Exact Finite Range Research Articles

Competition between direct and sequential two-neutron transfers in the O18+Si28 collision at 84 MeV

In this work we study the simultaneous and sequential two-neutron transfer mechanisms to the $^{28}$Si nucleus induced by (t,p) and ($^{18}$O, $^{16}$O) reactions. New experimental cross sections for the $^{28}$Si($^{18}$O,$^{16}$O)$^{30}$Si reaction at 84 MeV are also presented. Direct reaction calculations are carried out within the Exact Finite Range Coupled Reaction Channel, for the simultaneous transfer of the two-neutron cluster, and the second order Distorted Wave Born Approximation, for the sequential transfer. Two different models are considered to describe the two-neutron cluster. The spectroscopic information was obtained from shell model calculation with {\it psdmod} interaction for the target overlaps where the 1p$_{3/2}$, 1p$_{1/2}$, 1d$_{3/2}$, 1d$_{5/2}$ and 2s$_{1/2}$ orbitals are included as valence sub-space. We show that simultaneous and sequential two-neutron transfer are competing mechanisms for the population of the ground state in $^{30}$Si. A systematic analysis of the two-neutron transfer induced by the ($^{18}O,^{16}O$) indicates that static deformation of target nuclei impacts on the two-neutron transfer mechanism.

Long-range versus short-range correlations in the two-neutron transfer reaction Ni64(O18,O16)Ni66

Recently, various two-neutron transfer studies using the $(^{18}\mathrm{O},^{16}\mathrm{O})$ reaction were performed with a large success. This was achieved because of a combined use of the microscopic quantum description of the reaction mechanism and of the nuclear structure. In the present work we use this methodology to study the two-neutron transfer reaction of the $^{18}\mathrm{O}+^{64}\mathrm{Ni}$ system at 84 MeV incident energy, to the ground and first ${2}^{+}$ excited state of the residual $^{66}\mathrm{Ni}$ nucleus. All the experimental data were measured by the large acceptance MAGNEX spectrometer at the Instituto Nazionale di Fisica Nucleare --Laboratori Nazionali del Sud (Italy). We have performed exact finite range cross section calculations using the coupled channel Born approximation (CCBA) and coupled reaction channel (CRC) method for the sequential and direct two-neutron transfers, respectively. Moreover, this is the first time that the formalism of the microscopic interaction boson model (IBM-2) was applied to a two-neutron transfer reaction. From our results we conclude that for two-neutron transfer to the ground state of $^{66}\mathrm{Ni}$, the direct transfer is the dominant reaction mechanism, whereas for the transfer to the first excited state of $^{66}\mathrm{Ni}$, the sequential process dominates. A competition between long-range and short-range correlations is discussed, in particular, how the use of two different models (Shell model and IBM's) help to disentangle long- and short-range correlations.

Two-neutron transfer analysis of theO16(O18,O16)O18reaction

Recently a quantitative description of the two-neutron transfer reaction $^{12}\mathrm{C}(^{18}\mathrm{O},^{16}\mathrm{O})^{14}\mathrm{C}$ was performed and the measured cross sections were successfully reproduced [M. Cavallaro et al., Phys. Rev. C 88, 054601 (2013)]. This task was accomplished by combining nuclear structure calculations of spectroscopic amplitudes and a full quantum description of the reaction mechanism. Verification of such a theoretical approach to other heavy nuclear systems is mandatory in order to use ($^{18}\mathrm{O},^{16}\mathrm{O}$) reactions to assess pair configurations in nuclear states. In this work we apply this methodology to the $^{16}\mathrm{O}(^{18}\mathrm{O},^{16}\mathrm{O})^{18}\mathrm{O}$ reaction at 84 MeV. Experimental angular distributions for the two-neutron transfer to the ground state and ${2}_{1}^{+}$ state of $^{18}\mathrm{O}$ were obtained using the MAGNEX spectrometer at INFN-LNS. The roles of one- and two-step processes are analyzed under the exact finite range coupled reaction channel and the second order distorted wave Born approximation. We conclude that the one-step transfer mechanism is dominant in this system.

