We develop an OpenPET system which can provide an accessible open space to the patient during PET scanning. Our first-generation OpenPET geometry which we called dual-ring OpenPET consisted of two separated detector rings and it could extend its axial field of view (FOV) therefore enabling imaging the gap region in addition to the in-ring region. However, applications such as dose verification by in-beam PET measurement during particle therapy and real-time tumor tracking by PET require sensitivity focused onto the gap rather than on the wide FOV. In this paper, we propose a second-generation OpenPET geometry, single-ring OpenPET, which can provide an accessible and observable open space with higher sensitivity and a reduced number of detectors than the earlier one. The proposed geometry has a cylinder shape cut at a slant angle, in which the shape of each cut end becomes an ellipse. We provided a theoretical analysis for sensitivity of the proposed geometry, compared with the dual-ring OpenPET and a geometry where the conventional PET was positioned at a slant angle against the patient bed to form an accessible open space, which we called a slant PET. The central sensitivity depends on the solid angle of these geometries. As a result, we found that the single-ring OpenPET has a sensitivity 1.2 times higher than the dual-ring OpenPET and 1.3 times higher than the slant PET when designed for a 600 mm bed width with 300 mm accessible open space and about 200 detector blocks, each with a front area of 2500 mm². In addition, numerical simulation was carried out to show the imaging property of the proposed geometry realized with the ellipsoidal rings and these results indicate that the depth-of-interaction detector can provide uniform resolution even when the detectors are arranged in an ellipsoidal ring.