Distorted-wave Born Approximation Calculations Research Articles

Isospin forbidden ( alpha,d) transitions to the low-lying states in 26Al.

The $^{24}\mathrm{Mg}$(\ensuremath{\alpha},d${)}^{26}$Al reaction leading to the 0.23 MeV ${0}_{1}^{+}$, T=1 and the 3.16 MeV ${2}_{2}^{+}$, T=1 states were measured at ${\mathit{E}}_{\mathrm{\ensuremath{\alpha}}}$=64.7 MeV. Cross sections for these isospin-forbidden transitions were compared with exact-finite-range second-order distorted wave Born approximation (DWBA) calculations for successive-transfer processes (\ensuremath{\alpha}${\mathrm{\ensuremath{-}}}^{3}$He-d) and (\ensuremath{\alpha}-t-d). The DWBA calculation with spectroscopic amplitudes obtained from the full sd-shell model was found to underestimate the cross section for the ${0}^{+}$ state by a factor of 200, while a normalization factor of 10 was obtained for the ${2}^{+}$ state. About 5% isospin impurity in the ${0}^{+}$ state of $^{26}\mathrm{Al}$ was required to obtain the same normalization for the ${0}^{+}$ state.

Polarized-proton elastic scattering from polarized 13C.

The p\ensuremath{\rightarrow}${+}^{13}$C\ensuremath{\rightarrow} (polarized target) elastic-scattering spin observables ${\mathit{A}}_{000\mathit{n}}$ (target analyzing power) and ${\mathit{A}}_{00\mathit{n}\mathit{n}}$ (spin-correlation parameter) were determined at 497.5 MeV over the laboratory angular range 12\ifmmode^\circ\else\textdegree\fi{}--30\ifmmode^\circ\else\textdegree\fi{} with statistical uncertainties typically \ifmmode\pm\else\textpm\fi{}(0.02--0.06). Results of distorted-wave Born approximation calculations, based on either the relativistic or the nonrelativistic impulse approximation, are in reasonable agreement with these new data.

Existence of alpha -cluster structure in 44Ti via the (6Li,d) reaction.

{alpha}-cluster states in {sup 44}Ti have been investigated in the {sup 40}Ca({sup 6}Li,{ital d}){sup 44}Ti reaction at {ital E}=50 MeV. The angular distributions of 34 levels at excitation energies for {ital E}{sub {ital x}}=0--13 MeV allow us to analyze the data. The angular distributions of positive-parity members of the ground-state band (the {ital K}{sup {pi}}=0{sup +} band) in {sup 44}Ti were well reproduced by the finite-range distorted-wave Born approximation calculations up to the transferred angular momentum of {ital L}=8. For the members of the negative-parity band (the {ital K}{sup {pi}}=0{sup {minus}} band) with the primary quantum number {ital N}=13, three levels at 6.22, 7.34, and 9.43 MeV were identified as the 1{sup {minus}}, 3{sup {minus}}, and 5{sup {minus}} states, respectively. The existence of a negative-parity band in {sup 44}Ti has been investigated for a long time and persistently gives considerable support to {alpha}-cluster models for nuclei heavier than {ital A}=40.

Direct cluster transfer in 3He bombardment of 13C at sub-barrier energies.

The angular distributions of cross sections for the reaction $^{13}\mathrm{C}$${(}^{3}$He${,}^{4}$He${)}^{12}$C leading to ground state and first excited 4.44 MeV, ${2}^{+}$ state of $^{12}\mathrm{C}$ have been measured at sub-Coulomb energies of ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=1.20 and 1.05 MeV. The angular distributions are asymmetric with respect to 90\ifmmode^\circ\else\textdegree\fi{} and anisotropies are also found to be much larger than those expected from compound nuclear processes. Analyses of the data, with assumptions of direct transfer processes, by exact finite range distorted wave Born approximation calculations show the presence of interference of two modes of direct transfer mechanisms of neutron transfer and $^{9}\mathrm{Be}$ cluster transfer from the target $^{13}\mathrm{C}$ to the projectile $^{3}\mathrm{He}$. These direct transfer calculations are in good agreement with the angular distributions and yield the value of the ratio of three nucleon spectroscopic strengths of first excited state to ground state of $^{12}\mathrm{C}$ in good agreement with the value predicted from structure calculations.

