Microscopic Distorted-wave Born Approximation Calculations Research Articles

Two-neutron transfer in Sn isotopes beyond theN=82shell closure

We have performed microscopic distorted-wave Born approximation calculations of differential cross sections for the two reactions $^{136}\mathrm{Sn}(p,t)^{134}\mathrm{Sn}$ and $^{134}\mathrm{Sn}(t,p)^{136}\mathrm{Sn}$, which are within reach of near-future experiments with radioactive ion beams. We have described the initial and final nuclear states in terms of the shell model, employing a realistic low-momentum two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential that has already proved quite successful in describing the available low-energy spectrum of $^{134}\mathrm{Sn}$. We discuss the main features of the predicted cross sections for the population of the low-lying yrast states in the two nuclei considered.

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.

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.

Sn118levels studied by theSn120(p,t) reaction: High-resolution measurements, shell model, and distorted-wave Born approximation calculations

Cross-section angular distributions of 38 ($p$, $t$) transitions to final states of $^{118}\mathrm{Sn}$ up to an excitation energy of 3.597 MeV have been measured in a high-resolution experiment at an incident proton energy of 21 MeV. A distorted-wave Born approximation (DWBA) analysis of the 38 experimental differential cross sections, carried out by using conventional Woods-Saxon potentials, allowed us either 18 confirmations of previous spin and parity values or new assignments of spin and parity to 14 states of $^{118}\mathrm{Sn}$. A shell-model calculation has been performed by using a realistic two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential. The doubly-magic nucleus $^{132}\mathrm{Sn}$ is assumed as a closed core, with 14 valence neutron holes occupying the five levels of the 50--82 shell. Within this model space the calculations are performed by employing the seniority scheme including states with seniority up to 4. The energy spectrum of $^{118}\mathrm{Sn}$ has been calculated and compared with the experimental one. The theoretical two-neutron spectroscopic amplitudes are used in the microscopic DWBA calculations of some cross-section angular distributions.

Spectroscopy ofSn110via the high-resolutionSn112(p,t)Sn110reaction

The {sup 112}Sn(p,t){sup 110}Sn reaction was studied in a high-resolution experiment at an incident proton energy of 26 MeV. Angular distributions for 27 transitions to levels of {sup 110}Sn up to an excitation energy of {approx}4.3 MeV were measured. A distorted-wave Born approximation (DWBA) analysis of experimental angular distributions using conventional Woods-Saxon potentials were done, allowing either the confirmation of previous spin and parity values or the assignment of new spin and parity to a large number of {sup 110}Sn states. A shell-model study was performed using an effective interaction derived from the CD-Bonn nucleon-nucleon potential. The energy spectra are calculated and compared with experiment, whereas the theoretical two-nucleon spectroscopic amplitudes, evaluated in a truncated seniority space, are used in the microscopic DWBA calculation of some cross-section angular distributions.

12C(n,p)12B reaction at 56, 60, and 65 MeV.

The {sup 12}C({ital n},{ital p}){sup 12}B reaction has been studied at 60 and 65 MeV. Cross sections for the 1{sup +} ground state, the 2{sup +} first excited state at 0.95 MeV, an unresolved pair of 2{sup {minus}} and 4{sup {minus}} states at 4.4 MeV, and the analogs of the giant electric dipole and spin-dipole resonances around 7.7 MeV have been extracted and compared with previous data at 56 MeV and with microscopic distorted-wave Born approximation calculations. The shapes of angular distributions out to {ital q}{similar to}2 fm{sup {minus}1} are well reproduced by the calculations. A comparison of ({ital n},{ital p}), ({ital p},{ital n}), and ({ital p},{ital p}{prime}) cross sections near 60 MeV is made, and a value for {vert bar}{ital J}{sub {sigma}{tau}}{vert bar} (the volume integral of the central, spin-isospin part of the effective nucleon-nucleon interaction) is extracted. The magnitudes of cross sections for negative-parity states can be qualitatively understood when the loose binding of the {ital sd}-shell neutron in the final state and the effect of ground-state correlations on the dipole and spin-dipole strengths are taken into account.

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.

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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.

Neutron transition multipole moment for 88Sr( alpha, alpha ')88Sr (2(+), 1.84 MeV).

