Distorted-wave Born-approximation Predictions Research Articles

Multitude of2+discrete states inSn124observed via the(O17,O′17γ)reaction: Evidence for pygmy quadrupole states

A multitude of discrete 2+ states in Sn124 with energy up to 5 MeV were populated and identified with the (O17, O′17γ) reaction at 340 MeV. Cross sections were compared with distorted wave Born approximation predictions and in general a good agreement was found. The measured energy and intensity distributions of the 2+ states are very similar to the predictions based on self-consistent density functional theory and extended QRPA approach accounting for multiphonon degrees of freedom. This provides evidence of the excitation of the pygmy quadrupole resonance in skin nuclei.1 MoreReceived 9 June 2015DOI:https://doi.org/10.1103/PhysRevC.92.014330©2015 American Physical Society

Nuclear structure of 229,231Th studied with the 230,232Th( [formula omitted]) reactions

Detailed angular distributions for the 230,232Th( d , t ) 229,231Th reactions were measured with 17 MeV deuterons, using a magnetic spectrograph to analyze the reaction products. Comparisons with distorted wave Born approximation predictions were used to determine ℓ-values and spectroscopic strengths for many levels in both nuclides. These results reconfirm previous assignments for the 3 / 2 + [ 631 ] band in 229Th, with its bandhead unresolved from the 5 / 2 + [ 633 ] ground state, providing support for the existence of the much-sought “3.5 eV” isomer (for which the latest reported energy is 7.6 ± 0.5 eV ). Although 231Th was previously well studied, many new spin-parity assignments have been made and some changes to adopted model assignments are proposed. There is evidence in both isotopes for appreciable mixing of single-particle orbitals with other configurations, as predicted by the Quasiparticle Phonon Model. Single-nucleon transfer strengths are described much better with earlier values for the Nilsson model parameters κ and μ than later values that have been widely used. An earlier 232Th( d , t ) study concluded that serious errors could result in the commonly-used method of predicting cross sections by combining distorted wave Born approximation calculations using spherical form factors with Nilsson wave functions for a deformed potential, but the present work shows this conclusion is not valid because it was based on inadequate knowledge of the 231Th nuclear structure.

Mechanism of the 15N(p, α) 12C reaction at Ep=9.09–43.7 MeV

The spectroscopic-factor amplitudes for the triton-cluster transfer are used in distorted wave born approximation (DWBA) analyses for the first six 12C states, up to E x =17.76 MeV, in the reaction 15N(p, α) for E p=9.09–43.7 MeV. Agreements are obtained for most 12C states between the theoretically predicted spectroscopic factors ( S) and both of experimental and theoretical forward integrated cross-section values (at E p∼43.7 MeV) and their sequence states with the same nuclear parameters. The theoretical spectroscopic factors failed to predict the transition strengths for the two 12C states at 7.6542 and 17.76 MeV, while the DWBA predictions failed to reproduce the strengths of the three 12C states at 7.6542, 14.083 and 17.76 MeV. This is probably, in the first case, due to the inclusion of other direct mechanisms and (or) to the multi-step processes in their mechanism, while for the second case, it is may be due to either the angular momentum mismatching effect or the choice of the optical parameters. The agreement between theoretical and experimental data for the first six investigated 12C states indicate the success of the Cohen–Kurath wave-functions itself and their accuracy. They also indicate the success of the model of calculations of spectroscopic factors.

Effect of theα-nucleus potential on the28Si(α,p)31Preaction

The differential cross section of the ${}^{28}\mathrm{Si}(\ensuremath{\alpha}{,p)}^{31}\mathrm{P}$ reaction for 26 MeV incident energy has been analyzed in the distorted wave Born approximation (DWBA) with zero and full-finite range using a deep and shallow optical, Michel and molecular potentials in the incident channel, and a usual optical model potential for proton in the final channel. The parameters of potential in the entrance channel are determined from the elastic scattering data. The calculations done with the deep optical and Michel potentials reproduce the structure of the angular distributions reasonably well, but fail to account for the absolute magnitudes by a few orders. The shallow optical one is satisfactory up to about ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=100\ifmmode^\circ\else\textdegree\fi{}.$ The molecular potential, on the other hand, reproduces both the absolute cross sections and the pattern of the angular distributions. Coupled-channels Born approximation calculations improve fits to the data over the DWBA predictions.

