A comparison of DWBA and coupled channels in the 2s-1d shell
DWBA optical model coupled channels comparison in 2s-1d shell for predicting proton scattering elastic cross sections
Ascuitto, R. J.↗
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A comparison of DWBA and coupled channels in the 2s-1d shell
Comparing coupled channels and distorted wave Born approximation optical model parameters in 2s-1d shell to investigate inelastic nucleon scattering
Ascuitto, R. J.↗
Three-body Faddeev equations in two-particle Alt-Grassberger-Sandhas form with Distorted-Wave-Born-approximation amplitudes as effective potentials
A(d, p)B reactions on heavier nuclei are peripheral at sub-Coulomb energies and can be peripheral even at energies above the Coulomb barrier due to the presence of the distorted waves in the initial and final channels. Usually, to analyze such reactions the distorted-wave-Born-approximation (DWBA) is used. The DWBA amplitude for peripheral reactions is parametrized in terms of the asymptotic normalization coefficient (ANC) of the bound state B = (n A). However, in the DWBA, the coupling of the different channels is not taken into account explicitly. The three-body Faddeev equations written as the two-particle Alt-Grassberger-Sandhas (AGS) equations are very suitable for the analysis of the A(d, p)B reactions because they take into account explicitly the coupling of the different channels. It is well known that the overall normalization of the DWBA amplitude or even of the more advanced continuum-discretized coupled channels (CDCC) amplitude for peripheral reactions (both sub-Coulomb and above the Coulomb barrier) is determined by the ANC. However, it is not apparent that it is the case for the AGS solution due to the coupling of the (d, p) channel to other channels. In this paper, it is proved that the sub-Coulomb A(d, p)B reaction amplitude, which is a solution of the two-body AGS equations, is peripheral and is parametrized in terms of the ANC of the bound state B = (nA) if the corresponding DWBA amplitude is peripheral. Both nonlocal separable and local nuclear interaction potentials between the constituent particles are considered. To prove the peripheral character of the AGS amplitude for the sub-Coulomb A(d, p)B reactions the effective potentials are expressed in terms of the corresponding sub-Coulomb DWBA amplitudes of the different channels. The analysis of the A(d, p)B reactions above the Coulomb barrier requires the inclusion of the optical potentials. Hence, to analyze such reactions, the AGS equations are generalized by including the optical nuclear potentials in the same manner as it is done in the DWBA. The obtained AGS equations contain the DWBA effective potentials with distorted waves generated by the sum of the nuclear optical and the channel Coulomb potentials. It is shown that if the DWBA amplitude is peripheral than it is also the case for the AGS amplitude, which is also parametrized in terms of the ANC of the bound state B = (nA). Furthermore, the inclusion of the coupling of the different channels in the AGS formalism allows one to improve the treatment of the peripheral sub-Coulomb and above the Coulomb (d, p) reactions compared to the DWBA and CDCC method.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Uncertainty quantification due to optical potentials in models for ( d , p ) reactions
Recent work has studied the uncertainty in predictions for $A(d,p)B$ reactions using the distorted-wave Born approximation (DWBA), coming from the parametrization of the effective $dA$ interactions [Lovell et al. Phys. Rev. C 95, 024611 (2017)]. There are different levels of sophistication in reaction theories for one-nucleon transfer reactions, including the adiabatic wave approximation (ADWA) which takes deuteron breakup into account to all orders. In this paper, we quantify the uncertainties associated with the ADWA method that come from the parametrization of the NA interactions and compare ADWA with DWBA. Similar to Lovell et al., we use nucleon elastic-scattering data on a wide variety of targets at the appropriate incoming and outgoing energies to constrain the optical potential input to the ADWA theory. Pulling from the χ 2 distribution, we obtain 95% confidence bands for the elastic distributions. From the resulting parameters, we predict 95% confidence bands for the ( d , p ) transfer cross sections. Results obtained with the standard uncorrelated χ 2 are compared to those using the correlated χ 2 of Lovell et al. We also repeat the DWBA calculations for the exact same reactions for comparison purposes. We find that NA elastic-scattering data provide a significant constraint to the interactions, and, when the uncertainties are propagated to the transfer reactions using ADWA, predictions are consistent with the transfer data. The angular distributions for ADWA differ from those predicted by DWBA, particularly at small angles. As in Lovell et al., confidence bands obtained using the uncorrelated χ 2 function are unrealistically narrow and become much wider when the correlated χ 2 function is considered. For most cases, the uncertainty bands obtained in ADWA are narrower than DWBA when using elastic data of similar quality and range. However, given the large uncertainties predicted from the correlated χ 2 function, at this point, the transfer data cannot discriminate between these two methods.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Distorted-wave born approximation calculations for turbulence scattering in an upward-refracting atmosphere