17O(d

Differential cross sections and analyzing powers were measured for $^{17}\mathrm{O}$(d\ensuremath{\rightarrow},t${)}^{16}$O with polarized deuterons of 89 MeV. States of $^{16}\mathrm{O}$ up to 22.89 MeV excitation energy have been studied with an overall resolution of 60 keV. Discrimination between analyzing powers (${\mathit{A}}_{\mathit{y}}$) for different j transfers was found to be very good. The unique ${\mathit{A}}_{\mathit{y}}$(\ensuremath{\theta}) shapes were used to deduce ${\mathit{p}}_{1/2}$-${\mathit{p}}_{3/2}$ mixing ratios for those levels where it was significant. We find unexpectedly strong mixing for the 6.130 MeV, ${3}^{\mathrm{\ensuremath{-}}}$, and 8.872 MeV, ${2}^{\mathrm{\ensuremath{-}}}$, levels. Exact finite-range distorted-wave Born approximation calculations were used to identify l transfers and to extract spectroscopic strengths. Up to 23 MeV excitation, pickup strength is dominated by 1p transfer; less than 2% of the observed particle-hole strength results from 2s, 1d, or 1f transfer. Twelve particle-hole matrix elements for (${\mathit{p}}_{1/2}^{\mathrm{\ensuremath{-}}1}$${\mathit{d}}_{5/2}$) and (${\mathit{p}}_{3/2}^{\mathrm{\ensuremath{-}}1}$${\mathit{d}}_{5/2}$) configurations have been deduced. Comparison with previous work shows general agreement except for the T=0,${\mathit{J}}^{\mathrm{\ensuremath{\pi}}}$=${3}^{\mathrm{\ensuremath{-}}}$ term.

Structure of 4Li and 4He observed in the 1H( alpha,3He p)n reaction.

Kinematically complete measurements of the $^{1}\mathrm{H}$(\ensuremath{\alpha}${,}^{3}$He p)n reaction at ${\mathit{E}}_{\mathrm{\ensuremath{\alpha}}}$=170 MeV were made at several $^{3}\mathrm{He}$ and proton angles. Assuming an incoherent sum of different multipole contributions in different reaction channels, it was possible to describe all measured spectra consistently, taking into account sequential decay of states in $^{4}\mathrm{He}$ and $^{4}\mathrm{Li}$ and the p-n final state interaction. The parameters used to describe the p-n final state interaction and excited states in $^{4}\mathrm{He}$ are consistent with previous measurements. Resonance energies and widths for the ground state and the first excited state of $^{4}\mathrm{Li}$ were extracted which are considerably lower than assumed so far. The measured cross sections are in agreement with distorted-wave Born approximation calculations using folding form factors.

Dominance of the direct reaction process in the 12C( 7Li, 7Be) 12B reaction at θL=0° and [formula omitted

The 12C( 7Li, 7Be) 12B reaction is studied at projectile energies of 14, 21 and 26 MeV/ A. Emitted 7Be particles are detected at θ L∼0° with an energy resolution of about 200 keV which is enough to separate transitions leading to the first excited state of 7Be ( 7Be 1) from ones leading to the ground state of 7Be( 7Be 0). At incident energies higher than 21 MeV/ A, both zero-degree excitation functions for 7Be 0 and 7Be 1 are well predicted by microscopic distorted-wave Born approximation calculations, but at an incident energy of 14 MeV/ A there are large contributions from complex reaction processes other than the one-step process.

9Be(t,p)11Be and the structure of 11Be.

The $^{9}\mathrm{Be}$(t,p${)}^{11}$Be reaction has been used to populate the low-lying states with a 15-MeV triton beam. Differential cross sections were measured for nine low-lying states and distorted-wave Born-approximation calculations were used to analyze the data. Contributions from p-shell, $^{10}\ensuremath{\bigotimes}$(sd${)}^{1}$, and $^{9}\mathrm{Be}$(g.s.)\ensuremath{\bigotimes}(sd${)}^{2}$ configurations were investigated. The dominant structure is suggested for nearly all states investigated in the present work.

Investigation of spin-isospin strength in 48Ca-->48Sc and 90Zr-->90Nb using the (6Li,6He) reaction.

