6.2 11 Li Halo Nucleus as a Three-Body System …
71
Table 6.1 Parameters of the two-body input potentials
B E of 11 Li (MeV)
β/α
λ n /α 3
β 1 /α
λ c /α 3
λ c /α 3 from three body
0.34
5.8
18.6
5.0
10.32
12.92
6.255
23.4
5.0
10.32
12.91
5.8
18.6
5.5
14.00
17.01
0.20
5.8
18.6
5.0
10.32
12.39
5.8
18.6
5.5
14.00
16.38
Given the 11 Li binding energy, the strength parameter as obtained from the three-body equation is
matched with the corresponding value obtained from the two-body analysis
the results appear to be sensitive to the range parameter β 1 for the n
9 Li interaction,
whereas the corresponding parameter β for the n–n interaction is found to be not so
sensitive.
The solutions of the spectator functions F(P) and G(P) satisfying the integral
Eq. (4.26) describe the momentum distribution of the ‘spectator’ particles, i.e., of
the
9 Li core and of the halo neutron in the presence of the other two particles.
Figures 6.1 and 6.2 depict the behavior of F(p c ) and G(p 1 ) for the core and the halo
neutron, respectively, as plotted against their respective momenta in the laboratory
frame. The total laboratory momentum P L (= p c + p 1 + p 2 ) was chosen to correspond to a
11 Li projectile energy of 66 MeV/nucleon [67]. Experimentally, it has
been established that high-energy fragmentation of light nuclei closely reveals the
ground state momentum distribution of such fragments. Specifically, a large spatial
extent of the halo must be related, via the uncertainty relation, to a narrow momentum
spread. It has been experimentally observed that the momentum distribution of
9 Li
Fig. 6.1 Plot of the
spectator function F(p c ) (in
arb. Units) versus p c —the
9 Li core momentum in the
laboratory frame
71
Table 6.1 Parameters of the two-body input potentials
B E of 11 Li (MeV)
β/α
λ n /α 3
β 1 /α
λ c /α 3
λ c /α 3 from three body
0.34
5.8
18.6
5.0
10.32
12.92
6.255
23.4
5.0
10.32
12.91
5.8
18.6
5.5
14.00
17.01
0.20
5.8
18.6
5.0
10.32
12.39
5.8
18.6
5.5
14.00
16.38
Given the 11 Li binding energy, the strength parameter as obtained from the three-body equation is
matched with the corresponding value obtained from the two-body analysis
the results appear to be sensitive to the range parameter β 1 for the n
9 Li interaction,
whereas the corresponding parameter β for the n–n interaction is found to be not so
sensitive.
The solutions of the spectator functions F(P) and G(P) satisfying the integral
Eq. (4.26) describe the momentum distribution of the ‘spectator’ particles, i.e., of
the
9 Li core and of the halo neutron in the presence of the other two particles.
Figures 6.1 and 6.2 depict the behavior of F(p c ) and G(p 1 ) for the core and the halo
neutron, respectively, as plotted against their respective momenta in the laboratory
frame. The total laboratory momentum P L (= p c + p 1 + p 2 ) was chosen to correspond to a
11 Li projectile energy of 66 MeV/nucleon [67]. Experimentally, it has
been established that high-energy fragmentation of light nuclei closely reveals the
ground state momentum distribution of such fragments. Specifically, a large spatial
extent of the halo must be related, via the uncertainty relation, to a narrow momentum
spread. It has been experimentally observed that the momentum distribution of
9 Li
Fig. 6.1 Plot of the
spectator function F(p c ) (in
arb. Units) versus p c —the
9 Li core momentum in the
laboratory frame