The generator coordinate method as an approximation to the shell model: A comparison on 24Ne

The applicability of the generator coordinate method as an approximation to the complete shell model diagonalization is tested in the sd shell on ²⁴Ne. We use the quadrupole moment and the pairing energy as generator coordinates and choose as generating function a constrained Hartree-Bogoliubov solution projected on the subspace of good angular momentum and good proton and neutron number. The spectra obtained by the generator coordinate method and the complete diagonalization show good overall agreement. Also we draw some conclusions about the nature of some low-lying states in ²⁴Ne, interpreted in terms of vibrations.     

A study of even-parity states of the nuclei 19F, 21Ne and 23Na with the generator coordinate method and with mixing of projected Hartree-Fock determinants in comparison with complete diagonalization

The energies and electromagnetic properties of the even-parity states of the nuclei ¹⁹F, ²¹Ne and ²³Na are calculated with the generator coordinate method and with mixing of projected HartreeFock determinants, using the Kuo and the Preedom-Wildenthal two-body interactions. The two parameters β and ? of Nilsson's potential are chosen as generator coordinates and the subspace is enlarged with a few different configurations, i.e. one for A = 19 and three for A = 21 and 23 nuclei. Special care is taken in choosing the appropriate Hartree-Fock solution corresponding to possible occupied single-particle states. For both methods six basic functions are enough to obtain a good approximation to complete diagonalization within the same model space. The collective features of these nuclei are also investigated.     

The (3He,n) reaction on 16O and 18O

The (³He, n) reaction on ¹⁶O and ¹⁸O has been used to study low-spin states in ¹⁸Ne and ²⁰Ne up to E_x ≈ 8 and 20 MeV, respectively. The measured neutron angular distributions have been analysed using DWBA. By a comparison with shell-model calculations in the (s, d) shell it is found that most of the two-proton transfer strength can be explained within that shell. Important contributions, however, from the (f, p) shell in low-lying negative parity states are also present.     

Microscopic investigation of electric dipole transitions in the α + 16O system

A microscopic calculation of forbidden E1 transitions is presented in the framework of the generator coordinate method. Isovector and isoscalar origins of E1 transitions are studied in the case of the α + ¹⁶O system. Two-cluster T = 0 and T = 1 configurations are coupled by the exact microscopic Coulomb interaction. The γ- widths of the 1₁⁻ and 3₂⁻, states of ²⁰Ne are fairly reproduced by the model but the anomalous branching ratios observed experimentally remain unexplained. Simplified formulas for the isospin-mixing rates and reduced E1 transition probabilities are compared with the microscopic results and are employed to discuss them. The non-resonant E1 contribution to the ¹⁶O(α, γ)²⁰Ne reaction is shown to be almost negligible at astrophysical energies.     

The16O(α, γ)20Ne direct capture reaction at low energies

The¹⁶O(α, γ)²⁰Ne direct capture cross section has been calculated in a microscopically founded cluster model which reproduces simultaneously both the correct binding energies and the deformations of the²⁰Ne bound states. Theα+¹⁶O scattering states are derived from a microscopically derived local potential. The astrophysicalS-factor is found to increase linearly with energy in the energy rangeE _cm≈0.4–2 MeV and might therefore be determinable experimentally.     

The oscillator frequency in resonating-group-method calculations

For the example α-¹⁶O we present simple RGM calculations with equal (ω = ω′) and different (ω ≠ ω′) oscillator frequencies for the two nuclei. In the case ω ≠ ω′ and ω → ω′ the one-channel RGM space for angular momentum zero contains all ²⁰Ne states with four particles in the s-d shell and total spatial symmetry ($\text{[?] = [4]}$). These states form a basis for low-lying excited 0⁺ states of ²⁰Ne. The ω ≠ ω′ calculation (as well for ω → ω′ as for realistic ω, ω') exhibits, therefore, resonances corresponding to these states. We present also the calculation for ω = ω′ where these physically important resonances are missing.     

