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# Research Papers
**Published (newest first)**
Ch. Elster, L. Hlophe, V. Eremenko, F.M. Nunes, I.J. Thompson, G. Arbanas,
J.E. Escher, Separable Potentials
for (d,p) Reaction Calculations [pdf]
(12 Nov 2015)
An important ingredient for applications of nuclear physics
to e.g. astrophysics or nuclear energy are the cross sections for reactions
of neutrons with rare isotopes. Since direct measurements are often not
possible, indirect methods like (d,p) reactions must be used instead. Those
(d,p) reactions may be viewed as effective three-body reactions and
described with Faddeev techniques. An additional challenge posed by
(d,p)reactions involving heavier nuclei is the treatment of the
Coulomb force. To avoid numerical complications in dealing with the
screening of the Coulomb force, recently a new approach using the Coulomb
distorted basis in momentum space was suggested. In order to implement this
suggestion, one needs to derive a separable representation of neutron- and
proton-nucleus optical potentials and compute their matrix elements in this
basis.
I.J. Thompson, J.E. Escher, G. Arbanas, Ch. Elster, V. Eremenko, L. Hlophe,
and F.M. Nunes, One-nucleon
transfers to resonance states [pdf]
(18 June 2015)
We examine the contributions from interior, surface and
exterior parts of the matrix elements for (d,p) neutron-transfer matrix
elements, and show how their sum may be written as interior-post,
exterior-prior terms along with a surface term. If we locate our surface
according to the distance of the transferred neutron to the target, then the
three terms depend on the neutron wave function at specific radii, and the
surface and exterior terms depend only on that part of the neutron wave
function determined by R-matrix parameters for neutron-target scattering.
G. Arbanas, I. J. Thompson, J. E. Escher, Ch. Elster, F. M. Nunes and S.-S.
Zhang, A model of neutron
capture and deuteron stripping on deformed nuclei [pdf]
(16 June 2015)
A coupled channel model of direct neutron capture and
deuteron stripping reactions, which consistently accounts for effects of
nuclear deformations in both reactions, is constructed by coupling all
incoming and outgoing partitions of both reactions to the same set of
collective states. This model is demonstrated using the FRESCO
coupled-channels code [I. J. Thompson, *Comp. Phys. Rep*. 7, 167
(1988)], and it is applied to capture and stripping reactions on even-mass
calcium isotopes ^{40,42,44,46,48}Ca. All incoming and outgoing
partitions in capture and stripping reactions were coupled to 2+, 4+, and 3-
collective states using a consistent set of deformation lengths. Coupling to
these collective states significantly decreases the direct capture cross
section relative to the capture in a spherical model for the nuclides
considered. Similarly, deuteron stripping is approximately cut in half for
the same nuclides. These results suggest that single-particle spectroscopic
factors used in this model of direct capture ought to be refitted by
computing deuteron stripping with coupling to the same collective states.
Shi-Sheng Zhang, Jin-Peng Peng, M. S. Smith, G. Arbanas, and R. L. Kozub,
Exploration of direct neutron capture with covariant density functional theory
inputs [pdf], Phys. Rev. C
91, 045802 (10 April 2015)
Predictions of direct neutron capture are of vital importance
for simulations of nucleosynthesis in supernovae, merging neutron stars, and
other astrophysical environments. We calculated direct capture cross
sections using nuclear structure information obtained from a covariant
density functional theory as input for the fresco coupled reaction channels
code. We investigated the impact of pairing, spectroscopic factors, and
optical potentials on our results to determine a robust method to calculate
cross sections of direct neutron capture on exotic nuclei. Our predictions
agree reasonably well with experimental cross section data for the closed
shell nuclei ^{16}O and ^{48}Ca, and for the exotic nucleus
^{36}S. We then used this approach to calculate the direct neutron
capture cross section on the doubly magic unstable nucleus ^{132}Sn which
is of interest for the astrophysical r-process.
V. Eremenko, N. J. Upadhyay, I.J. Thompson, Ch. Elster, F.M. Nunes, G.
Arbanas, J.E. Escher and L. Hlophe,
Coulomb wave functions in
momentum space [pdf], Computer
Physics Communications, **187**, 195 (2015)
An algorithm to calculate non-relativistic partial-wave Coulomb functions
in momentum space is presented. The arguments are the Sommerfeld parameter
η, the angular momentum l, the asymptotic momentum q and the ‘running’
momentum p, where both momenta are real. Since the partial-wave Coulomb
functions exhibit singular behavior when p → q, different representations of
the Legendre functions of the 2nd kind need to be implemented in computing
the functions for the values of p close to the singularity and far away from
it. The code for the momentum-space Coulomb wave functions is applicable for
values of |η| in the range of 10−1 to 10, and thus is particularly suited
for momentum space calculations of nuclear reactions.
L. Hlophe, V. Eremenko, Ch. Elster, F.M. Nunes, G. Arbanas, J.E. Escher, and
I.J. Thompson,
Separable Representation
of Proton-Nucleus Optical Potentials [pdf],
Phys. Rev C. **90**, 061602(R) (9 Dec 2014)
Recently, a new approach for solving the three-body problem
for (d,p) reactions in the Coulomb-distorted basis in momentum space was
proposed. Important input quantities for such calculations are the
scattering matrix elements for proton- and neutron-nucleus scattering. We
present a generalization of the Ernst-Shakin-Thaler scheme in which a
momentum space separable representation of proton-nucleus scattering matrix
elements can be calculated in the Coulomb basis. The viability of this
method is demonstrated by comparing S-matrix elements obtained for p+^{48}Ca
and p+^{208}Pb for a phenomenological optical potential with
corresponding coordinate space calculations.
N. J. Upadhyay, V. Eremenko, L. Hlophe, F. M. Nunes, Ch. Elster, G. Arbanas,
J. E. Escher, and I. J. Thompson (TORUS Collaboration),
Coulomb problem in momentum space without screening [pdf],
Phys. Rev C. **90**, 014615
(28 July 2014)
**
Background:** The repulsive Coulomb
force poses severe challenges when solving the three-body problem for (d,p)
reactions on intermediate mass and heavy nuclei. Recently, a new approach
based on the Coulomb-distorted basis in momentum space was proposed.
