Microscopic Distorted-wave Born Approximation 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.

Properties of the First 1/2+Excitation State of 13C by 22 MeV Proton Inelastic Scattering

The differential cross sections of 22 MeV proton inelastic scatteringfor the first 1/2+ excitation state (Ex = 3.09 MeV) of13C have been measured between 9° and 130°. Thebroad peak located at ~120°, which has been systematicallyobserved in the 0+→0-, 1/2-→1/2+, and 1+→1- transitions for the 16O, 13C, and 14,15N(p,n) charge exchange reactions at Ep = 35 MeV, has beenobserved for the first time in the present proton inelastic scattering.The present experimental data are analysed by using microscopicdistorted-wave Born approximation. From the comparison ofpresent experimental data and theoretical results at forward angles,our analysis indicates the existence of neutron halo in the first1/2+ excitation state of the 13C nucleus. In addition, byreasonable modification of shell model wavefunction of the first1/2+ excitation state, we can well describe the experimentalform factors of (e,e') and the experimental differential cross sectionsof (p,p') at incident energy of 547 MeV.

Analog transitions insd- andf-shell nuclei and the isovector part of optical potentials studied by the(p,n)reaction at 35 MeV

Quasielastic $(p,n)$ reactions on $\mathrm{sd}$- and $f$-shell nuclei were studied at an incident proton energy of 35 MeV. Differential cross sections for isobaric analog $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}{=0}^{+}$ (Fermi-type) transitions and their angular distributions were measured in 13 $NgZ$ target nuclei ranging $17l~Al~48,$ ${}^{17,18}\mathrm{O},$ ${}^{22}\mathrm{Ne},$ ${}^{25,26}\mathrm{Mg},$ ${}^{27}\mathrm{Al},$ ${}^{30}\mathrm{Si},$ ${}^{34}\mathrm{S},$ ${}^{38,40}\mathrm{Ar},$ and ${}^{42,44,48}\mathrm{Ca}.$ Pure $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}{=0}^{+}$ Fermi-type transitions were observed in six of them. As for the other seven nuclei, contributions from mixed $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}\ensuremath{\ne}{0}^{+}$ components or those from unresolved transitions were evaluated by microscopic distorted-wave Born approximation (DWBA) calculations to subtract them from the raw data and extract pure Fermi-type transition strengths. Thus a total of 13 $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}{=0}^{+}$ angular distributions was fitted by macroscopic DWBA calculations with a Lane-model optical potential to derive systematically the isovector part of the potential. The best-fit parameters for each target are presented. $A$-dependent global parameters were obtained from these best-fit parameters by a least-squares fit.

In-plane polarization transfer in the 6Li(p,p') reaction and the effective NN interaction.

We have measured the in-plane polarization transfer coefficients for the $^{6}\mathrm{Li}$(p,p') reaction using a longitudinally polarized beam at 65 MeV. A microscopic distorted-wave Born-approximation analysis with the M3Y interaction has been performed for the excitation to the first ${0}^{+}$ state (T=1). The isovector tensor force ${\mathit{V}}_{\mathit{T}\mathrm{\ensuremath{\tau}}}$ and the isovector spin-orbit force ${\mathit{V}}_{\mathit{L}\mathit{S}\mathrm{\ensuremath{\tau}}}$ have been adjusted in order to reproduce the experimental differential cross sections, depolarization parameters, and in-plane polarization transfer coefficients. This analysis suggests that the high-momentum components of ${\mathit{V}}_{\mathit{T}\mathrm{\ensuremath{\tau}}}$ should be substantially reduced from the M3Y interaction and ${\mathit{V}}_{\mathit{L}\mathit{S}\mathrm{\ensuremath{\tau}}}$ needs to be more attractive.

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.

SPIN-FLIP ASYMMETRY IN THE PROTON INELASTIC SCATTERING TO THE FIRST 2+STATES OF48,50Ti

Angular distributions of the differential cross section σ (θ), analyzing power Ay (θ), spin-flip probability S(θ) and spin-flip asymmetry e (θ) in the excitation of the first 2+ states in 48Ti and 50Ti were measured at incident energies of 11 and 18 MeV using (p, p' γ) coincidence technique with polarized proton beam. The results were analyzed in terms of a macroscopic coupled channels method based on the vibrational model and of the microscopic distorted wave Born approximation (DWBA) based on shell-model wave functions and effective nucleon-nucleon interactions.