The ${(}^{6}$Li${,}^{6}$He) reaction was studied on the target nuclei $^{48}\mathrm{Ca}$ and $^{90}\mathrm{Zr}$ at ${\mathit{E}}_{\mathrm{Li}}$=156 MeV at extreme forward reaction angles. From the zero degree spectra Gamow-Teller strength was extracted for excitation energies 0\ensuremath{\le}${\mathit{E}}_{\mathit{x}}$\ensuremath{\lesssim}20 MeV. The results are compared with distorted-wave Born approximation calculations and (p,n) data.

One-nucleon-transfer reactions induced by 20Ne at 500 and 600 MeV.

The ${(}^{20}$Ne${,}^{19}$Ne), ${(}^{20}$Ne${,}^{21}$Ne), and ${(}^{20}$Ne${,}^{21}$Na) reactions on $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$ have been investigated at 500 and 600 MeV incident energies. Experimental spectra have been compared with predictions of distorted-wave Born approximation calculations. The different shapes observed for proton and neutron pickup spectra are explained quite well by the calculations. In particular, the broad peak observed at about 6.5 MeV in the ${(}^{20}$Ne${,}^{21}$Ne) spectra is shown to originate from ejectile excitation in the 1${\mathit{d}}_{3/2}$, 1${\mathit{f}}_{7/2}$, and 2${\mathit{p}}_{3/2}$ orbitals. An important component of the ${(}^{20}$Ne${,}^{19}$Ne) cross section is due to three-body processes, such as the elastic breakup of $^{20}\mathrm{Ne}$ into $^{19}\mathrm{Ne}$ and one neutron. In addition, bumps are observed at about 1.5 and 10 MeV excitation energy in $^{209}\mathrm{Pb}$ and 2.5 and 14 MeV in $^{91}\mathrm{Zr}$. The low energy peaks are shown to originate mainly from neutron transfer to high spin orbitals, i.e., 1${\mathit{i}}_{11/2}$ and 1${\mathit{j}}_{15/2}$ in $^{209}\mathrm{Pb}$ and 1${\mathit{g}}_{7/2}$ and 1${\mathit{h}}_{11/2}$ in $^{91}\mathrm{Zr}$. Because of the selectivity of the ${(}^{20}$Ne, $^{19}\mathrm{Ne}$) reaction for large angular momentum transfer, it is proposed that the structures observed at 14 MeV in $^{91}\mathrm{Zr}$ and 10 MeV $^{209}\mathrm{Pb}$ are due to a neutron transfer to high spin orbitals, such as 1${\mathit{i}}_{13/2}$ and 1${\mathit{k}}_{17/2}$ in $^{91}\mathrm{Zr}$ and $^{209}\mathrm{Pb}$, respectively.

0

Stretched particle-hole states of a 0\ensuremath{\Elzxh}\ensuremath{\omega} (\ensuremath{\pi}${\mathit{d}}_{5/2}$,\ensuremath{\nu}${\mathit{d}}_{5/2}^{\mathrm{\ensuremath{-}}1}$${)}_{5}^{+}$ type were observed as low-lying isolated peaks in the high-resolution (p,n) reactions on $^{22}\mathrm{Ne}$ and $^{26}\mathrm{Mg}$ at ${\mathit{E}}_{\mathit{p}}$=35 MeV. Angular distributions of the differential cross sections have been successfully interpreted, especially at large angles, or in high-momentum transfer regions (q\ensuremath{\sim}2 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$), by microscopic distorted-wave Born approximation calculations using shell-model wave functions and the M3Y interaction. No quenching of the (p,n) cross sections has been observed for these 0\ensuremath{\Elzxh}\ensuremath{\omega} stretched transitions in light nuclei.

Excitation of isovector states by the ( 7Li, 7Be) reaction on 12C and 13C

Isovector states in 12B and 13B are studied by using the ( 7Li, 7Be) reaction at a projectile energy of 21 MeV/nucleon. Angular distributions are measured at forward scattering angles of θ L ⩽ 10° and compared with one-step distorted-wave Born approximation (DWBA) calculations. The form factors are microscopically evaluated with effective nucleon-nucleon interactions and realistic transition densities. The DWBA calculations reproduce the observed cross sections with normalization factors near to unity. This suggests that the ( 7Li, 7Be) reaction at 21 MeV/nucleon proceeds mainly through the one-step direct reaction process. The excitation of the giant dipole resonance is confirmed at E x = 7.6 MeV in 12 B and at E x = 9.5 MeV in 13B, from which the isovector collective potential strength is obtained to be V 1 ∼ 50 MeV. The isovector octupole strength is observed in three states in 12B, but it is not distinctly observed in 13B.

