Distorted-wave Born Approximation Analysis Research Articles

Extracting the asymptotic normalization coefficient for the C14→B13+p overlap from the C14(B11,C12)B13 reaction

The availability of a comparatively complete data set for the elastic and inelastic scattering of a 45-MeV beam of $^{11}\mathrm{B}$ ions from a $^{14}\mathrm{C}$ target, together with an angular distribution for the $^{14}\mathrm{C}(^{11}\mathrm{B},^{12}\mathrm{C})^{13}\mathrm{B}$ proton pickup reaction enables a determination of the $\ensuremath{\langle}^{14}\mathrm{C}\ensuremath{\mid}^{13}\mathrm{B}+p\ensuremath{\rangle}$ asymptotic normalization coefficient (ANC) using the coupled reaction channel (CRC) technique. The complete nature of the data set allows two-step contributions to the reaction mechanism to be controlled while a set of $\ensuremath{\langle}^{12}\mathrm{C}\ensuremath{\mid}^{11}\mathrm{B}+p\ensuremath{\rangle}$ overlaps obtained from a consistent analysis of ($d,^{3}\mathrm{He}$) and ($e,{e}^{\ensuremath{'}}p$) data fixes the projectile overlaps. We find that the level of completeness of the modeling of the reaction mechanism has a significant effect on the value obtained for the ANC, with a distorted wave Born approximation analysis yielding a significantly larger ANC than the full CRC calculation. The final result obtained, when compared with the theoretical value calculated within the source term approach, is in accord with trends for proton removal from similar $p$-shell nuclei.

Observation of the near-threshold intruder 0− resonance in Be12

A resonant state at $3.21^{+0.12}_{-0.04}$\,MeV, located just above the one-neutron separation threshold, was observed for the first time in $^{12}$Be from the $^{11}$Be\,$(d,p)^{12}$Be one-neutron transfer reaction in inverse kinematics. This state is assigned a spin-parity of $0^-$, according to the distorted-wave Born approximation (DWBA) and decay-width analysis. Gamow coupled-channel (GCC) and Gamow shell-model (GSM) calculations show the importance of the continuum-coupling, which dramatically influences the excitation energy and ordering of low-lying states. Various exotic structures associated with cross-shell intruding configurations in $^{12}$Be and in its isotonic nucleus $^{11}$Li are comparably discussed.

Neutron-hole strength in N=81 nuclei

A systematic study of neutron-hole strength in the N = 81 nuclei 137Ba, 139Ce, 141Nd and 143Sm is reported. The single-neutron removal reactions (p,d) and (3He,4He) were measured at energies of 23 and 34 MeV, respectively. Spectroscopic factors were extracted from measured cross sections through a distorted-wave Born approximation analysis and centroids of single-particle strength have been established. The change in these centroid energies as a function of proton number have been compared to calculations of the monopole shift for the s1/2 and h11/2 orbitals, where the majority of the strength has been observed. Significant fragmentation of strength was observed for the d and g7/2 orbitals, particularly for the latter orbital which is deeply bound, with summed strengths that indicate a significant amount lies outside of the measured excitation energy range.

Halo-induced large enhancement of soft dipole excitation of 11Li observed via proton inelastic scattering

Proton inelastic scattering off a neutron halo nucleus, 11Li, has been studied in inverse kinematics at the IRIS facility at TRIUMF. The aim was to establish a soft dipole resonance and to obtain its dipole strength. Using a high quality 66 MeV 11Li beam, a strongly populated excited state in 11Li was observed at Ex=0.80±0.02 MeV with a width of Γ=1.15±0.06 MeV. A DWBA (distorted-wave Born approximation) analysis of the measured differential cross section with isoscalar macroscopic form factors leads us to conclude that this observed state is excited in an electric dipole (E1) transition. Under the assumption of isoscalar E1 transitions, the strength is evaluated to be extremely large amounting to 30∼296 Weisskopf units, exhausting 2.2%∼21% of the isoscalar E1 energy-weighted sum rule (EWSR) value. The large observed strength originates from the halo and is consistent with the simple di-neutron model of 11Li halo.

