The ${^3{rm He}}(alpha,gamma){^7{rm Be}}$ and ${^3{rm H}}(alpha,gamma){^7{rm Li}}$ astrophysical $S$ factors are calculated within the no-core shell model with continuum using a renormalized chiral nucleon-nucleon interaction. The ${^3{rm He}}(alpha,gamma){^7{rm Be}}$ astrophysical $S$ factors agree reasonably well with the experimental data while the ${^3{rm H}}(alpha,gamma){^7{rm Li}}$ ones are overestimated. The seven-nucleon bound and resonance states and the $alpha+{^3{rm He}}/{^3{rm H}}$ elastic scattering are also studied and compared with experiment. The low-lying resonance properties are rather well reproduced by our approach. At low energies, the $s$-wave phase shift, which is non-resonant, is overestimated.
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