Exact finite range calculations of light-ion induced two-neutron transfer reactions

Exact finite-range (EFR) distorted-wave Born approximation calculations were performed for light-ion induced two-neutron transfer reactions, by using a technique to calculate the form factors rather fast. The use of this method made it possible to carry out calculations even when realistic light-ion wave functions and multi-configurational two-neutron wave functions were used and large transferred angular momenta were considered. It was found that, at lower bombarding energies, the predictions of the EFR and zero-range calculations agree very closely both in angular distributions and relative magnitudes of the cross sections, though they differ significantly in absolute magnitude. As the bombarding energy increases, the discrepancy between the predicted absolute magnitude becomes still larger, and noticeable differences are seen even in relative cross sections. For all the energies considered, the EFR calculations predicted the absolute magnitudes of the experimental cross sections to within a factor of several units.     

Elastic and inelastic scattering of vector polarized deuterons from even samarium isotopes at 56 MeV

Differential cross sections and vector analyzing powers of deuteron elastic and inelastic scattering have been measured at 56 MeV over the whole range of the even samarium isotopes. Comprehensive analyses were performed with the optical model and the coupled-channels formalism. In the optical model analysis, calculations with a global parameter set could reproduce the experimental data only for the vibrational nuclei. The strong coupling approximation was applied assuming the ^{144, 148, 150}Sm to be harmonic vibrators and the ^152,154Sm symmetric rotators. The 2^λ (λ = 2, 3, 4, 6) pole deformation parameters were deduced from a systematic coupled-channels analysis. The transition strengths were extracted from the deformed optical potentials and compared with the corresponding electromagnetic ones. The transition rates for the rotational nuclei agreed with the electro-magnetic ones, but those for the vibrational nuclei gave the systematically smaller values. The latter fact was attributed to the difference between the proton and neutron transition matrix elements near the neutron-closed-shell nuclei. The ratios of the two matrix elements were obtained.     

The two-neutron transfer reactions (O, O) with O, C and Mg targets

Excitation functions, angular distributions and differential ranges were measured for the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction at ¹⁸O beam energies of 20–45 MeV. Excitation functions only were measured for the reactions ¹⁴C(¹⁸O, ¹⁹O)¹³C, ¹⁴C(¹⁸O, ¹⁶O)¹⁶C, ¹⁴C(¹⁸O, ²⁰O)¹²C, ¹⁴C(¹⁸O, ¹⁵N)¹⁷N and ¹⁸O(¹⁸O, ¹⁹O)¹⁷O, ¹⁸O(¹⁸O, ¹⁶O)²⁰O, ¹⁸O(¹⁸O, ¹⁵N)²¹F at ¹⁸O beam energies of 13–41 MeV. We have identified these as direct reactions in which a single neutron, a two-neutron cluster, a deuteron and a triton are transferred between projectile and target.

The cross sections for two-neutron transfer reactions were found to be relatively high and those for the ¹⁸O+¹⁸O and the ¹⁴C+¹⁸O reactions were higher than the ones of single-neutron transfers over most of the energy range.

Attempts were made to apply the theory of Buttle and Goldfarb for single-neutron transfer to the case of two-neutron transfer in the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction below the Coulomb barrier. It is shown that for those reactions for which the assumptions, implicit in the model, are valid, good agreement is obtained with experiment. We also tried to apply the diffraction model of Dar and Kozlovsky to the calculation of the angular distribution of these reactions. A good fit to the experimental results could be obtained if quite different sets of parameters were used in the calculations for the two bombarding energies.     

Energy levels in even actinide isotopes from (t,p) reactions

Energy levels in^{232, 234}Th,^{236, 238, 240}U and in²⁵⁰Cm have been measured using the (t, p) reaction. Angular distributions were obtained for the^{234, 238}U targets and evidence for second order effects in the direct reaction mechanism was found.     

