be interesting. For Br, however, laser spectroscopy (LS) measurements have not yet been reported in the literature. Thus direct information on the neutron-number dependence of the nuclear deformation in the bromine chain-as normally obtained from LS measurements of mean square radii and nuclear electric quadrupole moments-is not available. Concerning the ground-state properties of neutron-deficient Br isotopes, only the magnetic moments are known experimentally from nuclear orientation (NO) [16] and nuclear magnetic resonance on oriented nuclei (NMR-ON) measurements [17,18]. From these measurements Griffiths et al. drew the conclusion that their results pointed to a gradual increase in nuclear ground-state deformation from b 2 0.20, g 0 in 81 Br to b 2 0.33, g 0 in 75 Br [16]. Such a gradual increase of the deformation with decreasing N was actually in agreement with the change of the deformation of 36 Kr, 37 Rb, and 38 Sr. For bromine, however, the overall deformation may be influenced considerably by the single-particle properties of the valence proton.