Ab Initio Many-Body Calculations of Nucleon Scattering on 4He, 7Li, 7Be, 12C and 16O Page: 3 of 20
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to Digital Library by the UNT Libraries Government Documents Department.
The following text was automatically extracted from the image on this page using optical character recognition software:
Ab initio many-body calculations of nucleon scattering on 4He, 7Li, 7Be, '2C and 160
Petr Navratil1, Robert Roth2, and Sofia Quaglioni'
'Lawrence Livermore National Laboratory, P.O. Box 808, L-414, Livermore, CA 94551, USA
2lnstitut fur Kernphysik, Technische Universitdt Darmstadt, 64289 Darmstadt, Germany
(Dated: July 1, 2010)
We combine a recently developed ab initio many-body approach capable to describe simultane-
ously both bound and scattering states, the ab initio NCSM/RGM, with an importance truncation
scheme for the cluster eigenstate basis and demostrate its applicability to nuclei with mass numbers
as high as 17. Using soft similarity renormalization group (SRG) evolved chiral nucleon-nucleon
interactions, we first calculate nucleon-4He phase shifts, cross sections and analyzing power. Next,
we investigate nucleon scattering on 7Li, 7Be, 12C and 160 in coupled-channel NCSM/RGM calcula-
tions that include low-lying excited states of these nuclei. We check the convergence of phase shifts
with the basis size and study A = 8, 13, and 17 bound and unbound states. Our calculations predict
low-lying resonances in 8Li and 8B that have not been experimentally clearly identified yet. We are
able to reproduce reasonably well the structure of the A = 13 low lying states. However, we find
that A = 17 states cannot be described without an improved treatment of 160 one-particle-one-hole
excitations and the a clustering.
Nuclei are quantum many-body systems with both
bound and unbound states. A realistic ab initio de-
scription of light nuclei with predictive power must have
the capability to describe both classes of states within
a unified framework. Over the past decade, significant
progress has been made in our understanding of the
properties of the bound states of light nuclei starting
from realistic nucleon-nucleon (NN) interactions, see e.g.
Ref.  and references therein, and more recently also
from NN plus three-nucleon (NNN) interactions [2 4].
The solution of the nuclear many-body problem becomes
more complex when scattering or nuclear reactions are
considered. For A 3 and 4 nucleon systems, the Fad-
deev  and Faddeev-Yakubovsky  as well as the hyper-
spherical harmonics (HH)  or the Alt, Grassberger and
Sandhas (AGS)  methods are applicable and success-
ful. However, ab initio calculations for unbound states
and scattering processes involving more than four nu-
cleons in total are quite challenging. The first ab initio
many-body neutron-4He scattering calculations were per-
formed within the Green's Function Monte Carlo method
using the Argonne NN potential and the Illinois NNN
interaction . Also, resonances in He isotopes were in-
vestigated with some success within the coupled-cluster
method using the Gamow basis .
In a new development, we have recently combined
the ab initio no-core shell model (NCSM)  and the
resonating-group method (RGM) [12 17], into a new
many-body approach [18, 19] (ab initio NCSM/RGM)
capable of treating bound and scattering states of light
nuclei in a unified formalism, starting from fundamen-
tal inter-nucleon interactions. The NCSM is an ab ini-
tio approach to the microscopic calculation of ground
and low-lying excited states of light nuclei with realis-
tic two- and, in general, three-nucleon forces. The RGM
is a microscopic cluster technique based on the use of A-
nucleon Hamiltonians, with fully anti-symmetric many-
body wave functions built assuming that the nucleons are
grouped into clusters. Although most of its applications
are based on the use of binary-cluster wave functions,
the RGM can be formulated for three (and, in principle,
even more) clusters in relative motion . The use of the
harmonic oscillator (HO) basis in the NCSM results in
an incorrect description of the wave-function asymptotic
and a lack of coupling to the continuum. By combining
the NCSM with the RGM, we complement the ability
of the RGM to deal with scattering and reactions with
the use of realistic interactions, and a consistent ab ini-
tio description of the nucleon clusters, achieved via the
NCSM. Presently the NCSM/RGM approach has been
formulated for processes involving binary-cluster systems
only. However, extensions of the approach to include
three-body cluster channels are feasible, also in view
of recent developments on the treatment of both three-
body bound and continuum states (see, e.g., Refs. [20
24]). As described in detail in Refs. [18, 19], the ab
initio NCSM/RGM approach has been already applied
to study the n-3H, n-4He, n-10Be, and p-3,4He scatter-
ing processes, and addressed the parity inversion of the
11Be ground state, using realistic NN potentials. In that
work, we demonstrated convergence of the approach with
increasing basis size in the case of the A 4 and A 5
scattering. The n-10Be calculations were, on the other
hand, perfomed only in a limited basis due to the com-
plexity of the NCSM calculations of the 10Be eigenstates.
It is the purpose of the present paper to expand the ap-
plicability of the NCSM/RGM beyond the lightest nuclei
by using sufficiently large NhQ HO excitations to guar-
antee convergence of the calculation with the HO basis
expansion of both the cluster wave functions and the lo-
calized RGM integration kernels. The use of large NhQ
values is now feasible due to the recent introduction of
the importance truncated (IT) NCSM scheme [25, 26].
It turns out that many of the basis states used in the
NCSM calculations are irrelevant for the description of
any particular eigenstate, e.g., the ground state or a set
Here’s what’s next.
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Navratil, P; Roth, R & Quaglioni, S. Ab Initio Many-Body Calculations of Nucleon Scattering on 4He, 7Li, 7Be, 12C and 16O, article, July 1, 2010; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc871908/m1/3/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.