Analysing powers and differential cross sections of (3He,p) reactions on 6Li and 7Li at low energy

Angular distributions of the differential cross sections and analysing powers were measured at an energy of 4.6 MeV. The results are compared with the distorted wave Born approximation predictions for two-nucleon transfer and for a deuteron-cluster transfer. The agreement is qualitative at best, and a discussion of alternatives to improve it is presented.

Neutron-spectroscopic strength in Ru isotopes.

A systematic, high resolution (6--8 keV) study of (d,t) reactions on $^{100,102,104}\mathrm{Ru}$ is reported. Spectroscopic factors were extracted by comparison of experimental angular distributions with distorted wave Born approximation predictions. All of the information for $^{99}\mathrm{Ru}$ and, for excitation energies above 0.9 MeV, for $^{103}\mathrm{Ru}$ is new. Most of the strength expected for the 50--82 neutron shell was found. The strength distributions are discussed, also in comparison with the corresponding stripping reactions. Special attention is focused on extremely low and relatively intense l=3 excitations and on the l=4 transfer pattern observed.

Nuclear structure of 159Tb, 161Tb and 163Tb studied with the (t, α) reaction

The 160Dy(t, α) 159Tb, 162Dy(t, α) 161Tb, and 164Dy(t, α) 163Tb reactions have been studied using a 17 MeV triton beam from the McMaster University Tandem Accelerator. The α-spectra were analyzed with a magnetic spectrograph and the resolution obtained in the best spectra was 16–19 keV FWHM (full-width half maximum). Transferred l-values were determined by comparing the measured angular distributions with distorted-wave Born-approximation predictions. The results were interpreted in terms of the Nilsson model with pairing and Coriolis-mixing effects included. Prior to these experiments the only information available on excited states of 163Tb was from an unpublished (d, 3He) experiment. Now several rotational bands based on single-proton Nilsson states have been assigned. The 3 2 +[411] , 1 2 +[411] , 5 2 −[532] , 7 2 −[532] , 5 2 +[413], 1 2 +[420] and 3 2 −[541] bands have been observed.

Nuclear structure and medium effects in p

Nonrelativistic distorted-wave Born approximation predictions for polarized proton elastic scattering from polarized $^{13}\mathrm{C}$ are discussed and compared with data. Effects due to Pauli blocking, binding potentials in intermediate states, and shell-model configuration mixing are studied. The changes in the predicted polarized target spin observables are small at forward angles but can be significant at larger scattering angles.

Ground State Transition of (p,t) Reactions on Ni Isotopes

Angular distributions of 58,60,62,64Ni(p,t) ground state transitions at Ep = 25 MeV have been measured and compared with distorted wave Born approximation predictions. Relative enhancement factors for four Ni isotopes have been extracted. Comparison between the enhancement factors and the predictions of interacting boson approximation model has been made. It is found that a value of Ων = 6 is needed to describe the experimental result in SU(5) calculation.

Electron-photon angular correlation study of electron impact excitation of the 4p5(2P3/2)5s3P1 state of krypton

Excitation of the 4p5(2P3/2)5s3P1 state of krypton by 30 eV incident electrons has been studied using the electron-photon angular correlation technique. The alignment and orientation of this state can be completely described using four independent parameters, three of which can in principle be obtained from the present measurements of angular correlations with two detector geometries. Difficulties encountered in the extraction of the spin-dependent parameters are discussed. There is generally good agreement between the experimentally measured angular correlations and distorted-wave Born approximation predictions.

Analyzing powers and cross sections of inclusive polarized proton scattering on 208Pb

Inclusive polarized proton-nucleus scattering on 208Pb has been studied at 290 and 500 MeV. The measurements cover a broad range (0–250 MeV) of excitation energy over the 4°–27° angular range. The measured analyzing powers and cross sections for the continuum were compared with recent relativistic and nonrelativistic distorted-wave impulse approximation calculations. The cross section in the continuum region is found to be dominated by single-step quasi-free scattering. Differences of up to 40% between the analyzing powers measured at the quasi-free peak as opposed to free NN values strongly support the relativistic impulse approximation predictions for the quasi-free region, and indicate the presence of relativistic medium effects. Analyzing powers and cross sections of several low-lying states were compared with both nonrelativistic and relativistic distorted-wave Born approximation predictions.

Level structure of 101Ru from the 100Ru(d,p) reaction.

