J.F.A. van Hienen

High resolution investigation of 90Zr with (p, p') scattering at 25 MeV☆

Abstract The cross sections for inelastic proton scattering from 90Zr have been measured for levels up to 7.5 MeV excitation energy with a resolution of 12 to 16 keV. The measured angular distributions are compared with macroscopic DWBA calculations to determine L-values and deformation parameters. New spectroscopic information is obtained for levels above 4.0 MeV excitation energy, where conflicting information existed. The influence of two-step processes is investigated for some states. A number of states are investigated with microscopic distorted-wave calculations, which include antisymmetrization, using wave functions from broken-pair calculations. Reasonable agreement is obtained for the low-lying collective states and the 5− states when normalization factors for the transition amplitudes are used. The (p, d)(d, p) process is found to be important in the excitation of the members of the ν¦1g 9 2 −1 2d 5 2 〉 multiplet at 25 MeV incident energy, in contrast to results found at 65 MeV where such a process plays a minor role.

A study of 36S by high-resolution inelastic proton and alpha scattering

Abstract In an inelastic hadron scattering study of 36S both a high resolution (p, p′) experiment at Ep = 28.0 MeV and an (α, α′) experiment at Eα= 31.6 MeV were performed. A highly enriched target was used. Angular distributions for levels up to 6.55 MeV have been obtained. Five previously unknown levels have been observed. A macroscopic CC analysis with a phenomenological potential was performed for the inelastic levels, yielding Jπ assignments for several states. The different angular distributions for the 21+ and 22+ states could be accounted for by assuming a transition potential that has a contribution in the nuclear interior. Apart from the 3− state at Ex = 4.193 MeV a 4− state and 5− state were identified, for which phenomenological octupole band calculations have been performed. Explicit folding-model calculations, essential for a consistent description of 0+ and 1− states, have been performed for several levels, using the JLM nucleon-nucleon interaction both for (p, p′) and for (α, α′), A rather good description of the differential cross sections of several levels, including the 0+ and 1− states, is obtained. A direct comparison between the results from a (p, p′) and an (α, α′) folding-model analysis is made, resulting in isoscalar B(Eλ) values. Microscopic calculations have been performed for the (p, p′) results. The transition densities are obtained from shell-model (SM) and extended-RPA (E-RPA) calculations. No effective charges were introduced. The E-RPA calculations gave a fair description of the differential cross sections of several levels. In the SM calculations the neutron part of the transition density is severely underestimated.

Coupled-channels analysis of the 26Mg(p, p′)26Mg reaction at 24.0 MeV

Abstract Angular distributions from the 26 Mg(p, p′) 26 Mg reaction at E p = 23.95′ MeV have been measured with a split-pole magnetic spectrograph. The resolution obtained was 11–15 keV. Coupled-channels calculations have been performed for the 0 + , 2 + and 4 + members of the ground-state band and for the 2 + , 3 + and 4 + members of the lowest K π = 2 + and K π = 3 + bands. Calculations based on the rigid-rotator model yield no satisfactory descriptions. Much better results are obtained when the coupling strengths between the various states are allowed to be different from the values given by the rigid-rotator model. The results obtained from this analysis were used together with the results of electromagnetic studies to obtain the “true” proton and neutron transition matrix elements M p (E2) and M n (E2) for a number of L = 2 transitions between the low-lying states of 26 Mg. A comparison of the result found for M n (E2; 2 2 + → 0 1 + ) with the value for M p (E2; 2 2 + → 0 1 + ) in the mirror nucleus 26 Si as found from γ-ray studies shows a good agreement. The results for M p (E2), M n (E2) and for the transition matrix elements of the lowest four 4 + → 0 + 1 transitions have been compared to the results of shell-model calculations within the full (1s0d) shell. A satisfactory agreement is found, when effective charges consistent with the predictions of the schematic model of Brown and Madsen are used.