Second0+state of unboundO12: Scaling of mirror asymmetry

The unbound O12 nucleus was studied via the two-neutron transfer (p,t) reaction in inverse kinematics using a radioactive O14 beam at 51 MeV/u. Excitation energy spectra and differential cross sections were deduced by the missing mass method using MUST2 telescopes. We achieved much higher statistics compared to the previous experiments of O12, which allowed accurate determination of resonance energy and unambiguous spin and parity assignment. The O12 resonance previously reported using the same reaction was confirmed at an excitation energy of 1.62±0.03(stat.)±0.10(syst.). MeV and assigned spin and parity of 0+ from a distorted-wave Born approximation analysis of the differential cross sections. Mirror symmetry of O12 with respect to its neutron-rich partner Be12 is discussed from the energy difference of the second 0+ states. In addition, from systematics of known 0+ states, a distinct correlation is revealed between the mirror energy difference and the binding energy after carrying out a scaling with the mass and the charge. We show that the mirror energy difference of the observed 0+ state of O12 is highly deviated from the systematic trend of deeply bound nuclei and in line with the scaling relation found for weakly bound nuclei with a substantial 2s1/2 component. The importance of the scaling of mirror asymmetry is discussed in the context of ab initio calculations near the drip lines and universality of few-body quantum systems.

Experimental study of theNi66(d,p) Ni67one-neutron transfer reaction

The quasi-SU(3) sequence of the positive parity νg9/2,d5/2,s1/2 orbitals above the N=40 shell gap are assumed to induce strong quadrupole collectivity in the neutron-rich Fe (Z=26) and Cr (Z=24) isotopes below the nickel region. In this paper the position and strength of these single-particle orbitals are characterized in the neighborhood of Ni68 (Z=28,N=40) through the Ni66(d,p)Ni67 one-neutron transfer reaction at 2.95 MeV/nucleon in inverse kinematics, performed at the REX-ISOLDE facility in CERN. A combination of the Miniball γ-array and T-REX particle-detection setup was used and a delayed coincidence technique was employed to investigate the 13.3-μs isomer at 1007 keV in Ni67. Excited states up to an excitation energy of 5.8 MeV have been populated. Feeding of the νg9/2 (1007 keV) and νd5/2 (2207 keV and 3277 keV) positive-parity neutron states and negative parity (νpf) states have been observed at low excitation energy. The extracted relative spectroscopic factors, based on a distorted-wave Born approximation analysis, show that the νd5/2 single-particle strength is mostly split over these two excited states. The results are also compared to the distribution of the proton single-particle strength in the Zr90 region (Z=40,N=50).6 MoreReceived 25 February 2015Revised 28 April 2015DOI:https://doi.org/10.1103/PhysRevC.91.054321This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society

Breakup and finite-range effects on theB8(d,n)9Creaction

The astrophysical factor of $^{8}\mathrm{B}{(p,\ensuremath{\gamma})}^{9}\mathrm{C}$ at zero energy, ${S}_{18}(0)$, is determined by a three-body coupled-channels analysis of the transfer reaction $^{8}\mathrm{B}{(d,n)}^{9}\mathrm{C}$ at 14.4 MeV/nucleon. Effects of the breakup channels of $d$ and $^{9}\mathrm{C}$ are investigated with the continuum-discretized coupled-channels method. It is found that, in the initial and final channels, respectively, the transfer process through the breakup states of $d$ and $^{9}\mathrm{C}$, its interference with that through their ground states in particular, gives a large increase in the transfer cross section. The finite-range effects with respect to the proton-neutron relative coordinate are found to be about 20%. As a result of the present analysis, ${S}_{18}(0)=22\ifmmode\pm\else\textpm\fi{}6\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.16em}{0ex}}\mathrm{b}$ is obtained, which is smaller than the result of the previous distorted-wave Born approximation analysis by about 51%.

Structure of26Al studied by one - nucleon transfer reaction27Al(d,t)

The excited states of 26 Al have been produced and studied using 27 Al(d,t) reaction with 25 MeV deuteron as projectile. Optical model potential parameters were extracted from the measured elastic scattering angular distribution. Zero range distorted wave Born approximation analysis for the ground and 0.223 MeV states of 26 Al have been done. The spectroscopic factors calculated for these states are found to be in good agreement with the previously reported values.

