Interactions In Finite Nuclei Research Articles

Proton-nucleus elastic scattering: Comparison between phenomenological and microscopic optical potentials

Elastic scattering is a very important process to understand nuclear interactions in finite nuclei. Despite decades of efforts, the goal of reaching a coherent description of this physical process in terms of microscopic forces is still far from being completed. In previous papers (Phys. Rev. C93, 034619 (2016), Phys. Rev. C96, 044001 (2017)) we derived a nonrelativistic theoretical optical potential from nucleon-nucleon chiral potentials at fourth (N3LO) and fifth order (N4LO). We checked convergence patterns and established theoretical error bands. With this work we study the performances of our optical potential in comparison with those of a successful nonrelativistic phenomenological optical potential in the description of elastic proton scattering data on several isotopic chains at energies around and above 200 MeV. We use the same framework and the same approximations of our previous papers, where the nonrelativistic optical potential is derived at the first-order term within the spectator expansion of the multiple scattering theory and adopting the impulse approximation and the optimum factorization approximation. The cross sections and analyzing powers for elastic proton scattering off calcium, nickel, tin, and lead isotopes are presented for several incident proton energies, exploring the range $156 \le E \le 333$ MeV, where experimental data are available. In addition, we provide theoretical predictions for Ni56 at 400 MeV, which is of interest for the future experiments at EXL. Our results indicate that microscopic optical potentials derived from nucleon-nucleon chiral potentials at N4LO can provide reliable predictions for the cross section and the analyzing power both of stable and exotic nuclei, even at energies where the reliability of the chiral expansion starts to be questionable.

Successive variational method of the tensor-optimized antisymmetrized molecular dynamics for central interaction in finite nuclei

Tensor-optimized antisymmetrized molecular dynamics (TOAMD) is the basis of the successive variational method for nuclear many-body problem. We apply TOAMD to finite nuclei to be described by the central interaction with strong short-range repulsion, and compare the results with the unitary correlation operator method (UCOM). In TOAMD, the pair-type correlation functions and their multiple products are operated to the AMD wave function. We show the results of TOAMD using the Malfliet-Tjon central potential containing the strong short-range repulsion. Adding the double products of the correlation functions in TOAMD, the binding energies are converged quickly to the exact values of the few-body calculations for s-shell nuclei. This indicates the high efficiency of TOAMD for treating the short-range repulsion in nuclei. We also employ the s-wave configurations of nuclei with the central part of UCOM, which reduces the short-range relative amplitudes of nucleon pair in nuclei to avoid the short-range repulsion. In UCOM, we further perform the superposition of the s-wave configurations with various size parameters, which provides a satisfactory solution of energies close to the exact and TOAMD values.

Regularization of zero-range effective interactions in finite nuclei

The problem of the divergences which arise in beyond mean-field calculations, when a zero-range effective interaction is employed, has not been much considered so far. Some of us have proposed, quite recently, a scheme to regularize a zero-range Skyrme-type force when it is employed to calculate the total energy, at second-order perturbation theory level, in uniform matter. Although this scheme looked promising, the extension for finite nuclei is not straightforward. We introduce such procedure in the current paper, by proposing a regularization procedure that is similar, in spirit, to the one employed to extract the so-called V_{\rm low-k} from the bare force. Although this has been suggested already by B.G. Carlsson and collaborators, the novelty of our work consists in setting on equal footing uniform matter and finite nuclei; in particular, we show how the interactions that have been regularized in uniform matter behave when they are used in a finite nucleus with the corresponding cutoff. We also address the problem of the validity of the perturbative approach in finite nuclei for the total energy.

Extended relativistic chiral mean field model for nuclear matter

We study nuclear matter properties based on the chiral sigma model. We formulate the extended relativistic chiral mean-field model by using the tensor optimized shell-model prescription developed for the description of the tensor interaction in finite nuclei. We apply further the unitary correlation operator model prescription to the treatment of the short-range repulsion in the pion channel. The remaining effects are treated phenomenologically in terms of the \ensuremath{\omega}-meson coupling term in the relativistic mean-field approximation. We discuss the equation of state and the chiral properties of nuclear matter.