Wave functions for low-lying states of light deformed nuclei using a “realistic” hamiltonian and their test by inelastic scattering: The case of 20Ne

Nuclear structure wave functions for the ground and low-lying excited states of ²⁰Ne, obtained from the angular momentum projected deformed particle-hole model using a “realistic” many-nucleon hamiltonian (kinetic energy plus a Brueckner G-matrix based on the Hamada-Johnston potential), are used as input to microscopic antisymmetrised DWBA analyses of inelastic proton scattering from ²⁰Ne. This nuclear structure model, which has been previously shown able to describe the essential features of the giant multipole resonances of both ²⁰Ne and ²⁸Si, predicts angular distributions for inelastic proton scattering, exciting a number of states below 9 MeV in ²⁰Ne, in qualitative agreement with the available data; a somewhat surprising result given the nuclear structure model's completely microscopic formulation. Anomalies observed in the assignment of some predicted levels to experimental states suggest some shortcomings in the form adopted for the hamiltonian.     

Influence of left-right asymmetry degrees of freedom in self-consistent calculations of 20Ne

Within a constrained Hartree-Fock calculation we investigate the effects of left-right asymmetric degrees of freedom associated with the channel ¹⁶O + ⁴He ? ²⁰Ne. We find a large softness of ²⁰Ne against octupole deformation. The optimal solution after restoration of the parity by means of a projection shows a pronounced ¹⁶O + ⁴He clustering. A generator coordinate calculation along the collective path confirms this conclusion. Once center-of-mass motion effects are taken into account a good agreement with experiment is found.     

Search for highly deformed shape isomers in 28Si, 24Mg and 20Ne linked by successive alpha decays

Measurements of the ¹²C(¹⁶O,²⁰Neα)α, ¹²C(¹⁶O,αα)²⁰Ne, ¹²C(¹⁶O,⁸Be)²⁰Ne and ¹²C(¹⁶O,¹⁶Oα)⁸Be reactions have been performed at E_c.m. = 27.0 MeV. For decays proceeding through resonant states in the intermediate ²⁴Mg nucleus, angular correlation measurements have enabled spin assignments to be made and the dominant entrance channel angular momentum to be determined. The results are inconsistent with recent similar experiments which were interpreted as arising from successive α-decays from deformed shape isomeric states in ²⁸Si and ²⁴Mg.     

Microscopic treatment of the coupled monopole and quadrupole vibrations in light nuclei

The coupled monopole and volume-conserving quadrupole oscillations in ⁴He, ¹²C, ¹⁶O, ²⁰Ne and ⁴⁰Ca have been studied within the framework of the Hill-Wheeler generator coordinate method.     

Gamov states in the generator coordinate method

Starting from the generator coordinate theory, a method is developed for calculatingα-decay widths within a microscopic dynamical theory. Antisymmetrization is taken into account exactly between all nucleons of the decaying system. For illustration, the method is applied to theα-decay of⁸Be and²⁰Ne.     

Recoil-distance measurements of g-factors for 24Mg(21+) and 20Ne(21+)

Time-differential recoil-into-vacuum measurements have been performed with a plunger on the first-excited I^π = 2⁺ states of ²⁴Mg and ²⁰Ne. The states were populated by the reactions ¹²C(¹⁶O, α)²⁴Mg and ¹²C(¹²C, α)²⁰Ne. The measured anisotropy of the α-γ angular correlation was greatly increased by means of a vertical slit on the annular particle detector. Values of $\text{¦g¦= 0.51 ± 0.02}\text{and}\text{0.54 ± 0.04}$ have been deduced for the ²⁴Mg and ²⁰Ne g-factors, respectively. The mean lives of these states have been determined as τ_m = 2.09 ± 0.13 ps and 0.8 ± 0.2 ps, respectively. Various theoretical calculations are discussed and compared with the measured g-factors.The analysis of the measurement also yields values for the populations of electronic states contributing to the hyperfine interaction. For ²⁰Ne the populations of the different electronic configurations are compared with the results of a separate time-integral measurement, in which the correlations were measured for each ionic state separately. Large fractions of two-electron excited states are found to contribute.     

SU(3) coupling for negative-parity states of 16O

Results of a shell-model calculation for negative-parity T = 0 states of ¹⁶O are reported. Comparison with earlier work on the problem of low-lying collective states suggests that the difficulty in getting these states low enough in energy is probably related to the strong truncations of the vector space.     