Proton spectroscopic factor of the12Cground state from the12C(11B,12C)11Belastic transfer reaction

The angular distributions of the ${}^{12}\mathrm{C}{{(}^{11}\mathrm{B},{\phantom{\rule{0.16em}{0ex}}}^{11}\mathrm{B})}^{12}\mathrm{C}$ and ${}^{12}\mathrm{C}{{(}^{11}\mathrm{B},{\phantom{\rule{0.16em}{0ex}}}^{12}\mathrm{C})}^{11}\mathrm{B}$ reactions have been measured at an incident energy of 50 MeV by using the high resolution Q3D magnetic spectrometer of the HI-13 tandem accelerator at China Institute of Atomic Energy, Beijing. The optical potential parameters of the ${}^{11}\mathrm{B}+{}^{12}\mathrm{C}$ system are determined by fitting the angular distribution of the elastic scattering and then used to predict the cross sections of the elastic transfer reaction leading to the ground state in ${}^{12}\mathrm{C}$ based on distorted-wave Born approximation (DWBA) analysis. Taking into account the interference between the elastic scattering and the elastic transfer processes, the proton spectroscopic factor of the ${}^{12}\mathrm{C}$ ground state is extracted to be 2.15 $\ifmmode\pm\else\textpm\fi{}$ 0.23 by constraining the geometrical parameters ${r}_{0}$ and $a$ using the rms radius of the valence proton in the ${}^{12}\mathrm{C}$ ground state.

Proton widths of the low-lying16Fstates from the15N(7Li,6Li)16Nreaction

All the 16F levels are unbound by proton emission. To date the four low-lying 16F levels below 1 MeV have been experimentally identified with well established spin-parity values and excitation energies with an accuracy of 4 - 6 keV. However, there are still considerable discrepancies for their level widths. The present work aims to explore these level widths through an independent method. The angular distributions of the 15N(7Li, 6Li)16N reaction leading to the first four states in 16N were measured using a high-precision Q3D magnetic spectrograph. The neutron spectroscopic factors and the asymptotic normalization coefficients for these states in 16N were then derived based on distorted wave Born approximation analysis. The proton widths of the four low-lying resonant states in 16F were obtained according to charge symmetry of strong interaction.

Spectroscopic factors for low-lyingN16levels and the astrophysicalN15(n,γ)N16reaction rate

Background: Fluorine is a key element for nucleosynthetic studies since it is extremely sensitive to the physical conditions within stars. The astrophysical site to produce fluorine is suggested to be asymptotic giant branch stars. In these stars the N15(n,γ)N16 reaction could affect the abundance of fluorine by competing with N15(α,γ)F19. Purpose: The N15(n,γ)N16 reaction rate depends directly on the neutron spectroscopic factors of the low-lying states in N16. Shell model calculations and two previous measurements of the (d,p) reaction yielded the spectroscopic factors with a discrepancy by a factor of ∼2. The present work aims to explore these neutron spectroscopic factors through an independent transfer reaction and to determine the stellar rate of the N15(n,γ)N16 reaction. Methods: The angular distributions of the N15(Li7,Li6)N16 reaction populating the ground state and the first three excited states in N16 are measured using a Q3D magnetic spectrograph and are used to derive the spectroscopic factors of these states based on distorted wave Born approximation analysis. Results: The spectroscopic factors of these four states are extracted to be 0.96 ± 0.09, 0.69 ± 0.09, 0.84 ± 0.08, and 0.65 ± 0.08, respectively. Based on the new spectroscopic factors we derive the N15(n,γ)N16 reaction rate. Conclusions: The accuracy and precision of the spectroscopic factors are enhanced due to the first application of high-precision magnetic spectrograph for resolving the closely spaced N16 levels which cannot be achieved in most recent measurements. The present result demonstrates that two levels corresponding to neutron transfers to the 2s1/2 orbit in N16 are not good single-particle levels although N15 is a closed neutron-shell nucleus. This finding is contrary to the shell model expectation. The present work also provides an independent examination to shed some light on the existing discrepancies in the spectroscopic factors and the N15(n,γ)N16 rate.Received 21 November 2013DOI:https://doi.org/10.1103/PhysRevC.89.012801©2014 American Physical Society

