Ab Initio Many-Body Calculations Of n-3H, n-4He, p-3,4He, And n-10Be Scattering Page: 4 of 6
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n-3H (Ek1n = 0.75 MeV)
i+ (3S1) 1- (1p1)
Nmax
9
11
13
15
17
19
Nmax
9
11
13
15
173H
Eg.s.
-7.80
-7.96
-8.02
-8.11
-8.12
-8.16
4He
Eg.s.
-27.00
-27.41
-27.57
-27.75
-27.770+ (1s0)
-27.8
-31.3
-32.4
-33.2
-34.2
-34.81 (3p 1)
4.96
5.93
6.17
6.12
6.30
6.491- (E) 2+ (3P2)
17.5
12.7
-9.1
-9.5
10.7
10.17.51
6.42
5.75
6.08
6.19
6.02at
1.06
1.20
1.25
1.33
1.41
1.440- (3po)
2.30
2.39
2.15
2.45
2.60
2.49TABLE I: Calculated 3H and 4He g.s. energies (in MeV), n-3H, n-4He and p-4He phase shifts (in degrees), and n-3H and
n-4He total cross sections (in barns) for increasing Nmax at hQ = 18 MeV, obtained using the Vo,0k NN potential (derived
from AV18 with cutoff A = 2.1 fm-1) [8]. Only the g.s. of the 3H and 4He nuclei were included in the scattering calculations.by the maximum number, Nmax, of HO quanta above
the lowest configuration shared by the nucleons. Thanks
to the unique properties of the HO basis, we can make
use of Jacobi-coordinate wave functions [4] for both nu-
clei or only for the lightest of the pair (typically a < 4),
and still preserve the translational invariance of the prob-
lem. In the second case we expand the heavier cluster on
a Slater-determinant (SD) basis, and remove completely
the spurious c.m. components in a similar fashion as in
Refs. [5, 6]. We exploited this dual approach to verify our
results. The use of the SD basis is computationally ad-
vantageous and allows us to explore reactions involving p-
shell nuclei. In calculating (4), all "direct" terms arising
from the identical permutations in both A~ and A,,, are
treated exactly with the exception of (<DKT I Vrel 1< ,).
The latter and all remaining terms are obtained by ex-
panding the Dirac 6 of Eq. (2) on a set of HO radial
wave functions with identical frequency Q, and model-
space size Nmax consistent with those used for the two
clusters. In this respect we note that Vreu is localized
also in presence of the Coulomb force. We solve Eq. (3)
by means of the coupled-channel R-matrix method on a
Lagrange mesh [7] imposing either bound-state or scat-
tering boundary conditions for glrT(r) at large r.
All calculations in the present paper were carried out
using binary-cluster channels (2) with a 1. We first dis-
cuss results obtained limiting the expansion (1) to config-
urations with the (A - 1)-cluster in its g.s. Table I shows
the behavior with respect to Nmax of selected A 4, 5
data obtained using the V10,, NN potential [8]. A satis-
factory convergence of both g.s. energies and scattering
data is reached starting from Nmax 17, for the four-,
and Nmax 15 for the five-nucleon systems, respectively.In what follows we present results obtained using ef-
fective interactions derived from the underlying realis-
tic NN potential, VN, through a unitary transformation.
Starting from the relevant two-nucleon Hamiltonian (for
notation and definitions see Ref. [4]) H = Ho2 + V12,
with V12 VN( 2) --Q m252/A, the cluster eigenstates
are obtained employing the usual NCSM two-body effec-
tive interaction V2eff H2eff - Ho2, where H2eff is the20
L 10tA
Lv49
30
15
0-30
-60- 3P +
---
3P1 +
+
- . Nmq -
""13
15
-- 17
- 19
f. flf2 = 22 MeV
10 -0 1 2 3 4 5
Eki~ [MeV]1P1
- + + . 3 -
. - .
- - -
+
+. n +3H .
- 3p + .. - -
. + .
- .* N3LO~
- s -0 1 2 3 4 5
Eki~ [MeV]6
FIG. 1: (Color online.) Calculated phase shifts for n -3H scat-
tering as a function of the relative kinetic energy in the c.m.
frame Ekin, using the N3LO NN potential [9]. Only the g.s.
of the (A - 1)-cluster was included in the present calculation.
Dependence on the model-space truncation Nmax at h?= 22
MeV compared to AGS results of Ref. [10, 11].2.19
2.63
3.10
3.46
3.74
4.00
at
1.95
1.98
1.98
1.97
1.97p-41He (Ein = 5.0 MeV)
2+ (251/2) 2 (2p1/2) 2 (2p3/2)
-45.8 31.3 76.5
-46.4 31.9 80.2
-46.6 32.0 80.0
-46.6 32.1 79.9
-46.5 32.0 79.92
n-41He (Eun = 5.0 MeV)
+ (2$1/2) 2 (2P1/2) 2 (2P3/2)
-57.9 33.5 81.8
-58.6 33.7 86.1
-58.7 34.0 85.7
-58.7 33.9 84.6
-58.6 33.9 84.826.2
28.1
28.8
29.9
30.9
31.3
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Quaglioni, S & Navratil, P. Ab Initio Many-Body Calculations Of n-3H, n-4He, p-3,4He, And n-10Be Scattering, article, March 26, 2008; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc902262/m1/4/: accessed May 13, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.