ner_tags: O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: the deeper optical potential of antikaons , the earlier onset of K − and condensations in NS matter. Moreover, condensation in comparison with K − condensation always occurs at a higher density. It can be seen from equation ( 10 ) that the threshold condition for condensations is more difficult to fulfill compared with the threshold condition for K − condensation in NSs. In our model, condensations only appear in stable NSs when the optical potential of antikaons = −100, −110, −120 and −130 MeV, and the presence of them suppresses the increase of the fraction of K − mesons as indicated in Fig. 2 (a) and Table 1 . Besides, it can be also seen from Figs 2(b) and (c) that the increase of K − mesons makes the dramatical decrease of e and μ fractions in NSs. It is because that K − meson is boson in the lowest energy state, replacing negatively charged particles, makes the system energy lower. In order to keep the conditions of the electrical neutrality, the proton fraction grows faster and then the growth is suppressed when mesons appears in NSs. Eventually, the proton fraction turns out to be almost identical neutron fraction in NS matter. Therefore, according to equation ( 15 ), the Fermi momenta of neutrons decrease and the corresponding values of protons increase including K − and condensations in NS matter, which are displayed in Fig. 3 (a). Figure 1. EOSs and NSs masses as a function of nucleon density n N . In the paper, the black, red, blue, dark cyan, magenta, dark yellow and green lines represent the seven cases of = −80, −90, −100, −110, −120, −130 and 0 MeV, respectively. The dots stand for the maximum masses of NSs for the seven cases. Figure 2. Composition of NSs as a function of nucleon density n N with and without antikaon condensations. We take the optical potential of antikaons = −80, −90, −100, −110, −120, −130 and 0 MeV. Figure 3. The nucleon Fermi momentum, the effective mass and the single particle energy E N ( p F ) at the Fermi surface versus nucleon density n N in npeμ and npe matter. We take the optical potential of antikaons = −80, −90, −100, −110, −120, −130 and 0 MeV. Table 1. Maximum masses m max = M max /M ⊙ , and the corresponding radii R and the centre densities n C as well as the threshold densities and of K − and condensations for the optical potential of antikaons = −80, −90, −100, −110, −120, −130 and 0 MeV, respectively. Fig. 3 gives the nucleon Fermi momentum p FN , the effective mass and the single particle energy E N ( p F ) at the Fermi surface as a function of nucleon density n N including and not including K − and condensations in npeμ matter. We could see that the nucleon effective mass with K − and condensations is smaller than the corresponding values without K − and condensations, and it gradually declines along with the optical potential of antikaons growth in npe matter in Fig. 3 (b). The individual single particle energies of neutrons and protons in npe matter are all much less than their values in