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Residue Coulomb interaction among isobars and its influence in symmetry energy of neutron-rich fragment

The residue Coulomb interaction (RCI), which affects the results of symmetry energy of neutron-rich nucleus in isobaric yield ratio (IYR) methods, is difficult to be determined. Four RCI approximations are investigated: (1) the M1--RCI adopting the $a_{c}/T$ (the ratio of Coulomb energy coefficient to temperature) determined from the IYR of mirror-nuclei fragment; (2) the M2--RCI by fitting the difference between IYRs; (3) the M3--RCI by adopting the standard Coulomb energy at a temperature $T=2$MeV; and (4) neglecting the RCI among the three isobars. The M1--, M2-- and M3--RCI is found to no larger than 0.4. In particular, the M2--RCI is very close to zero. The effects of RCI in the $a_{sym}/T$ of fragment are also studied. The M1-- and M4--$a_{sym}/T$ are found to be the lower and upper limitations of $a_{sym}/T$, respectively. The M2--$a_{sym}/T$ overlaps the M4--$a_{sym}/T$, which indicates that the M2--RCI is negligible, at the same time the RCI among the three isobars can be neglected. A relative consistent low values of M3--$a_{sym}/T$ ($7.5\pm2.5$) are found in very neutron-rich isobars.