Research on neutron-rich nuclei in the region of the nuclear shells N=20 and N=28

The results of the joint experiments carried out by the Dubna-GANIL (France) and the Dubna-RIKEN (Japan) collaborations aimed at synthesizing new isotopes close to the neutron shells N=20 and N=28 and at studying their properties are presented. Gamma-spectroscopic methods were used to study low-lying states in ^30,32Mg, ^26–28Ne, ²²O, and ¹⁸C. The ratios E(4⁺)/E(2⁺) were determined. A direct method was used to measure the masses of 20 nuclides located between the shells N=20 and N=28. The decay properties were determined for ³⁰Ne and ^26,27,29F. Information obtained in this way suggests the existence of a deformation close to the neutron shell N=20. The results of experiments devoted to searches for the doubly magic nucleus ²⁸O are also presented. Only the upper limit on the cross section for its production was deduced, which can be taken as evidence of its instability.     

Radiative decays of unbound levels in 20Ne

Nine levels in the range 8.7 to 12.5 MeV in ²⁰Ne have been investigated with the ¹⁶O(α, γ)²⁰Ne and ¹⁶O(α, α')¹⁶O¹(6.13 MeV) reactions using a differentially pumped windowless gas target. Three of the levels have not been observed previously in these reactions, and new information has been obtained for most of the others. In particular, the 11.27 MeV 1^? level is shown to have T = 1, a result of relevance to a proposed parity violation experiment, and the analogue of the 1.97 MeV (3^?T = 1) level in ²⁰F is shown to lie at 12.25 MeV in ²⁰Ne rather than at 12.39 MeV as proposed previously. In addition, the 12.25 MeV level has a width Γ < 1 keV, in contrast to the value Γ ～ 5 keV reported in other work. The electromagnetic transition rates for positive parity T = 1 states in ²⁰Ne are compared with shell-model calculations.     

Evidence for boson-mode excitations in the16O(α,n) and20Ne(α,n) excitation functions

Excitation functions for¹⁶O(α,n) and²⁰Ne(α,n) have been measured from threshold to 26 and 31 MeV compound excitation energy, respectively. The dominating compound states are interpreted as boson excitation modes of nuclei with α-particle structure.     

Nonstatistical structures in the excitation functions of20Ne(16O,12C)24Mg and20Ne(16O,20Ne)16O reactions

The data on the excitation functions of²⁰Ne(¹⁶O,¹²C)²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(1.37, 2⁺),²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(4.12, 4⁺+4.24, 2⁺) +²⁰Ne(¹⁶O,¹²C^*(4.44, 2⁺))²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(6.01, 4⁺+6.43, 0⁺),²⁰Ne(¹⁶O,²⁰Ne)¹⁶O,²⁰Ne(¹⁶O,²⁰Ne^*(1.63, 2⁺))¹⁶O, and²⁰Ne(¹⁶O,²⁰Ne^*(4.25, 4⁺))¹⁶O reactions atθ _lab=13° fromE _c.m.=22.8 to 38.6 MeV have been subjected to a statistical analysis comprising of the calculations of the distribution of cross sections, deviation functions, cross-correlation functions, summed excitation functions, cross-channel correlation coefficients and coherence widths. The analysis confirms the existence of nonstatistical structures atE _c.m.=24.6, 27.8, 31.7 and 35.5 MeV, and identifies a new structure of the same nature atE _c.m. =25.6 MeV.     

Quadrupole collectivity of neutron-rich neon isotopes

The Angular Momentum Projected Generator Coordinate Method, with the quadrupole moment as collective coordinate and the Gogny force (D1S) as the effective interaction, is used to describe the properties of the ground state and low-lying excited states of the even-even neon isotopes ^20-34Ne, that is, from the stability valley up to the drip line. It is found that the ground state of the N = 20 nucleus ³⁰Ne is deformed but to a lesser extent than the N = 20 isotope of the magnesium. In the calculations, the isotope ³²Ne is at the drip line in good agreement with other theoretical predictions. On the other hand, rather good agreement with experimental data for many observables is obtained. Received: 19 Novemeber 2002 / Accepted: 24 January 2003 / Published online: 8 April 2003