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The charge-dependent Bonn potentials with pseudovector pion-nucleon coupling

To apply the high-precision realistic nucleon-nucleon ($NN$) potentials on the investigations of relativistic many-body methods, the new versions of charge-dependent Bonn (CD-Bonn) $NN$ potential are constructed within the pseudovector pion-nucleon coupling instead of the pseudoscalar type in the original CD-Bonn potential worked out by Machleidt [Phys. Rev. C 63, 024001 (2001)]. Two effective scalar mesons are introduced, whose coupling constants with nucleon are independently determined at each partial wave for total angular momentum $J\leq 4$, to describe the charge dependence of $NN$ scattering data precisely, while the coupling constants between vector, pseudovector mesons and nucleon are identical in all channels. Three revised CD-Bonn potentials adopting the pseudovector pion-nucleon couplings (pvCD-Bonn) are generated by fitting the Nijmegen PWA phase shift data and deuteron binding energy with different pion-nucleon coupling strengths, which can reproduce the phase shifts at spin-single channels and low-energy $NN$ scattering parameters very well, and provide the significantly different mixing parameters at spin-triplet channels. Furthermore, the $D$-state probabilities of deuteron from these potentials range from $4.22\%$ to $6.05\%$. It demonstrates that these potentials contain different components of tensor force, which will be useful to discuss the roles of tensor force in nuclear few-body and many-body systems.