Finite-range Distorted-wave Born Approximation Research Articles

Radiative Neutron Capture Rate of 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B(n,γ)12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n,\\gamma )^{12}$$\\end{document}B Reaction from the Coulomb Dissociation of 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12}$$\\end{document}B

We calculate the 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B(n,γ)12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n,\\gamma )^{12}$$\\end{document}B reaction rate which is an important constituent in nucleosynthesis networks and is contributed by resonant as well as non-resonant capture. For the resonant rate, we use the narrow resonance approximation whereas the non-resonant contribution is calculated with the Coulomb dissociation method for which we use finite-range distorted wave Born approximation theory. We then compare our calculated rate of 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B(n,γ)12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n,\\gamma )^{12}$$\\end{document}B reaction with those reported earlier and with other charged particle reactions on 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B.

Analyses of α–nucleus interaction on the 28Si(α, d)30P reaction at 40 and 50 MeV

The angular distributions of the 28Si(α, d)30P reaction at 40 and 50 MeV incident energies have been analyzed using the full finite-range (FFR) distorted-wave Born approximation (DWBA) method. Three forms of the optical model potentials namely, Woods-Saxon, Michel, and molecular potentials are used to analyze the bound states of the 30P nucleus for 8 and 21 transitions at 40 and 50 MeV, respectively. The two-nucleon spectroscopic factors that have been obtained for the three optical model potentials are compared with the previous experimental and theoretical calculations. The χN2 values have been calculated for the optical model potentials to estimate the quality of fits for the α+28Si elastic scattering and the 28Si(α, d)30P reaction at two different incident energies. These analyses show that the Michel and the molecular potentials describe the elastic scattering data more satisfactorily than the Woods-Saxon potential at 40 and 50 MeV incident energies, but for the reaction analyses at 40 MeV the Woods-Saxon potential takes over the other two forms of potential. These investigations also show that the direct two nucleons transfer reaction mechanism with the angular distributions of the admixture of L transfers in most of the states of 30P is seemingly sufficient for all forms of the optical model potential at these incident energies.

Exploring the structure of 29Ne

We apply a fully quantum mechanical Coulomb breakup theory under the aegis of post form finite-range distorted wave Born approximation to analyze the elastic Coulomb breakup of 29Ne on 208Pb at 244MeV/u. We calculate several reaction observables to quantify its structural parameters. One-neutron removal cross section is calculated to check the consistency of the ground state configuration of 29Ne with the available experimental data. A scrutiny of the parallel momentum distribution of the charged fragment reveals a full width at half maximum of 82MeV/c, which is in good agreement with the experimental value and indicates a moderate halo for a nearly spherical 29Ne in the 28Ne(0+)⊗2p3/2ν ground state. The energy-angular distributions and average momentum of the charged fragment point to the absence of post-acceleration effects in the breakup process, a desirable result for elastic breakup.

Scaling with deformation in probable p-wave halo 34Na

We investigate the electric dipole response of 34Na, a probable p-wave one-neutron halo nucleus, lying in the “island of inversion” and having a deformed structure. We use a semi-analytic approach to probe the dipole response and further compare the results obtained from a post form finite-range distorted wave Born approximation theory of Coulomb breakup. The effects of deformation are figured out on the peak positions of the electric dipole strength distribution which further constraint the one-neutron separation energy of the deformed projectile and it leads to a two-dimensional scaling of total B(E1) strength with parameters: separation energy and deformation.

