Search Results (28 total)

We apply the Lee-Suzuki iteration method to calculate the linked-folded diagram series for a new Nijmegen local NN potential. We obtain an exact starting-energy-independent effective two-body interaction for a multishell, no-core, harmonic-oscillator model space. It is found that the resulting effective-interaction matrix elements can be well approximated by the Brueckner G-matrix elements evaluated at starting energies selected in a simply way. These starting energies are closely related to the energies of the initial two-particle states in the ladder diagrams. The ‘‘exact’’ and approximate effective interactions are used to calculate the energy spectrum of ⁶Li in order to test the utility of the approximate form.

We perform large-space shell-model calculations for the low-lying energy spectra of a few light nuceli,⁴He, ⁵He, ⁶Li, and ⁷Li, in a no-core model space with a realistic effective two-body interaction (Brueckner G matrix). Our G matrices are calculated for the Reid-soft-core potential in a harmonic-oscillator basis. Single-particle ‘‘-U’’ insertions are replaced by two-particle ‘‘-U’’ insertions and are included in the G-matrix calculations, which sum them to all orders. With the starting energy of the G matrix chosen to give approximately the experimental binding energy, we obtain nuclear energy spectra which are in reasonable agreement with experiment. We also investigate the dependence of our results on the size of the model space and on the harmonic-oscillator basis parameter (ħΩ).

We compare density-dependent distorted-wave impulse-approximation (DD-DWIA) calculations with experimental (p,n) cross-section angular distributions at 135 MeV for ten nuclei from A=14 to 208. The DD-DWIA calculations use a G-matrix interaction based on the Bonn one-boson-exchange potential and empirical optical-model parameters. The agreement between the calculations and the experimental results is excellent with normalization factors required that are within 10% of unity; these factors are within the experimental scale uncertainties.

The ⁴⁵Sc(p,n)⁴⁵Ti reaction was studied at 135 MeV with a beam-swinger system. Neutron kinetic energies were measured by the time-of-flight technique, with neutron detectors located in three detector stations at 0°, 24°, and 45° with respect to the undeflected beam. Flight paths of 131.0, 131.1, and 81.3 m were used. The overall timing resolution was about 825 ps, providing energy resolutions of 320 keV in the first two stations and 520 keV in the third. The wide-angle spectra are dominated by a complex at E_x=4.3 MeV. The angular distribution for this complex is fitted well by a distorted-wave impulse approximation calculation for an assumed J^π=17/2^-,19/2^- (πf_7/2²,νf_7/2^-1) doublet. The spectra and angular distribution are consistent with (p,π^-) excitations of the same states and are in good agreement with a full 1f-2p shell-model calculation. The 17/2^-,19/2^- strength predicted by distorted-wave impulse approximation calculations using these shell-model wave functions is in good agreement with the experimental measurements.

Gamow-Teller transition probabilities are extracted for eight nuclei with masses between A=13 and 39 from medium-energy (p, n) reactions via the distorted-wave impulse approximation, and compared with experimental β-decay and with free-nucleon transition probabilities. These comparisons indicate strongly that the renormalization of the Gamow-Teller operator needed for (p, n) reactions on finite nuclei is different from that needed for β decay.

The ⁴⁸Ca(p,n)⁴⁸Sc reaction was studied at 134 and 160 MeV. Neutron energy spectra were measured by the time-of-flight technique with resolutions from 320 to 460 keV at 11 angles from 0° to 60° spaced approximately 6° apart. The neutron spectra reveal strong excitation of the (πf_7/2,νf_7/2^-1) band of states at low excitation energies; five of the known eight members of the band are excited strongly, generally consistent with distorted-wave-impulse-approximation calculations with 1f-2p shell-model wave functions. The normalization of the distorted-wave-impulse-approximation calculations to the extracted angular distributions at 135 MeV vary from 0.40 for the 5⁺ state to 0.93 for the 0⁺, isobaric analog state. The normalization factor of 0.60 required for the 7⁺, stretched-state transition is significantly larger than those required for similar distorted-wave-impulse-approximation calculations of various stretched-state excitations observed in inelastic proton scattering, which involve promoting a nucleon up into the next major shell (a ‘‘1 ħω’’ excitation). The larger normalization factor required for the (πf_7/2,νf_7/2^-1) 7⁺ excitation (a ‘‘0 ħω’’ excitation) indicates that this strength is more highly concentrated in a single state. The 4⁺ and 6⁺ states of this band are observed to be only weakly excited, consistent with predictions that transitions dominated by the tensor term of the nucleon-nucleon interaction will predominantly excite non-normal parity states. The excitation of the 2⁺ member of this band shows both Δl=0 and Δl=2 contributions to the angular distribution and may indicate significant two-step processes for this transition.