**
**
Purpose: In this work, we demonstrate the feasibility of using the
Coulomb-distorted basis in momentum space for calculating matrix elements
expected in a wide range of nuclear reactions.
**
**
Method: We discuss the analytic forms of the Coulomb wave function in
momentum space. We analyze the singularities in the Coulomb-distorted form
factors and the required regularization techniques. Employing a separable
interaction derived from a realistic nucleon-nucleus optical potential, we
compute and study the Coulomb-distorted form factors for a wide range of
cases, including charge, angular momentum, and energy dependence. We also
investigate in detail the precision of our calculations.
**
**
Results: The Coulomb-distorted form factors differ significantly from
the nuclear form factors except for the very highest momenta. Typically, the
structure of the form factor is shifted away from zero momentum due to the
Coulomb interaction. Unlike the Yamaguchi forms typically used in three-body
methods, our realistic form factors have a short high-momentum tail, which
allows for a safe and efficient truncation of the momentum grid.
**
**
Conclusions: Our results show that the Coulomb-distorted basis can be
effectively implemented.
I.J. Thompson and G. Arbanas,
Coupled-channel Treatment of Isobaric Analog Resonances in (p,p′) Capture
Processes [pdf], Nuclear Data Sheets **118**,
298 (2014)
With the advent of nuclear reactions on unstable isotopes,
there has been a renewed interest in using isobaric analogue resonances (IAR)
as a tool for probing the nuclear structure. The position and width of
isobaric analogue resonances in nucleon-nucleus scattering are accurate and
detailed indicators of the positions of resonances and bound states with
good single-particle characters. We report on implementation within our
coupled-channels code FRESCO of the charge-exchange interaction term that
transforms an incident proton into a neutron. Isobaric analog resonances are
seen as peaks in g-ray spectrum when the proton is transformed into a
neutron at an energy near a neutron bound state. The Lane coupled-channels
formalism was extended to follow the non-orthogonality of this neutron
channel with that configuration of an inelastic outgoing proton, and the
target being left in a particle-hole excited state. This is tested for ^{
208}Pb, for which good (p,p'g) coincidence data exists.
B.V. Carlson, J.E. Escher, and M.S. Hussein,
Theoretical descriptions of
compound-nuclear reactions: open problems & challenges [pdf], J.
Phys. G focus issue on Open Problems in Reaction Theory, **41**, 094003 (15
July 2014)
Compound-nuclear processes play an important role for
nuclear physics applications and are crucial for our understanding of the
nuclear many-body problem. Despite intensive interest in this area, some of
the available theoretical developments have not yet been fully tested and
implemented. We revisit the general theory of compound-nuclear reactions,
discuss descriptions of pre-equilibrium reactions, and consider extensions
that are needed in order to get cross section information from indirect
measurements.
I.J. Thompson,
Computational challenges to the development of modern theories of nuclear
reactions [pdf], J.
Phys. G focus issue on Open Problems in Reaction Theory, **41**, 094009 (15
July 2014)
Detailed theories of nuclear reactions now lead to and
require extensive computations. Only then can their results be used to make
verifiable predictions and to contribute to the development of nuclear
physics. I focus on low-energy reactions of nucleons and light clusters on
heavier nuclei, and discuss the computational challenges in the evaluation
of coupled-channel theories of those reactions.
I.J. Thompson, J.E. Escher and G. Arbanas,
Coupled-Channel Models of Direct-Semidirect Capture via Giant-Dipole Resonances
[pdf], Nuclear Data Sheets **118**,
292 (2014)
Semidirect capture, a two-step process that excites a
giant-dipole resonance followed by its radiative de-excitation, is a
dominant process near giant-dipole resonances, that is, for incoming neutron
energies within 5–20 MeV. At lower energies such processes may affect
neutron capture rates that are relevant to astrophysical nucleosynthesis
models. We implement a semidirect capture model in the coupled-channel
reaction code Fresco and validate it by comparing the cross section for
direct-semidirect capture ^{208}Pb(n,g)^{209}Pb
to experimental data. We also investigate the effect of low-energy electric
dipole strength in the pygmy resonance. We use a conventional
single-particle direct-semidirect capture code Cupido for comparison.
Furthermore, we present and discuss our results for direct-semidirect
capture reaction ^{130}Sn(n,g)^{131}Sn,
the cross section of which is known to have a significant effect on nucleosynthesis models.
J.E. Escher, I.J. Thompson, G. Arbanas, Ch. Elster, V. Eremenko, L. Hlophe,
F.M. Nunes,
Reexamining surface-integral formulations for one-nucleon transfers to bound and
resonance states [pdf],
Phys. Rev C. **89**, 054605
(8 May 2014)
One-nucleon transfer reactions, in particular (d,p)
reactions, have played a central role in nuclear structure studies for many
decades. Present theoretical descriptions of the underlying reaction
mechanisms are insufficient for addressing the challenges and opportunities
that are opening up with new radioactive beam facilities. We investigate a
theoretical approach that was proposed recently to address shortcomings in
the description of transfers to resonance states. The method builds on ideas
from the very successful R-matrix theory; in particular it uses a similar
separation of the parameter space into interior and exterior regions, and
introduces a parameterization that can be related to physical observables,
which, in principle, makes it possible to extract meaningful spectroscopic
information from experiments. We carry out calculations, for a selection of
isotopes and energies, to test the usefulness of the new approach.
L. Hlophe, Ch. Elster, R.C. Johnson, N.J. Upadhyay, F.M. Nunes, G. Arbanas,
V. Eremenko, J.E. Escher, and I.J. Thompson,
Separable Representation of
Phenomenological Optical Potentials of Woods-Saxon Type [pdf],
Phys. Rev C **88**, 064608 (11 Dec 2013)
Background: One important ingredient for many applications of
nuclear physics to astrophysics, nuclear energy, and stockpile stewardship
are cross sections for reactions of neutrons with rare isotopes. Since
direct measurements are often not feasible, indirect methods, e.g. (d,p)
reactions, should be used.} Those (d,p) reactions may be viewed as
three-body reactions and described with Faddeev techniques.
Purpose: Faddeev equations in momentum space have a long tradition of
utilizing separable interactions in order to arrive at sets of coupled
integral equations in one variable. While there exist several separable
representations for the nucleon-nucleon interaction, the optical potential
between a neutron (proton) and a nucleus is not readily available in
separable form. The purpose of this paper is to introduce a separable
representation for complex phenomenological optical potentials of
Woods-Saxon type.