Weiner and Keast observed that in an upward-refracting atmosphere, the relative sound pressure level versus range follows a characteristic 'step' function. The observed step function has recently been predicted qualitatively and quantitatively by including the effects of small-scale turbulence in a parabolic equation (PE) calculation. (Gilbert et al., J. Acoust. Soc. Am. 87, 2428-2437 (1990)). The PE results to single-scattering calculations based on the distorted-wave Born approximation (DWBA) are compared. The purpose is to obtain a better understanding of the physical mechanisms that produce the step-function. The PE calculations and DWBA calculations are compared to each other and to the data of Weiner and Keast for upwind propagation (strong upward refraction) and crosswind propagation (weak upward refraction) at frequencies of 424 Hz and 848 Hz. The DWBA calculations, which include only single scattering from turbulence, agree with the PE calculations and with the data in all cases except for upwind propagation at 848 Hz. Consequently, it appears that in all cases except one, the observed step function can be understood in terms of single scattering from an upward-refracted 'skywave' into the refractive shadow zone. For upwind propagation at 848 Hz, the DWBA calculation gives levels in the shadow zone that are much below both the PE and the data.
Gilbert, Kenneth E.↗
Analytical Proton Transfer Amplitude for Heavy Ion Induced Nuclear Reactions
Direct reactions between heavy ions have been studied widely using semi-classical theories. The Distorted Wave Born Approximation or DWBA has been extensively applied to analyse transfer reaction processes. Initial attempts to gain insights into the simple semi-classical parametrisation starting from the DWBA had focused mainly on neutron transfer reactions. An analytical formula for the semi-classical amplitude for the transfer of a single neutron between bound classical orbits states in heavy ion collisions that agrees well with the DWBA calculations has been successfully derived. In this paper, we have successfully derived the corresponding analytical expression for the proton transfer amplitude by using a technique analogous to the transfer of a single neutron between bound states. Our result reduces to the well known expression for the neutron transfer amplitude in the limit that the nuclear charge tends to zero.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Core excitation effects in the breakup of halo nuclei
The role of core excitation in the structure and dynamics of two-body halo nuclei is investigated. We present calculations for the resonant breakup of {sup 11}Be on protons at an incident energy of 63.7 MeV/nucleon, where core excitation effects were shown to be important. To describe the reaction, we use a recently developed extension of the DWBA formalism which incorporates these core excitation effects within the no-recoil approximation. The validity of the no-recoil approximation is also examined by comparing with DWBA calculations which take into account core recoil. In addition, calculations with two different continuum representations are presented and compared.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Neutrino-induced reactions and neutrino scattering with nuclei in low and high neutrino energy
We reviewed present status regarding theoretical approaches for neutrino-induced reactions and neutrino scattering. With a short introduction of relevant data, our recent calculations by distorted-wave Born approximation (DWBA) for quasielastic region are presented for MiniBooNE data. We also discussed that one step-process estimated by the DWBA is comparable to the two-step process, which has been usually used in the neutrino-nucleosynthesis. For much higher energy neutrino data, such as NOMAD data, elementary process approach was shown to be useful instead of using complicated nuclear models. But, in the low energy region, detailed nuclear structure model, such as QRPA and shell model, turn out to be inescapable to explain the reaction data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
High-resolution measurement of the {sup 118,124}Sn(p,t){sup 116,122}Sn reactions: Shell-model and microscopic distorted-wave Born approximation calculations