The neutron transition multipole moment, ${M}_{n}$, for (${0}^{+}$\ensuremath{\rightarrow}${2}^{+}$, 1.84 MeV) transition is inferred by measuring the (\ensuremath{\alpha},\ensuremath{\alpha}') angular distribution at ${E}_{\ensuremath{\alpha}}$=50 MeV and comparing it with a microscopic distorted-wave Born approximation calculation. Proton transition densities are taken from electron scattering data. ${M}_{n}$/${M}_{p}$ is found to be substantially less than N/Z in agreement with the (p,p') result.

Isovector and isoscalar spin-flip excitations in even-even s-d shell nuclei excited by inelastic proton scattering.

Forward-angle cross sections for ${1}^{+}$ states have been measured in $^{24}$,26Mg, $^{28}\mathrm{Si}$, and $^{32}\mathrm{S}$ by 201 MeV proton inelastic scattering. Comparisons are made with (\ensuremath{\gamma},\ensuremath{\gamma}'), (e,e'), and (p,n) results. The measured strength is compared with microscopic distorted-wave Born approximation calculations using large-scale shell-model wave functions. Ratios of experimental to theoretical ${1}^{+}$ strengths are given. Almost no quenching is observed.

Spin-flip transitions in 16O and 18O excited by inelastic proton scattering.

Inelastic proton scattering at forward angles has been carried out on /sup 16/O and /sup 18/O at a bombarding energy of 201 MeV. The (p,p') spin-flip transitions to 1/sup +/ and 2/sup -/ states are compared with (e,e'), (p,..gamma..), and charge exchange data, and with microscopic distorted-wave Born approximation calculations using shell model wave functions. The ratios of orbital to spin contributions are deduced for the known 1/sup +/ states in /sup 16/O.

Analyzing powers for proton inelastic scattering to unnatural-parity states inCa40andSi28

Cross sections and analyzing powers in proton inelastic scattering leading to unnatural parity states of ${2}^{\ensuremath{-}}$, $T=0$ (6.025 and 6.75 MeV), ${2}^{\ensuremath{-}}$, $T=1$ (8.42 MeV) in $^{40}\mathrm{Ca}$ and ${6}^{\ensuremath{-}}$, $T=0$ (11.58 MeV) and ${6}^{\ensuremath{-}}$, $T=1$ (14.36 MeV) in $^{28}\mathrm{Si}$ were measured at 65 MeV. These states are pair states of different isospin with the same spin and parity. The analyzing powers for a pair of $T=0$ and $T=1$ excitations in $^{40}\mathrm{Ca}$ show an isospin dependence not observed in $^{28}\mathrm{Si}$. The measured angular distributions were compared with microscopic distorted-wave Born approximation calculations using two versions of the effective nucleon-nucleon interaction. As expected, the interaction emphasizing the tensor contribution predicts analyzing powers and cross sections in better agreement with the experimental data. As factors to produce a difference in the analyzing powers between the $T=0$ and the $T=1$ states, the effect of two transferred orbital angular momentum amplitudes allowed in a transition and the energy dependence of the isoscalar spin-dependent terms in the effective interaction are discussed.NUCLEAR REACTIONS $^{40}\mathrm{Ca}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}, {p}^{\ensuremath{'}})^{40}\mathrm{Ca}$, $^{28}\mathrm{Si}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}, {p}^{\ensuremath{'}})^{28}\mathrm{Si}$, $^{24}\mathrm{Mg}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}, {p}^{\ensuremath{'}})^{24}\mathrm{Mg}$, $E=65$ MeV, unnatural parity states of ${E}_{x}=6\ensuremath{-}15$ MeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$, analyzing power ${A}_{y}(\ensuremath{\theta})$, resolution \ensuremath{\sim}35 keV, DWBA analysis.

Observation of1+state inCa48by hadron inelastic scattering

The 10.2 MeV state in $^{48}\mathrm{Ca}$ has been confirmed to be ${J}^{\ensuremath{\pi}}={1}^{+}$ by ($p$,${p}^{\ensuremath{'}}$) and ($\ensuremath{\alpha}$, ${\ensuremath{\alpha}}^{\ensuremath{'}}$) experiments. The state was strongly excited by the ($p$,${p}^{\ensuremath{'}}$) reaction at ${E}_{p}=65$ MeV. Differential cross sections of the state are compared with a microscopic distorted-wave Born approximation calculation based on a shell model. The calculation overestimates the cross sections by a factor of 4.NUCLEAR REACTIONS $^{48}\mathrm{Ca}$($p$,${p}^{\ensuremath{'}}$), $E=65$ MeV, $^{48}\mathrm{Ca}$($\ensuremath{\alpha}$,${\ensuremath{\alpha}}^{\ensuremath{'}}$), $E=70$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; ${J}^{\ensuremath{\pi}}={1}^{+}$ assigned for the 10.2 MeV level. Enriched target. DWBA analysis.