Important Influence of Entrance Channel Reorientation Coupling on Proton Stripping

While it is well established that the ground state reorientation coupling can have a significant influence on the elastic scattering of deformed nuclei, the effect of such couplings on transfer channels has been much less well investigated. In this letter we demonstrate that the ^{208}hbox {Pb}(^7hbox {Li},^6hbox {He})^{209}hbox {Bi} proton stripping reaction at an incident energy of 52 MeV can be well described by the inclusion of the ^7hbox {Li} ground state reorientation coupling within the coupled channels Born approximation formalism. Full finite-range distorted wave Born approximation calculations were previously found to be unable to describe these data. Addition of coupling to the 0.478-MeV 1/2^- excited state of ^7hbox {Li}, together with the associated two-step transfer path, has little or no influence on the shape of the angular distributions (except that for stripping leading to the 1.61-MeV 13/2^+ level of ^{209}hbox {Bi} which is significantly improved) but does affect appreciably the values of the ^{209}mathrm {Bi} rightarrow {^{208}mathrm {Pb}} + p spectroscopic factors. Implications for experiments with weakly-bound light radioactive beams are discussed.

Multistep processes in heavy-ion-induced single-nucleon transfer reactions

It was first noted during the 1970s that finite-range distorted wave Born approximation (FR-DWBA) calculations were unable satisfactorily to describe the shape of the angular distributions of many single-proton (and some single-neutron) transfer reactions induced by heavy ions, with calculations shifted to larger angles by up to ~ 4 degrees compared with the data. These reactions exhibited a significant mismatch, either of the reaction Q value or the grazing angular momentum of the entrance and exit channels, and it was speculated that the inclusion of multi-step transfer paths via excited state(s) of the projectile and/or ejectile could compensate for the effect of this mismatch and yield good descriptions of the data by shifting the calculated peaks to smaller angles. However, to date this has not been explicitly demonstrated for many reactions. In this work we show that inclusion of the two-step transfer path via the 4.44-MeV 2+ excited state of the 12C projectile in coupled channel Born approximation calculations enables a good description of the 208Pb(12C,11B)209Bi single-proton stripping data at four incident energies which could not be described by the FR-DWBA. We also show that inclusion of a similar reaction path for the 208Pb(12C,13C)207Pb single-neutron pickup reaction has a relatively minor influence, slightly improving the already good description obtained with the FR-DWBA.

Neutron transfer in reaction 18O + 181Ta with formation of neutron-rich oxygen isotopes

Differential cross sections for the formation of oxygen isotopes in the reaction 18O + 181Ta have been measured at projectile nucleus energy 10 A⋅MeV on the high-resolution magnetic spectrometer MAVR. Theoretical analysis of product yields has been performed in the finite-range distorted-wave Born approximation formalism using the FRESCO code under the assumption of sequential neutron transfer mechanism. The results of calculations are in good agreement with experimental data.

Differential Production Cross Sections for Isotopes of Light Nuclei in the $$\boldsymbol{{}^{18}\textrm{O}+^{181}}$$Ta Reaction

The results of experiments performed at a high-resolution magnetic spectrometer (MAVR) are presented. The differential production cross sections for oxygen isotopes in the $${}^{18}\textrm{O}+^{181}$$ Ta reaction at the projectile energy of 10 MeV per nucleon were measured at the MAVR facility. The yield of reaction products is analyzed theoretically in the finite-range distorted-wave Born approximation (FR-DWBA method) by means of the FRESCO code. The theoretical differential cross sections are calculated for sequential neutron transfer. The contributions of the mechanisms of sequential neutron transfer and dineutron-cluster transfer to the production cross sections for the neutron-rich oxygen isotopes $${}^{20,22,24}$$ O are studied.

Asymptotic normalization coefficients from transfer reactions and R -matrix analysis of direct capture in the Ne22(p,γ)Na23 reaction