Single-neutron excitations in18N

States in ${}^{18}$N have been populated in the neutron-adding $(d,p)$ reaction on the short-lived ${}^{17}$N beam. Previously observed levels, found in this work at excitation energies of 0.12(1) MeV and 0.74(1) MeV, have been identified as those expected from a proton $0{p}_{1/2}$ hole coupled to the ${}^{19}$O $5/{2}^{+}$ ground state. A new state at 1.17(2) MeV is consistent with the coupling of the $1/{2}^{\ensuremath{-}}$ proton-hole state to the excited $1/{2}^{+}$ state in ${}^{19}$O. Orbital angular momentum assignments and spectroscopic factors were determined from the measured angular distributions through a distorted wave Born approximation analysis. Systematics for the ${(0{d}_{5/2}1{s}_{1/2})}^{3}$ neutron configurations in the $N=11$ isotones, ${}^{17}$C, ${}^{18}$N, and ${}^{19}$O are discussed and comparisons to $p$-$sd$ shell-model calculations are made.

Neutron-hole strength in the N = 81 isotones

The distribution of neutron-hole strength has been studied in the N = 81 isotones 137Ba, 139Ce, 141Nd and 143Sm through the single-neutron removing reactions (p,d) and (3He,α), at energies of 23 and 34 MeV, respectively. Systematic cross section measurements were made at angles sensitive to the transferred angular momentum, and spectroscopic factors extracted through a distorted-wave Born approximation analysis. Application of the MacFarlane-French sum rules indicate an anomalously low summed g7/2 spectroscopic factor, most likely due to extensive fragmentation of the single-particle strength. Single-particle energies, based upon the centroids of observed strength, are presented.

28Si(p,3He) reaction for spectroscopy of26Al

The ${}^{28}\text{Si}{(p{,}^{3}\text{He})}^{26}\text{Al}$ reaction was utilized for the first time to study the levels in ${}^{26}$Al, using a proton beam from the Holifield Radioactive Ion Beam Facility. Five previously unreported states in ${}^{26}$Al are observed and discussed, including Distorted Wave Born Approximation analysis. Proton-decay branching ratios consistent with previous studies and theoretical expectations were found by detecting decay protons from highly excited ${}^{26}$Al states in coincidence with the ${}^{3}$He particles.

High resolution spectroscopy of112Sn through the114Sn(p,t)112Sn reaction

The ${}^{114}$Sn($p$,$t$)${}^{112}$Sn reaction has been investigated in a high resolution experiment at incident proton energy of 22 MeV. Angular distributions for 28 transitions to levels of ${}^{112}$Sn up to the excitation energy of 3.624 MeV have been measured. The spin and parity identification has been carried out by means of a distorted-wave Born approximation (DWBA) analysis, performed by using conventional Woods-Saxon potentials. A shell-model study of ${}^{112}$Sn nucleus has been performed using a realistic two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential. The energy spectra have been calculated and compared with the experimental ones, while the theoretical two-nucleon spectroscopic amplitudes, evaluated in a truncated seniority space, have been used in the microscopic DWBA calculation of the cross-section angular distributions.

Indirect study of the12C(α,γ)16O reaction via the12C(7Li, t)16O transfer reaction

