Empirical Effective Interaction Research Articles

Lifetime measurement of the Ex = 2485.3 keV level of 25Al populated through 24Mg(p,γ)25Al resonance reaction

Results of our experimental study of the 24Mg(p,γ)25Al resonance reaction at E=plab223 keV are presented. The proton beam energy is varied from 220 to 265 keV. An evaporated Mg target with thick Ta backing is used. We remeasure a mean lifetime of τ=6.04−2.65+3.03 fs for the E=x2485.3 keV level of 25Al, using Doppler shift attenuation (DSA) method. Three most successfully used empirical effective interactions developed for the sd shell by Wildenthal (w), Chung-Wildenthal (cw) and Preedom-Wildenthal (pw), are utilized to calculate energy spectra, spectroscopic factors, beta decay properties, transition probabilities and the lifetime of the resonance state in 25Al within the framework of nuclear shell model. The theoretical results agree reasonably well with the experimental data. However, a detailed study for each set to identify the most preferred interaction for this nucleus is performed. Calculated lifetimes using two of the interactions (w, cw) agree better with the central value of the experimental lifetime of the resonance state measured in the present work.

Reaction mechanism for natural parity (p,p') transitions inB10

We report angular distribution measurements of the cross section, analyzing power, induced polarization, and all polarization transfer coefficients for the natural parity transitions in $^{10}\mathrm{B}$($\stackrel{\ensuremath{\rightarrow}}{p},{\stackrel{\ensuremath{\rightarrow}}{p}}^{'}){}^{10}$B at 197 MeV. All of the transitions closely follow the pattern for spin-1/2 scattering from spin-0, namely $A=P,{D}_{{\mathit{SS}}^{'}}={D}_{{\mathit{LL}}^{'}}$, and ${D}_{{\mathit{SL}}^{'}}=\ensuremath{-}{D}_{{\mathit{LS}}^{'}}$. Small deviations from ${D}_{{\mathit{NN}}^{'}}=1$ reflect spin-flip contributions to these transitions. Distorted wave impulse approximation calculations were generally successful, supporting the use of an empirical effective nucleon-nucleon interaction, the inclusion of channel-coupling in the ground state and the ${3}^{+}\ensuremath{\leftrightarrow}{4}^{+}$ transition, and the procedure of increasing the $L=2$ strength of shell-model particle-hole matrix elements to match the collective contribution to these transitions.

Equations of state and thermodynamic properties of rare-gas solids under pressure calculated using a self-consistent statistical method

Equations of states (EOS's) and thermodynamic properties of rare gas solids (RGS's) under pressure are studied by a statistical method. On the basis of empirical effective two-body interactions for Ar, Kr, and Xe close agreement is obtained with experimental data for the pressure dependencies of the Gr\"uneisen parameter and sound velocities as well as for the temperature dependence of the interatomic distance, the heat capacities, the bulk modulus, and Gr\"uneisen parameter at ambient pressures. All these thermodynamic quantities are finally also calculated for 2, 5, and 10 GPa. Most remarkably a strong suppression of the intrinsic anharmonic contributions to the Gibbs free energy is noticed under strong compression and quantitatively evaluated.

Importance of isovector effects in reproducing neutron total cross section differences in the W isotopes

Cross section differences among the isotopes ${}^{182,184,186}\mathrm{W}$ have been measured as a part of a study of total cross sections in the 5--560 MeV energy range. These difference measurements show oscillations up to 150 mb between 5 and 100 MeV. Calculations with spherical and deformed phenomenological optical potentials employing standard radial and isospin dependences show much smaller oscillations than the experimental data. In a simple Ramsauer model, this discrepancy can be traced to a cancellation between radial and isospin effects. Understanding this problem requires a more detailed model that incorporates a realistic description of the neutron and proton density distributions. This has been done with the results of Hartree-Fock-Bogoliubov calculations using the Gogny force, together with a microscopic folding model employing a modification of the Jeukenne, Lejeune, and Mahaux potential as an effective interaction. This treatment yields a satisfactory interpretation of the observed total cross section differences up to 200 MeV. The calculations have been extended above that energy with a folding model based on an empirical effective interaction.

100Sncore excitations in102In

Nuclei in the vicinity of the doubly-magic Sn-100 nucleus have been studied, and an extended level scheme for In-102 has been established. The level structure comprises both the negative parity states involving the nuh(11/2) orbital, and levels due to the breakup of the doubly-magic Sn-100 core. Results of a large-scale shell model calculation, using realistic and empirical effective interactions with Sr-88 as a core, are in very good agreement with the experimental data.