The distribution of Gamow-Teller strength in the ¹⁸O(p, n)¹⁸F reaction was studied at a bombarding energy of 135 MeV. Five 1⁺, T=0 states are identified below E_x=7 MeV and a concentration of 1⁺ states of presumed T=1 character is observed between E_x=9.5 and 12 MeV. Approximately 82% of the 1⁺ strength is concentrated into the ground-state transition and only 5.5% is seen in the T=1 component. Normalization of the ground-state transition to the known Gamow-Teller matrix element from the analogous beta decay of ¹⁸Ne allows the (p, n) cross sections to be related to the Gamow-Teller strength. The resulting total Gamow-Teller strength observed in the (p, n) reaction is about two-thirds of the minimum value required by the sum rule for a T=1 nucleus. This result is in reasonable agreement with the total Gamow-Teller strength predicted from a shell-model calculation which uses empirically renormalized single-particle Gamow-Teller matrix elements. The concentration of the T=0 strength predominantly into the ground state and the observed ratio of T=1 to T=0 strength also are consistent with these calculations.

NUCLEAR REACTIONS ¹⁸O(p, n)¹⁸F, E=135 MeV; neutron spectra measured in ∼3° steps between 0° and 69°; angular distributions extracted for separate transitions. Strengths of forward-peaked transitions compared with shell-model predictions of Gamow-Teller strength.

We present the ratio of experimental 0° (p, n) cross sections with the measured B(M1) values for transitions in several nuclei. Taking the strong spin-flip transition in ¹²C for normalization, we find overall good agreement with shell-model predictions for ²⁴Mg, ²⁸Si, and ⁴⁸Ca. The values of the ratios vary considerably and are very sensitive to the relative amounts of spin and current contributions to each transition. Experimental ratios are also presented for ¹⁶O and ²⁶Mg.

NUCLEAR REACTIONS Charge exchange (p, n) at 0°, E_p=62-160 MeV, cross sections; targets ¹²C, ¹⁶O, ²⁴Mg, ²⁶Mg, ²⁸Si, ⁴⁸Ca. Compared σ_p,n(0°) with B(M1) values from inelastic electron scattering.

We measured neutron energy spectra and extracted angular distributions for eleven separate transitions for the ¹⁶O(p,n)¹⁶F reaction at 99.1 and 135.2 MeV. Several new spin and parity assignments are obtained for states in ¹⁶F by comparison of the excitation energy spectra with known analog states in ¹⁶O and with a shell-model prediction and by analysis of the neutron angular distributions. The most strongly-excited states are two 2^- states at E_x=0.40±0.05 and 7.6±0.1 MeV, a 4^- state at 6.37±0.05 MeV, and two broad 1^- states at 9.4±0.1 and 11.5±0.1 MeV. These states are analogs of known 2^- (M 2) states, a 4^- "stretched" state, and 1^- (E 1) strength, respectively, in ¹⁶O. Three weakly excited 1⁺ states are observed at E_x=3.75±0.05, 4.65±0.05, and 6.23±0.05 MeV. These states are analogs of known 1⁺ (M 1) states in ¹⁶O and directly indicate correlations in the ground state of ¹⁶O. A weakly excited 4^- state is seen at 5.93±0.05 MeV in good agreement with a 4^- state observed in ¹⁶O (e,e^′) measurements. All of the most strongly excited states align (to within ±200 keV) with known T=1 analog states in ¹⁶O for a common net displacement energy of 12.6 MeV. The (p,n) reaction at medium energies is shown to be an important spectroscopic tool.