Results: Starting from a global optical potential, a separable
representation thereof is introduced based on the Ernst-Shakin-Thaler (EST)
scheme. This scheme is generalized to non-hermitian potentials. Applications
to n+48Ca, n+132Sn and n+208Pb are investigated for energies from 0 to 50
MeV and the quality of the representation is examined.
Conclusions: We find a good description of the on-shell t-matrix for all
systems with rank up to 5. The required rank depends inversely on the
angular momentum. The resulting separable interaction exhibits a different
off-shell behavior compared to the original potential, reducing the high
momentum contributions.
A. Orazbayev, Ch. Elster, S.P. Weppner,
Open Shell Effects in a Microscopic
Optical Potential for Elastic Scattering of 6(8)He, [pdf]
Phys. Rev C 88,034610 (2013)
Elastic scattering observables (differential cross section
and analyzing power) are calculated for the reaction 6He(p,p)6He at
projectile energies starting at 71 MeV/nucleon. The optical potential needed
to describe the reaction is based on a microscopic Watson first-order
folding potential, which explicitly takes into account that the two neutrons
outside the 4He-core occupy an open p-shell. The folding of the
single-particle harmonic oscillator density matrix with the nucleon-nucleon
t-matrix leads for this case to new terms not present in traditional folding
optical potentials for closed shell nuclei. The effect of those new terms on
the elastic scattering observables is investigated. Furthermore, the
influence of an exponential tail of the p-shell wave functions on the
scattering observables is studied, as well as the sensitivity of the
observables to variations of matter and charge radius. Finally elastic
scattering observables for the reaction 8He(p,p)8He are presented at
selected projectile energies.
T.J. Ross, R.O. Hughes, C.W. Beausang, J.M. Allmond, C.T. Angell, M.S.
Basunia, D.L. Bleuel, J.T. Burke, R.J. Casperson, J.E. Escher, P. Fallon, R.
Hatarik, J. Munson, S. Paschalis, M. Petri, L.W. Phair, J.J. Ressler, and N. D.
Scielzo, Remnants of
spherical shell structures in deformed nuclei: The impact of an N = 64 neutron
subshell closure on the structure of N ≈ 90 gadolinium nuclei, [pdf]
Phys. Rev C **88**, 031301(R) (2013)
Odd-mass gadolinium isotopes around N=90
were populated by the (p,d)
reaction, utilizing 25-MeV protons, resulting in population of low-spin
quasineutron states at energies near and below the Fermi surface.
Systematics of the single quasineutron levels populated are presented. A
large excitation energy gap is observed between levels originating from the
2d_{3/2},
1h_{11/2},
and 3s_{1/2} spherical
parents (above theN=64
gap), and the 2d_{5/2} (below
the gap), indicating that the spherical shell model level spacing is
maintained at least to moderate deformations.
Ch. Elster, A. Orazbayev, S. P. Weppner,
Microscopic Optical Potentials for
Helium-6 Scattering off Protons, [pdf]
Few Body Systems, **54**, 1399 (2013) (13 Jan 2013)
The differential cross section and the analyzing power are
calculated for elastic scattering of^{ 6}He from a proton target
using a microscopic folding optical potential, in which the ^{6}He
nucleus is described in terms of a ^{4}He-core with two additional
neutrons in the valence p-shell. In contrast to previous work of that
nature, all contributions from the interaction of the valence neutrons with
the target protons are taken into account.
M. Gulino, C. Spitaleri, X. D. Tang, G. L. Guardo, L. Lamia, S. Cherubini, B.
Bucher, V. Burjan, M. Couder, P. Davies, R. deBoer, X. Fang, V. Z. Goldberg, Z.
Hons, V. Kroha, L. Lamm, M. La Cognata, C. Li, C. Ma, J. Mrazek, A. M.
Mukhamedzhanov, M. Notani, S. O’Brien, R. G. Pizzone, G. G. Rapisarda, D.
Roberson, M. L. Sergi, W. Tan, I. J. Thompson, and M. Wiescher,
Suppression of the
centrifugal barrier effects in the off-energy-shell neutron + ^{17}O
interaction [pdf], PRC **87**, 012801(R) (4 Jan 2013)
The reaction ^{17}O(n,α)^{14}C
was studied at energies from E_{c.m.}=0
to E_{c.m.}=350 keV
by using the quasifree deuteron breakup in the three-body reaction ^{17}O+d→α+^{14}C+p,
which extended the Trojan Horse indirect method (THM) to neutron-induced
reactions. It is found that the ^{18}O
excited state at E^{*}=8.125±0.002 MeV,
observed in THM experiments, is absent in the direct measurement because of
its high centrifugal barrier. The angular distributions of the populated
resonances have been measured by using this method. The results
unambiguously indicate the ability of the THM to overcome the centrifugal
barrier suppression effect and to pick out the contribution of the bare
nuclear interaction.
T.J. Ross, C.W. Beausang, R.O. Hughes, N.D. Scielzo, J.T. Burke, J.M. Allmond,
C.T. Angell, M.S. Basunia, D.L. Bleuel, R.J. Casperson, J.E. Escher, P. Fallon,
R. Hatarik, J. Munson, S. Paschalis, M. Petri, L. Phair, and J. J. Ressler,
Spectroscopy of ^{88}Y
by the (p,dγ) reaction, [pdf]
PRC **86**, 067301 (4 Dec 2012)
Low-spin, high-excitation energy states in ^{88}Y
have been studied using the^{ 89}Y(p,dγ)
reaction. For this experiment a 25 MeV proton beam was incident upon a
monoisotopic ^{89}Y
target. A silicon telescope array was used to detect deuterons, and
coincident γ rays
were detected using a germanium clover array. Most of the known
low-excitation-energy low-spin states populated strongly via the (p,d)
reaction mechanism are confirmed. Two states are seen for the first time and
seven new transitions, including one which bypasses the two low-lying
isomeric states, are observed.
