We show that it is possible to change not only s-wave but also higher partial wave atom-atom interactions in cold collision in the presence of relatively intense laser fields tuned near a photoassociative transition.PACS numbers: 34.80. Qb, 34.50.Cx, 32.80.Qk, 34.20.Cf Ability to control particle-particle interaction is important for exploring quantum physics of many-particle systems in various interaction regimes. Ultracold atoms offer a unique opportunity for such explorations with unprecedented control over atom-atom interaction. There are two methods of manipulating interaction in cold atoms. The most popular one is magnetic field Feshbach resonance (MFR) [1] which has been extensively used to tune s-wave scattering length over a wide range. This has facilitated the recent demonstration of s-wave fermionic superfluidity in strongly interacting atomic gases [2]. In fact, MFR has become an essential tool in experimental investigations on the effects of large s-wave scattering length on the properties of atomic Fermi gases [3] and Bose-Einstein condensates (BEC) [4]. The other method of modifying atomic interaction is optical Feshbach resonance (OFR) proposed by Fedichev et al. [5] and implemented in recent experiments [6,7,8]. While MFR relies on magnetic effects of Zeeman and hyperfine interactions, OFR uses off-resonant continuum-bound optical dipole transitions. In the case of resonance or near-resonance, OFR can lead to photoassociation (PA) [9] of two atoms into an excited molecule. Recently, p-wave MFR [10] in fermionic atoms has been observed. Enhanced scattering in higher partial waves by magnetic-field induced dissociation of Feshabch molecule has been shown [11]. There is a proposal [12] for generating anisotropic interaction by static electric field. Both the methods of magnetic and optical Feshbach resonances are so far primarily used to tune s-wave scattering length in ultracold atoms. To go beyond s-wave physics of cold atoms, it is now essential to devise methods of controlling p-, d-and other higher partial-wave interactions. This is particularly important for testing models of unconventional superconductivity or superfluidity in atomic Fermi gases. Superfluidity and superconductivity are related phenomena. Conventional low temperature superconductivity can be explained by Bardeen-Cooper-Schrieffer theory which is based on s-wave Cooper-pairing. It is assumed that higher partial-wave interactions can lead to unconventional and high temperature superconductivity. Studies on Fermi superfluidity in cold atomic gases with controllable p-and d-wave interactions will help us to develop new insight about high temperature superconductivity which requires a proper theoretical understanding.Here we show that it is possible to change not only ℓ = 0 (s-wave) but also nonzero partial-wave scattering amplitudes of two cold atoms by OFR with a relatively intense laser field. At low energy, the light-shift (or Stark-shift) due to laser-induced free-bound coupling can greatly exceed the spontaneous as well a...