NUCLEAR REACTIONS ¹⁶O(p,n)¹⁶F, E=99.1 and 135.2 MeV; measured neutron spectra in ∼3° steps between 0° and 69°; extracted σ(θ) for eleven separate transitions to discrete states in ¹⁶F. Compared excitation energies with analog states in ¹⁶O and with a shell-model prediction. Deduced several new J^π assignments.

We measured the analyzing power for the ¹⁶O(p→,n)¹⁶F (4^-,6.37 MeV) reaction at 134.0 MeV and the differential cross section for the same reaction at 135.2 MeV. The shape of the cross section for the transition to this unnatural parity stretched state is described well by a distorted-wave impulse-approximation calculation using a (πd_{5 / 2},νp_{3 / 2}^-1)_4^- configuration and the effective interaction derived by Love and Franey from nucleon-nucleon phase shifts. The analyzing power from this calculation reproduces all of the qualitative features of the data and supports the use of the impulse approximation as an excellent starting point for describing the reaction mechanism. Quantitative agreement between the experimental and theoretical analyzing power can be improved by eliminating the imaginary tensor term of this interaction and taking the real part to be that derived by Love from the Sussex matrix elements. The sensitivity of the calculations to the choice of optical potentials and the importance of spin-orbit distortion is explored.

NUCLEAR REACTIONS ¹⁶O(p→,n)¹⁶F, E=134 MeV; measured neutron spectra at 12 angles between θ=0° and 62.9°; extracted σ(θ) and A(θ) to J^π=4^-,6.37 MeV state of ¹⁶F. Compared angular distributions of σ(θ) and A(θ) with calculations based on a nucleon-nucleon effective interaction.

We find large corrections to the ¹⁷O magnetic form factor arising from a two-pion exchange three-body force. These corrections are comparable in magnitude to meson exchange current contributions. The phases of the M1, M3, and M5 amplitudes due to the three-body force are favorable for improving agreement between theory and experiment, especially in the region of momentum transfer between 1.5 and 3.0 fm^-1.

NUCLEAR REACTIONS ¹⁷O(e,e); magnetic form factor, theory including higher order effects and three body force effects.

We obtain the magnetic form factor of ¹⁷O in a microscopic effective operator approach which includes self-consistency effects, first order core polarization, and second order number conserving sets of effective operator diagrams. The self-consistency effects yield a reduction in the cross section ranging from 10% to 20% through the region of experimental data. Core polarization reduces the M3 contribution by a factor of 2 as compared to a factor of 3 reduction obtained by Arima, Horikawa, Hyuga, and Suzuki. In addition, we find the core polarization yields a slight M1 enhancement at its peak and a substantial M5 reduction so that the overall agreement with experiment is poor. We then explore second order core polarization effects and evaluate the two number conserving sets of diagrams. Their contributions are non-negligible but fail to resolve the discrepancy between theory and experiment. We also include an exchange current amplitude. The lack of agreement between theory and experiment invites theoretical attention to additional corrections and to phenomena which may enhance magnetic scattering.

NUCLEAR REACTIONS ¹⁷O(e,e); magnetic form factor, theory including higher order effects. Effective operator within self-consistent framework.

The orbital current and spin contributions to isovector M1 excitations in light nuclei are studied microscopically by combining information from inelastic electron scattering at small momentum transfers with that obtained from recent measurements of (p,n) cross sections at forward angles. The (p,n) reaction is studied within the distorted-wave approximation using a G-matrix interaction and shell model wave functions and the (e,e^′) scattering is calculated in a plane wave approximation.

NUCLEAR REACTIONS Charge exchange scattering, E_p=62 MeV, cross sections; inelastic electron scattering; targets ¹²C, ²⁴Mg, ²⁸Si.