Vacuum polarizations and meson exchange interactions in finite nuclei

Abstract First we solve the relativistic Hartree problem for a finite nucleus: We obtain the relativistic single particle states of positive and negative energy nucleons in 16O, treating these nucleons on the equal footing, and compare the results with those of the mean field theory. We solve the simultaneous mean field equations as matrix equations on the wave packet basis. This method needs not rely on the derivative expansion to renormalize the divergent sums of the densities and of the energies of negative energy nucleons. The contribution of these nucleons suppresses the mean meson fields and increases the nuclear radius. Secondly, taking the positive energy nucleon state sector picture of a nucleus to elucidate the results of the above relativistic Hartree calculation, we derive the effective nuclear interactions between positive energy nucleons which are corrected by the N N vacuum polarizations. The polarizations suppress the meson exchange interactions and increase their ranges.

Derivative scalar coupling model versus sigma - omega model.

The relativistic derivative scalar coupling model of Zimanyi and Moszkowski, which is based on the original \ensuremath{\sigma}-\ensuremath{\omega} model, is investigated both for infinite symmetric nuclear matter and finite spherical nuclei. We find that while this model yields satisfactory compressibility in nuclear matter, and consequently gives good total binding energies for finite nuclei, it however fails to give the right spin-orbit interaction in finite nuclei. Calculated results are shown for $^{16}\mathrm{O}$ and compared to the \ensuremath{\sigma}-\ensuremath{\omega} model and experimental data; the origin of the discrepancy is discussed.

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 in Finite Nuclei Based on Reaction Matrix Theory. II: Properties of Reaction Matrix and Core-Phonon-Exchange Interaction

Effective Interactions in Finite Nuclei Based on Reaction Matrix Theory. II: Properties of Reaction Matrix and Core-Phonon-Exchange Interaction

Effective Interactions in Finite Nuclei Based on Reaction Matrix Theory. I: Reaction Matrix Consistent with Model Space

Reaction matrix is calculated in rigorous ways, special attentions being paid to the consistency with the chosen model space. In our treatment of the reaction matrix, there occurs no ambiguity concerning the double counting. Core-polarization corrections to the effective interactions are considered in second order. The energy spectra of 42Sc are calculated from two types of free nucleon-nucleon potentials, H-J and OBEP-K, with a model space chosen as (fp)2-configurations, at first, and then extended to ((fp)2 + (sdg)2)-configurations. This extension of the model space is found to be important to push down the lowest (JπT) = (1+0) state and (0+1) state; the former has the strongest correlation in bare G and the correlation of the latter is most enhanced through the core-polarization. For the lowest (1+0) state, however, the binding is still weaker compared with the experimental result, even for the OBEP-K potential which is more favourable for the deuteron-like correlation in nuclei.

Density-dependent effective interactions in finite nuclei (II)

The effect of the density dependence of the effective forces on spherical nuclear calculations is examined. Calculations have been made with forces giving different nuclear matter saturation densities and compressibilities and also with interactions having different long-range density dependence. The results have been compared with experiments.

Density-dependent effective interactions in finite nuclei (I)

Finite nuclei ranging from 16O to 208Pb are calculated using the Hartree-Fock theory and the local-density approximation. The energy of the nucleus is separated into a volume term, which can be calculated directly in terms of the nuclear matter energy density, and a residual surface term which contains a starting energy correction and to which only the long-range part of the effective interaction contributes. The results obtained are compared with experiment and with other calculations.

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.

Effective interactions in finite nuclei

Effective interactions in finite nuclei

The free reaction matrix as a residual interaction in finite nuclei

The individual particle spectra of O 18 and Ca 42 are calculated using as a residual interaction the reaction matrix of two isolated nucleons. The reaction matrix is determined by the demand that it correctly predicts the tangents of the phase shifts in the isobaric triplet states of the two-nucleon system. A reasonable fit to the spectra is obtained if the residual short range repulsion (above 100 MeV) in the two-nucleon 1S 0 state is ignored.

A study of effective nuclear interactions in finite nuclei

A shell-model analysis of T = 1 levels in the nuclei Li5, O16 and Ti18 is presented in appropriate configuration space and coupling scheme. The important feature of this analysis is that the matrix elements of various energy states are calculated in terms of the matrix elements of the effective interaction (i.e. the reaction matrix in Brueckner's theory) in two-nucleon states of definite relative orbital angular momentum I and total spin S. The nature of the effective interactions thus derived is discussed: the results throw some light on possible non-locality and configuration-dependence of the elements of the reaction-matrix in finite nuclei.

On the effective interaction in finite nuclei

The expectation values of the two nucleons interaction are calculated using Brueckner's matrix and shell model wave functions. These values are compared with phenomenological ones. The discrepancies can be explained by the effected approximations.