Continuum Shell-model Calculations Research Articles

Spectroscopy ofC9via resonance scattering of protons onB8

The structure of the neutron-deficient $^{9}\mathrm{C}$ isotope was studied via elastic scattering of radioactive $^{8}\mathrm{B}$ on protons. An excitation function for resonance elastic scattering was measured in the energy range from 0.5 to 3.2 MeV in the center-of-momentum system. A new excited state in $^{9}\mathrm{C}$ was observed at an excitation energy of 3.6 MeV. An $R$-matrix analysis indicates spin-parity $5/{2}^{\ensuremath{-}}$ for the new state. The results of this experiment are compared with continuum shell-model calculations.

Origin of anomalous values ofσ(π+,π+′p)/σ(π−,π−′p)

Results of recoil-corrected continuum shell model calculations are presented for {sup 4}He({pi},{pi}{sup {prime}}p){sup 3}H. The extremely large values of {sigma}({pi}{sup +},{pi}{sup +{prime}}p)/{sigma}({pi}{sup {minus}},{pi}{sup {minus}{prime}}p) are shown to be a result of neutron excitations which couple to outgoing proton channels. The large ratio will occur in regions where neutron excitations increase rapidly in a particular channel and, therefore, may be a signal for giant resonances. {copyright} {ital 1997} {ital The American Physical Society}

Radiative proton capture to discrete states in 31N at 98 and 176 MeV

A high resolution magnetic pair spectrometer for medium energy photons has been used for studies of the exclusive (p,γ) reaction on 12C at 98 and 176 MeV. We present angular distributions of the differential cross section for transitions to the ground state and the first three excited states of 13N. The distributions from these four states are compared with predictions from a microscopic continuum shell model calculation using a realistic finite-ranged effective interaction with tensor components. In general, reasonable agreement is obtained for reactions to states described by p shell single particle wave functions, but poor agreement is obtained for transitions described by sd shell single particle wave functions. Nevertheless we find, however, that the dominant reaction mechanism is a direct capture process. We also compare the (p,γ) data with existing data on the exclusive (p,π) reaction at 185 MeV revealing notable differences between the two reactions.

Radiative proton capture to discrete states in 12C at 98 and 176 MeV

A high-resolution magnetic pair spectrometer for medium energy photons has been used for studies of the exclusive (p, γ) reaction on 11B at 98 and 176 MeV. We present angular distributions of the differential cross section for transitions to the ground and first three excited states of 12C. The distributions from the three lowest lying states are compared with predictions from a microscopic continuum shell-model calculation using a realistic finite-ranged effective interaction with tensor components. Exchange current effects are examined in detail as both Δ(1232) isobar and pion exchange currents are rigorously included. In general, a good theoretical description of the data is obtained. The predominant reaction mechanism involves photon emission by the nucleonic one-body current.

Effective interactions and nucleon scattering from light nuclei

Effective interactions have been constructed from several nucleon-nucleon potentials. The interactions are obtained from Brueckner calculations for the appropriate finite nucleus and are, therefore, nucleus-dependent. A prescription for the starting energies in the interactions is determined by comparing the results of translationally invariant, continuum shell model calculations to nucleon-scattering data for A=3 and 4 targets. The different nucleon-nucleon potentials give similar results, and the calculations for the A=3 and 4 targets agree well with data up to EN=60 MeV. Mid-angle cross-sections begin to deviate from data at EN=85 MeV, and calculated analysing powers at EN=154 MeV are not able to reproduce the forward angle peak found in the data. Therefore, these interactions should be appropriate for nucleon reactions below 85 MeV.

Radiative proton capture and exchange currents in light nuclei

A new type of high resolution pair spectrometer for medium energy photons has been used for studies of the exclusive (p,γ) and (p,e+e−) reactions on light nuclei in the energy region 100 to 200 MeV. From the current experiments we present angular distributions of the differential cross section for transitions to the ground state and first three excited states in 12C. The distributions from the ground state and first excited state are compared with predictions from a microscopic continuum shell model calculation which uses a realistic finite-range effective interaction with tensor components. Based on preliminary data, the salient features of the (p,γ) reaction on 12C and the (p,e+e−) reaction on 11B are also discussed.

Radiative proton capture to individual states in 12C

A new type of high resolution pair spectrometer for medium energy photons has been used for studies of the exclusive ( p, γ)reaction on 11B at 98 MeV. Angular distributions of the differential cross section for transitions to the ground state and first excited state in 12C are presented. The distributions show good agreement with predictions from a microscopic continuum shell model calculation which uses a realistic finite-range effective interaction with tensor components.

Electroexcitation of 4He in the near continuum.

Inelastic electron scattering cross sections for /sup 4/He have been measured at 180/sup 0/ for incident electron energies of 130 and 200 MeV. Spectra measured up to excitation energies of 54 MeV are relatively featureless and show no evidence for resolvable excitations. The data are compared with continuum shell-model calculations which include all one-body breakup channels.