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.

Asymmetry of spin-flip of polarized protons in the inelastic scattering to the first 2(+) states of 48Ti and 50Ti.

Angular distributions of the differential cross section, analyzing power, spin-flip probability, and spin-flip asymmetry in the excitation of the first ${2}^{+}$ states in $^{48}\mathrm{Ti}$ and $^{50}\mathrm{Ti}$ were measured at incident energies of 11 and 18 MeV using the (p,p'\ensuremath{\gamma}) coincidence technique with a polarized proton beam. The angular distributions show strong incident energy and target dependence. The results were analyzed in terms of a macroscopic coupled-channels method based on the vibrational model and of the microscopic distorted wave Born approximation based on shell-model wave functions and effective nucleon-nucleon interactions. The spin-flip asymmetry is quite sensitive to the spin-dependent part in the interaction that causes inelastic scattering.

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.

10B(7Li, 7Be)10Be charge-exchange reaction.

${\mathrm{The}}^{10}$B${(}^{7}$Li,${\mathrm{}}^{7}$Be${)}^{10}$Be charge-exchange reaction has been measured at ${E}_{\mathrm{lab}=39}$ MeV. Calculations were performed using a microscopic distorted-wave Born approximation with both central and tensor forces with an optical model potential obtained by fitting measured elastic scattering data. Several residual two-body interactions were used for which the absolute cross-section magnitudes varied at most within factors of two. The calculations showed that the one-step mechanism is very important for this particular reaction even at this low bombarding energy.

34S(p,n)34Cl reaction at 35 MeV and its microscopic distorted-wave Born approximation analysis: Stringent test of the shell model.

Differential cross sections for the /sup 34/S(p,n)/sup 34/Cl reaction were measured at E/sub p/ = 35 MeV. Remarkable differences were observed among the angular distribution shapes for the known 1/sup +/ states in /sup 34/Cl at 0.441, 0.666, 2.581, and 3.128 MeV. Distorted-wave Born approximation calculations using the recent full sd-shell wave functions of Brown and Wildenthal successfully reproduce such differences, whose origin was traced back to the different contributions of the ..delta..J(..delta..L,..delta..S) = 1(0,1) and 1(2,1) transition amplitudes. The 1/sup +/ transitions with dominant 1(0,1) amplitudes required a renormalization factor N of about 0.8, which agrees well with that obtained for the ..beta../sup +/ decay of /sup 34/Ar. The 1/sup +/ and 2/sup +/ transitions with dominant 1(2,1) and 2(2,1) amplitudes required N of about 0.5. Similar distorted-wave Born approximation calculations gave a good description of the ..delta..S = 0 and ..delta..L = 0 and 2 transitions without any renormalization.

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.

Isovector effects in nucleon inelastic scattering in a density-dependent folding model

Differential cross section data for inelastic proton and neutron scattering to the first ${2}^{+}$ states in $^{54}\mathrm{Fe}$ and $^{56}\mathrm{Fe}$ at several energies in the 11-26 MeV range have been analyzed using a microscopic distorted-wave Born approximation model. The entrance- and exit-channel optical potentials and the transition form factors were calculated consistently in a folding model using a density-dependent interaction obtained from nuclear matter calculations based upon a free nucleon-nucleon interaction. These microscopic calculations yield reasonable agreement with the data. The model was used to determine the ratio of neutron and proton transition matrix elements $\frac{{M}_{\mathrm{n}}}{{M}_{\mathrm{p}}}$ for these excitations.

Giant resonance excitation in theAl27(Li6,He6)Si27reaction at 93 MeV

A giant resonance in /sup 27/Si is observed in the excitation energy region of 10--18 MeV in the spin-isospin flip /sup 27/Al(/sup 6/Li, /sup 6/He)/sup 27/Si reaction. A microscopic distorted-wave Born approximation analysis using a G-matrix nucleon-nucleon force and a local energy approximation knockout exchange correction indicates multipolarities between lambda = 3 and lambda = 5 for the giant resonance.