Contribution of 2h̷ω transitions to the excitation of 0+ states in 58Ni and 26Mg in inelastic electron scattering

Abstract The excitation of 0+ states in 58Ni and 26Mg has been investigated by inelastic electron scattering. Shell model calculations in a 1&ℏ;ω model space are not able to reproduce the data, which clearly show contributions from 2&ℏ;ω, i.e. giant monopole resonance-like, excitations.

Observation of the second 4+ state in 28Si by means of proton inelastic scattering and analysis of the Kπ = 01+and 31− bands

Abstract High-resolution data from the 28 Si(p, p′) reaction have been obtained at E p = 26.3 MeV. Separate cross sections for the 3 1 − and 4 2 + states at 6.879 and 6.889 MeV have been obtained. The strength of the 4 2 + state is much larger than reported in previous experimental papers. The 3 1 − state is well described in a coupled-channels calculation based on the rotation-vibration model.

Consistent macroscopic treatment of L = 0 and L = 1 transitions in inelastic proton scattering☆

Abstract The nuclear transition density for L = 0 and L = 1 transitions is constrained by conservation of mass and centre of mass, respectively. It is shown that the usual procedure to apply these constraints directly to the transition potential is not correct if a density-dependent effective nucleon—nucleon interaction is used to calculate the transition potential via a folding prescription.

The role of the sequential-transfer process in natural-parity transitions in the 208Pb(p, t)206Pb reaction†

Abstract Data for natural-parity transitions in the 208 Pb(p, t) 206 Pb reaction measured at E p = 20 and 50.5 MeV plus existing data at E p = 26.2, 35, 40 and 80 MeV have been analysed in zero-range as well as exact finite-range DWBA. The extracted enhancement factors exhibit a similar strong dependence on the bombarding energy, with a relative minimum at E p = 35 MeV. It is demonstrated that this energy dependence is largely removed when sequential transfer (p, d)(d, t) is included in the calculations, except at E p = 35 MeV. At this bombarding energy a phasing problem between the direct- and sequential-transfer amplitudes is encountered which seems to be related to resonances in the intermediate deuteron channel.

The role of sequential transfer in unnatural-parity transitions in the 208Pb(p, t)206Pb reaction

Abstract Angular distributions have been obtained for several unnatural-parity transitions in the 208 Pb(p, t) 206 Pb reaction at E p = 20.0 and 50.5 MeV. It is found that the sequential (p, d) (d, t) process provides an adequate description of these transitions at both energies.

Coupled-channels analysis of proton inelastic scattering from 26Mg at 24 MeV

Abstract The validity of a rotational description of low-lying levels in 26 Mg was investigated by inelastic proton scattering. A coupled-channels analysis based on pure rotational models proves to be insufficient. Further analysis indicates the occurence of antistretching and band mixing and leads to coupling strengths which are in good agreement with known B (E λ ) values and with the results of shell-model calculations.

Folding-model analysis of inelastic proton scattering off 28Si

Abstract Expressions are derived for the use of an explicit folding model in the analysis of inelastic proton scattering. It is shown that the use of phenomenological (transition) potentials can be considered to be a form of implicit folding. Differential cross sections from the 28 Si(p,p′) 28 Si reaction at E p = 26.3 and 65 MeV have been analyzed with a folding model based on the effective nucleon-nucleon interaction of Jeukenne, Lejeune and Mahaux. Coupled-channels calculations with a rotation-vibration model have been performed for the 0 + , 2 + , 4 + and 6 + members of the (rotational) ground-state band, the 3 − , 4 − and 5 − members of a K π = 3 − octupole band and the 1 − and 3 − members of a K π = 0 − or 1 − octupole band. For most states a satisfactory description could be obtained. However, the situation with respect to the 1 − state is quite unsatisfactory. Two excited 0 + states can also be described reasonably with a macroscopic nuclear model. The members of the ground-state band, the two excited 0 + states and several other positive-parity states were also analyzed in coupled-channels calculations using transition densities obtained with a microscopic model. The ground-state band is described reasonably, for the other states the description is less satisfactory.