Empirical Effective Interaction Research Articles

Effective interactions and nuclear structure using 180 MeV protons. II. 28Si(p,p').

Differential cross sections and analyzing powers for the scattering of 180 MeV protons have been measured for 14 states of $^{28}\mathrm{Si}$ for momentum transfers between about 0.4 and 2.1 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. Medium modifications to the effective interaction for normal-parity isoscalar transitions were studied using transition densities fitted to electroexcitation data to minimize uncertainties due to nuclear structure. An empirical effective interaction, guided by nuclear matter theory, was fitted to inelastic scattering data for five states of $^{28}\mathrm{Si}$ using self-consistent distorted waves. A good fit to the inelastic scattering data was achieved with an interaction similar to previous results for $^{16}\mathrm{O}$. The elastic data, which were not fitted, are also described well. In addition, we tested for mass dependence in the empirical effective interaction by repeating the analysis using data for both $^{16}\mathrm{O}$ and $^{28}\mathrm{Si}$ simultaneously. This global analysis produced an interaction intermediate between the two independent results without compromising the fit to either data set. Therefore, the effective interaction in finite nuclei appears to depend strongly upon local density but only weakly upon target.

Effective interactions and nuclear structure using 180 MeV protons. I. 16O(p,p').

Differential cross sections and analyzing powers for scattering of 180 MeV protons by $^{16}\mathrm{O}$ have been measured for all narrow states below 12.1 MeV of excitation. Medium modifications to the effective interaction for normal-parity isoscalar transitions were studied using transition densities determined by electron scattering to minimize nuclear structure uncertainties. An empirical effective interaction, guided by nuclear matter theory, was fitted to inelastic scattering data for six states simultaneously. Distorted waves were generated from self-consistent optical potentials computed from the same effective interaction. The isoscalar effective interaction determined by this procedure provides a good global fit to the inelastic scattering data and is consistent with elastic scattering data that were not included in the fit. The results are consistent with earlier results for 135 MeV and show that the effective interaction is suppressed at low density but is less density dependent than predicted by nuclear matter theory and the local density approximation. These comparisons suggest effects in finite nuclei beyond the local density approximation. Finally, we compare data for ${0}^{\mathrm{\ensuremath{-}}}$ and ${2}^{\mathrm{\ensuremath{-}}}$ states at both 135 and 180 MeV with representative calculations.

Effective interactions and nuclear structure using 180 MeV protons. III. 30Si(p,p').

Differential cross sections and analyzing powers for low-lying states of $^{30}\mathrm{Si}$ have been measured using 180 MeV protons. The data were analyzed using an empirical effective interaction previously fitted to inelastic scattering data for $^{16}\mathrm{O}$ and $^{28}\mathrm{Si}$ at the same energy. Proton transition densities for the ${2}_{1}^{+}$, ${2}_{2}^{+}$, ${3}_{1}^{\mathrm{\ensuremath{-}}}$, and ${4}_{2}^{+}$ states were fitted to the available electron scattering data. Neutron transition densities for these states were then extracted from the proton scattering data. The fitted matrix elements ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$ agree well with lifetime data for the A=30 T=1 multiplet. Results for the positive-parity states are also compared with shell-model calculations. We find that neutron densities for the ${2}_{2}^{+}$ and ${4}_{2}^{+}$ states are considerably stronger than predicted. We also find ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$=1.3\ifmmode\pm\else\textpm\fi{}0.1 for the ${3}_{1}^{\mathrm{\ensuremath{-}}}$ state and that the neutron form factor is consistent with a dominant 2${\mathit{s}}_{1/2}$\ensuremath{\rightarrow}1${\mathit{f}}_{7/2}$ transition.

Empirical effective interaction for 135 MeV nucleons

A model for medium modifications to the two-nucleon effective interaction, based upon the results of nuclear matter theory, is proposed for the analysis of proton inelastic scattering to normal-parity isoscalar states of self-conjugate nuclei. An empirical effective interaction is fitted to cross section and analyzing power data for the excitation by 135 MeV protons of six states of $^{16}\mathrm{O}$ simultaneously. Transition densities determined by electron scattering minimize uncertainties due to nuclear structure. Distorted waves are generated from the self-consistent optical potential computed from the same effective interaction, corrected for rearrangement effects. We find that a unique effective interaction provides a good global fit to all inelastic scattering data and is consistent with data for elastic scattering, which were not included in the fit. The density dependence of the empirical interaction is similar to, but somewhat smaller than, that of the Paris-Hamburg G matrix. However, we also find that the interaction strength is reduced at zero density. These comparisons suggest effects due to nonlocal density dependence beyond the local density approximation.

