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We study $^5$He variationally as the first $p$-shell nucleus in thetensor-optimized antisymmetrized molecular dynamics (TOAMD) using the barenucleon--nucleon interaction without any renormalization. In TOAMD, the centraland tensor correlation operators promote the AMD's Gaussian wave function to asophisticated many-body state including the short-range and tensor correlationswith high-momentum nucleon pairs. We develop a successive approach by applyingthese operators successively with up to double correlation operators to getconverging results. We obtain satisfactory results for $^5$He, not only for theground state but also for the excited state, and discuss explicitly thecorrelated Hamiltonian components in each state. We also show the importance ofthe independent optimization of the correlation functions in the variation ofthe total energy beyond the condition assuming common correlation forms used inthe Jastrow approach.

Successive variational approach with the tensor-optimized antisymmetrized molecular dynamics for the $^5$He nucleus