The $^{22}$Ne(p,$\gamma$)$^{23}$Na reaction in NeNa cycle plays an important role in the production of only stable sodium isotope $^{23}$Na. This nucleus is processed by the NeNa cycle during hot bottom burning (HBB) in asymptotic giant branch (AGB) stage of low metallicity intermediate mass stats (4 M$_O$ $\leq$ M $\leq$ 6 M$_O$). Recent measurements have addressed the uncertainty in the thermonuclear reaction rate of this reaction at relevant astrophysical energies through the identification of low lying resonances at E$_p$ = 71,105, 156.2, 189.5 and 259.7 keV. In addition, precise measurements of low energy behaviour of the non-resonant capture has also been performed and the contribution of the sub-threshold resonance at 8664 keV excitation in $^{23}$Na has been established. Here, in this article, we have presented a systematic R-matrix analysis of direct capture to the bound states and the decay of the sub-threshold resonance at 8664 keV to the ground state of $^{23}$Na. A finite range distorted wave Born approximation (FRDWBA) calculation has been performed for $^{22}$Ne($^3$He,d)$^{23}$Na transfer reaction data to extract the asymptotic normalization coeeficients (ANC-s) required to estimate the non-resonant capture cross sections or astrophysical S-factor values in R-matrix analysis. Simultaneous R-matrix analysis constrained with ANC-s from transfer calculation reproduced the astrophysical S-factor data over a wide energy window. The S$_{tot}^{DC}$(0) = 48.8$\pm$9.5 keV.b compares well with the result of Ferraro, {\it et al.} and has a lower uncertainty. The resultant thermonuclear reaction is slightly larger in 0.1 GK $\le$ T $\le$ 0.2 GK temperature range but otherwise in agreeent with Ferraro, {\it et al.}.

Neutron capture rates of C18

Background: Small changes in reaction rates due to neutron capture, $\ensuremath{\alpha}$ capture, and $\ensuremath{\beta}$ decay by exotic nuclei in the low and medium mass region can direct the $r$-process path in different ways, thereby affecting the abundance pattern. In this context, it is important to find the most abundant carbon isotope closer to the neutron drip line. It was postulated that the $(n,\ensuremath{\gamma})$ reaction network will be broken at the $^{18}\mathrm{C}$ isotope and follow the $^{18}\mathrm{C}(\ensuremath{\alpha},n)^{21}\mathrm{O}$ reaction path [Terasawa et al., Astrophys. J. 562, 470 (2001)].Purpose: In this paper, we calculate the radiative capture cross section of $^{18}\mathrm{C}(n,\ensuremath{\gamma})^{19}\mathrm{C}$, taking into consideration the halo character of $^{19}\mathrm{C}$. Eventually, we calculate the reaction rate for the same reaction and compare it with Hauser-Feshbach estimates of $(n,\ensuremath{\gamma})$ and $(\ensuremath{\alpha},n)$ to determine the abundance pattern of carbon isotopes.Method: We compute the relative energy spectrum for elastic Coulomb breakup of $^{19}\mathrm{C}$ on a Pb target at a beam energy of 67 MeV/u using the finite-range distorted-wave Born approximation (FRDWBA) theory. We use the principle of detailed balance to calculate the radiative capture cross section from the photo disintegration cross section, and subsequently we calculate the reaction rate.Results: We report the $^{18}\mathrm{C}(n,\ensuremath{\gamma})^{19}\mathrm{C}$ capture cross section as a function of relative energy. Estimation of the energy range contributing to the reaction rates is done by calculating the integrand of the reaction rate expression. A comparison of the $^{18}\mathrm{C}(n,\ensuremath{\gamma})^{19}\mathrm{C}$ with $^{18}\mathrm{C}(\ensuremath{\alpha},n)^{21}\mathrm{O}$ (extracted from the Hauser-Feshbach estimates) shows the domination of the neutron radiative capture reaction in the relevant temperature range ${T}_{9}=0.1--4$.Conclusion: The radiative capture cross section of $^{18}\mathrm{C}$ calculated using FRDWBA theory agrees well with the experimental data, whereas the statistical model calculation lies orders of magnitude lower. We conclude that at equilibrium temperature of ${T}_{9}=0.62$, the $^{18}\mathrm{C}(n,\ensuremath{\gamma})^{19}\mathrm{C}$ reaction rate is orders of magnitude higher than that of the $^{18}\mathrm{C}(\ensuremath{\alpha},n)^{21}\mathrm{O}$ reaction, thereby pushing the carbon isotope abundance towards the neutron drip line.