Measurement of neutron total cross sections up to 560 MeV

We have completed a new set of total cross section measurements of 31 elements and isotopes spanning the periodic table from A=1 to 238. We employed the same technique as in Finley et al. [Phys. Rev. C 47, 237 (1993)] with refinements intended to allow measurements on separated isotopes and improved systematic error control. The goal of the new measurement was 1% statistical accuracy in 1% energy bins with systematic errors less than 1%. This was achieved for all but the thinnest samples. Stringent checks of systematic errors in this measurement resulted in a reassignment of systematic uncertainties to the neutron total cross sections reported in Finley et al. Microscopic optical model calculations were carried out to interpret the results of the experiment. Two specific types of optical models were employed. The Jeukenne-Lejeune-Mahaux model was used in the range of 5--160 MeV, and a model based on the empirical effective interaction of Kelly was used from 135 to 650 MeV. These models are shown to be useful for predicting both neutron total cross sections and proton reaction cross sections. They are particularly important for light nuclei, for which standard global phenomenological parametrizations of the optical potential are insufficiently accurate.

Neutron transition densities for low lying states in58Niobtained by using 200 MeV inelastic proton scattering

Differential cross section and analyzing power measurements have been made for 200 MeV inelastic proton scattering from ${}^{58}\mathrm{Ni}.$ Using the code LEA, neutron transition densities have been obtained for four ${2}^{+},$ one ${3}^{\ensuremath{-}},$ and five ${4}^{+}$ low lying states. Charge transition densities obtained from electron scattering were used in order to minimize the nuclear structure uncertainty, along with a recent 200 MeV empirical effective interaction. Two types of calculations have been used in comparison to the data, one in which the neutron transition densities are obtained by scaling the charge transition densities by $N/Z,$ the other in which the neutron transition densities are allowed to vary to obtain a best fit to the data. Multipole matrix elements are obtained and compared to collective model analyses using both intermediate energy protons and pion scattering results. The radial shapes of the neutron transition densities for the lowest lying ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states are compared to those calculated using the energy density method.

Nuclear transparency to intermediate-energy protons.

Nuclear transparency in the ({ital e},{ital e}{sup {prime}}{ital p}) reaction for 135{le}{ital T}{sub {ital p}}{le}800 MeV is investigated using the distorted-wave approximation. Calculations using density-dependent effective interactions, both empirical and theoretical, are compared with phenomenological optical potentials. We find that nuclear transparency is well correlated with proton absorption and neutron total cross sections and that calculations using density-dependent effective interactions provide the best agreement with data. Nuclear transparency calculations are compared with recent electron scattering data for {ital Q}{sup 2}{lt}2 (GeV/{ital c}){sup 2}. For {ital T}{sub {ital p}}{approx_lt}200 MeV we find that there is considerable sensitivity to the choice of optical model and that the empirical effective interaction provides the best agreement with the data, but remains 5{endash}10{percent} low. For {ital T}{sub {ital p}}{approx_gt}300 MeV we find that there is much less difference between these models, but that the calculations significantly underpredict transparency data and that the discrepancy increases with {ital A}. The differences between Glauber and optical model calculations are related to their respective definitions of the semi-inclusive cross section. By using a more inclusive summation over final states the Glauber model emphasizes nucleon-nucleon inelasticity, whereas with a more restrictive summation the optical model emphasizes nucleon-nucleus inelasticity; experimental definitionsmore » of the semi-inclusive cross section lie between these extremes. {copyright} {ital 1996 The American Physical Society.}« less

Test of a density-dependent interaction using in-plane 28Si(p

We report measurements of in-plane polarization transfer for nine natural-parity isoscalar transitions in the $^{28}\mathrm{Si}$(p\ensuremath{\rightarrow},p${\ensuremath{\rightarrow}}^{\ensuremath{'}}$${)}^{28}$Si reaction using a 198.5 MeV polarized proton beam. These measurements test in a new way the validity of an empirical effective NN interaction derived from cross section and analyzing power measurements for similar transitions. The test is successful, demonstrating the need to modify the free NN interaction in the nuclear medium. \textcopyright{} 1996 The American Physical Society.

Effects of multiple ionization on the Kα spectrum of aluminum in intense lithium beam experiments

The effect of multiple ionization on Kα spectra is investigated for aluminum targets irradiated by intense lithium beams. Multiple ionization cross sections have been calculated using a formulation incorporating single-electron ionization probability in the binomial distribution. In contrast to conventional binary-encounter approximation (BEA) theory, the single-electron ionization probabilities for each atomic shell have been calculated using a combination of modified plane-wave Born approximation (MPWBA) and an empirical effective interaction radius which is dependent on both the target ion and the projectile. Our calculations show that the effect of multiple inner-shell ionization on aluminum Kα spectra observed in intense lithium beam experiments is important. Multiple ionization effects become less important as the target ionization state increases. Nevertheless, even for highly ionized species up through Be-like Al multiple ionization effects can be significant and must be considered in the analysis of spectra obtained in intense Li beam-plasma interaction experiments.