Ad hoc Coulomb corrections to the radiation tail.

We give an empirically derived correction factor to an ad hoc procedure of including Coulomb corrections in the plane-wave calculation of the radiation tail accompanying elastic electron scattering from the atomic nucleus. Apart from regions of the radiation tail with very large Coulomb distortion effects, our corrected ad hoc results agree with a distorted-wave Born approximation calculation of the radiation tail to better than 5%.

Neutron pickup strength in 87Sr from the (p

Differential cross section and analyzing power angular distributions have been obtained for the $^{87}(\mathit{p}\ensuremath{\rightarrow}$,d${)}^{86}$Sr reaction in two measurements using different magnetic spectrometers at incident proton energies of 94.2 and 91.8 MeV. Typical energy resolutions of 70 and 40 keV, respectively, were achieved. Optical-model parameters were obtained by fitting the elastic scattering data measured to laboratory angles of 90\ifmmode^\circ\else\textdegree\fi{} for protons at 94.2 MeV and to 120\ifmmode^\circ\else\textdegree\fi{} for deuterons at 88.0 MeV. Standard exact finite range distorted-wave Born approximation calculations using these optical-model parameters failed to describe the experimental data, while the adiabatic approximation improved the description to some extent. Orbital and total angular momenta, l and j, of the picked-up neutron were extracted from the angular distributions of the differential cross section and analyzing power for all the residual states observed. The rms radius of the 1${g}_{9/2}$ neutron orbital, obtained from magnetic electron scattering, was used in the extraction of strength for this orbital, while rms radii from Hartree-Fock calculations were used for the 2${p}_{1/2}$, 2${p}_{3/2}$, 1${f}_{5/2}$, and 1${f}_{7/2}$ orbitals. The observed 1${g}_{9/2}$ strength, spread over 20 states up to 5.4-MeV excitation, indicates a depletion of about 43% compared to simple shell-model expectations. Similarly, the observed 1${f}_{5/2}$ strength, spread over 17 states, indicates a depletion of about 32%. The weighted summed spectroscopic strength for the 1${g}_{9/2}$ orbital, deduced from the present study, is lower than that obtained from magnetic electron scattering.

Inelastic scattering of 210 MeV 6Li ions from 12C, 28Si, and 58Ni: Test of unique 6Li potentials.

Measurements of the inelastic scattering of 210 MeV $^{6}\mathrm{Li}$ ions from $^{12}\mathrm{C}$, $^{28}\mathrm{Si}$, and $^{58}\mathrm{Ni}$ have been made. Differential cross sections leading to the first excited (${2}^{+}$) states of the target nuclei were obtained. The angular distributions for $^{12}\mathrm{C}$ (6.8\ifmmode^\circ\else\textdegree\fi{}--60.6\ifmmode^\circ\else\textdegree\fi{}), $^{28}\mathrm{Si}$ (4.9\ifmmode^\circ\else\textdegree\fi{}--45.9\ifmmode^\circ\else\textdegree\fi{}), and $^{58}\mathrm{Ni}$ (7.2\ifmmode^\circ\else\textdegree\fi{}--48.3\ifmmode^\circ\else\textdegree\fi{}) are similar in shape to those for elastic scattering, with diffractive oscillations at forward angles followed by smooth exponential falloff, characteristic of refractive nuclear scattering, at the larger angles. Distorted-wave Born approximation calculations provide good fits to the data when unique $^{6}\mathrm{Li}$ optical-model potentials, derived from elastic scattering data, are used. Calculations with discrete ambiguous potentials deviate from the data at large angles. Coupled-channels calculations reproduce both the elastic and inelastic scattering data without significant changes in the unique potentials. The deformation lengths, ${\ensuremath{\beta}}_{2}$R, derived from the analyses are compared with results of previous measurements. The deduced quadrupole moments, ${q}_{20}$, are in excellent agreement with those obtained from electromagnetic measurements.