Ch. Elster, L. Hlophe, Nuclear Reactions: A
Challenge for Few- and Many-Body Theory, Proceedings of the
HITES 2012 Conference,
J. Phys.: Conf. Ser.
403, 012025, arxiv.org/abs/1209.0838
A current interest in nuclear reactions, specifically with
rare isotopes concentrates on their reaction with neutrons, in particular
neutron capture. In order to facilitate reactions with neutrons one must use
indirect methods using deuterons as beam or target of choice. For adding
neutrons, the most common reaction is the (d,p) reaction, in which the
deuteron breaks up and the neutron is captured by the nucleus. Those (d,p) reactions may be viewed as a three-body problem in a many-body context. This
contribution reports on a feasibility study for describing phenomenological
nucleon-nucleus optical potentials in momentum space in a separable form, so that they may be used for Faddeev calculations of (d,p) reactions.
J E Escher, A M Mukhamedzhanov and I J Thompson,
Exploring R-matrix ideas for the
description of one-nucleon transfer reactions, Proceedings of the
HITES 2012 Conference
, J. Phys.: Conf.
Ser. 403 012026
Deuteron-induced reactions, in particular (d,p) one-neutron
transfer reactions, have been used for decades to investigate the structure of
nuclei. These reactions, carried out in inverse kinematics, are expected to play
a central role in the study of weakly-bound systems at modern radioactive beam
facilities. While the theoretical framework and its computational implementation
for describing (d,p) reactions have seen much progress over the decades, open
questions remain and need to be addressed, including the proper treatment of
transfers to resonance states. Recently, a new formalism was proposed [1] that,
in principle, describes transfers to both bound and resonance states. The new
formalism is summarized here and illustrated; implications are discussed.
F.M. Nunes and N.J. Upadhyay, Status of
reaction theory for studying rare isotopes, Proceedings of the
HITES 2012 Conference,
J. Phys.: Conf. Ser.
403, 012029
Reactions are an important tool to study nuclear structure and
for extracting reactions relevant for astrophysics. In this paper we focus on
deuteron induced reactions which can provide information on neutron shell
evolution as well as neutron capture cross sections. We review recent work on
the systematic comparison of the continuum discretized coupled channel method,
the adiabatic wave approximation and the Faddeev momentum-space approach. We
also explore other aspects of the reaction mechanism and discuss in detail
difficulties encountered in the calculations.
M. La Cognata, C. Spitaleri, O. Trippella, G. G. Kiss, G. V. Rogachev, A. M.
Mukhamedzhanov, M. Avila, G. L. Guardo, E. Koshchiy, A. Kuchera, L. Lamia, S. M.
R. Puglia, S. Romano, D. Santiago, and R. Spartŕ,
Measurement of the -3 keV
resonance in the reaction ^{13}C(a,n)^{16}O
of importance in the s-process [pdf], Phys. Rev. Lett.
109, 232701 (4 Dec 2012)
The ^{13}C(α,n)^{16}O
reaction is the neutron source for the main component of the s-process,
responsible for the production of most nuclei in the mass range 90<A<204.
It is active inside the helium-burning shell in asymptotic giant branch
stars, at temperatures <=10^{8} K,
corresponding to an energy interval where the ^{13}C(α,n)^{16}O
is effective from 140 to 230 keV. In this region, the astrophysical S(E)-factor
is dominated by the -3 keV subthreshold resonance due to the 6.356 MeV
level in ^{17+}O,
giving rise to a steep increase of the S(E)-factor.
Notwithstanding that it plays a crucial role in astrophysics, no direct
measurements exist inside the s-process
energy window. The magnitude of its contribution is still controversial as
extrapolations, e.g., through the R matrix
and indirect techniques, such as the asymptotic normalization coefficient
(ANC), yield inconsistent results. The discrepancy amounts to a factor of 3
or more right at astrophysical energies. Therefore, we have applied the
Trojan horse method to the ^{13}C(^{6}Li,n^{16}O)d quasifree
reaction to achieve an experimental estimate of such contribution. For the
first time, the ANC for the 6.356 MeNV level has been deduced through the
Trojan horse method as well as the n-partial
width, allowing to attain an unprecedented accuracy in the ^{13}C(α,n)^{16}O
study. Though a larger ANC for the 6.356 MeV level is measured, our
experimental S(E)-factor
agrees with the most recent extrapolation in the literature in the 140–230 keV
energy interval, the accuracy being greatly enhanced thanks to this
innovative approach.
A.M. Mukhamedzhanov, Coulomb
renormalization and ratio of proton and neutron asymptotic normalization
coefficients for mirror nuclei [pdf]
PRC 86, 044615 (15 Oct 2012)
Asymptotic normalization coefficients (ANCs) are
fundamental nuclear constants playing important role in nuclear reactions,
nuclear structure and nuclear astrophysics. In this paper the physical
reasons of the Coulomb renormalization of the ANC are addressed. Using
Pinkston-Satchler equation the ratio for the proton and neutron ANCs of
mirror nuclei is obtained in terms of the Wronskians from the radial overlap
functions and regular solutions of the two-body Schrödinger
equation with the short-range interaction excluded. This ratio allows one to
use microscopic overlap functions for mirror nuclei in the internal region,
where they are the most accurate, to correctly predict the ratio of the ANCs
for mirror nuclei, which determine the amplitudes of the tails of the
overlap functions. Calculations presented for different nuclei demonstrate
the Coulomb renormalization effects and independence of the ratio of the
nucleon ANCs for mirror nuclei on the channel radius. This ratio is valid
both for bound states and resonances. One of the goals of this paper is to
draw attention on the possibility to use the Coulomb renormalized ANCs
rather than the standard ones especially when the standard ANCs are too
large.
R. L. Kozub, G. Arbanas, A. S. Adekola, D. W. Bardayan, J. C. Blackmon, K.Y.
Chae, K. A. Chipps, J. A. Cizewski, L. Erikson, R. Hatarik, W. R. Hix, K. L.
Jones, W. Krolas, J. F. Liang, Z. Ma, C. Matei, B. H. Moazen, C. D. Nesaraja, S.
D. Pain, D. Shapira, J. F. Shriner, Jr., M. S. Smith, and T. P. Swan, *
Neutron
single particle structure in *^{131}Sn and direct neutron capture cross
sections [pdf], PRL **109**,
172501 (2012).