We develop a systematic approach to the calculation of self-consistency effects in core plus valence nucleon systems. A detailed calculation of the effective one-body Hamiltonian for A=17 in an 11ℏΩ model space is readily extrapolated to a 20ℏΩ model space which is sufficient to develop accurate tails for the single-particle wave functions. The effective one-body interaction is found using a Brillouin-Wigner type perturbation theory which eliminates folded diagrams and leads to a manifestly Hermitian interaction. A renormalized Brueckner calculation is performed for A=16 and the results are employed in a shell-model study of A=17. The self-consistent results still have a weak dependence on the initial unperturbed Hamiltonian. However, we find a single unperturbed Hamiltonian which yields a reasonable binding energy for A=16 and, except for a weak spin-orbit splitting, reasonable results for the lowest states in the A=17 system. This agreement is important for continued valence s-d shell studies.

NUCLEAR STRUCTURE Brueckner theory, self-consistency effects, ¹⁷O spectra and wave functions, ¹⁶O properties.

Several commonly made approximations in microscopic effective interaction calculations have been found to result in serious inaccuracies. Recent improved second-order calculations for A=18 nuclei suggested somewhat better order by order convergence in the reaction matrix G than indicated previously. A selected third-order term has been calculated to study further this possibility. The convergence of the intermediate-state summation was also investigated for this diagram. Our improved calculational technique results in a greater reduction of the third-order term than the reduction found earlier for the second-order term. The outlook for the (asymptotic) convergence of the expansion is much improved, but the prospects for a complete third-order calculation of the effective interaction are dim due to the difficulties of the calculation.

[NUCLEAR STRUCTURE Effective interaction, theory; convergence of the intermediate-state sums; convergence of the diagram series through third-order in the nuclear reaction matrix; shell-model matrix elements in the sd shell.]

The muon capture matrix elements M_v², M_a², and M_p² are calculated for ⁴He and ¹⁶O using the closure approximation and utilizing the linked cluster expansion to introduce correlations in the nuclear target wave functions. An important set of diagrams is summed by replacing uncorrelated wave functions with Bethe-Goldstone wave functions. However, we also find it necessary to include diagrams insuring that the pair number operator is unchanged and (for ¹⁶O) particle-hole diagrams to account for the fact that oscillator orbitals rather than Hartree-Fock orbitals are used for the uncorrelated basis. Typical results for ¹⁶O are M_v^2(corr)=0.82M_a^2(corr)=0.74M_p^2(corr)=0.58M^2(osc), while for ⁴He, M_v^2(corr)=0.88M_a^2(corr)=0.78M_p^2(corr)=0.76M^2(osc). The bulk of the effects arise from correlations induced by the tensor component of the nucleon-nucleon interaction. We find that including correlations reduces the predicted total capture rate by ∼30% in ¹⁶O and ∼20% in ⁴He.

NUCLEAR REACTIONS ⁴He, ¹⁶O, calculated total muon capture rate, closure and nuclear correlations.

Renormalized Brueckner-Hartree-Fock and density dependent Hartree-Fock calculations in the literature have been difficult to compare because they involve both different physical approximations and also technical computational differences. Hence, results obtained in both calculations for ⁴⁰Ca are corrected for technical differences and compared in detail. It is shown that comparable Brueckner-Hartree-Fock calculations using an oscillator basis and using the local density approximation are in good numerical agreement, and that three mechanisms are of roughly equal importance in obtaining the proper interior density: occupation probabilities, the potential arising from the variation of the pauli operator, and the phenomenological parametrization of higher order corrections to the effective nuclear interaction. The renormalized oscillator basis calculations include only the effect of occupation probability diagrams. The "bare" local density approximation results are an improvement over the renormalized results since the former includes the effects of both occupation probabilities and the variation of the Pauli operator. The adjusted local density approximation calculations then give further improvement due to the phenomenological parametrization of the force, simulating the effect of higher-order diagrams.

NUCLEAR STRUCTURE Renormalized Brueckner-Hartree-Fock and density dependent Hartree-Fock theory. Application to ⁴⁰Ca.

Correlated wave functions obtained by solving the Bethe-Goldstone equation with the Hamada-Johnston potential are used to calculate Coulomb matrix elements for use in the nuclear 1p shell. When proper attention is given to the Pauli operator we find that Coulomb matrix elements are not appreciably larger than those obtained using uncorrelated wave functions, in contrast to conclusions reached by previous investigators.