Quantitative analysis of two-neutron correlations in the12C(18O,16O)14C reaction

The ${}^{12}$C(${}^{18}$O,${}^{16}$O)${}^{14}$C and ${}^{12,13}$C(${}^{18}$O,${}^{17}$O)${}^{13,14}$C reactions are studied at 84 MeV. Mass distributions and energy spectra of the ejectiles are measured, indicating the selectivity of these reactions to populate two- and one-neutron configurations in the states of the residual nucleus, respectively. The measured absolute cross-section angular distributions are analyzed by exact finite range coupled reaction channel calculations based on a parameter free double-folding optical potential. The form factors for the (${}^{18}$O,${}^{16}$O) reaction are extracted within an extreme cluster and independent particles scheme with shell-model-derived coupling strengths. The results show that the measured cross sections are accurately described for the first time without the need for any arbitrary scaling factor. The (${}^{18}$O,${}^{16}$O) reaction is thus found to be a powerful tool for quantitative spectroscopic studies of pair configurations in nuclear states.

Fusion cross sections for 7Li + 12C system at near barrier energies

Elastic scattering and alpha particle angular distributions for the reaction 7Li + 12C have been measured at E lab = 7.5 , 9 , 12 , and 15 MeV. Statistical and direct reaction model calculations have been performed to deduce the fusion and direct reaction cross sections. The fusion cross sections measured in the present work are found to be consistent with those obtained by measurement of characteristic γ-rays, which are very different from those measured by direct detection of evaporation residues. The contribution from direct reactions to the alpha particle cross section has been quantified by exact finite range transfer calculations and found to be negligible ( < 6 % ) at all the bombarding energies studied. The measured fusion cross sections at all the energies studied are nearly equal to the reaction cross sections which imply that the direct reaction contributions are less and fusion is the dominant process.

Five-nucleon simultaneous and sequential transfer in theC12(11B,6Li)17O andC12(d,7Li)7Be reactions

Measurements of the angular distributions of the {sup 12}C({sup 11}B,{sup 6}Li){sup 17}O reaction were performed at three energies of a {sup 11}B beam: 28, 35, and 40 MeV. The results were analyzed in the frame of the exact finite range distorted wave Born approximation of the first and the second order assuming the simultaneous and sequential transfer of the neutron and the {alpha} particle. Such an analysis was also performed for previously measured angular distributions of the {sup 12}C({ital d},{sup 7}Li){sup 7}Be reaction at {ital E}{sub lab} = 78 MeV. In both reactions under investigation dominance was found of the simultaneous transfer of the {alpha} particle and the nucleon correlated to the {sup 5}He ({sup 5}Li) cluster in the ground or the first excited state. {copyright} {ital 1996 The American Physical Society.}

Neutron pair and proton pair transfer reactions between identical cores in the sulfur region.

Optical model and exact finite range distorted-wave Born approximation analyses were performed on neutron pair exchange between identical cores for $^{32}\mathrm{S}$ and $^{34}\mathrm{S}$ nuclei and on proton pair exchange between identical cores for $^{30}\mathrm{Si}$ and $^{32}\mathrm{S}$. The extracted spectroscopic factors were compared with theoretical ones deduced from Hartree-Fock calculations on these pairs of nuclei. The enhancement of the experimental cross sections with respect to the theoretical ones strongly suggests evidence for a nuclear Josephson effect. \textcopyright{} 1996 The American Physical Society.

Study of ( alpha ,3He) and ( alpha ,t) reactions on 28Si at 45 MeV

The 28Si( alpha ,3He)29Si, 28Si( alpha ,t)29P and Si( alpha , alpha )Si reactions were studied at Ealpha =45 MeV. Exact finite-range (EFR) DWBA analysis was carried out for the transitions to the ground state and to five excited states in 29Si and 29P. Spectroscopic strengths G were extracted for all the states and were compared with the predictions from shell-model and quasi-particle core-coupling calculations. Similar EFR-DWBA analyses were carried out from available (unpublished) data for the 28Si( alpha ,3He)29Si reaction at Ealpha =64.9 and 120 MeV, and for the 28Si( alpha ,t)29P reaction at Ealpha =50 and 64.9 MeV. The comparison of experimental and theoretical values of G are provided.