Recent calculations suggest that the rate of neutron capture by^{
}^{130}Sn
has a significant impact on late-time nucleosynthesis in the r-process.
Direct capture into low-lying bound states is expected to be significant in
neutron capture near the N=82 closed shell, so r- process reaction rates may
be strongly impacted by the properties of neutron single particle states in
this region. In order to investigate these properties, the (d,p)
reaction has been studied in inverse kinematics using a 630 MeV beam of
^{130}Sn
(4.8 MeV/u) and a (CD2)n
target. An array of Si strip
detectors, including the SIDAR and an early implementation of the ORRUBA,
was used to detect reaction products. Results for the ^{
130}Sn(d,p)^{131}Sn
reaction are found to be very similar to those from the previously reported
^{132}Sn(d,
p)^{133}Sn
reaction. Direct-semidirect (n, γ)
cross section calculations, based for the first time on experimental data,
are presented. The uncertainties in these cross sections are thus reduced by
orders of magnitude from previous estimates.
Shi-Sheng Zhang, M. S. Smith, G. Arbanas, and R. L. Kozub,
Structures of exotic
^{131,133}Sn isotopes and effect on r-process nucleosynthesis [pdf], PRC
**86**,
032802 (2012)
Background: Four
strong single-particle bound levels with strikingly similar level spacings
have recently been measured in ^{131}Sn
and ^{133}Sn.
This similarity has not yet been addressed by a theoretical nuclear
structure model. Information on these single-particle bound levels, as well
as on resonant levels above the neutron capture threshold, is also needed to
determine neutron capture cross sections—and corresponding capture reaction
rates—on ^{130,132}Sn.
The ^{130}Sn(n,γ)
rate was shown in a recent sensitivity study to significantly impact the
synthesis of heavy elements in the r-process
in supernovae.
Purpose: Understand
the structure of bound and resonant levels in ^{131,133}Sn,
and determine if the densities of unbound resonant levels are sufficiently
high to warrant statistical model treatments of neutron capture on ^{130,132}Sn.
Method: Single-particle
bound and resonant levels for ^{131,133}Sn
are self-consistently calculated by the analytical continuation of the
coupling constant (ACCC) method based on a relativistic mean field (RMF)
theory with BCS approximation.
Results:We
obtain four strong single-particle bound levels in both ^{131,133}Sn
with an ordering that agrees with experiments and spacings that, while
differing from experiment, are consistent between the Sn isotopes. We also
find at most one single-particle level in the effective energy range for
neutron captures in the r-process.
Conclusions:Our
RMF+ACCC+BCS model successfully reproduces observed single-particle bound
levels in ^{131,133}Sn
and self-consistently predicts single-particle resonant levels with
densities too low for widely used traditional statistical model treatments
of neutron capture cross sections on ^{130,132}Sn
employing Fermi gas level density formulations.
A.M. Mukhamedzhanov, V. Eremenko, A.I. Sattarov,
Generalized Faddeev equations in the
AGS form for deuteron stripping with explicit inclusion of target excitations and
Coulomb interaction [pdf],
PRC **86**, 034001 (2012)
Theoretical description of reactions in general, and the theory for (d,p)
reactions, in particular, needs to advance into the new century. Here
deuteron stripping processes off a target nucleus consisting of A nucleons
are treated within the framework of the few-body integral equations theory.
The generalized Faddeev equations in the AGS form, which take into account
the target excitations, with realistic optical potentials provide the most
advanced and complete description of the deuteron stripping. The main
problem in practical application of such equations is the screening of the
Coulomb potential, which works only for light nuclei. In this paper we
present a new formulation of the Faddeev equations in the AGS form taking
into account the target excitations with explicit inclusion of the Coulomb
interaction. By projecting the (A + 2)-body operators onto target states,
matrix three-body integral equations are derived which allow for the
incorporation of the excited states of the target nucleons. Using the
explicit equations for the partial Coulomb scattering wave functions in the
momentum space we present the AGS equations in the Coulomb distorted wave
representation without screening procedure. We also use the explicit
expression for the off-shell two-body Coulomb scattering T-matrix which is
needed to calculate the effective potentials in the AGS equations. The
integrals containing the off-shell Coulomb T-matrix are regularized to make
the obtained equations suitable for calculations. For NN and nucleon-target
nuclear interactions we assume the separable potentials what significantly
simplifies solution of the AGS equations.
K. T. Schmitt, K. L. Jones, A. Bey, S. H. Ahn, D.W. Bardayan, J.C. Blackmon,
S.M. Brown, K.Y. Chae, K. A. Chipps, J.A. Cizewski, K.I. Hahn, J.J. Kolata, R.L.
Kozub, J.F. Liang, C.Matei, M. Matoš, D. Matyas, B. Moazen, C. Nesaraja, F.M. Nunes,
P.D. O’Malley, S.D. Pain, W.A. Peters, S.T. Pittman, A. Roberts, D. Shapira, J.F.
Shriner, Jr., M.S. Smith, I. Spassova, D.W. Stracener, A.N. Villano, and G.L. Wilson,
Halo Nucleus 11Be: A
Spectroscopic Study via Neutron Transfer [pdf].
(Phys. Rev. Letts, **108**, 192701 (2012))
The best examples of halo nuclei, exotic systems with a diffuse
nuclear cloud surrounding a tightly bound core, are found in the light, neutron-rich
region, where the halo neutrons experience only weak binding and a weak, or
no, potential barrier. Modern direct-reaction measurement techniques provide
powerful probes of the structure of exotic nuclei. Despite more than four decades
of these studies on the benchmark one-neutron halo nucleus ^{11}Be,
the spectroscopic factors for the two bound states remain poorly constrained.
In the present work, the ^{10}Be(d,p)
reaction has been used in inverse kinematics at four beam energies to study
the structure of ^{11}Be.
The spectroscopic factors extracted using the adiabatic model were found to
be consistent across the four measurements and were largely insensitive to the
optical potential used. The extracted spectroscopic factor for a neutron in
an nℓj=2s_{1/2} state coupled to the ground state of ^{10}Beis 0.71(5). For the fist excited state at 0.32 MeV, a spectroscopic factor
of 0.62(4) is found for the halo neutron in a 1p_{1/2}
state.