The {sup 118,124}Sn(p,t){sup 116,122}Sn reactions have been investigated in high-resolution experiments at incident proton energies of 24.6 and 25 MeV, respectively. Angular distributions for 55 transitions to levels of {sup 116}Sn and 63 transitions to levels of {sup 122}Sn, up to excitation energies of {approx}3.850 and {approx}4.000 MeV, respectively, have been measured. The spin and parity identification was carried out by means of a distorted-wave Born approximation (DWBA) analysis, performed by using conventional Woods-Saxon potentials. A shell-model study of {sup 116}Sn and {sup 122}Sn nuclei was performed using a realistic two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential. The doubly magic nucleus {sup 132}Sn was assumed as a closed core, with the 16 and 10 valence neutron holes occupying the five levels of the 50-82 shell. The energy spectra have been calculated and compared with the experimental ones, and the theoretical two-nucleon spectroscopic amplitudes, evaluated in a truncated seniority space, have been used in the microscopic DWBA calculation of some cross-section angular distributions of both reactions.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Effects of the Grazing Incidence Geometry on X-ray Photon Correlation Spectroscopy Measurements
X-ray photon correlation spectroscopy (XPCS) is a versatile tool to measure dynamics on the nanometer to micrometer scale in bulk samples. XPCS has also been applied in grazing incidence (GI) geometry to examine the dynamics of surface layers. However, considering GI scattering experiments more universally, the GI geometry leads to a superposition of signals due to reflection and refraction effects, also known from the distorted-wave Born approximation (DWBA). In this paper, the impact of these reflection and refraction effects on the correlation analysis is determined experimentally by measuring grazing incidence transmission XPCS (GT-XPCS) and grazing incidence XPCS (GI-XPCS) simultaneously for a thin film sample, showing non-equilibrium dynamics. Here the results of the GI and GT geometry comparisons are combined within the framework of the standardly applied, simplified DWBA. These calculations allow identifying the main contributions of the detected signal from the leading scattering terms along the out-of-plane direction q z , which dominate the measured intensity pattern on the detector. In combination with the calculation of the non-linear effect of refraction in GTSAXS and GISAXS, it is possible to identify experimental conditions that can be chosen to run experiments and data analysis as close as possible to transmission XPCS and to explain which limitations for data interpretations are observed. Consequently, the beam exposure can be significantly reduced by using GI geometry only. Calculations of experimental settings prior to experiments are detailed to determine suitable q z regions for a variety of material systems measured in bulk-sensitive GI-XPCS experiments, allowing us to determine the scaling behavior of typical decay times as a function of q that is comparable to the scaling behavior obtained in distortion-free GT-XPCS or transmission XPCS experiments.
36 MATERIALS SCIENCE↗
Sub-Coulomb He 3 transfer and its use to extract three-particle asymptotic normalization coefficients
In this work, data for the 13 C( 6 Li,t) 16 O reaction, obtained in inverse kinematics at a 13 C incident energy of 7.72 MeV, are presented. A distorted wave Born approximation (DWBA) analysis was used to extract spectroscopic factors and asymptotic normalization coefficients (ANCs) for the < 16 O | 13 C + 3 He> overlaps, subject to the assumption of a fixed < 6 Li | 3 He + 3 H> overlap. The variation of the extracted spectroscopic factors and ANCs as a function of various inputs to the DWBA calculations was explored. The extracted ANCs were found to vary as a cubic function of the radius of the potential well binding the transferred 3 He to the 13 C core while the spectroscopic factors varied as a quartic function of the radius. Finally, the ANC values could be determined to within a factor of two for this system.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Large longitudinal spin alignment generated in inelastic nuclear reactions
Large longitudinal spin alignment of E/A = 24 MeV 7 Li projectiles inelastically excited by Be, C, and Al targets was observed when the latter remain in their ground state. This alignment is a consequence of an angular-momentum-excitation-energy mismatch, which is well described by a DWBA cluster-model (α + t). The longitudinal alignment of several other systems is also well described by DWBA calculations, including one where a cluster model is inappropriate, demonstrating that the alignment mechanism is a more general phenomenon. Finally, predictions are made for inelastic excitation of 12 C for beam energies above and below the mismatch threshold.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation
Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ 2 = (2) 2 and (71) 2 Å 2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of q z = 0.05 and 0.10 Å −1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both q z values simultaneously, that is, identical fitting parameters were applied at both values of q z . The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for q z = 0.04, 0.05, and 0.06 Å −1 . Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of q z . Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Energy density functional and sensitivity of energies of giant resonances to bulk nuclear matter properties
The development of a modern and more realistic nuclear energy density functional (EDF) for accurate predictions of properties of nuclei is the subject of enhanced activity, since it is very important for the study of properties of nuclear matter (NM), giant resonances and, in particular, of properties of rare nuclei with unusual neutron-to-proton ratios. Here, we provide a short review of the current status of the nuclear EDF and the theoretical results obtained for properties of nuclei and nuclear matter. We will first describe a method for determining the parameters of the EDF, associated with the Skyrme type effective interaction, by carrying out a Hartree-Fock based fit to extensive set of data of ground state properties and constraints. Next we will describe the fully self-consistent Hartree-Fock (HF) based random-phase-approximation (RPA) theory for calculating the strength functions S(E) and centroid energies E CEN of giant resonances and the folding model (FM) distorted wave Вorn approximation (DWBA) to calculate the excitation cross section of giant resonances by α scattering. Then we will provide results for: (i) the Skyrme parameters of the KDE0v1 EDF; (ii) consequences of violation of self-consistently in HF-based RPA; (iii) FM-DWBA calculation of excitation cross section; (iv) values of the E CEN of isoscalar and isovector giant resonances of multipolarities L=0–3 for a wide range of spherical nuclei, using 33 EDFs associated with standard form of the Skyrme type interactions, commonly employed in the literature; and (v) the sensitivities E CEN of the giant resonances to bulk properties of NM. We also determine constraints on NM properties, such as the incompressibility coefficient and effective mass, by comparing with experimental data on E CEN of giant resonances.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Investigation of the role of 10 Li resonances in the halo structure of 11 Li through the 11 Li(p,d) 10 Li transfer reaction
Here, the first measurement of the one-neutron transfer reaction 11 Li(p,d) 10 Li performed using the IRIS facility at TRIUMF with a 5.7A MeV 11 Li beam interacting with a solid H 2 target is reported. The 10 Li residue was populated strongly as a resonance peak with energy E r = 0.62 ± 0.04 MeV having a total width Γ = 0.33 ± 0.07 MeV. The angular distribution of this resonance is characterized by neutron occupying the 1p 1/2 orbital. A DWBA analysis yields a spectroscopic factor of 0.67 ± 0.12 for p 1/2 removal strength from the ground state of 11 Li to the region of the peak.
10,11Li↗
Theory of Nuclear Reactions with RIBs
This is a review of the basic formalism for the high energy scattering and the eikonal approximation and of some of the methods to obtain the optical potentials necessary in breakup calculations. We make also the connection to the surface imaginary part of the optical potential for halo and weakly bound nuclei. Semiclassical reductions of the DWBA approximation for inclusive and exclusive breakup are then presented. Methods to study resonances at threshold in unbound nuclei and the relation to R-matrix theory are finally introduced.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Possible experimental evidence for the presence of double octupole states in {sup 240}Pu
Excited states in the {sup 240}Pu nucleus have been studied by means of the (p,t) reaction using the Q3D spectrometer and the focal plane detector from Munich. The comparison between experimental angular distributions and the DWBA calculations allowed the extraction of relative two-neutron transfer strengths. These observables may reveal important information about the structure of different states. The experimental two neutron strength for the 0{sup +}{sub 2} and 0{sup +}{sub 3} states is found in good agreement with the predictions of the IBA model, confirming the double octupole nature for the 0{sup +}{sub 2} state proposed in the previous studies.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
{sup 16}O resonances near 4α threshold through {sup 12}C({sup 6}Li,d) reaction
Several narrow alpha resonant {sup 16}O states were detected through the {sup 12}C({sup 6}Li,d) reaction, in the range of 13.5 to 17.5 MeV of excitation energy. The reaction was measured at a bombarding energy of 25.5 MeV employing the São Paulo Pelletron-Enge-Spectrograph facility and the nuclear emulsion technique. Experimental angular distributions associated with natural parity quasi-bound states around the 4α threshold are presented and compared to DWBA predictions. The upper limit for the resonance widths obtained is near the energy resolution (15 keV)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