6.3 Resonant States of 11 Li, Probability Distributions and β-decay of Halo Analog States
81
This distribution which is compared with the latest experimental data [80] is
shown in Fig. 6.9. Here, the overall agreement with the experimental data shows that
the inner structure of
9 Li core has only marginal role to play at large momenta in
so far as the longitudinal component of the momentum distribution is considered.
To derive the longitudinal momentum distribution of halo neutron, we first express
the three-body wave function in terms of momentum vectors
p 31 and
p 2 . Then, the
longitudinal momentum distribution of halo neutron is simply defined as:
dN
d p I I
=
d p 31 d 31 d 2 p
2
31 |ψ(
p 31 ,
p 2 )|
2
(6.22)
The longitudinal momentum distribution of halo neutron is shown in Fig. 6.10.
However, the corresponding experimental data, to the best of our knowledge, are
not yet available. From Fig. 6.9, the FWHM is estimated to be 46 MeV/c, which is
in agreement with the experimental value of 45 ± 3 MeV/c [62]. From Fig. 6.10,
FWHM is found to be 35 MeV/c for the halo neutron. Comparison of the two widths
shows that
(FWHM) 9 Li
(FWHM) n
= 1.314,
(6.23)
which is only slightly less than the value for uncorrelated neutron pair, i.e.,
√
2 [81].
It can thus be inferred that the two halo neutrons in
11 Li are nearly uncorrelated.
Fig. 6.9 Longitudinal momentum distribution of 9 Li (along Y-axis) versus p e|| , which is expressed
in MeV/c