Experimental survey of the (d

Differential cross sections, vector and tensor analyzing powers of the (d\ensuremath{\rightarrow},t) reaction on $^{120}\mathrm{Sn}$, $^{116}\mathrm{Sn}$, $^{90}\mathrm{Zr}$, $^{58}\mathrm{Ni}$, $^{16}\mathrm{O}$, and $^{12}\mathrm{C}$ have been measured at 200 MeV bombarding energy. Deuteron elastic scattering measurements have been performed on $^{116}\mathrm{Sn}$ and $^{208}\mathrm{Pb}$ at the same energy. These data have been analyzed together with previous ones on $^{58}\mathrm{Ni}$ and $^{16}\mathrm{O}$ to get best fit optical parameters describing deuteron elastic scattering. The (d\ensuremath{\rightarrow},t) experimental survey bears on 28 transitions populating well known valence levels, including previous data in $^{207}\mathrm{Pb}$ and $^{27}\mathrm{Si}$. The vector and tensor analyzing powers exhibit striking similarities for transitions measured in different nuclei. The angular distributions are found to strongly depend on the number of nodes in the neutron form factor and on the coupling of spin and angular momentum ${\mathit{j}}_{\mathrm{\ensuremath{-}}}$=l-1/2 versus ${\mathit{j}}_{+}$=l+1/2. The j effect is especially pronounced, for both analyzing powers for n=1 transitions. The slopes of the differential cross sections in different nuclei depend mainly on the number of nodes. Exact finite range calculations including S and D components have been performed, using two sets of deuteron parameters together with a deep triton potential. Both analyses reproduce rather well the differential cross sections and currently adopted spectroscopic factors. The conventional analyses with deuteron parameters fitting elastic scattering data reproduce rather well analyzing powers of ng1 transitions (with l=0,1,2), but disagree with the data for n=1 transitions (except for ${\mathit{j}}_{+}$${\mathit{A}}_{\mathit{y}\mathit{y}}$ values). Good or qualitative agreement is achieved for all transitions with the second deuteron potential, characterized by larger spin orbit terms and an additional imaginary tensor term. This allows using the reaction as a spectroscopic tool.

CONTRIBUTION OF THE PARITY DEPENDENT POTENTIAL IN HEAVY ION TRANSFER REACTIONS

The theory of heavy ion reactions with particle transfer is considered in the framework of the exact finite-range distorted wave Born approximation (EFR-DWBA). Modified Woods-Saxon potentials which include a parity dependent interaction and an angular momentum absorptive term have been used as the ion-ion interactions in the initial and final channels. The bound state interactions are represented by nucleus-nucleus inter-actions which include repulsive and attractive Yukawa type components. The present numerical calculations of the differential cross-sections are in good agreement with the experimental measurements. The distorting parity dependent potentials are found very important in reproducing the cross-sections at backward as well as at intermediate angles. The obtained extracted values of the spectroscopic factors are reasonable.

DWBA analyses of the (t,6He) reaction at 38 MeV

New differential cross section data are presented for the (t,6He) reaction on targets of 7Li and 19F at an incident energy of 38 MeV. Existing data for the (t,6He) reaction on 12,13C have been re-extracted and revised values are reported for 12C. Exact finite range DWBA calculations are presented using Woods-Saxon potentials for the projectile and target wavefunctions; the effect of the choice of geometry parameters is examined. The spectroscopic factors are compared with shell-model and microscopic-model calculations.

Computation of Nuclear Reactions with Light-Heavy Ions

The computer code OLYMPS for calculation of the inclusive cross sections for nuclear reactions induced by light heavy ions on medium-mass nuclei at beam energies of 10–20 MeV per nucleon is developed. Our calculations are based on the description of the massive transfer reactions in the spectator model. In view of the fact that most of the considered reactions have more than two particles in the final state and require an allowance for the continuum spectrum, the standard distorted wave Born approximation (DWBA) code fails to work. In our method the transition amplitude is witten in a prior-form of exact finite range DWBA and an exact numerical integration over the transfer momentum is carried out. This requires knowledge of the optical potentials between interacting light and heavy ions in a wide energy range. In addition, OLYMPS provides for the alternative ways of calculation of the wave functions of the relative motion of the heavy ions.

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.

A study of the (3He,α) reaction on 60Ni

The (3He, alpha ) reaction on 60Ni has been studied using a beam of 33 MeV 3He particles. Angular distributions have been measured for twenty-two levels, including five analogues, up to Ex approximately=10.5 MeV over the angular range 12.5 degrees -115 degrees (lab) in steps of 2.5 degrees . DWBA analysis was carried out using the code DWUCK4 with non-locality and finite range corrections introduced in the local energy approximation. The large angle data call for the incorporation of exact finite range including target recoil and the angular distributions were re-analysed using the full finite range DWBA code DWUCK5. Spectroscopic factors have been extracted.

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.

Direct reaction mechanism for heavy ion reactions with particle transfer

The theory of direct nuclear reactions is considered. Heavy ion reactions with particle transfer are treated using a direct reaction mechanism. The exact finite-range distorted wave Born approximation (EFR-DWBA) is used in investigating these direct heavy ion reactions. The particle-nucleus interactions for the bound states in the target and residual nuclei and represented by Yukawa plus exponential potentials. Theoretical expressions are evaluated for the differential cross sections of the particle transfer heavy ion reaction process. Numerical calculations are carried out for the form factors and angular distributions for different heavy ion reactions with different particle transfer. The present theoretically calculated differential cross sections are in good agreement with the experimental measurements. The obtained values of the extracted spectroscopic factors are reasonable.

