4.4 Derivation of Three-Body Scattering Amplitude …
55
Z 1 ( p, k; E) =
1
pk
ln
p
2
/2a + k
2
/2a + pk − m E
P 2 /2a + k 2 /2a − pk − m E
,
Z 2 ( p, k; E) =
1
pk
ln
p
2
+ k
2
/2a + pk − m E
p 2 + k 2 /2a − pk − m E
,
Z 3 ( p, k; E) =
1
pk
ln
k
2
+ p
2
/2a + kp − m E
k 2 + p 2 /2a − kp − m E
(4.46)
Having derived these equations for the n-dimer scattering amplitude within the
framework of effective field theory, we defer further discussion on the computational
work including the subtraction procedure to the subsequent Chap. 6 on halo nuclei.
There we study the bound state properties of
20 C as a three-body (n–n–
18 C) bound
state and n–
19 C scattering using separable potential at low energies and find some
exciting results. It would, therefore, be interesting to undertake a comparative study
to see, using effective field theory, how far these results are model independent.
55
Z 1 ( p, k; E) =
1
pk
ln
p
2
/2a + k
2
/2a + pk − m E
P 2 /2a + k 2 /2a − pk − m E
,
Z 2 ( p, k; E) =
1
pk
ln
p
2
+ k
2
/2a + pk − m E
p 2 + k 2 /2a − pk − m E
,
Z 3 ( p, k; E) =
1
pk
ln
k
2
+ p
2
/2a + kp − m E
k 2 + p 2 /2a − kp − m E
(4.46)
Having derived these equations for the n-dimer scattering amplitude within the
framework of effective field theory, we defer further discussion on the computational
work including the subtraction procedure to the subsequent Chap. 6 on halo nuclei.
There we study the bound state properties of
20 C as a three-body (n–n–
18 C) bound
state and n–
19 C scattering using separable potential at low energies and find some
exciting results. It would, therefore, be interesting to undertake a comparative study
to see, using effective field theory, how far these results are model independent.