Effective interaction for N=50 isotones.

Standard shell-model techniques of constructing and diagonalizing Hamiltonians in finite Hilbert spaces have been used to treat the N=50 isotones with an expanded model space and a new empirical effective interaction. A vector space with active 0${f}_{5/2}$, 1${p}_{3/2}$, 1${p}_{1/2}$, and 0${g}_{9/2}$ proton orbits is used to model the low-lying excitations of these nuclei. The effective interaction is obtained by varying 35 parameters, distributed over the 65 two-body matrix elements and four single particle energies of the model space, to fit over 170 experimental energy levels in nuclei from $^{82}\mathrm{Ge}$ through $^{96}\mathrm{Pd}$. Nearly all of the experimental level energies of N=50 nuclei involved in the fit are well reproduced by the final interaction.

Static moments and phenomenological interactions

A method is presented which in addition to energy spectra, used conventionally, can make use of electromagnetic properties for the determination of an empirical effective nucleon-nucleon interaction. The method is applied to the static moments of the 0p-shell nuclei. Compared to results obtained with other phenomenological interactions the accuracy of the calculated static moments is strongly improved, without destroying the agreement for energy levels.

Effective interaction analysis of 500 MeV (p

A nonrelativistic distorted wave Born approximation analysis, using a phenomenological effective proton-nucleon interaction to generate both optical and transition potentials, is made of new 500 MeV (p\ensuremath{\rightarrow},p') data for excitation of low-lying states in $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$. The data, differential cross section and analyzing power angular distributions for 5\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.\mathrm{\ensuremath{\le}}30\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$, are well described using this effective interaction. Calculations using the impulse approximation to generate the optical and transition potentials do not adequately describe the data. As a further test of the 500 MeV empirical effective interaction, model-dependent neutron transition densities are deduced for excitations which are expected to be purely isoscalar, such as the first ${3}^{\mathrm{\ensuremath{-}}}$ states of $^{40}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$. These are found to be qualitatively similar in strength and overall shape to the renormalized (\ifmmode\times\else\texttimes\fi{}N/Z) model-independent proton densities determined from analysis of (e,e') data. Model-dependent neutron transition densities are also deduced for other excitations and are in reasonable agreement with results of analyses of other hadron plus nucleus scattering data. These results indicate that the 500 MeV isoscalar effective interaction is better than the free proton-nucleon scattering amplitudes (impulse approximation) as a starting point for analysis of (p,p') data aimed at detailed extraction of neutron transition densities and other nuclear structure information.

Mutual support of magicities and residual effective interactions near 208Pb

We summarize experimental evidence in the lead region on the increased stability associated with neutron magic number when the proton number is magic, and vice versa. The effect is interpreted in the framework of the nuclear shell model with empirical effective interactions. Its relation to spherical Hartree-Fock calculations is pointed out and used to test Skyrme-type forces. None of the considered Skyrme interactions reproduce the effect.

Role of the antisymmetric spin-orbit component in effective interactions in thesdshell

The antisymmetric spin-orbit interaction proposed for $\mathrm{sd}$-shell nuclei is investigated. It is shown that the important contribution of the antisymmetric spin-orbit component to the effective interactions is to give the proper centroid energy of the ${d}_{\frac{5}{2}}\ensuremath{-}{d}_{\frac{3}{2}}$ interactions which plays a crucial role in reproducing the excited band spectra of $A=18\ensuremath{-}24$ nuclei. Also proposed is an empirical effective interaction without the antisymmetric spin-orbit component to reproduce the observed spectra of light $\mathrm{sd}$-shell nuclei.NUCLEAR STRUCTURE $^{24}\mathrm{Mg}$; calculated levels; $0{d}_{\frac{5}{2}}\ensuremath{-}1{s}_{\frac{1}{2}}\ensuremath{-}0{d}_{\frac{3}{2}}$ shell model. Effective interactions; Kuo, Chung-Wildenthal, and NOALS; antisymmetric spin-orbit component.