N. J. Upadhyay, A. Deltuva, F. M. Nunes,
Testing the continuum discretized
coupled channel method for deuteron induced reactions [pdf]
(PRC **85**, 054621, 2012)
The continuum-discretized coupled channels (CDCC) method is a well established
theory for direct nuclear reactions which includes breakup to all orders. Alternatively,
the three-body problem can be solved exactly within the Faddeev formalism which
explicitly includes breakup and transfer channels to all orders. With the aim
to understand how CDCC compares with the exact three-body Faddeev formulation,
we study deuteron- induced reactions on (i) 10Be at Ed = 21.4, 40.9 and 71 MeV;
(ii) 12C at Ed = 12 and 56 MeV; and (iii) 48Ca at Ed = 56 MeV. We calculate
elastic, transfer, and breakup cross sections. Overall, the discrepancies found
for elastic scattering are small with the exception of very backward angles.
For transfer cross sections at low energy, ∼10 MeV/u, CDCC is in good agreement
with the Faddeev-type results and the discrepancy increases with beam energy.
In contrast, breakup observables obtained with CDCC are in good agreement with
Faddeev-type results for all but the lower energies considered here.
T. J. Ross, C. W. Beausang, R. O. Hughes, J. M. Allmond, C. T. Angell. M. S.
Basunia, D. L. Bleuel, J. T. Burke, R. J. Casperson, J. E. Escher, P. Fallon, R.
Hatarik, J. Munson, S. Paschalis, M. Petri, L. Phair, J. J. Ressler, N. D.
Scielzo, and I. J. Thompson,
Measurement of the
entry-spin distribution imparted to the high excitation continuum region of
gadolinium nuclei via (p,d) and (p,t) reactions*
*[pdf],
Phys. Rev. C **85**, 051304(R), (2012)
Over the last several years, the surrogate reaction technique has been
successfully employed to extract (n,f ) and (n,γ ) cross sections in the
actinide region to a precision of ∼5%
and ∼20%,
respectively. However, attempts to apply the technique in the rare earth
region have shown large (factors of 2–3) discrepancies between the directly
measured (n,γ ) and extracted surrogate cross sections. One possible origin
of this discrepancy lies in differences between the initial spin-parity
population distribution in the neutron induced and surrogate reactions. To
address this issue, the angular momentum transfer to the high excitation
energy quasicontinuum region in Gd nuclei has been investigated. The (p,d)
and (p,t) reactions on 154,158Gd at a beam energy of 25 MeV were utilized.
Assuming a single dominant angular momentum transfer component, the measured
angular distribution for the (p,d) reactions is well reproduced by
distorted-wave Born approximation (DWBA) calculations for L
= 4
h ̄ transfer, whereas the (p,t ) reactions are better characterized by L
=
5 h ̄ . A linear combination of DWBA
calculations, weighted according to a distribution of L transfers (peaking
around L =
4–5 h ̄ ), is in excellent agreement with
the experimental angular distributions.
S.P. Weppner, Ch. Elster,
Elastic Scattering of
^{6}He based on a Cluster Description [pdf].
(Phys. Rev. C **85**, 044617 (2012))
Elastic scattering observables (differential cross section and analyzing
power) are calculated for the reaction ^{6}He(p,p)^{6}He at
projectile energies starting at 71 MeV/nucleon. The optical potential needed
to describe the reaction is derived describing ^{6}He in terms of a
^{4}He-core and two neutrons. The Watson first order multiple scattering
ansatz is extended to accommodate the internal dynamics of a composite cluster
model for the ^{6}He nucleus scattering from a nucleon projectile. The
calculations are compared with the recent experiments at the projectile energy
of 71 MeV/nucleon. In addition, differential cross sections and analyzing powers
are calculated at selected higher energies.
P. Capel, H. Esbensen and F.M. Nunes,
Comparing
nonperturbative models of the breakup of neutron-halo nuclei [pdf], Phys. Rev. C
**85**, 044605 (2012)
Breakup reactions of loosely bound nuclei are often used to
extract structure and/or astrophysical information. Here we compare three
nonperturbative reaction theories often used when analyzing breakup
experiments, namely the continuum discretized coupled channel model, the
time-dependent approach relying on a semiclassical approximation, and the
dynamical eikonal approximation. Our test case consists of the breakup of
^{15}C
on Pb at 68 MeV/nucleon and 20 MeV/nucleon.
R. O. Hughes, C. W. Beausang, T. J. Ross, J. T. Burke, N. D. Scielzo, M. S.
Basunia, C. M. Campbell, R. J. Casperson, H. L. Crawford, J. E. Escher, J.
Munson, L. W. Phair, and J. J. Ressler, *
Utilizing (p,d) and
(p,t) reactions to obtain (n,f) cross sections in uranium nuclei via the
surrogate-ratio method *[pdf],
Phys. Rev. C **84**, 024613 (2012)
The surrogate ratio method has been tested for (p,d) and (p,t) reactions
on uranium nuclei. 236U and 238U targets were bombarded with 28-MeV protons
and the light ion recoils and fission fragments were detected using the
Silicon Telescope Array for Reaction Studies detector array at the 88-Inch
Cyclotron at Lawrence Berkeley Na- tional Laboratory. The (p,df ) reaction
channels on 236U and 238U targets were used as a surrogate to determine the
σ [236 U(n,f )]/σ [234 U(n,f )] cross-section ratio. The (p,tf ) reaction
channels were also measured with the same
targetsasasurrogatefortheσ[235U(n,f)]/σ[(233U(n,f)]ratio.Forthe(p,df)and(p,tf)surrogatemeasurements,
there is good agreement with accepted (n,f ) values over equivalent neutron
energy ranges of En = 0–7 MeV and En =
0–5.5 MeV, respectively. An internal surrogate ratio method comparing the (p,d)
and (p,t) reaction channels on a single target is also discussed. The
σ[234U(n,f)]/σ[233U(n,f)] and σ[236U(n,f)]/σ[235U(n,f)] cross-section ratios
are extracted using this method for the 236U and 238U targets, respectively.
