80
6 Three-Body Approach to Structural Properties …
Fig. 6.8 Probability density P (along Y-axis) versus p 3 . Here, p 12 , and p 3 are expressed in units
of α
r
2
matter
=
A c
A
r
2
core
+
1
A
ρ
2
,
(6.20)
originally given by Fedorov et al. [53]. Taking the value of the radius of
9 Li and
substituting the values of r 12 and r 3 from Eqs. (6.18) and (6.19) into Eq. (6.20), we
obtain the value of the matter radius to be 3.27 fm which is to be compared with
3.2 ± 0.1 fm recently established by Garrido et al. [79].
The study of the behavior of probability amplitude with respect to the angle
between vectors
p 12 and
p 3 shows that the ground state of
11 Li has a maximum
probability for a configuration when the n–n relative motion and the recoil motion of
9 Li are at right angles to each other in such a way that the halo neutrons when away
from the core are closer and they are far away when closer to the core.
6.3.3 n–n Correlations in 11 Li from Momentum Distributions
One can also find the behavior of longitudinal momentum distributions of
9 Li and
that of the halo neutrons by defining
p = =
p I I + +
p ⊥ . The longitudinal or parallel
momentum distribution of
9 Li is by definition the momentum distribution of
9 Li
in the beam direction in fragmentation reaction of
11 Li beam on a target at certain
beam energy. In the present model, this implies that one should take − → p 3 along beam
direction only and integrate over the solid angle. Thus, longitudinal momentum
distribution of
9 Li is given as:
dN
d p 3I I
=
d p 12 d 12 d 3 p
2
12 |ψ(
p 12 ,
p 3 )|
2
(6.21)
6 Three-Body Approach to Structural Properties …
Fig. 6.8 Probability density P (along Y-axis) versus p 3 . Here, p 12 , and p 3 are expressed in units
of α
r
2
matter
=
A c
A
r
2
core
+
1
A
ρ
2
,
(6.20)
originally given by Fedorov et al. [53]. Taking the value of the radius of
9 Li and
substituting the values of r 12 and r 3 from Eqs. (6.18) and (6.19) into Eq. (6.20), we
obtain the value of the matter radius to be 3.27 fm which is to be compared with
3.2 ± 0.1 fm recently established by Garrido et al. [79].
The study of the behavior of probability amplitude with respect to the angle
between vectors
p 12 and
p 3 shows that the ground state of
11 Li has a maximum
probability for a configuration when the n–n relative motion and the recoil motion of
9 Li are at right angles to each other in such a way that the halo neutrons when away
from the core are closer and they are far away when closer to the core.
6.3.3 n–n Correlations in 11 Li from Momentum Distributions
One can also find the behavior of longitudinal momentum distributions of
9 Li and
that of the halo neutrons by defining
p = =
p I I + +
p ⊥ . The longitudinal or parallel
momentum distribution of
9 Li is by definition the momentum distribution of
9 Li
in the beam direction in fragmentation reaction of
11 Li beam on a target at certain
beam energy. In the present model, this implies that one should take − → p 3 along beam
direction only and integrate over the solid angle. Thus, longitudinal momentum
distribution of
9 Li is given as:
dN
d p 3I I
=
d p 12 d 12 d 3 p
2
12 |ψ(
p 12 ,
p 3 )|
2
(6.21)