Nuclear structure of 49Ca above 5 MeV excitation from n + 48Ca and astrophysics for 30keV neutrons

The level structure of 49Ca has been investigated above the neutron separation energy by measurements of the total and capture cross sections for neutron energies up to 2 MeV. Transmission data were obtained for two 48CaCO 3 samples enriched to 96% in 48Ca and were analyzed in the R-matrix formalism for neutron energies up to 2 MeV. An upper limit of 0.07 × 10 −4 was placed upon the s-wave strength function (〈 Γ n o 〉/ D) and an optical model real potential was deduced from the low energy total cross section. Approximately 45% of the 2 d 5 2 single particle strength is observed in the region below 2 MeV neutron energy. Model configurations based on continuum shell model calculations which describe this strength and its distribution are presented. Combined low energy results are used to obtain the maxwellian averaged capture cross section and the result is discussed in relation to the nucleosynthesis of 49Ca and the anomalous abundances observed in an inclusion of the Allende meteorite.

Continuum shell-model calculation for 14C including core excitations

Elastic and inelastic cross sections for neutron scattering on 13C have been calculated up to 10 MeV including excitations of the 12C core. The core properties are taken from experiment while the additional neutrons are described in a shell-model basis. Antisymmetrization between the valence particles and the core is taken into account as a second-order perturbation effect. All results including those for the target and the bound states of 14C are compared to experimental data. The differences between a gaussian and a δ interaction for the valence particles is investigated. The calculation was only feasible with a modified continuum shell model, i.e. approximating the single-particle resonances by bound states. The remaining modified continuum states are damped in amplitude within the resonance region. The residual interaction between modified continuum states is neglected.

Continuum shell model calculations and the resonances below the GDR in12C

The excitation functions in the11B(p, n0),11B(p, p1) and11B(p, γ) reaction channels predicted by a continuum shell model calculation are compared to facilitate isospin assignments forJ− resonances in the (19÷22) MeV region of excitation in12C. Model predictions are also tested against differential cross-section data in the particle channels. It is shown that definitive spin, isospin and parity assignments can be made for several dominant resonances reported in the literature. Comparison with recent (e, e′) data analysis not only confirms our model predictions but also demonstrates that level energies are well reproduced within the multiconfiguration shell model only if continuum effects are included.

Fast neutron radiative capture in silicon

Using the28Si(n, γ)29Si reaction, transitions to the ground state and first excited state in29Si have been studied in the neutron energy range 3–14 MeV with improved neutron energy resolution (of about 100 keV). The 90° cross sections show considerable structure in the entire neutron energy range. Comparison with theoretical calculations shows that compound-nucleus and direct-semidirect processes account for the non-resonant part (smoothly varying part) of the cross section. A microscopic model is, however, required to describe the resonance structure. Continuum shell-model calculations have proven to be a very promising means towards a better understanding of the capture process in, and below, the giant resonance region in light nuclei. The angular distributions of gamma rays in the neutron energy range 8–14 MeV indicate that the capture reaction is mainly of direct character and that the effect of interference between the electric dipole and isoscalar quadrupole resonance is weak.

Determination of unbound states inS35from neutron total and capture cross-section measurements onS34

The high neutron resolution capability of the Oak Ridge Electron Linear Accelerator has been used to investigate the unbound region of $^{35}\mathrm{S}$ via neutron resonance spectroscopy studies of the $^{34}\mathrm{S}$+n system. The total cross section of $^{34}\mathrm{S}$ was measured over the neutron energy range from 90 to 1500 keV, and the capture cross section was measured over the range from 30 to 1100 keV. Analysis of the data yielded spectroscopic factors for the $s$ states in the unbound region for excitation energies from 7 to 8 MeV. Continuum shell model calculations of the $s$ and $d$ states were also performed for both the bound and the unbound regions of $^{35}\mathrm{S}$. In general, the measured and calculated neutron strengths for $s$ waves in the unbound region are in reasonable agreement, although the fragmentation of single-particle strength seen experimentally is somewhat higher than that predicted. Core-particle calculations for the $p$ states in the unbound region of $^{35}\mathrm{S}$ were also performed, and, on the basis of all these results, plus those of others, we have summarized our understanding of the distributions of single-particle neutron strengths in the $s$, $p$, and $d$ states of $^{35}\mathrm{S}$ for excitation energies up to 8.5 MeV.