The resulting fission cross-section ratios show relatively good agreement
with accepted values up to En ∼
5 MeV.
A.M. Mukhamedzhanov, Theory of deuteron
stripping. From surface integrals to generalized *R*-matrix approach [pdf-v4]
(Phys. Rev. C **84**, 044616 (2011))
There are two main reasons for absence of the practical theory of stripping
to resonance states which could be used by experimental groups: numerical problem
of the convergence of the DWBA matrix element when the full transition operator
is included and it is unclear what spectroscopic information can be extracted
from the analysis of transfer reactions populating the resonance states. The
purpose of this paper is to address both questions. The theory of the deuteron
stripping is developed, which is based on the post continuum discretized coupled
channels (CDCC) formalism going beyond of the DWBA and surface integral formulation
of the reaction theory [A. S. Kadyrov et al., Ann. Phys. **324**, 1516 (2009)].
First, the formalism is developed for the DWBA and then extended to the CDCC
formalism, which is ultimate goal of this work. The CDCC wave function takes
into account not only the initial elastic $d+ A$ channel but also its coupling
to the deuteron breakup channel $p + n + A$ missing in the DWBA. Stripping to
both bound states and resonances are included. The convergence problem for stripping
to resonance states is solved in the post CDCC formalism. The reaction amplitude
is parametrized in terms of the reduced width amplitudes (ANCs), inverse level
matrix, boundary condition and channel radius, that is the same parameters which
are used in the conventional $R$-matrix method. For stripping to resonance states
many-level, one and two-channel cases are considered. The theory provides a
consistent tool to analyze both binary resonant reactions and deuteron stripping
in terms of the same parameters.
N.B.Nguyen, S.J.Waldecker, F.M.Nunes, R.J.Charity, W.H.Dickhoff,
Transfer reactions and
the dispersive optical-model [pdf]
(Phys. Rev. C **84**, 044611 (2011)).
The dispersive optical-model is applied to transfer reactions. A systematic
study of (*d,p*) reactions on closed-shell nuclei using the finite-range
adiabatic reaction model is performed at several beam energies and results are
compared to data as well as to predictions using a standard global optical-potential.
Overall, we find that the dispersive optical-model is able to describe the angular
distributions as well as or better than the global parameterization. In addition,
it also constrains the overlap function. Spectroscopic factors extracted using
the dispersive optical-model are generally lower than those using standard parameters,
exhibit a reduced dependence on beam energy, and are more in line with results
obtained from (*e,e'p*) measurements.
L.J. Titus, P. Capel, F.M. Nunes,
Asymptotic normalization
of mirror states and the effect of couplings [pdf]
(PRC **85**, 035805, 2011)
Assuming that the ratio between asymptotic normalization coefficients
of mirror states is model independent, charge symmetry can be used to indirectly
extract astrophysically relevant proton capture reactions on proton-rich nuclei
based on information on stable isotopes. The assumption has been tested for
light nuclei within the microscopic cluster model. In this work we explore the
Hamiltonian independence of the ratio between asymptotic normalization coefficients
of mirror states when deformation and core excitation is introduced in the system.
For this purpose we consider a phenomenological rotor + N model where the valence
nucleon is subject to a deformed mean field and the core is allowed to excite.
We apply the model to 8Li/8B, 13C/13N, 17O/17F, 23Ne/23Al, and 27Mg/27P. Our
results show that for most studied cases, the ratio between asymptotic normalization
coefficients of mirror states is independent of the strength and multipolarity
of the couplings induced. The exception is for cases in which there is an s-wave
coupled to the ground state of the core, the proton system is loosely bound,
and the states have large admixture with other configurations. We discuss the
implications of our results for novae.
F.M. Nunes and A. Deltuva,
Adiabatic versus Faddeev
for (d,p) and (p,d) reactions [pdf]
(Phys. Rev. C **84**, 034607 (2011))
The finite range adiabatic wave approximation provides a practical
method to analyze (d,p) or (p,d) reactions, however until now the level of accuracy
obtained in the description of the reaction dynamics has not been determined.
In this work, we perform a systematic comparison between the finite range adiabatic
wave approximation and the exact Faddeev method. We include studies of $^{11}$Be(p,d)$^{10}$Be(g.s.)
at $E_p=$5, 10 and 35 MeV; $^{12}$C(d,p)$^{13}$C(g.s.) at $E_d=$7, 12 and 56
MeV and $^{48}$Ca(d,p)$^{49}$Ca(g.s.) at $E_d=$19, 56 and 100 MeV. Results show
that the two methods agree within $\approx 5%$ for a range of beam energies
($E_d \approx 20-40$ MeV) but differences increase significantly for very low
energies and for the highest energies. Our tests show that ADWA agrees best
with Faddeev when the angular momentum transfer is small $\Delta l=0$ and when
the neutron-nucleus system is loosely bound.
M. La Cognata, A.M. Mukhamedzhanov, C. Spitaleri, et al.,
The Fluorine Destruction
In Stars: First Experimental Study Of The ^{19}F(p,a_{0})^{16}O
Reaction at Astrophysical Energies. (Ap.J.Letts, **738**,
L54, 2011)
The ^{19}F(p,a)^{16}O reaction
is an important fluorine destruction channel in the proton-rich outer layers
of asymptotic giant branch (AGB) stars and it might also play a role in hydrogen-deficient
post-AGB star nucleosynthesis. So far, available direct measurements do not
reach the energy region of astrophysical interest (Ecm <~ 300 keV), because
of the hindrance effect of the Coulomb barrier. The Trojan Horse (TH) method
was thus used to access this energy region, by extracting the quasi-free contribution
to the 2H(19F, α16O)n and the 19F(3He, α16O)d reactions. The TH measurement
of the α0 channel shows the presence of resonant structures not observed before,
which cause an increase of the reaction rate at astrophysical temperatures up
to a factor of 1.7, with potential consequences for stellar nucleosynthesis.