Energy levels of /sup 101/Ru have been studied by the /sup 100/Ru(d,p)/sup 101/Ru reaction at an incident deuteron energy of 12 MeV. Outgoing particles were momentum analyzed by a magnetic spectrograph and detected in nuclear emulsion plates, with an energy resolution of 7.5 keV. A total of 68 levels up to 3.2 MeV excitation energy was identified, about two-thirds of them reported for the first time. Experimental angular distributions were compared to distorted-wave Born approximation predictions and reduced spectroscopic factors obtained. The total l = 2 and 75% of l = 0, 4, and 5 spectroscopic strengths were located. Attention is drawn to transitions to low-lying states in /sup 101/Ru (below E/sub exc/ = 0.75 MeV) with l = 3 and l = 1 character.

Single-nucleon transfer reactions induced by 376-MeV 17O on 208Pb.

The one-nucleon $^{208}\mathrm{Pb}$${(}^{17}$O${,}^{16}$O) and $^{208}\mathrm{Pb}$${(}^{17}$O${,}^{18}$F) transfer reactions have been investigated at ${E}_{\mathrm{lab}{(\mathrm{}}^{17}\mathrm{O})=376}$ MeV. The data were analyzed in terms of the distorted-wave Born approximation. The distorted-wave Born approximation predictions reproduce fairly well the bell shape of the various angular distributions and the relative intensities of the various single-particle and single-hole transitions.

Analyzing powers for 207Pb(t

Analyzing powers and differential cross sections for $^{207}\mathrm{Pb}$(t\ensuremath{\rightarrow},p${)}^{209}$Pb have been studied at 17 MeV in order to identify the effects of second-order (t\ensuremath{\rightarrow},p) transfer mechanisms. Angular distributions for transitions to seven single-particle states in $^{209}\mathrm{Pb}$ and to the first pairing vibration state in $^{209}\mathrm{Pb}$ were measured for the angular range 6?(de\ensuremath{\le}theta\ensuremath{\le}70\ifmmode^\circ\else\textdegree\fi{}. The observed L dependence of the differential cross sections is adequately reproduced by one-step finite-range distorted-wave Born approximation calculations, but the absolute magnitude of these transitions is underpredicted by factors ranging from 1.25 to 2.5.The analyzing powers for the transitions to the seven well-known single-particle states are significantly different from each other and do not follow one-step distorted-wave Born approximation predictions or any other simple dependence on the transferred angular momentum L. The observed analyzing powers for the L=5 transfers to the ${(9/2)}^{+}$ ground state and the ${(11/2)}^{+}$ state at 0.778 MeV differ even in sign. It is found that the inclusion of two-step second-order distorted-wave Born approximation channels, which treat the dominant single-neutron stripping channels as intermediate states, can yield qualitatively correct analyzing powers. In agreement with experiment, two-step calculations predict analyzing powers which depend strongly on the spins (${j}_{1}$,${j}_{2}$) of the transferred neutrons.However, quantitatively satisfactory results have only been obtained if an ``adiabatic'' scattering potential for the intermediate projectile is used. The adiabatic potential, obtained as the sum of a proton and a neutron potential, gives a considerably deeper absorptive part than the empirical deuteron optical model potential. This representation of the intermediate scattering state is supported by a recent two-nucleon transfer model by Austern and Kawai. The inclusion of sequential stripping channels also gives a needed enhancement of the absolute cross sections, although zero-range calculations do not always give quantitatively correct enhancements.

The [formula omitted] residual interaction from 87Sr(d, t) 86Sr

Differential cross sections for 87Sr(d, t) 86Sr transitions to the (1 g 9 2 ) −2 states of 86Sr were obtained with the Pittsburgh 18 MeV deuteron beam and the Enge split-pole spectrograph. States of 86Sr up to 3.82 MeV in excitation were studied with a total resolution of 12 keV. Successful distorted-wave Born approximation (DWBA) predictions for 87Sr(d, t) 86Sr angular distributions permitted the extraction of l-values and spectroscopic strengths. The sum-rule value agrees with the observed value for the (1 g 9 2 ) −2 configuration. The observed g 9 2 strength is spread over 13 states. Contrary to an earlier interpretation, the 0 + ground state is found to contain only 65% of the ( g 9 2 ) 2 0 + strength. Similarly, the full 4 + strength is not located in a single state. The new data change the interpretation of the ( g 9 2 ) −2 spectrum of 86Sr. They significantly alter the deduced low-spin matrix elements and bring them into much closer agreement with those derived from 88Y. Several new negative-parity states dominated by l = 1 orbital angular momentum transfer have also been identified.

