Mass-18 Nuclei Research Articles

A study of the mass-18 nuclei and the effective interaction in the sd shell

Abstract Using Q -box techniques, linked expansions in terms of number of folds are carried out for all states of the mass-18 nuclei, where the complete 0 + 2 ħω space is considered. These expansions are shown to converge quickly. However, the series involved in obtaining the Q -box and the Rayleigh-Schrodinger series are found to converge slowly and only with the use of a shift operator that modifies the harmonic-oscillator potential.

Effective interactions through third order for mass-18 nuclei with the Paris potential

We have studied the behavior of the effective interaction in the (sd)-shell through third order for mass-18 with the meson-theoretical Paris potential. All JT states are considered. The results are compared with those obtained with the G -matrix of Kuo and Brown, based on the phenomenological Hamada-Johnston potential. The excitation spectra obtained with both these potentials are rather similar, though the Paris potential gives a better fit through third order, whereas it produces more binding for low-lying states through second order. Still, evidence for non-convergent behavior is found in T =0 states for the Paris potential.

The one-boson-exchange potential and the shell-model spectra of mass-18 nuclei

The one-boson-exchange potentials in the momentum representation of Holinde and Machleidt (see Nucl. Phys. A, vol.256, p.497, 1976) are used in a shell-model calculation of the spectra of mass-18 nuclei in order to gain an insight into the possibilities of convergence of the effective interaction expansion for these nucleon-nucleon interactions. The spectra are calculated in first order, and also in first order including the core polarisation term, which is the most important second-order correction. Comparison is made with the Reid soft-core potential results.

Three-particle one-hole multiple scattering contribution to the nuclear effective interaction in mass-18 nuclei

Within the systematic framework of the double partition approach, the three-particle one-hole multiple scattering andQ-☐ formalisms are combined to give the valence-linked and connected energy-independent effective interaction. All low-lying [2p + 3p1h] contributions to the mass-18 effective interaction are evaluated using an essentially exact energy-dependent reaction matrix based on the Reid SC potential. The low-lying one-body field of the core nucleus is treated consistently with the underlying reaction matrix G through particle- and hole-line self-energy insertions. Center-of-mass motion, folded diagrams and starting energy dependence are properly taken into account throughout. The low-lying [2p + 3p1h] correlations are stongly damped by self-energy insertions. By incorporating only the folded diagram contributions with origins in the low-lying space, the net effect of all low-lying [2p + 3p1h] correlations is to give back the bare-G plus second-order core-polarization spectra which are found to be in respectable agreement with the experimental spectra. However, including the full folded diagram contribution, which has additional contributions from the high-lying space through the energy dependence of G, leads to final spectra which deviate sizably from experiment. The present results are conclusive in the sense that the treatment is essentially exact for low-lying [2p + 3p1h] correlations which originate from the high-lying two-particle correlations through the reaction matrix G

Importance of high-lying intermediate excitations on the nuclear effective interaction

A particular third-order diagram which contributes to the effective two-body interaction in mass-18 nuclei is computed up to intermediate excitations of 26h..omega... We find that our results have not converged by 26h..omega.. and that the slow decrease in the higher-lying contributions is mainly due to the strong short-range repulsion in the central components of the nucleon-nucleon force.

