  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.