Effective proton-neutron interaction in the singly closed shell region

The empirical effective proton-neutron interaction was investigated in the singly closed shell region. It was found that the quadrupole component of the effective interaction is about twice as strong in this region as in the doubly magic one. The presence of the additional quadrupole-quadrupole interaction was explained as the first experimental evidence for the existence of the polarization interaction predicted by Bohr and Mottelson as a second order consequence of the particle-vibration coupling. It was shown that the renormalization of higher order multipole coefficients is also necessary to take into account all effects of the particle-vibration coupling. We pointed out that this renormalization can be approximated by lengthening the range of the effective interaction.

Empirical Effective Interaction in 22MeV Proton Scattering

Inelastic differential cross sections of 22 MeV proton scattering for 5 excited states of 28Si have been measured from 10° to 115°. Empirical effective interactions were extracted within the frame of DWBA from the normal parity state data which transition densities were known from electron scattering. The fitting is good except for the forward angle of 41+ and 02+ states. The results are discussed.

Comparison between relativistic and nonrelativistic models of the nucleon-nucleon effective interaction. I. Normal-parity isoscalar transitions

Relativistic density-dependent effective interactions for nucleon-nucleus scattering based upon a complete set of Lorentz-invariant NN amplitudes are used in calculations of elastic and inelastic scattering to normal-parity states of self-conjugate targets. Owing to distortion of Dirac spinors by the relativistic mean fields, the effective interaction appropriate for use in a Schr\odinger formalism incorporates relativistic density dependence, which is stronger for inelastic than elastic scattering. The dominant effect for normal-parity transitions is equivalent to a short-ranged repulsive contribution to the real central interaction that is proportional to density and nearly independent of energy. Pauli blocking of occupied intermediate states is included and gives results similar to the familiar Clementel-Villi damping of the absorptive potential. The relativistic effective interaction is compared with nonrelativistic G-matrix calculations and with empirical effective interactions fitted to data for proton elastic and inelastic scattering. Calculations for elastic and inelastic scattering are compared with data for 200, 318, and 500 MeV and we find that the agreement with data improves as the energy increases. The density dependence of the relativistic model is much stronger at low energies than either the G matrix or the empirical interaction; its repulsive contribution to the central interaction is too strong to give a good description of the data for 200 MeV. Near 500 MeV the relativistic interaction is closer to the empirical interaction and better agreement with the data is obtained, whereas the density dependence of nonrelativistic effective interactions is too small.

Effective interaction for 16O(p,p') and 40Ca(p,p') at Ep=200 MeV.

Differential cross sections and analyzing powers for scattering of 200 MeV protons have been measured for states of $^{16}\mathrm{O}$ up to 14.4 MeV and for states of $^{40}\mathrm{Ca}$ up to 7.2 MeV of excitation. The data cover c.m. momentum transfers from approximately 0.4 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ to 3.0 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. Calculations were performed using several density-dependent effective interactions in the local density approximation. Empirical effective interactions from isoscalar normal-parity transitions were fitted to elastic and inelastic scattering data for $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ either individually or simultaneously. Transition densities from electron scattering were used to minimize uncertainties due to nuclear structure. The fitted interactions were iterated to generate optical potentials self-consistently. We find that the empirical interaction, although strongly dependent on the local density, is essentially independent of target or state. We also find that the empirical interaction is reduced in strength at zero density. Finally, the results were compared with a relativistic impulse approximation model and with a recent global optical potential from Dirac phenomenology.

Microscopic coupled-channels analysis of 9Be(p,p') for 100

Microscopic coupled-channels calculations for the ground-state rotational band of {sup 9}Be are performed using the folding model and density-dependent effective interactions. Transition densities are obtained either from the shell model or from fits to electron scattering data. The quadrupole contribution to elastic scattering enhances the cross section and damps the analyzing power for momentum transfers larger than about 1.2 fm{sup {minus}1}. Channel coupling is more important for the 7/2{sup {minus}} than for the 5/2{sup {minus}} state and roughly follows the energy dependence of the interaction strength. Comparisons are made between calculations using either theoretical effective interactions or empirical effective interactions previously fitted to data for {sup 16}O or {sup 40}Ca. The results demonstrate that medium modifications are quite important and well described by the local density approximation. Therefore, the effective interaction depends primarily upon local density and is almost independent of nucleus, state, or deformation.

Effective interaction for 40Ca(p,p') at Ep=318 MeV.

