Asymptotics of three-body bound state radial wave functions of halo nuclei

Three-body asymptotic normalization factors for halo nuclei and their determination

“…One notes that when m 3 → ∞ (a heavy particle 3 for which m j /m 3 <<1), the asymptotics formula for Ψ a; ν 1 (r 1 , r 2 ) passes to the same form for Ψ (as) ν (r, ρ) at r → ∞ and ρ → ∞ given by (1) since for the limit at m 3 → ∞ R (j) = R and C (j) a; ν 1 = C a; ν [2]. As is seen from Egs.…”

“…Therefore, systematic collection of data about TBANFs for different three-body halo nuclei must be extremely encouraged nowadays. For this end, at the present time a comparative analysis of the approximate model wave functions with the obtained asymptotic expressions [1][2][3][4][5] is usually done to extract the TBANF values. 6 He and 9 Be nuclei In this section, we present the result of the analysis of the asymptotic behaviour of the approximate three-body (αnn) and (nαα) radial wave functions for the ground state of 6 He and 9 Be nuclei obtained in [2,[7][8][9] and [10], respectively, as well as the results of the TBANF values for α+n+n → 6 He and n+α+α → 9 Be obtained in Refs.…”

“…6 He and 9 Be nuclei In this section, we present the result of the analysis of the asymptotic behaviour of the approximate three-body (αnn) and (nαα) radial wave functions for the ground state of 6 He and 9 Be nuclei obtained in [2,[7][8][9] and [10], respectively, as well as the results of the TBANF values for α+n+n → 6 He and n+α+α → 9 Be obtained in Refs. [2,5] and in Ref. [3], respectively.…”

“…At this, in [9] the Sack-Biedeharn-Breit for αN -interaction and the hard-core Reid for the NN potential (M1-model; ε He =0.3048 MeV, ε Be =1.56 MeV) were applied. In [2,7,8], the radial wave function Ψ a; ν 1 (r 1 , r 2 ) were obtained within the Lagrange-mesh approach by using the Kanada et al for αN -interaction and the Minnesota NN potential.…”

“…In this review work, we will briefly present the true asymptotic forms derived in works [1][2][3][4][5] for the three-body (3+1+2) halo nucleus a, which is also denoted by 3+1+2→ a below, and the results for the three-body asymptotic normalization factors(TBANFs) for α + n + n → 6 He and n + α + α → 9 Be obtained from the comparative analysis of these asymptotic forms with the specific approximate model wave functions for asymptotic regions. We useh = c =1 throughout the paper.…”