Low-lying dipole strengths for probable p-wave one-neutron halos in the medium mass region

The one-neutron halos lying in the island of inversion around $N=20$ has provided the podium, to study the variation of total low-lying dipole strength with the neutron separation energy. We study three probable p-wave one-neutron halo candidates 31Ne and 34Na and 37Mg lying in the island of inversion. A simple analytic model has been used for the calculation of the total low-lying dipole strength for the medium mass p-wave one-neutron halos. A correction factor to this analytical model has been estimated with a realistic Woods-Saxon potential. A comparison of these analytic calculations has been made with the those performed by a finite-range distorted-wave Born approximation theory of the Coulomb dissociation. We also make an estimate of the one-neutron separation energies of 31Ne, 34Na and 37Mg.

Excited-state one-neutron halo nuclei within a parallel momentum distribution analysis

Using a fully quantum mechanical post-form finite-range distorted-wave Born approximation theory of Coulomb breakup, I study the parallel momentum distribution of the core in the Coulomb breakup of suggested excited-state one-neutron halo nuclei considered in their different bound excited states. Narrow momentum distributions obtained in the present calculations for some cases indicate the possibilities of the excited-state halo structure in the nuclei under consideration and therefore favor the previous predictions.

Single-particle strength in neutron-richCu69from theZn70(d,He3)Cu69proton pick-up reaction

We have performed the $^{70}\mathrm{Zn}(d,^{3}\mathrm{He})^{69}\mathrm{Cu}$ proton pick-up reaction in direct kinematics using a deuteron beam at 27 MeV. The outgoing $^{3}\mathrm{He}$ particles were detected at the focal-plane detection system of an Enge split-pole spectrometer. The excitation-energy spectrum was reconstructed up to 7 MeV and spectroscopic factors were obtained after analysis of the angular distributions in the finite-range distorted-wave Born approximation. The results show three new angular distributions for which the $\ensuremath{\pi}{f}_{7/2}$ strength was measured and a lower limit of the centroid is established. State-of-the-art shell-model calculations are performed and predict a $\ensuremath{\pi}{f}_{7/2}$ strength that lies too high in energy in comparison to our experimental results.

Analysis of the normal optical, Michel and molecular potentials on the 40Ca(6Li, d)44 Ti reaction

Full finite-range (FFR) distorted-wave Born approximation (DWBA) method has been applied to analyse the angular distributions of cross-sections of the 40Ca(6Li, d) 44Ti reaction at 28 MeV incident energy for the 22 transitions involving both the bound and unbound states of 44Ti by using the normal optical, Michel and molecular potentials. The extracted spectroscopic factors for the three optical potentials are compared with those of some previous studies of zero-range (ZR) calculations of the 40Ca(6Li, d) 44Ti reaction using the normal optical potential. The χ 2 values of all the levels are obtained for the three optical potentials to estimate the quality of the fits. Molecular and Michel potentials have been used for the first time to analyse the four-nucleon transfer reaction and it seems that the molecular potential fits the experimental data more satisfactorily for some of the states than the normal optical and Michel potentials.

Evolution of single-particle strength in neutron-rich 71Cu

The strength functions of the πf5/2, πp3/2 and πf7/2 orbitals in neutron-rich 71Cu were obtained in a 72Zn(d,3He)71Cu proton pick-up reaction in inverse kinematics using a radioactive beam of 72Zn at 38 MeV/u. A dedicated set-up was developed to overcome the experimental challenges posed by the low cross section of the reaction and the low energy of the outgoing 3He particles. The excitation-energy spectrum was reconstructed and spectroscopic factors were obtained after analysis of the angular distributions with the finite-range Distorted-Wave Born Approximation (DWBA). The results show that unlike for the πf5/2 orbital and contrary to earlier interpretation, the πf7/2 single-particle strength distribution is not appreciably affected by the addition of neutrons beyond N=40.