The (g) residual interaction from Sr(d, t)Sr

Differential cross sections for 87Sr(d, t)86Sr transitions to the (1g 92)−2 states of 86Sr were obtained with the Pittsburgh 18 MeV deuteron beam and the Enge split-pole spectrograph. States of 86Sr up to 3.82 MeV in excitation were studied with a total resolution of 12 keV. Successful distorted-wave Born approximation (DWBA) predictions for 87Sr(d, t) 86Sr angular distributions permitted the extraction of l-values and spectroscopic strengths. The sum-rule value agrees with the observed value for the (1g 92)−2 configuration. The observed g 92 strength is spread over 13 states. Contrary to an earlier interpretation, the 0+ ground state is found to contain only 65% of the (g92)20+ strength. Similarly, the full 4+ strength is not located in a single state. The new data change the interpretation of the (g92)−2 spectrum of 86Sr. They significantly alter the deduced low-spin matrix elements and bring them into much closer agreement with those derived from 88Y. Several new negative-parity states dominated by l = 1 orbital angular momentum transfer have also been identified.

Pb206(α,d)Bi208at 48 MeV

The $^{206}\mathrm{Pb}(\ensuremath{\alpha},\mathrm{d})^{208}\mathrm{Bi}$ reaction was investigated at 48.2 MeV with about 25 keV resolution. Angular distributions were obtained for 48 levels at excitation energies up to 5 MeV. Many previously unknown levels were seen and most seem to have two-particle---two-hole structure and spins above 6; however, the relatively structureless angular distributions permit only approximate $L$ assignments. Transitions to six low-lying one-particle---one-hole states were analyzed in detail. Distorted-wave Born approximation predictions agreed with the observed angular distributions, but the absolute cross sections computed from published $^{206}\mathrm{Pb}$ and $^{208}\mathrm{Bi}$ wave functions are generally larger than observed, particularly those for the ${J}_{max}$ states. Contributions of the dominant two-step sequential stripping channels to the one-step results were investigated. They were important and gave varying amounts of enhancement for all six levels. The observed quenching of the ${J}_{max}$ cross sections was not reproduced.

Quasielastic transfer reactions induced byFe56onNi58,Ni64, andSn122

Differential cross sections sigma(Z,A,E,theta) for the quasielastic projectilelike reaction products from the bombardment of /sup 56/Fe on /sup 58,64/Ni and /sup 122/Sn at 5.9 and 8.5 MeV/nucleon have been measured with a channel-plate time-of-flight telescope followed by a ..delta..E-E gas-ionization chamber. Angular intervals of 10/sup 0/--15/sup 0/ centered at the grazing angles were covered. The differential cross sections for one-proton transfer with Q values near zero were analyzed using the distorted-wave Born approximation, which can account for the shape of the angular distributions and, to better than a factor of 5, for the absolute cross sections. At Q values more negative than -10 MeV the measured angular distributions begin to deviate from the distorted-wave Born approximation predictions. Substructures were observed in the energy spectra near Q = -25 MeV. A model for unfolding the effects of particle evaporation from the reaction products is developed. It is shown that, within the limitations of the model, the observed substructures cannot be accounted for by evaporation effects alone but must be present in the primary energy spectra. Finally the optimum Q values are analyzed with a one-body dissipation model. The model is reasonably successful if the concept of a local Fermi momentum ismore » introduced.« less