Exact finite range evaluation of breakup-fusion cross section in the post form

Post-form breakup-fusion cross sections are calculated for several alpha - and d-induced reactions by using the exact finite range method. It is shown that the calculated cross sections overpredict the experimental cross sections by a factor that can become as large as 30, a problem that is not encountered if the prior-form calculation is done. The reason for this troublesome post-form result is discussed in some detail.

(16O,14C) reaction on some even N=28 isotones.

The two-proton stripping reaction ${(}^{16}$O${,}^{14}$C) has been measured on some of the even N=28 isotones: $^{48}\mathrm{Ca}$, $^{52}\mathrm{Cr}$ at 160 MeV and $^{50}\mathrm{Ti}$, $^{54}\mathrm{Fe}$ at 150 MeV bombarding energy. States of excitation up to 10 MeV have been extracted over an angular range 4\ifmmode^\circ\else\textdegree\fi{}--10\ifmmode^\circ\else\textdegree\fi{} in the center-of-mass system. The angular distributions have been compared to transfer calculations that consist of both the simultaneous and successive transfer processes and were performed in exact finite range. Only the simple, (1${f}_{7/2}$${)}^{n}$ dominated states have been analyzed to investigate whether this reaction mechanism can account for the data. The absolute magnitude of the $^{48}\mathrm{Ca}$${(}^{16}$O${,}^{14}$C) $^{50}\mathrm{Ti}$ ground-state reaction has been reproduced. However, the experimental and theoretical uncertainties are larger than the sensitivity to different structure descriptions of the target/residual nuclei. Therefore, we have not been able to probe the pairing correlations in the ground state of $^{50}\mathrm{Ti}$. The calculations fail to reproduce the magnitude of the transitions to other states in $^{50}\mathrm{Ti}$. Similar problems occurred for the other reactions, leading to $^{52}\mathrm{Cr}$, $^{54}\mathrm{Fe}$, and $^{56}\mathrm{Ni}$. The discrepancy ranges from a factor of 2 to nearly 30. In addition, there are phase differences between the calculations and the measured cross sections. Some systematics of the disagreement are investigated. It is suggested that the simultaneous/successive mechanism can account for the data when the transition is kinematically well matched. In cases of poor matching, inelastic/transfer mechanisms may be kinematically enhanced and contribute to the cross section with significant strength.

Cross section and analyzing power measurements for the (p,d) reaction onO16andCa40at 200 MeV

Cross sections and analyzing powers for the reactions $^{16}(\mathit{p}\ensuremath{\rightarrow}$,d${)}^{15}$O and $^{40}(\mathit{p}\ensuremath{\rightarrow}$,d${)}^{39}$Ca at ${T}_{p}$=200 MeV have been measured for the ${1/2}^{\mathrm{\ensuremath{-}}}$ (0 MeV) and ${(3/2}^{\mathrm{\ensuremath{-}}}$ (6.18 MeV) levels in $^{15}\mathrm{O}$ and for the ${(3/2}^{+}$ (0 MeV) and ${1/2}^{+}$ (2.47 MeV) levels in $^{39}\mathrm{Ca}$. The angular ranges covered are 3\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.\mathrm{\ensuremath{\le}}47\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ and 4\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.\mathrm{\ensuremath{\le}}21\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$, respectively, for the two reactions. Exact finite range distorted-wave Born approximation calculations are in poor agreement with the measured angular distributions of cross sections and analyzing powers. The angular distributions of the cross sections are featureless and decrease exponentially with increasing scattering angle.

Study of the one-neutron transfer reactions induced by polarized 7Li ON 26Mg and 120Sn

Abstract Angular distributions of the cross sections and analyzing powers up to third rank have been measured for the one-neutron transfer reactions 26Mg(7Li,6Li)27Mg, 120Sn(7Li,6Li)121Sn and 120Sn(7Li, 8Li)129Sn initiated by polarized 7Li ions of 44 MeV. Third-rank analyzing power has been measured for the first time in transfer reactions. Coupled-channels calculations in which the ground and first excited states of 7Li are coupled together by collective interactions and one-neutron transfers are calculated in exact finite range explain the experimental data for low-lying states in final nuclei. Extracted spectroscopic factors are in good agreement with those obtained from other one-neutron transfer reactions on the same targets.