Enhanced isospin dependence of the empirical particle-hole effective interaction

The separation betweenT=0 andT=1 centroids of the empirical effective interaction is fairly large for the (d 3 2/−1 f 7/2)JT particle-hole interaction as compared to nearby (f 7/2)2 JT and (d 5/2)2 JT particle-particle interactions. This interesting feature of the empirical effective interaction is shown to arise as a consequence of renormalization of the effective interaction as one truncates the configuration space from (s−d)−1(f−p)1 to (d 3 2/−1 f 7/2) and from (f−p)2 and (s−d)2 configurations to (f 7/2)2 and (d 5/2)2 respectively.

Family of nuclear mass relations

A family of simple nuclear mass relations, which includes as members the Garvey-Kelson transverse and longitudinal relations, is presented. Each member of this family gives a prediction of roughly equal statistical accuracy for the unknown mass of a given nuclide. The average of this family is statistically more reliable than is any single prediction. The essential physical observation that leads to these relations is that the empirical neutron-proton effective interaction is generally weak and that the strength of this interaction is strongly correlated separately for neighboring even-A and for neighboring odd-A nuclei.

The deformation producing tendency of (d 3/2−f 7/2) empirical effective interaction

The effective matrix elements in (d 3/2−f 7/2)2 configuration have been recently defined by Erskineet al. and Sherret al. assuming shell clcsures for S32 and Ca40. We have attempted to verify whether this empirically deduced (d 3/2−f 7/2)2 interaction permits thed 3/2 shell to remain closed when nucleons are added to Ca40. It is found that the Erskine interaction gives rise to ground states of thef 7/2 shell nuclei in which thed 3/2 orbit is completely filled. However that interaction over-binds Ca40. If the centroid of the (d 3/2)2 interaction is modified to fit the Ca40 binding energy, the ground states of Cr48 and Fe52 become deformed and thed 3/2 orbit is not completely filled.

Microscopic effective interaction for 155-MeV protons

An empirical nucleon-nucleon effective interaction is derived by fitting the angular distributions of various (J/sup $pi$/,T) transitions from the $sup 12$C(p,p')$sup 12$C* reaction. (AIP)

Translationally invariant and non-translationally invariant empirical effective interactions

In this work we examine empirical deficiencies of the core-renormalized realistic effective interactions and seek simple corrective potentials. We note the inability of the current realistic interactions to account for the energies of isobaric analog states; likewise they are unable to reproduce the changes in the single-particle energies, as one goes from one closed shell to another. We note that the Schiffer interaction gives better results for these gross properties and we attribute this to a combination of several facts. First, to the inclusion of long range terms in the Schiffer potential, then to the presence of relative p-state terms ( l = 1), in addition to the usual relative s-state terms ( l = 0). We further attribute the strange shape of the above interaction to the fact that it is translationally invariant, whereas the theory of core-polarization yields non-translationally invariant potentials. Consequently, as a correction to the monopole deficiencies of the realistic interactions we propose the term V mon = ar 2(1) r 2(2)+ β[ r 4(1) r 2(2)+ r 2(1) r 4(2)].

Reaction matrix elements for the 0f-1p shell nuclei

The shell-model reaction matrix elements for the 0f-1p shell are calculated and tabulated. The matrix elements consist of two parts; the bare reaction matrix elements and the renormalizations due to core polarizations which are both calculated with the Hamada-Johnston nucleon-nucleon potential. The core polarizations are evaluated for two cases; first for a 40Ca core and then for a 48Ca core. As a preliminary test, these matrix elements have been compared with available empirical effective interactions and used to calculate (i) the spectra of the valence particles of 42Ca, 42Sc, 50Ca, 50Sc and 50Ti, (ii) the changes of single-particle (hole) levels such as the changes of single-neutron levels from 41Ca to 49Ca and (iii) the 0 f 7 2 −0 d 3 2 particle-particle states of 38Cl and the corresponding particle-hole states of 40K. In general, the calculated results are in good agreement with the experimental values, and the core polarization effects are usually of great importance.