(t→,p) reaction onFe56,Ni58,60,64: Structure and reaction-mechanism effects

Differential cross sections and analyzing powers have been measured for the ($\stackrel{\ensuremath{\rightarrow}}{t}$,$p$) reaction on $^{56}\mathrm{Fe}$, $^{58,60,64}\mathrm{Ni}$ at an incident energy of 17 MeV. Data were obtained for states up to an excitation of 3.7, 3.13, 2.8, and 4.9 MeV in $^{58}\mathrm{Fe}$, $^{60,62,66}\mathrm{Ni}$, respectively, including about ten states each with spin and parity ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$, and two states each with ${3}^{\ensuremath{-}}$ and ${5}^{\ensuremath{-}}$. The measured analyzing powers show angular distributions characteristic of the $L$ transfer, with variations from state to state comparable to those observed for cross sections of a given $L$. Angular distributions of the differential cross sections for strong transitions were generally fitted well by a standard distorted-wave Born approximation calculation. There appear to be significant discrepancies between the data and distorted-wave Born approximation predictions for excited ${0}^{+}$ states and for most ${4}^{+}$ states. Distorted-wave Born approximation predictions of analyzing power were in qualitative agreement with the data for ground-state transitions and for strong $L=2$ transitions but this was not true for $L=0$ transitions to excited states and for transitions with $L>2$. The effect of varying the optical parameters used in the distorted-wave Born approximation calculations was investigated; it was found that predictions of analyzing power for $L>0$ were quite sensitive to the choice of proton potential. The effects of two-step reaction processes were also investigated. These were found to produce large changes in predicted cross sections and analyzing powers, which could account for some of the discrepancies between these results and distorted-wave Born approximation predictions.NUCLEAR REACTIONS $^{56}\mathrm{Fe}$,$^{58,60,64}\mathrm{Ni}$($\stackrel{\ensuremath{\rightarrow}}{t}$,$p$) $E=17$ MeV; polarized beam; enriched targets; measured $\ensuremath{\sigma}({E}_{p},\ensuremath{\theta})$, ${A}_{y}({E}_{p},\ensuremath{\theta})$; DWBA; coupled reaction channel analysis.

Hole states excited by theMg24(p,d)Mg23reaction at 95 MeV

Experimental excitation energies and angular distributions have been obtained for 33 deuteron groups from the $^{24}\mathrm{Mg}$($p$,$d$) reaction at 94.8-MeV bombarding energy with 80-keV experimental resolution. Energies obtained for states in $^{23}\mathrm{Mg}$ are in agreement with the sixth compilation of Endt and van der Leun up to 7.25 MeV and the recent unpublished ($p$,$t$) study of Nann et al. up to 9.72 MeV. Energies are determined in the present work for 18 additional groups corresponding to excitations between 9.8 and 13.28 MeV. Angular distributions from 6\ifmmode^\circ\else\textdegree\fi{} to 88\ifmmode^\circ\else\textdegree\fi{} laboratory (momentum transfers up to 660 MeV/c) show characteristic oscillatory signatures for $l=0$ transitions and broad peaked nonoscillatory behavior for presumed multistep transitions. $l=1 \mathrm{and} 2$ transitions show a very similar exponential falloff with large momentum transfer, but they can be clearly distinguished by their small-angle behavior after division by an empirical exponential factor or by the dominant momentum transfer dependence from a plane-wave analysis. $l=1$ transitions are observed to deep-hole states at 8.91-, 9.02-, 9.67-, and 10.57-MeV excitation. The angular distributions also lead to very probable assignments of $\frac{5}{{2}^{\ensuremath{-}}}$ and $\frac{7}{{2}^{+}}$ to the 3.97- and 4.68-MeV states of $^{23}\mathrm{Mg}$, and are consistent with $\frac{9}{{2}^{+}}$ and $\frac{11}{{2}^{+}}$ assignments to the 2.71- and 5.45-MeV states. Distorted-wave Born approximation (DWBA) predictions using optical potentials from published elastic scattering results show rather good agreement with the shapes of the observed angular distributions for $l=2$ transitions, but spectroscopic factors vary by up to a factor of 3 depending on the deuteron potential employed. $l=0$ transitions are not fitted in either shape or position of the oscillations, which may be due to the fact that deuteron wave functions derived from elastic scattering are not accurate in the nuclear interior. Reasonable shapes are predicted by preliminary coupled-channel Born approximation (CCBA) analyses for transitions believed to proceed in two steps.NUCLEAR REACTIONS $^{24}\mathrm{Mg}$ ($p$,$d$), $E=94.8$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$. $^{23}\mathrm{Mg}$ levels deduced $l$, $J$, $\ensuremath{\pi}$. $S$. DWBA analysis, resolution 80 keV, $\ensuremath{\theta}=6\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}88\ifmmode^\circ\else\textdegree\fi{}$, $\ensuremath{\Delta}\ensuremath{\theta}=2\ifmmode^\circ\else\textdegree\fi{} or 4\ifmmode^\circ\else\textdegree\fi{}$, ${E}_{x}=0\ensuremath{-}13.28$ MeV.