Energy levels inMg23from theMg25(p,t)Mg23reaction

Angular distributions of the $^{25}\mathrm{Mg}(p,t)^{23}\mathrm{Mg}$ reaction have been measured at 40 MeV bombarding energy. An energy resolution of 10-15 keV permitted the observation of about 40 new levels in $^{23}\mathrm{Mg}$ up to 9.72 MeV of excitation. Unambiguous spin and parity assignments of ${5/2}^{+}$ are made to the levels at 0.045(3), 5.662(8), 6.566(8), 6.899(5), 6.982(5), 7.582(6), 7.795(6), and 8.155(6) MeV on the basis of an $L=0$ admixture in the angular distributions. Values of the orbital angular momentum $L$ transferred to several states have been deduced. Microscopic distorted-wave Born approximation calculations for the transitions to the first eight ${5/2}^{+}$ states have been performed using spectroscopic amplitudes from recent shell model calculations and are compared to the experimental data.[NUCLEAR REACTIONS $^{25}\mathrm{Mg}(p,t)$, ${E}_{P}$ MeV; measured $\ensuremath{\sigma}({E}_{t},\ensuremath{\theta})$. $^{23}\mathrm{Mg}$ deduced levels, $L$, ${J}^{\ensuremath{\pi}}$. DWBA analysis. Enriched target.]

Giant monopole and quadrupole resonances and other multipole excitations inPb208studied in 43 MeV/nucleonα-particle and deuteron scattering

Inelastic excitations of $^{208}\mathrm{Pb}$ up to the giant resonance region were investigated in 172 MeV $\ensuremath{\alpha}$ and 86 MeV $d$ scattering. In the spectra, the giant resonance bump exhibits a double structure; the well known isoscalar giant quadrupole resonance at 10.9 \ifmmode\pm\else\textpm\fi{} 0.3 MeV, and the new resonance at 13.8 \ifmmode\pm\else\textpm\fi{} 0.3 MeV, for which evidence exists for $L=0$. Both resonances have a full width at half maximum of 2.6 \ifmmode\pm\else\textpm\fi{} 0.3 MeV. Below the giant resonances two new structures were found at excitation energies of 7.4 and 8.1 MeV which were identified as hexadecapole excitations with a strength of 3 and 2.7 single particle units, respectively. Angular distributions have been obtained for highlying excitations as well as for the low-lying ${3}^{\ensuremath{-}}$, ${5}^{\ensuremath{-}}$, ${2}^{+}$, and ${4}^{+}$ states. Microscopic distorted-wave Born-approximation calculations have been performed using double folding form factors. In this approach a good description of our scattering data has been achieved. For low-lying excitations our results are consistent with electron and proton scattering analyses. For the giant quadrupole resonance the angular distributions cannot be described assuming pure $L=2$ excitation. Different assumptions about other contributing multipole strengths are discussed. Assuming the 13.8 MeV resonance to be the giant monopole excitation, several models yield differential cross sections which are inconsistent with the data. A consistent description of $\ensuremath{\alpha}$ and $d$ scattering is obtained if, in addition to the compressional $L=0$ mode, diffuseness effects are considered as well as other contributing multipole strength ($L=1$). With the transition density used, the monopole strength corresponds to about 90% of the energy weighted sum rule limit. The result of a recent $^{16}\mathrm{O}$ scattering experiment suggesting a pronounced $L=3 \mathrm{and} 5$ resonance at ${E}_{x}\ensuremath{\simeq}20$ MeV in $^{208}\mathrm{Pb}$ is not confirmed.NUCLEAR REACTIONS $^{208}\mathrm{Pb}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, ${E}_{\ensuremath{\alpha}}=172$ MeV, $^{108}\mathrm{Pb}(d, {d}^{\ensuremath{'}})$, ${E}_{d}=86$ MeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$. Deduced strength of multipole excitation up to the giant resonance region.

