Physics Letters B 742 (2015) 285–289
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Deuteron–deuteron scattering above four-nucleon breakup threshold
A. Deltuva
a,∗
, A.C. Fonseca
b
a
Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania
b
Centro de Física Nuclear da Universidade de Lisboa, P-1649-003 Lisboa, Portugal
a r t i c l e i n f o a b s t r a c t
Article history:
Received
26 September 2014
Received
in revised form 11 January 2015
Accepted
29 January 2015
Available
online 3 February 2015
Editor:
J.-P. Blaizot
Keywords:
Four-nucleon
Scattering
Transfer
reactions
Polarization
Deuteron–deuteron elastic scattering and transfer reactions in the energy regime above four-nucleon
breakup threshold are described by solving exact four-particle equations for transition operators. Several
realistic nuclear interaction models are used, including the one with effective many-nucleon forces
generated by the explicit -isobar excitation; the Coulomb force between protons is taken into account as
well. Differential cross sections, deuteron analyzing powers, outgoing nucleon polarization, and deuteron-
to-neutron
polarization transfer coefficients are calculated at 10 MeV deuteron energy. Overall good
agreement with the experimental data is found. The importance of breakup channels is demonstrated.
© 2015 The Authors. 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
.
1. Introduction
The pursuit for numerical solutions of the three- and four-
nucleon
scattering problems has been, since the early seventies of
the last century, one of the most challenging endeavors in nuclear
reaction theory, following the development of formal exact N-body
equations using momentum or configuration space representations
[1,2]. Progress advanced slowly at first and limited to the use of
separable representations of subsystem operators, but with the
advent of powerful computational tools, both in terms of algo-
rithms
(spline interpolation, Padé summation, special integration
meshes and weights, etc.) and hardware advances, three-nucleon
(3N) calculations with realistic nucleon–nucleon (NN) force models
reached state-of-the-art status in the early 1990s due to the effort
of a number of independent groups [3–7]. Due to its higher di-
mensionality
and multichannel complexity, the four-nucleon (4N)
scattering problem took twenty years longer to reach the same
status as the three-nucleon system except for the calculation of
breakup amplitudes. These developments are mainly due to the
works of the Pisa [8–11], Grenoble–Strasbourg [12–15], and Lisbon
[16–19] groups. Because the first two groups use the coordinate-
space
representation, they were able to include, not only realistic
two-body interactions, but also realistic three-body force models.
Nevertheless they have had a major difficulty in calculating mul-
tichannel
reactions and going beyond breakup threshold, particu-
*
Corresponding author.
E-mail
address: arnoldas.deltuva@tfai.vu.lt (A. Deltuva).
larly when the Coulomb interaction is included between protons.
The Lisbon group uses the momentum space Alt, Grassberger and
Sandhas (AGS) equations for transition operators [2] that can be
solved for multichannel reactions both below and above breakup
and with the Coulomb force included. The only stumbling block
has been the inclusion of irreducible three-body forces. As alterna-
tive
the nuclear force model with explicit excitation of a nucleon to
a isobar was used. This coupling generates both effective three-
and
four-nucleon forces (3NF and 4NF) that have been successfully
included in 4N calculations by the Lisbon–Hannover Collaboration
[20].
The calculations using potentials derived from chiral effective
field theory have been performed as well [16,17] but so far includ-
ing
only the NN part of the interaction.
In
the last 40 years progress in nuclear reaction theory has
most often succeeded experimental developments to the point
that, when calculations achieved a solid ground, the instrumen-
tation
that gave rise to the data was no longer in operation.
Therefore inconsistencies between different data cannot anymore
be resolved by repeating the experiments or developing new ones
guided by the theoretical predictions. The 4N scattering problem
has suffered from this much more than the 3N system for the
reasons mentioned above. Nevertheless, new 4N scattering calcula-
tions
are worth pursuing because they lead the way to the solution
on complex multiparticle scattering problems, not just in nuclear
physics but also in cold atom physics [21].
In
this work we present first results for 4N reactions initiated
by the collision of two deuterons (d) at energies above four-particle
breakup threshold. In this energy domain there are a few shallow
resonances [22]; therefore one does not expect the same problems
http://dx.doi.org/10.1016/j.physletb.2015.01.052
0370-2693/
© 2015 The Authors. 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
.
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