Differential cross sections and analyzing powers have been measured for the excitation by 318 MeV protons of states of $^{40}\mathrm{Ca}$ below 7.2 MeV. The data for those normal-parity excitations for which transition densities are available from electroexcitation measurements are analyzed in terms of medium modifications to the nucleon-nucleon interaction. We find that the empirical effective interaction previously fitted to $^{16}\mathrm{O}$(p,p') data at the same energy predicts $^{40}\mathrm{Ca}$(p,p') very well. Density-dependent modifications of the effective interaction fitted to data for $^{40}\mathrm{Ca}$ or $^{16}\mathrm{O}$, either independently or simultaneously, are virtually identical. The density dependence of the empirical interaction is considerably stronger than that of interactions based upon nonrelativistic nuclear matter theory and persists to lower density. The most significant differences are that the empirical interaction has a stronger repulsive core and that absorption is enhanced at high density, contrary to expectations based upon Pauli blocking. We also find substantial suppression of the spin-orbit interaction at low density and enhancement at high density. Nevertheless, the independence of the effective interaction from the target supports the concept of local nuclear matter density. We also find that optical potentials based upon the empirical effective interaction are very similar to Schr\"odinger-equivalent potentials based upon a relativistic impulse approximation model, suggesting that the empirical density dependence is similar to the equivalent density dependence that arises from elimination of lower components from Dirac wave functions. Finally, the results are compared with global optical potentials from Dirac phenomenology.

Empirical density-dependent effective interaction for nucleon-nucleus scattering at 500 MeV.

We report new cross-section and analyzing-power data for the excitation by 498-MeV protons of all narrow normal-parity states of {sup 16}O below 12.1-MeV excitation. In addition, spin-rotation measurements for elastic scattering and depolarization measurements for the 1{sub 1}{sup {minus}}, 2{sub 1}{sup +}, and 3{sub 1}{sup {minus}} states of {sup 16}O have been performed. These data are used in conjunction with existing data for {sup 40}Ca to study medium corrections to the effective interaction for nucleon-nucleus scattering at 500 MeV. Systematic differences between the data and nonrelativistic impulse approximation calculations based upon either the free {ital t} matrix or a recent density-dependent effective interaction are interpreted within the framework of the local-density approximation. An empirical effective interaction has been constructed which parametrizes the density dependence of the medium modifications in a simple form amenable to phenomenological analysis of data.

Effective interaction for 16O(p,p') at Ep=318 MeV.

We report new cross-section and analyzing power data for the excitation by 318 MeV protons of 20 states of $^{16}\mathrm{O}$ below 14 MeV. The data for normal-parity isoscalar excitations are compared with calculations based upon the nonrelativistic impulse approximation using both density-independent and density-dependent interactions in the local-density approximation. These comparisons clearly indicate that density-dependent modifications of the effective interaction are required. Although the Paris-Hamburg, Nakayama-Love, and Ray interactions all predict significant medium modifications, none describes the data particularly well. Therefore, we fitted an empirical effective interaction to the data for five inelastic transitions simultaneously using a self-consistency cycle that maintains consistency between transition potentials and microscopic distorting potentials. This interaction describes the inelastic data as well as elastic data and data for $^{40}\mathrm{Ca}$ which were not included in the fitting procedure. Therefore, the local-density approximation is supported by the phenomenology. However, medium modifications of the effective interaction are substantially stronger than predicted and persist to low density. The optical potentials are similar to the Schr\"odinger-equivalent potentials from the relativistic IA2 model, showing that the equivalent density dependence due to virtual NN\ifmmode\bar\else\textasciimacron\fi{} pairs is comparable to the short-range repulsion fitted to inelastic-scattering data.

P-shell nuclei in a (0+2)

An empirical effective interaction for the {ital A}=4--16 {ital p}-shell nuclei in the complete (0+2){h bar}{omega} model space is presented, which also reproduces the predominant 2{h bar}{omega} intruder states. The results are not spoiled by the mixing catastrophe. The inclusion of 2{h bar}{omega} states also leads to a new feature not encountered before in smaller model spaces, i.e., the appearance of radially excited states. The latter can be observed experimentally in certain cases.

Shell-model calculation for two-neutrino double beta decay of 48Ca.

The 2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta} decay matrix element of $^{48}\mathrm{Ca}$ has been studied in a large basis shell-model space. The theoretical and experimental ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{\ensuremath{\beta}}}^{+}$ spectra and their relation to 2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta} are discussed. A new empirical effective interaction is found to give the best agreement to ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{\ensuremath{\beta}}}^{+}$ spectra with the effective Gamow-Teller operator \ensuremath{\sigma}\ifmmode \tilde{}\else \~{}\fi{}t=0.77\ensuremath{\sigma}t. The predicted ${\mathit{T}}_{1/2}$=1.9\ifmmode\times\else\texttimes\fi{}${10}^{19}$ yr differs by a factor of 2 from the present experimental limit of ${\mathit{T}}_{1/2}$g3.6\ifmmode\times\else\texttimes\fi{}${10}^{19}$ yr. We also compare the matrix elements obtained at various levels of the truncation in the shell-model space.