Retarded IsoscalarM2Strength Observed in the ReactionO16(ppol, ppol′)O16(2−, 8.88 MeV)atEp=40MeV

Measurement of the spin-flip probability in the reaction $^{10}\mathrm{O}({p}_{\mathrm{pol}}, {{p}_{\mathrm{pol}}}^{\ensuremath{'}})^{16}\mathrm{O}({2}^{\ensuremath{-}}, 8.88 \mathrm{MeV})$ at ${E}_{p}=40$ MeV yields values that are significantly smaller than those predicted by microscopic distorted-wave Born-approximation calculations. This is interpreted as direct evidence for the dominance of multistep processes in this reaction. Analysis of the data in terms of the spin-flip cross section (spin-flip probability times the differential cross section) yields an isoscalar $M2$ strength for the ${2}^{\ensuremath{-}}$ which is significantly smaller than that predicted by random-phase-approximation wave functions.

Inelastic scattering of 40 MeV protons fromMg24. II. Microscopic calculations for positive parity states

Proton inelastic scattering data at 40 MeV bombarding energy are compared to microscopic distorted-wave Born-approximation calculations for positive parity states in $^{24}\mathrm{Mg}$ utilizing shell-model wave functions spanning the full $2s1d$ shell basis. Both empirical forces and forces derived from free nucleon-nucleon potentials are used in the calculations. Except for four transitions for which strong coupling effects are evident, the agreement between theory and experiment is quite good. Enhancement factors extracted for the natural parity transitions are consistent with the effective charges obtained from electromagnetic transition rates. Levels corresponding to the giant $M1$ resonance in $^{24}\mathrm{Mg}$ have been resolved in the present experiment. The fact that the renormalization factor between theory and experiment is close to unity for the 10.713 MeV 1+; $T=1$ state indicates that little or no renormalization of the two-body force is necessary for this inelastic transition. It is argued that little renormalization is also involved for magnetic-type inelastic transitions of multi polarities higher than $M1$.

(p,t) and (p,He3) reactions onK39

Angular distributions of the $^{39}\mathrm{K}(p,t)^{37}\mathrm{K}$ and $^{39}\mathrm{K}(p,^{3}\mathrm{He})^{37}\mathrm{Ar}$ reactions between 3\ifmmode^\circ\else\textdegree\fi{} and 55\ifmmode^\circ\else\textdegree\fi{} have been measured at 40 MeV bombarding energy. The experimental differential cross sections of the transitions to several of the low-lying mirror pairs of even-parity final states in $^{37}\mathrm{K}$ and $^{37}\mathrm{Ar}$ are compared to results of microscopic distorted-wave Born-approximation calculations based on current shell-model wave functions. The sensitivity of these distorted-wave Born-approximation calculations to optical model parameters is studied.NUCLEAR REACTIONS $^{39}\mathrm{K}(p,t)$, $^{39}\mathrm{K}(p,^{3}\mathrm{He})$, ${E}_{p}=40$ MeV; measured $\ensuremath{\sigma}({E}_{t},{E}_{3\mathrm{He}},\ensuremath{\theta})$; natural target; DWBA analysis.

Comparison of theLi6(t,He3)He6andLi6(t,t′)Li6reactions to supermultiplet members

The /sup 6/Li(t, /sup 3/He)/sup 6/He(0.0) and /sup 6/Li(t,t')/sup 6/Li(3.56) transitions have been studied at 17 MeV triton incident energy. Differential cross sections have been obtained from 10degree to 90degree c.m. angle, with 12 angles common to both reactions. The experimental ratio of sigma (t, /sup 3/He) to sigma (t,t') is 2.28 +- 0.16, while geometrical isospin considerations for this reaction pair would predict a ratio of 2.0. Corrections based on a microscopic distorted-wave Born-approximation calculation of charge exchange and inelastic scattering do not account for a deviation of this magnitude. (AIP)

Two-nucleon transfer reactions induced byO16onCa42andCa48

The reactions $^{42,48}\mathrm{Ca}$ ($^{16}\mathrm{O}$, $^{18}\mathrm{O}$) $^{40,46}\mathrm{Ca}$ and $^{42,48}\mathrm{Ca}$ ($^{16}\mathrm{O}$, $^{14}\mathrm{C}$) $^{44,50}\mathrm{Ti}$ were studied at 56-MeV bombarding energy. Angular distributions for transitions to the ground and excited states of the residual nuclei and of the outgoing particles are analyzed in the framework of both cluster and microscopic distorted-wave Born-approximation calculations. The measured transfer cross sections are not described by calculations using optical-model parameters which fit elastic scattering. Agreement is substantially improved by a systematic change in the exit channel parameters. Cross sections for excited states relative to ground-state transitions are compared to relative strengths obtained from light-ion reactions and from simple shell-model calculations.