The ${}^{12}$C($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)${}^{16}$O reaction plays a crucial role in stellar evolution. The rate of this reaction determines directly the ${}^{12}$C-to-${}^{16}$O abundance ratio at the end of the helium burning phase of stars and consequently has a big effect on the subsequent nucleosynthesis and even on the evolution of massive stars. However, despite many experimental studies, the low-energy cross section of ${}^{12}$C($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)${}^{16}$O remains uncertain. The extrapolation of the measured cross sections to stellar energies ($E\ensuremath{\sim}300$ keV) is made particularly difficult by the presence of the 2${}^{+}$ (${E}_{x}=6.92$ MeV) and 1${}^{\ensuremath{-}}$ (${E}_{x}=7.12$ MeV)subthreshold states of ${}^{16}$O. To further investigate the contribution of these two subthreshold resonances to the ${}^{12}$C($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)${}^{16}$O cross section, we determine their $\ensuremath{\alpha}$-reduced widths via a measurement of the transfer reaction ${}^{12}$C(${}^{7}$Li, $t$)${}^{16}$O at two incident energies, 28 and 34 MeV. The uncertainties on the determined $\ensuremath{\alpha}$-spectroscopic factors and the $\ensuremath{\alpha}$-reduced widths were reduced thanks to a detailed distorted-wave Born approximation analysis of the transfer angular distributions measured at the two incident energies. The $R$-matrix calculations of ${}^{12}$C($\ensuremath{\alpha}$,$\ensuremath{\gamma}$)${}^{16}$O cross section using our obtained $\ensuremath{\alpha}$-reduced widths for the 2${}^{+}$ and 1${}^{\ensuremath{-}}$ subthreshold resonances lead to an $E1$ $S$ factor at 300 keV of $100\ifmmode\pm\else\textpm\fi{}28$ keV b, which is consistent with values obtained in most of the direct and indirect measurements as well as the NACRE collaboration compilation while the result for the $E2$ component ${S}_{E2}\phantom{\rule{0.28em}{0ex}}(300\phantom{\rule{4.pt}{0ex}}\text{keV})=50\ifmmode\pm\else\textpm\fi{}19$ keV b disagrees with the NACRE adopted value.

Astrophysical Rates for the 6He(p, γ)7Li Reaction

Angular distribution of the 6He(d,n)7Li reaction at Ec.m.=9.1 MeV is measured in inverse kinematics for the first time. The proton spectroscopic factors for the ground and first excited states of 7Li are derived by using the distorted wave Born approximation analysis. The astrophysical rates of 6He(p, γ)7Li reaction are then deduced and fitted with an expression of REACLIB.

High-resolution measurement of theSn118,124(p,t)Sn116,122reactions: Shell-model and microscopic distorted-wave Born approximation calculations

The $^{118,124}\mathrm{Sn}$($p$,$t$)$^{116,122}\mathrm{Sn}$ 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 $^{116}\mathrm{Sn}$ and 63 transitions to levels of $^{122}\mathrm{Sn}$, up to excitation energies of $~3.850$ and $~4.000$ 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 $^{116}\mathrm{Sn}$ and $^{122}\mathrm{Sn}$ nuclei was performed using a realistic two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential. The doubly magic nucleus $^{132}\mathrm{Sn}$ 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.

Spin assignments to excited states inNa22through aMg24(p,He3)Na22reaction measurement

The level structure of $^{22}\mathrm{Na}$ has been studied at the Holifield Radioactive Ion Beam Facility in Oak Ridge National Laboratory using the $^{24}\mathrm{Mg}$($p$,$^{3}\mathrm{He}$)$^{22}\mathrm{Na}$ reaction. Proton beams of 41 and 41.5 MeV were generated by the 25-MV tandem accelerator and bombarded isotopically enriched $^{24}\mathrm{Mg}$ targets. Angular distributions of recoiling $^{3}\mathrm{He}$ particles were extracted by using a segmented annular silicon strip detector array. Spins and parities for 10 levels were constrained through a distorted-wave Born approximation analysis of angular distributions, including three levels above the proton threshold at 6.739 MeV.

Microscopic study of the isoscalar giant resonances in 208Pb induced by inelastic α scattering

The energetic beam of (spin and isospin zero) α-particles remains a very efficient probe for the nuclear isoscalar giant resonances. In the present work, a microscopic folding model study of the isoscalar giant resonances in 208Pb induced by inelastic α + Pb 208 scattering at E lab = 240 and 386 MeV has been performed using the (complex) CDM3Y6 interaction and nuclear transition densities given by both the collective model and Random Phase Approximation (RPA) approach. The fractions of energy weighted sum rule around the main peaks of the isoscalar monopole, dipole and quadrupole giant resonances were probed in the Distorted Wave Born Approximation analysis of inelastic α + Pb 208 scattering using the double-folded form factors given by different choices of the nuclear transition densities. The energy distribution of the E0, E1 and E2 strengths given by the multipole decomposition analyses of the ( α , α ′ ) data under study are compared with those predicted by the RPA calculation.