6.3 Resonant States of 11 Li, Probability Distributions and β-decay of Halo Analog States
87
Fig. 6.13 Spectator function H 5 (p) versus p for 11 Be* excited state at 18.3 MeV. Here, p along
X-axis is in units of α
H 5 ( p) = (E1 × p) × exp(−E2 × p), E1 = −0.101α
−3
, E2 = 0.800α
−1
(6.39)
The three-body wave function is then normalized requiring that
ψ 11 Be (
p 12 ,
p 3 ; E)ψ11 Be
∗ (
p 12 ,
p 3 ; E)d p 12 d
p 3 = 1
(6.40)
Using the algebraic representations for the spectator functions Eqs. (6.35)–
(6.39), we compute the quadrature of the integral and determine the value of the
normalization constant, N 1 = 0.157α
4 .
6.3.6 β-Decay of 11 Li to Halo Analog 11 Be* (18.3 MeV) State
Equipped with the required details to write the complete three-body wave functions
for
11 Li and
11 Be
∗ states, we are now in a position to calculate the transition probabilities of β-decay
11 Li to different decay channels. Experimental studies [74, 75, 85,
86] of β-delayed charged particles like deuterons, tritons,
4 He and
9 Be and neutrons
and γ -rays that follow the
11 Li β-decay indicate a β-feeding to an excited state at
excitation energy of 18.3 MeV in
11 Be with a large Gamow–Teller strength, B GT ≥ 1.
Now such a large value of B GT implies a large spatial overlap of the
11 Be
∗ state and
the ground state of
11 Li. Using the three-body wave functions obtained above, we
calculate the value of the overlap integral
M fi =
ψ 11 Be ∗
ψ 11 Li
=
ψ
∗
11Be ∗ (
p 12 ,
p 3 ; E)ψ 11 Li (
p 12 ,
p 3 ; E)d
p 12 d
p 3 (6.41)