Deeply bound hole states and isobaric analog states observed by neutron pickup reactions on even tin isotopes

Deeply bound hole states in the odd tin isotopes ^{115, 117, 119, 123}Sn were investigated by using 81 MeV (³He, α) and 52 MeV (p, d) reactions. Excitation of low-spin states was largely suppressed in (³He, α) reactions due to the angular-momentum mismatch so that the excitation energies and widths of the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ states have been clearly determined. DWBA analyses showed that the deeply bound hole states have spectroscopic factors less than 20% of the sum-rule limit. Isobaric analog states $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{, 2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ corresponding to the ground and two lowest excited states of In isotopes were investigated in ^{115, 117, 119, 121, 123}Sn isotopes. Coulomb displacement energies were deduced. DWBA analyses of these states were used to check the calculations for the deeply bound states. The spectroscopic factors of the analog states are in good agreement with the sum-rule prediction.     

Comparative spectroscopy with the (d, τ) reaction on even Ar isotopes

The (d, τ) proton pick-up reactions on ³⁶Ar and ³⁸Ar have been studied at an incident energy of 52 MeV. Differential cross sections were measured and spectroscopic factors were extracted for transitions to 14 states of ³⁵Cl and 13 states of ³⁷Cl, respectively. Many new $\text{5}\text{2}$⁺ states and nearly the complete $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ strength have been observed in both nuclei. The width of the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ spectral distribution is appreciably smaller for the semi-closed shell nucleus ³⁸Ar than for ³⁶Ar and ⁴⁰Ar. The results are compared with those from the ⁴⁰Ar(d, τ) reaction and proton stripping reactions on each of the three argon isotopes. Recent shell model calculations proved to be well suited to describe excitation energies as well as spectroscopic factors for the low-lying positiveparity states. Mirror relations were established for the nuclei ³⁵Ar and ³⁵Cl. In ³⁷Cl we succeeded in observing a weak component of a 1p proton hole state at a separation energy of only 18 MeV.     

Octupole vibrations in the even mercury and lead isotopes

Prominent groups are observed corresponding to excited states in the region of 2.6 MeV in the scattering of 24 and 27 MeV α-particles from ^{198, 200, 202, 204}Hg and ^{204, 206, 208}Pb. For each of the Pb isotopes the state concerned is identified with the known 3^? octupole vibration. Angular distribution measurements for scattering to the Pb and ²⁰⁴Hg states are in agreement with octupole-vibration coupled-channels predictions, and systematic trends suggest that the states observed in the isotopes ^{198, 200, 202}Hg can also be attributed to octupole vibrations.     

The (t,p) reaction on the even isotopes of neodymium

The Aldermaston multi-angle magnetic spectrograph and tandem Van de Graaff accelerator have been used to study the (t, p) reactions leading to the neodymium isotopes ^{144,146,148,150, 152}Nd bombarding energy of 13 MeV. The Q-values were measured for final states with excitation energies up to about 3 MeV.     

Nuclear reactions between oxygen isotopes

Elastic and inelastic cross sections have been measured for the system ¹⁶O + ¹⁷O at c.m. energies from 12.5 to 15.5 MeV, and for ¹⁶O + ¹⁸O at c.m. energies from 12 to 20 MeV, at angles between 60° and 125°. Position-sensitive detectors were employed, using the kinematic coincidence technique. The data have been analyzed with particular attention to the contributions of multiple-exchange processes.     

Electron scattering studies of low-lying collective states of even Zn isotopes

The inelastic electron scattering cross sections for the excitation of the low-lying collective states in the even Zn isotopes ⁶⁴Zn, ⁶⁶Zn, ⁶⁸Zn and ⁷⁰Zn have been measured in the momentum transfer region q = 0.3–1.1 fm^?1. Strong transitions to the first 2⁺ and 3^? states have been observed and the modified Tassie model with a two parameter Fermi charge distribution for the ground state was used to extract the values for the reduced transition probability B↑ (Eλ). Besides the investigation of these states, which in the framework of the vibrational model are considered as one-phonon states, special effort was made to measure the transition to the 2⁺ two-phonon states in ⁶⁴Zn (ε = 1.80 MeV) and ⁷⁰Zn (ε = 1.76 MeV). We have applied the anharmonic vibrator model to these two nuclei and have extracted values for the static quadrupole moment of the first excited state.     