Implications of the experimental results on the photodisintegration ofHe4

The photoproton and photoneutron cross sections for $^{4}\mathrm{He}$ are evaluated in the light of several recent measurements, and are found to be substantially different in the energy region below 30 MeV. Because these cross sections are dominated by $\ensuremath{\Delta}S=0$, $\ensuremath{\Delta}T=1$ $E1$ transitions, this result implies strong isospin mixing in the four-nucleon system. Furthermore, since available continuum shell-model calculations including Coulomb effects predict only small differences in the photoproton and photoneutron cross sections except near threshold, this result suggests that a nonzero charge asymmetry is present in the nuclear force.NUCLEAR REACTIONS $^{4}\mathrm{He}(\ensuremath{\gamma}, p)^{3}\mathrm{H}$, $^{4}\mathrm{He}(\ensuremath{\gamma}, n)^{3}\mathrm{He}$, evaluated cross sections, cross-section ratio; isospin mixing, charge asymmetry.

Structure of 12B from measurement and R-matrix analysis of σ(θ) for 11B(n, n) 11B and 11B(n, n') 11B ∗(2.12 MeV), and shell-model calculations

Differential cross sections for neutrons elastically scattered from 11B and inelastically scattered to the first excited state 11B∗ (2.12 MeV) have been measured at 13 incident energies for 4.8 ≦ E n ≦ 7.6 MeV corresponding to excitation energies in 12B of 7.8 to 10.3 MeV. The cross sections were measured at nine laboratory angles per energy from 20° to 160° and show considerable resonance structure. Differential inelastic cross sections were also measured for the 4.45 and 5.02 MeV levels of 11B for 2 to 9 angles at several incident energies. These new elastic and inelastic 2.12 MeV level data have been analyzed together with previously published cross sections for 2 ≦ E n ≦ 7.5 MeV using a multilevel-multichannel R-matrix program to determine J, π, E λ and γ λc for states in 12B. The shell model was used to calculate states in 12B as well as spectroscopic amplitudes for reactions leading to these states. The results of this model calculation are compared to those of the R-matrix analysis. Much of the structure observed in the experimental work is predicted by the model for E x ≲ 7 MeV. For levels of higher excitation the agreement is not as good. The experimental data are also compared to continuum shell-model calculations.

Polarized neutron capture onHe3atEn=9.0MeV

A polarized neutron beam has been used to measure the angular distribution of the analyzing power for the $^{3}\mathrm{He}$($\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}$,$\ensuremath{\gamma}$)$^{4}\mathrm{He}$ reaction at ${E}_{n}$ $({E}_{x})=9.0 (27.3)$ MeV. The angular distribution of the cross section, obtained with an unpolarized beam, is combined with these data to obtain the ${b}_{k}$ coefficients. These coefficients are compared to the results of a previous measurement performed for the $^{3}\mathrm{H}$($\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$,$\ensuremath{\gamma}$)$^{4}\mathrm{He}$ reaction, and to the results of a recent continuum shell model calculation.NUCLEAR REACTIONS $^{3}\mathrm{He}$($\stackrel{\ensuremath{\rightarrow}}{\mathrm{n}}$,$\ensuremath{\gamma}$)$^{4}\mathrm{He}$, measured $\ensuremath{\sigma}(\ensuremath{\theta})$ and $A(\ensuremath{\theta})$ at ${E}_{n}=9.0$ MeV. Compared results to previous $^{3}\mathrm{H}$($\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$,$\ensuremath{\gamma}$)$^{4}\mathrm{He}$ measurements and to recent continuum shell model calculations.

Threshold states in schematic models

The possibility of strength decoupling from the giant dipole resonance is shown in the Brown-Bolsterli and Goswami-Pal schematic models, modified to incorporate the features of the threshold states, and in continuum shell-model calculations. Two essential features are considered: the threshold states have lower particle-hole energy than the other normal states and the coupling between the threshold and the normal states via the residual interaction is weaker than between states of identical type.

The centre-of-mass spuriosity in continuum shell-model calculations

A method proposed previously to eliminate the centre-of-mass (CM) spuriosity in continuum shell-model (SM) calculations of 4He is generalised to adapt to the cases of heavier nuclei. It is applied to study the (p,p) and (p,n) reactions involving the one-particle-one-hole excitation of the dipole resonances in 12C and 16O. The effect is non-negligible and the results show features not observed previously. The Pauli term is also studied and is found to be less important in 16O as compared with the lighter nucleus 12C.

Prediction of Observable Polarization-Analyzing-Power Differences inB11(p,n)C11

Polarization-analyzing power differences in /sup 11/B(p,n)/sup 11/C are predicted to be observable at selected energies below E/sub p/ approx. 10 MeV at the level of vertical-bar P-A vertical-bar> or approx. =0.1. This result is derived from recoil corrected continuum shell model calculations in the lp-lh approximation, using a realistic g-matrix interaction.

Recoil corrected continuum shell model calculations for four-nucleon systems

The continuum shell model with full correction for target recoil is extended to 1p-1h configurations. The procedure is discussed in a framework which allows generalization to more complicated configurations. An application is made to nucleon reaction channels in 4He using the g-matrix interaction of Bertsch et al. Excellent agreement with the data is obtained.