Some higher-order corrections to renormalized Brueckner-Hartree-Fock calculations are estimated for the nuclei ¹⁶O, ⁴⁰Ca, and ²⁰⁸Pb. The diagrams of interest are the potential insertions in particle lines and the two-body correlation corrections to the rms radii. Studies are made of the sensitivity of these corrections to the shift in the intermediate spectrum used to calculate the G matrix. The correlation corrections to the radii are small and seem to increase somewhat as the intermediate spectrum is lowered, but there is no appreciable change in the over-all saturation properties. The errors involved in estimating the corrections are discussed. "Off-diagonal occupation probabilities" are also calculated and found to be small, thereby justifying ignoring such diagrams as is usually done in renormalized Brueckner calculations.

Calculations of the spherical nuclei ¹⁶O, ⁴⁰Ca, and ²⁰⁸Pb are presented for G matrices which differ in the definition of the particle spectrum. Detailed comparisons are made using pure harmonic-oscillator, shifted oscillator, and QTQ intermediate-state spectra. Attention is particularly focused on the saturation properties of the various G matrices. The QTQ prescription seems to give somewhat better saturation properties than the oscillator prescriptions. A comparison is made in ⁴⁰Ca between the QTQ results and some results obtained by Negele. A study is also made of the importance of the relative partial waves not defined in the Reid soft-core potential.

A G matrix derived from the Reid soft-core potential is used in a series of Brueckner-Hartree-Fock calculations of spherical nuclei. The G matrix is calculated using an intermediate-state spectrum and Pauli operator appropriate to pure oscillator orbitals, with options to shift the entire spectrum or the low-lying levels from unperturbed oscillator energies. The Pauli operator takes into account the filling of different neutron and proton subshells in N≠Z nuclei. Self-consistent occupation probabilities are included in the calculations and results are presented for ¹⁶O, ⁴⁰Ca, ⁴⁸Ca, and ²⁰⁸Pb. Various systematics and convergences are studied. Good results can be obtained for the binding energies, but the experimental binding energy and charge radius cannot be fitted simultaneously. It is shown that renormalization with occupation probabilities is crucial for calculating a reasonable single-particle spectrum. The difficulty of comparing single-particle energies with experiment is discussed with particular emphasis on heavy and superheavy nuclei. The nuclei ²⁹⁸114 and ³¹⁰126 are calculated for a simple force.

A new, simple, and exact method is given for calculating the reaction matrix G in a two-particle harmonic-oscillator basis. The method makes use of an expansion of the Bethe-Goldstone wave function in terms of solutions of the Schrödinger equation for two interacting particles in a harmonic-oscillator well. Since a two-particle basis is used, the Pauli operator Q is diagonal and can be treated exactly. Reaction matrix elements based on the Hamada-Johnston potential are used in a shell-model calculation of A=18 nuclei. The results are compared with those of earlier calculations using approximate Pauli operators. The dependence of the reaction matrix on the starting energy is studied, and the relationship of this energy to the intermediate-state spectrum and to the Pauli operator Q is discussed. In this same context the difference between using a Brueckner Q and a shell-model Q is also discussed.

The new method of Truelove and Nicholls for obtaining reaction matrix elements for nuclear-structure calculations is discussed. In this method, the Bethe-Goldstone wave function is expanded in terms of eigenfunctions of two interacting nucleons bound in a common potential well. The Bethe-Goldstone equation, which is written in terms of an expansion over noninteracting two-particle states, is then solved iteratively. In practice, the method is most easily applied when a harmonic-oscillator basis is used; the Pauli operator Q can then be treated exactly. The convergence of the Truelove-Nicholls iteration scheme and of the above two expansions is investigated. It is shown that the original method is incorrect for nucleon-nucleon potentials with an infinite hard core. A simple way of correcting the method is presented.

A method is developed for evaluating self-consistent occupation probabilities in Brueckner-Hartree-Fock calculations of finite nuclei. The method does not involve explicitly the overlaps of defect wave functions but is based instead on the energy dependence of the G matrix elements. Results are presented for ¹⁶O using a G matrix which shifts only the low-lying intermediate-particle spectrum.