A.M. Mukhamedzhanov, L. D. Blokhintsev, B.F. Irgaziev,
Reexamination of the astrophysical
S factor for the α+ d -> ^{6}Li +g reaction (arxiv,
PRC **83**, 055805, 2011)
Recently, a new measurement of the ^{6}Li (150 A MeV)
dissociation in the field of ^{208}Pb has been reported [Hammache
et al., Phys. Rev. C 82, 065803 (2010)]
to study the radiative capture α+d→^{6}Li+γ
process. However, the dominance of the nuclear breakup over the Coulomb one
prevented the information about the α+d→^{6}Li+γ
process from being obtained from the breakup data. The astrophysical
S_{24}(E)
factor has been calculated within the α-d
two-body potential model with potentials determined from the fits to the
α-d
elastic scattering phase shifts. However, the scattering phase shift, according
to the theorem of the inverse scattering problem, does not provide a unique
α-d
bound-state potential, which is the most crucial input when calculating the
S_{24}(E)
astrophysical factor at astrophysical energies. In this work, we emphasize the
important role of the asymptotic normalization coefficient (ANC) for ^{6}Li→α+d,
which controls the overall normalization of the peripheral
α+d→^{6}Li+γ
process and is determined by the adopted α-d
bound-state potential. Since the potential determined from the elastic scattering
data fit is not unique, the same is true for the ANC generated by the adopted
potential. However, a unique ANC can be found directly from the elastic scattering
phase shift, without invoking intermediate potential, by extrapolation the scattering
phase shift to the bound-state pole [Blokhintsev
et al., Phys. Rev. C 48, 2390 (1993)].
We demonstrate that the ANC previously determined from the
α-d
elastic scattering s-wave phase shift
[Blokhintsev et al., Phys.
Rev. C 48, 2390 (1993)], confirmed
by ab initio calculations, gives
S_{24}(E),
which at low energies is about 38% less
than the other one reported [Hammache
et al., Phys. Rev. C
82, 065803 (2010)]. We recalculate
also the reaction rates, which are lower than those obtained in that same study
[Hammache
et al., Phys. Rev. C
82, 065803 (2010)].
F.M. Nunes, A. Deltuva, and June Hong,
Improved description of ^{34;36;46}Ar(p,d)
transfer reactions (Phys. Rev. C **83**, 034610 (2011)).
An improved description of single neutron stripping from
^{34;36;46}Ar beams at 33 MeV/nucleon by a hydrogen target is presented
and the dependence on the neutron-proton asymmetry of the spectroscopic factors
is further investigated. A finite range adiabatic model is used in the analysis
and compared to previous zero range and local energy approximations. Full three-body
Faddeev calculations are performed to estimate the error in the reaction theory.
In addition, errors from the optical potentials are also evaluated. From our
new spectroscopic factors extracted from transfer, it is possible to corroborate
the neutron-proton asymmetry dependence reported from knockout measurements.
A.M. Mukhamedzhanov and A.S. Kadyrov,
Unitary correlation in nuclear
reaction theory: divorce of reaction theory and spectroscopic factors (PRC
**82**,
051601(R), 2011)
Future exact many-body theory will allow us to calculate nuclear
reactions based on the adopted NN and many-body nuclear potentials. But NN potentials
are not observable and there are infinite number of the phase-equivalent NN
potentials related via finite-range unitary transformations. We show that asymptotic
normalization coefficients, which are the amplitudes of the asymptotic tails
of the overlap functions are invariant under finite-range unitary transformations
but spectroscopic factors are not. We prove also that the exact amplitudes for
the (d,p), (d,pn) and (e, e′p) reactions determining the asymptotic behavior
of the exact scattering wave functions in the corresponding channels, in contrast
to spectroscopic factors, are invariant under finite-range unitary transformations.
Moreover, the exact reaction amplitudes are not parametrized in terms of the
spectroscopic factors and nuclear reactions in the exact approach cannot provide
a tool to determine spectroscopic factors which are not observable.
**Preprints**
Ch. Elster, L. Hlophe, V. Eremenko, F.M. Nunes, G. Arbanas, J.E. Escher, I.J.
Thompson, Separable Optical
Potentials for (d,p) Reactions [pdf],
Contribution to the Proceedings of the International Conference on Nuclear
Theory in the Supercomputing Era (NTSE 2014)
An important ingredient for applications of nuclear
physics to e.g. astrophysics or nuclear energy are the cross sections for
reactions of neutrons with rare isotopes. Since direct measurements are
often not possible, indirect methods like (d,p) reactions must be used
instead. Those (d,p) reactions may be viewed as effective three-body
reactions and described with Faddeev techniques. An additional challenge
posed by (d,p) reactions involving heavier nuclei is the treatment of the
Coulomb force. To avoid numerical complications in dealing with the
screening of the Coulomb force, recently a new approach using the Coulomb
distorted basis in momentum space was suggested. In order to implement this
suggestion, one needs not only to derive a separable representation of
neutron- and proton-nucleus optical potentials, but also compute the Coulomb
distorted form factors in this basis..
**Review Papers**
F. Nunes,
Continuum-Discretised Coupled Channels methods (Scholarpedia)
One of the most common methods to study rare isotopes with
large proton/neutron asymmetry, is through breakup reactions. These exotic
nuclei are so loosely bound they can break up very easily while leaving
the target in its ground state. While the first efforts to study breakup
assumed the process could be treated perturbatively, it was soon realized
that multi-step effects are important. Also, it is not simple to isolate
Coulomb effects from nuclear effects. A non perturbative method that treats
breakup to all orders, and includes Coulomb and nuclear effects on equal
footing is the Continuum discretized coupled channel method (CDCC). Over
the last two decades this method has become increasingly popular. Here we
present the method as it was originally introduced, address implementation
aspects and provide some applications. We also discuss limitations of the
method as well as new developments that allow to solve more complicated
problems.
**Related Research Papers**
P. Capel and P. Danielewicz and F. M. Nunes,
Deducing spectroscopic
factors from wave-function asymptotics
In a coupled-channel model, we explore the effects of coupling
between configurations on the radial behavior of the wave function and,
in particular, on the spectroscopic factor (SF) and the asymptotic normalization
coefficient (ANC). We evaluate the extraction of a SF from the ratio of
the ANC of the coupled-channel model to that of a single-particle approximation
of the wave function. We perform this study within a core+n collective model,
which includes two states of the core that connect by a rotational coupling.
To get additional insights, we also use a simplified model that takes a
δ function for the coupling potential. Calculations are performed for11Be.
Fair agreement is obtained between the SF inferred from the single-particle
approximation and the one obtained within the coupled-channel models. Significant
discrepancies are observed only for large coupling strength and/or large
admixture, that is, a small SF. This suggests that reliable SFs can be deduced
from the wave-function asymptotics when the structure is dominated by one
configuration, that is, for a large SF. |