Single-particle strength in neutron-rich 71Cu from the (d,3He) proton pick-up reaction

We have measured the 72Zn(d,3He)71Cu proton pick-up reaction in inverse kinematics at 38 MeV/u. A dedicated set-up was developed to overcome the experimental challenges posed by the low cross section of the reaction and the low energy of the outgoing 3He particles. The excitation-energy spectrum was reconstructed and spectroscopic factors were obtained after analysis of the angular distributions in the finite-range Distorted-Wave Born Approximation (DWBA). The results show that unlike for the πf5/2 orbital, the πf7/2 singleparticle strength is not appreciably affected by the addition of neutrons beyond N = 40.

Study of the 1p transfer channel in the 12C + 27Al reaction at 6–7 MeV per nucleon

The 27Al(12C,11B)28Si reactions have been studied at 73, 81 and 85 MeV to extract spectroscopic factors for the ground (0+), first (2+) and second (4+) excited states of 28Si using a transfer reaction. The elastic scattering angular distributions have been fitted using the computer code ECIS94, and finite range distorted-wave Born approximation calculations have been performed using DWUCK5. The extracted spectroscopic factors are compared with shell model calculations.

The ANC of 16O subthreshold states from 12C(6Li, d) reaction at energies near the barrier

The ANC of the 2+ (6.92 MeV) and 1− (7.12 MeV) subthreshold states of 16O have been extracted from the normalization of 12C(6Li, d) angular distribution to a Finite Range Distorted Wave Born Approximation (FRDWBA) calculation. The theoretical analysis indicates a peripheral reaction and the extracted ANCs are not sensitive to the number of nodes in the bound state potential. The uncertainty from the entrance channel potential is minimized to 8% for the 6.92 and 11% for the 7.12 MeV state if the normalization is performed at the grazing angle. The uncertainty from the exit channel potential at the grazing angle is found to be 10% and 12% respectively for the 7.12 and 6.92 MeV states.

Interaction of loosely bound radioactive 7Be and stable 7Li with 9Be

Quasielastic scattering angular distributions have been measured for the 7Be + 9Be system at Elab = 17 , 19 and 21MeV in the angular range \( \theta_{{cm}}^{}\) = 24° - 57° . An optical model (OM) analysis of these data has been carried out in order to extract optical potential parameters and reaction cross-sections. One-proton stripping cross-sections were also measured for this system at Elab = 19 and 21MeV. These transfer angular-distribution data were compared with the finite-range distorted-wave Born approximation (FRDWBA) calculations. For the 7Li + 9Be system quasielastic scattering angular distributions were measured and emitted light charged particles were detected at Elab = 15.75 , 24.00 and 30.00MeV in the angular range \( \theta_{{cm}}^{}\) = 7° - 70° . Fusion cross-sections were obtained by reproducing the measured \( \alpha\) -evaporation spectra from the compound nucleus at backward angles with the statistical model calculations. The ratios of the experimental fusion cross-sections to the total reaction cross-sections (obtained from OM analysis) were found to be small. This result suggests that the break-up process has a strong influence on the fusion process leading to a reduction in the fusion cross-section.

Optical Potential Parameters of Weakly Bound Nuclear System 17F+13C

Elastic scattering angular distributions of the 14N+16O system and the angular distributions of transfer reaction 16O(14N,13 C)17 F at ELab = 76.2 MeV and 57MeV have been measured and calculated by means of the exact finite-range distorted-wave Born approximation with the PTOLEMY code. The optical potential parameters for the weakly bound nuclear system 17F+13 C have been deduced and applied to analyse the elastic scattering angular distributions of the similar systems 17F+12C and 17F+14N which are taken from literature. The result shows that the transfer reaction with stable projectile and target combination can be used as an alternative method to extract the optical potential parameters for the weakly bound nuclear system.