B10-induced2nand2ptransfer reactions on light targets

A systematic study is made of 100 MeV $^{10}\mathrm{B}$-induced $2n$ and $2p$ transfer reactions on light targets of $^{12}\mathrm{C}$, $^{14}\mathrm{N}$, and $^{16}\mathrm{O}$. These reactions are seen to selectively populate only a few states in the residual nuclei, showing them to be useful for studying states of particular structures. Known states with ${({p}_{\frac{1}{2}}{d}_{\frac{5}{2}})}_{3}$- and $({d}_{\frac{5}{2}})_{}^{2}{}_{{4}^{+}}{}^{}$ structures are strongly populated in the $T=1$ mass-14 nuclei. The known $({d}_{\frac{5}{2}})_{}^{2}{}_{{4}^{+}}{}^{}$ states in the $T=1$ mass-18 nuclei are also strongly populated. The lowest ${2}^{+}$ states (also of a $d_{\frac{5}{2}}^{}{}_{}{}^{2}$ nature) in these latter nuclei are populated more weakly. Exact finite-range distorted-wave Born-approximation calculations, assuming a cluster transfer of the two neutrons or protons, are presented for the strongly populated levels in the mass-14 and -18 residual nuclei, and for the ${2}^{+}$ level in $^{18}\mathrm{O}$. With the exception of this ${2}^{+}$ state and the unbound ${4}^{+}$ state in $^{14}\mathrm{O}$, the shapes of the angular distributions are well fitted by the cluster approximation. The distorted-wave Born-approximation normalizations to the data are compared to cluster spectroscopic factors calculated from shell model wave functions for the various states involved. In most cases, the extracted factors agree with the calculated spectroscopic factors to within a factor of 3. This agreement suggests that the reaction mechanism is predominantly a one-step transfer of a $T=1$, $S=0$ pair of neutrons or protons. The known structures of the strongly populated states in the mass-14 and -18 nuclei can be used to interpret newly observed states in the mass-16 spectra, in which there are two groups of strongly populated levels in each nucleus. The doublet in the low excitation region corresponds to the known ${2}^{\ensuremath{-}}$ and ${3}^{\ensuremath{-}}$ states presumably populated through the transfer of the nucleon pair into a ${({p}_{\frac{1}{2}}{d}_{\frac{5}{2}})}_{3}$- configuration coupled to the $^{14}\mathrm{N}_{1+}$ target core. The higher group of states is predicted to arise from the transfer of the nucleon pair into a $({d}_{\frac{5}{2}})_{}^{2}{}_{{4}^{+}}{}^{}$ configuration coupled to the ${1}^{+}$ core. The results of a Bansal-French-Zamick weak coupling model calculation for the center of gravity of the triplet of states from this $({d}_{\frac{5}{2}})_{}^{2}{}_{{4}^{+}}{}^{}$ configuration in the $T=1$ mass-16 nuclei are presented. These are seen to be in agreement with the observed energies of the high excitation peaks in the data.[NUCLEAR REACTIONS $^{12}\mathrm{C}$, $^{14}\mathrm{N}$, $^{16}\mathrm{O}$($^{10}\mathrm{B}$, $^{8}\mathrm{Li}$), $E=100$ MeV; $^{12}\mathrm{C}$, $^{14}\mathrm{N}$, $^{16}\mathrm{O}$($^{10}\mathrm{B}$, $^{8}\mathrm{B}$), $E=100$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; DWBA analysis; extracted and calculated $2n$ and $2p$ spectroscopic factors; weak coupling model predictions.]

Negative-parity spectra for mass-18 nuclei in the dynamic-interaction propagator approach

The energy spectra and two-particle strengths of negative-parity states in mass-18 nuclei are calculated by using a Green-function formulation which includes energy-dependent two-particle interactions. The energy dependence is induced by the dynamic exchange of the octupole phonon which appears at 6.13 MeV in 16O. This state is described within a normal static particle-hole RPA. The two-body interaction parameters are chosen to provide the correct phonon energy and reasonable negative parity mass-17 and positive-parity mass-18 spectra. The negative-parity states are then calculated in a parameter-free way. In order to avoid redundant solutions or ghosts, the fermion lines must be dressed in a way consistent with the phonon exchange.

Average effective-interaction calculations in a simulated Hartree-Fock basis

The averaged effective interaction for mass-18 nuclei is computed through fourth-order perturbation theory in both a pure harmonic-oscillator basis and a simulated Hartree-Fock basis. Going to a Hartree-Fock basis does not eliminate the large fourth-order averages found earlier by Goode and Koltun using an harmonic-oscillator basis.

Some convergence properties of the perturbation series for the effective nuclear interaction:: The stability of results under double partitioning in mass-18 nuclei

The Bloch-Horowitz-Brandow (BHB) expansion for the effective interaction in mass-18 nuclei is evaluated by the method of double partitioning. That is, the BHB expansion for the effective interaction is divided into two calculations for the purpose of approximating separately the high- and low-energy (long- and short-range, respectively) effects so as to improve the approximation of each. This is done by approximating a high-energy effective interaction (for a larger, or “outer”, model space) and then using that for the potential in terms of which the low-energy BHB expansion (for a smaller, or “inner”, model space: the sd shell) is evaluated. The size of the outer model space is 4 h ̷ Ω larger than the smaller. The results, by comparision with earlier works by Barrett, show a trend that suggests that the (intermediate-range) tensor force is being poorly accounted for and as a result the convergence of the intermediate-excitation sums is poor, a finding similar to that found by Vary, Sauer and Wong. The convergence of the order-by-order sum, however, seems to be improved as the outer model space is enlarged. The suggestion is made that the use of a better approximation, if one can be found, to the effective interaction for the outer model space (appropriate for including the effects of the tensor force) might improve the intermediate excitation convergence.

The average effective interaction in linked cluster theory

We derive a theoretical method for calculating the averages (over J and T) of matrix elements of the nuclear effective interaction, in any order of the linked cluster expansion. We apply this to calculate all terms through fourth order in the G-matrix, for the averages in mass-6 and mass-18 nuclei. We find that the averages in fourth order are as large as in second and third order. This behavior is associated with a small number of terms, which suggests a partial summation method of improving the series. The relation to other work is discussed.