Excitation of spin- and isospin-flip states with the (d, d s=0 ) reaction

The (d, ds=0) reaction has been studied for the first time at Ed = 56 MeV and 70 MeV. It is demonstrated that the reaction is a useful tool for the study of the inelastic excitation of the spin- and isospin-flip mode. Several states in 12C with T= 1 and S= 1 are strongly excited. The differential cross sections and vector analyzing powers are reasonably reproduced by the distorted-wave Born-approximation calculation.

Ca48(d,n)49Sc reaction at 79 MeV

We measured differential cross sections and vector analyzing powers for the $^{48}\mathrm{Ca}$(d,n${)}^{49}$Sc reaction at 79 MeV. An overall energy resolution of about 325 keV was achieved, and data were extracted for states up to 3.4 MeV of excitation. Both distorted-wave Born approximation and Johnson-Soper adiabatic approximation calculations were performed; in general, the Johnson-Soper adiabatic approximation calculations provide a better description of the data, and yield reasonable spectroscopic factors.

Elastic and inelastic scattering of 6li from 70,72Ge AT 44 MeV

The ( 6Li, 6Li') scattering on 70Ge and 72Ge has been studied at 44 MeV using a tandem Van de Graaff accelerator and a split-pole magnetic spectrometer, with an overall energy resolution of 80 keV. Angular distributions have been obtained for 10 states in 70Ge and 72Ge. The 2 1 + and 3 1 − states are strongly excited in comparison with the 0 2 +, 2 2 +, and 4 1 + states. The data have been analysed with the distorted-wave Born approximation and coupled-channels calculations based on the (harmonic and anharmonic) vibrational model and asymmetric rotor model.

(p148,t)146Gd reaction: Neutron states inGd146

We have used the $^{148}(\mathit{p}$,t${)}^{146}$Gd reaction with protons of 34.6 and 24.9 MeV to study levels in $^{146}\mathrm{Gd}$ below ${E}_{x}$=5.6 MeV. The radioactive target material was deposited on the carbon support foil from an isotope separator. Triton spectra were analyzed by a magnetic quadrupole-dipole-dipole-dipole spectrometer (Q3D) at 11 angles between 10\ifmmode^\circ\else\textdegree\fi{} and 60\ifmmode^\circ\else\textdegree\fi{}. By comparing the angular distributions with the results of distorted-wave Born approximation calculations we obtained definitive L-transfer values for 11 excited states, including a strongly populated ${0}^{+}$ state at 4534 keV, and approximate L values for about 50 additional states. A search for members of the two-octupole-phonon quartet of states expected to occur at \ensuremath{\sim}3.2 MeV of excitation (twice the single-phonon energy) revealed no convincing evidence of the ${0}^{+}$ component, but the ${2}^{+}$ component could be one of the four new ${2}^{+}$ states identified in this region. A comparison between the most strongly populated low-lying states of $^{142}\mathrm{Sm}$ in the $^{144}(\mathit{p}$,t) reaction and states in the pairing-vibrational region of $^{146}\mathrm{Gd}$ reveals a possible set of states whose energies and (p,t) cross sections are in reasonable agreement with predictions of the harmonic pairing-vibration model.

Evaluation of E2 form factor: 24Mg.

Longitudinal and transverse electron scattering form factors for the ${2}^{+}$ state at 1.37 MeV of the $^{24}\mathrm{Mg}$ nucleus were evaluated with rotational model wave functions. Four different approaches were used for the transverse E2 form factor: projected Hartree Fock, cranking model, rigid rotor, and irrotational flow. For the nuclear intrinsic wave function, the Nilsson model was assumed in all approaches yielding the calculation of the form factor in the plane-wave and distorted-wave Born approximations. The results are discussed and compared with a recent measurement performed for 180\ifmmode^\circ\else\textdegree\fi{} electrons scattered from this state. The distorted-wave Born approximation calculation, taking into account first-order corrections due to 〈${J}_{\ensuremath{\perp}}^{2}$${〉}^{\mathrm{\ensuremath{-}}1}$, shows that projected Hartree Fock and irrotational flow models give the best agreement with the available data and compete in quality with more complex calculations performed in the ``shell model'' approach.