Transition charge densities of low-lying collective states in even Zn isotopes

The inelastic electron scattering cross sections for the quadrupole transitions to the 2₁⁺ and 2₂⁺ states in the even Zn isotopes ⁶⁴Zn, ⁶⁶Zn and ⁶⁸Zn and for the hexadecapole transition to the 4⁺₁ state in ⁶⁴Zn have been measured in a momentum transfer range up to q = 2.2 fm^?1. In the frame-work of the vibrational model these states are considered as one- and two-quadrupole-phonon states. The measurements are characterized by high statistical accuracy and by an overall resolution of δE/E₀ = 10^?3 which permitted separation of almost all members of the two-phonon triplet. The measured cross sections are analyzed with phenomenological models as well as with a Fourier-Bessel expansion of the transition charge density. The latter analysis yields realistic error bands for the transition charge densities and model-independent values for the reduced transition probabilities and transition radii.     

One- and two-neutron transfer reactions on 12C with the weakly bound 6He projectile

Using the framework of the coupled reaction channels (CRC) the one- and two-neutron transfer process initiated by the weakly bound nucleus ⁶He on ¹²C at an energy of E _L = 5.9 MeV is studied. The absolute cross-sections for a few states in ¹⁴C are well reproduced within a factor 2 in second order, using microscopic wave functions of ⁶He and ¹²C. Only a small dependence of the cross-section on details of the ⁶He wave function is observed. Good fits to the data are obtained in a calculation with full coupling (25 iterations) with renormalised optical potential parameters and spectroscopic amplitudes of ⁶He. Received: 13 June 2000 / Accepted: 24 July 2000     

Coulomb and nuclear excitation effects on 16O scattering from samarium isotopes

Elastic scattering of ¹⁶O on ^{148, 150, 152}Sm isotopes and inelastic scattering leading to the first 2⁺ state for the three isotopes and the 4⁺ state for ¹⁵²Sm have been measured at several energies in the vicinity of the Coulomb barrier. The whole set of data was reproduced at forward angles with an effective potential taking into account Coulomb excitation and in the full angular range by CCBA calculations including separate nuclear and Coulomb deformations.     

A study of the giant dipole resonance in doubly even tellurium and cerium isotopes

The partial photoneutron cross sections [σ(γ, n) + σ(γ, pn)] and σ (γ, 2n) of ^{124, 126, 128, 130}Te and ^{140, 142}Ce were measured in the giant dipole resonance region by means of the monochromatic photon beam installation at SACLAY. Absolute total photoneutron cross sections, Lorentz line parameters and integrated cross sections are evaluated. The experimental behaviour of the GDR for the above nuclei and in particular its spreading, is then tentatively interpreted in terms of the improved dynamic collective model using the concept of potential energy surfaces.     

Neutron total and scattering cross sections of some even Mo isotopes and the optical model

Neutron total cross sections of ⁹²Mo, ⁹⁶Mo, ⁹⁸Mo and ¹⁰⁰Mo were measured at intervals of ? 10 keV from 1.6 to 5.5 MeV with resolutions of ≈ 10 keV. Neutron elastic and inelastic scattering cross sections of these isotopes were measured from 1.8 to 4.0 MeV at intervals of 0.2 MeV. Neutron groups corresponding to the excitation of forty states were identified. The experimental results were examined in the context of optical and statistical nuclear models. It was concluded that the real part of the optical potential includes a term proportional to [(N-Z)/A] and suggested that the imaginary part of the potential was shell dependent with decreasing magnitude as N = 50 is approached. Comparison of measured and calculated inelastic neutron excitation cross sections suggested a number of J^π assignments extending previous knowledge.