Two-particle ladder diagrams and double-counting in effective interaction calculations

It is shown that including the two-particle ladder diagrams, computed with the Barrett, Hewitt, McCarthy G matrix elements at a starting energy of 47 MeV and for intermediate excitations of 2ℏΩ, in the perturbation expansion for the effective two-body interaction in mass-18 nuclei involves a double-counting of roughly 42%. It is argued by comparison that the double-counting should be roughly the same when the Kuo G matrix elements are used.

Convergence properties of the perturbation expansion for the effective two-particle interaction in mass-18 nuclei in a doubly partitioned Hilbert space

The theory for calculating the effective interaction ov for finite nuclei in a doubly partitioned Hubert space is discussed and then applied to the calculation of ov through third order in the nuclear reaction matrix G for the J = 0, T = 1 states in mass-18 nuclei. The G-matrix elements were computed using the technique of Barrett, Hewitt and McCarthy, which allowed an acccurate treatment of the Pauli projection operator. Calculations were first performed using the standard procedure for computing ov. These calculations were then repeated employing the double-partition procedure, and its results were compared with those from the standard procedure. The convergence of the perturbation expansion for ov through third order in G was improved in the double-partition approach but was not conclusive. However, the double-partition procedure allows the possibility of performing much more sophisticated and accurate calculations of ov than the standard procedure. All calculations were performed as a function of the starting energy ω of G, which is related to constant shifts between the energy levels of the occupied and unoccupied single-particle states. For all calculations a value of ω was found at which the 0 + ground state agreed with experiment. A procedure is proposed for determining in advance the value of ω at which G and ov should be computed.

Second Coulomb energy differences of isospin triplets in the 2s-1d shell

Abstract Second Coulomb energy differences, which in the present case are proportional to the tensor Coulomb energy, are calculated for 0 + , T = 1 ground states in the region 18 ≦ A ≦ 42 using a shell model that includes a pairing interaction. The calculation is done with a mathematical formalism that includes p-n pairs as well as p-p and n-n pairs. Besides an enhancement of proton-pair Coulomb energies, the pairing interaction is responsible for lowering the Coulomb energy of N = Z members of isospin triplets and also gives rise to an important term in the second energy difference. Using pairing strengths derived from fitting energy levels for mass-18 and mass-42 nuclei, results of the calculation reproduce experimental second energy differences extremely well.

4p-2h intermediate states and the effective interaction in mass-18 nuclei

Abstract A set of diagrams with 4p-2h intermediate states is summed. The result is more attractive than the lowest order, the effect being mainly on J = 0 T = 1 and J = 1 T = 0 states. The ground states are depressed, somewhat improving the fit to experiment.

Higher-order terms and the apparent non-convergence of the perturbation expansion for the effective interaction in finite nuclei

We have calculated all significant terms through third order in the reaction matrix G which contribute to the perturbation series for the J = 0, T = 1 effective interaction between two valence nucleons in the mass-18 nuclei and also a few selected fourth-order terms. We have shown that the perturbation series does not converge order-by-order to third order in G and that certain large third-order terms tend to cancel the second-order contribution. An intuitive physical picture of the process giving rise to this effect and to analogous effects in related calculations of the effective charge is given. This picture suggests a rearrangement of the perturbation series into physically significant groups of diagrams, so that each group converges order-by-order in G. However, one must then find some way to sum all these groups of diagrams. We conclude that simple perturbation theory is not a reliable method for calculating the effective two-nucleon interaction in mass-18 nuclei, when currently standard calculational techniques are used, and that the success of first- plus second-order perturbation theory in fitting experimental spectra for these nuclei is unexplained.

A study of deformation in light nuclei: (II). Application to the even-parity states of the mass-18 nuclei

The properties of the low-lying even-parity levels of 18F and 18O are shown to be well understood in terms of an extended shell-model calculation in which deformed (4-particle-2-hole) states are mixed with the usual two-particle states. The properties of the levels investigated are their energies, electromagnetic decays and reduced widths. The deformed states are constructed by first forming a representation for the ground state band of 20Ne and then coupling on to this a complete set of two-hole states formed from (1p) −2 oscillator configurations. It is shown that admixtures derived from configurations which include p 3 2 holes are of much greater importance in the low-lying T = 0 states than in the T = 1 states. It is found that the observed E2 decay strengths in both 18O and 18Ne require the adoption of an effective charge of about 0.3 e for their explanation. The observed E2 decays in 18F between the lower T = 0 levels, however, are well reproduced without effective charge. This feature, for which there is no explanation in terms of the normal effective charge concept, is discussed in terms of second order perturbation theory, which takes into account states in which one particle from the core is promoted through two major shells.

Mass-18 nuclei

A shell-model calculation was carried out for the singly excited states of mass-18 nuclei using the group SU 3 to classify the states. The effect of the spin-orbit coupling in mixing these states is examined, and the structure of the dipole resonances is elucidated. The division of the dipole strength from the various excited configurations to the ground state is calculated. The lowest of these dipole states is found to occur in the region of 12 MeV.