Physics Letters B 736 (2014) 119–123
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Ab initio path to heavy nuclei
Sven Binder
∗
, Joachim Langhammer, Angelo Calci, Robert Roth
Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstr. 2, 64289 Darmstadt, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received
24 March 2014
Received
in revised form 1 July 2014
Accepted
7 July 2014
Available
online 9 July 2014
Editor:
J.-P. Blaizot
Keywords:
Ab
initio nuclear structure theory
Chiral
effective field theory
Coupled-cluster
theory
Heavy
nuclei
We present the first ab initio calculations of nuclear ground states up into the domain of heavy
nuclei, spanning the range from
16
O to
132
Sn, based on two- plus three-nucleon interactions derived
within chiral effective field theory. We employ the similarity renormalization group for preparing
the Hamiltonian and use coupled-cluster theory to solve the many-body problem for nuclei with closed
sub-shells. Through an analysis of theoretical uncertainties resulting from various truncations in this
framework, we identify and eliminate the technical hurdles that previously inhibited the step beyond
medium-mass nuclei, allowing for reliable validations of nuclear Hamiltonians in the heavy regime.
Following this path we show that chiral Hamiltonians qualitatively reproduce the systematics of nuclear
ground-state energies up to the neutron-rich Sn isotopes.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP
3
.
1. Introduction
Hamiltonians derived within chiral effective field theory [1,2]
represent
a milestone in the endeavor to describe nuclear proper-
ties
in a universal framework based on QCD. Already at the current
stage, chiral two-nucleon (NN) plus three-nucleon (3N) Hamilto-
nians
have successfully been applied in a wide range of ab initio
nuclear
structure [3–10] and reaction calculations [11]. Particu-
larly
the medium-mass regime has seen amazing progress over the
past few years: several ab initio many-body methods can nowa-
days
access this regime. The importance-truncated no-core shell
model [12,13] provides quasi-exact solutions that serve as bench-
mark
points for computationally efficient medium-mass meth-
ods [8].
In addition to its success in quantum chemistry, coupled-
cluster
theory [4,6] has emerged as one of the most efficient and
versatile tools for the accurate computation of (near-)closed-shell
nuclei.
Alternative approaches are the self-consistent Green’s func-
tion
methods [14–16] and the in-medium similarity renormaliza-
tion
group [8,17,18], which also have been generalized to open-
shell
systems. While most of the many-body methods above can be
applied to heavier systems, challenges regarding the preparation of
the Hamiltonian have prevented ab initio theory from entering this
mass range so far.
*
Corresponding author.
E-mail
addresses: sven.binder@physik.tu-darmstadt.de (S. Binder),
joachim.langhammer@physik.tu-darmstadt.de (J. Langhammer),
angelo.calci@physik.tu-darmstadt.de (A. Calci), robert.roth@physik.tu-darmstadt.de
(R. Roth).
In this Letter we overcome these limitations and present ab
initio calculations of nuclei up to
132
Sn using similarity renormal-
ization
group (SRG)-transformed chiral NN + 3N interactions. We
present key developments in the treatment of the Hamiltonian that
enable these calculations, and discuss the remaining uncertainties
due to truncations. For the solution of the many-body problem we
use coupled-cluster (CC) theory including a non-iterative treatment
of triply excited clusters.
2. Preparation of the Hamiltonian
With ab initio nuclear structure theory advancing towards heav-
ier
systems, the preparation of the NN + 3N Hamiltonian prior
to the many-body calculations becomes increasingly important.
We start from the chiral NN interaction at N
3
LO [19] and a lo-
cal
form of the chiral 3N interaction at N
2
LO [20] with regulator
cutoff of 400 MeV/c [13,21,22]. To enhance the convergence be-
havior
of the many-body calculations, we soften this initial Hamil-
tonian
through an SRG transformation, formulated as flow equa-
tion
in terms of a continuous flow parameter α [21,23–25]. The
SRG allows to consistently evolve the NN and 3N interactions [13]
and
yields a model-space independent Hamiltonian. One of the
challenges is the many-body interactions induced during the SRG
flow. For practical reasons we truncate these interactions at the
3N level and consequently violate the unitarity of the transfor-
mation,
which introduces a flow-parameter dependence of ob-
servables.
This α-dependence carries information about the rel-
evance
of omitted many-nucleon interactions and allows conclu-
sions
about their origins and importance. We consider two types
of Hamiltonians in order to distinguish between the effects of
http://dx.doi.org/10.1016/j.physletb.2014.07.010
0370-2693/
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by
SCOAP
3
.
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