Physics Letters B 769 (2017) 227–232
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Resonance and continuum Gamow shell model with realistic nuclear
forces
Z.H. Sun, Q. Wu, Z.H. Zhao, B.S. Hu, S.J. Dai, F.R. Xu
∗
School of Physics, and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
11 November 2016
Received
in revised form 21 March 2017
Accepted
21 March 2017
Available
online 30 March 2017
Editor:
J.-P. Blaizot
Keywords:
Realistic
nuclear forces
Gamow
shell model
Unstable
nuclei
Spectra
Resonance
Continuum
Starting from realistic nuclear forces, we have developed a core Gamow shell model which can describe
resonance and continuum properties of loosely-bound or unbound nuclear systems. To describe properly
resonance and continuum, the Berggren representation has been employed, which treats bound, resonant
and continuum states on equal footing in a complex-momentum (complex-k) plane. To derive the model-
space
effective interaction based on realistic forces, the full
ˆ
Q -box folded-diagram renormalization has
been, for the first time, extended to the nondegenerate complex-k space. The CD-Bonn potential is
softened by using the V
low-k
method. Choosing
16
O as the inert core, we have calculated sd-shell neutron-
rich
oxygen isotopes, giving good descriptions of both bound and resonant states. The isotopes
25,26
O are
calculated to be resonant even in their ground states.
© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
Resonance is a general phenomenon happening in classic or
quantum systems. It plays a special role in weakly-bound or un-
bound
quantum systems. An unbound quantum system, such as
atomic cluster or unbound nucleus, can emerge in the form of in-
trinsic
resonance. Nuclear resonances are usually followed by par-
ticle
emissions as the Gamow quantum tunneling. Weakly-bound
or unbound nuclei are complex open quantum systems (OQS) in
which the coupling to the scattering continuum is crucial and
should be properly treated. A small uncertainty in modeling would
change the conclusions of physics.
In
the standard shell model (SM), harmonic oscillator (HO)
wave functions are always bound and localized, while a loosely-
bound
nucleus has small separation energy and large spatial
spread, in which the continuum plays a critical role. To over-
come
the shortcoming of the conventional SM, the continuum
shell model (CSM) [1–3] has been developed, taking into account
the continuum effect by projecting the model space onto the sub-
spaces
of bound and scattering states in a real-energy basis. The
continuum effect has also been well treated in the continuum cou-
pled
cluster [4] and the continuum-coupled shell model [5].
The
Gamow resonance is in fact a time-dependent problem, as-
sociated
with a decaying process. However, the exact treatment of
the time-dependent problem is difficult. Berggren generalized the
*
Corresponding author.
E-mail
address: frxu@pku.edu.cn (F.R. Xu).
time-independent Schrödinger equation to a complex-k plane, giv-
ing
single-particle (SP) bound states, unbound resonant states and
nonresonant continuum states [6]. The three types of the SP states
construct a complete set of basis states, called the Berggren en-
semble
[6]. Using the Berggren basis, the so-called Gamow shell
model (GSM) has been advanced recently. With phenomenologi-
cal
interactions, the GSM has been successfully applied to nuclear
structure calculations [7–10].
It
is pursued currently to perform the first-principles calcula-
tions
of nuclear structure. Such calculations require two funda-
mental
elements: (i) using realistic nuclear forces and (ii) rigor-
ously
treating many-body correlations. The shell model which is
beyond mean-field approach provides a good platform to handle
many-body correlations. Starting from realistic forces, traditional
core shell model [11,12] or no core shell model (NCSM) calcula-
tions
[13] have obtained great success, while the GSM calculation
faces big challenges. For example, the wave functions of resonant
SP states are not square integrable, which complicates severely the
treatments of the complex non-Hermitian Hamiltonian and other
mechanical quantities. It is even more challenging to establish a
GSM based on realistic nuclear forces with an inert core. In this
case, one has to strive to build the model-space effective interac-
tion
in the complex-k basis. Nevertheless, the realistic core GSM
(CGSM) calculation has been proposed with limit to two- or three-
particle
systems [14,15]. The effective interaction was built by us-
ing
the degenerate
ˆ
Q -box approach but neglecting folded diagrams
http://dx.doi.org/10.1016/j.physletb.2017.03.054
0370-2693/
© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
资源评论
