Hamada-Johnston Potential Research Articles

Nucleon-nucleon potentials from Δ -full chiral effective-field-theory and implications

We closely investigate NN potentials based upon the Delta-full version of chiral effective field theory. We find that recently constructed NN potentials of this kind, which (when applied together with three-nucleon forces) were presented as predicting accurate binding energies and radii for a range of nuclei from A=16 to A=132 and providing accurate equations of state for nuclear matter, yield a chi^2/datum of 60 for the reproduction of the pp data below 100 MeV laboratory energy. This chi^2 is more than three times what the Hamada-Johnston potential of the year of 1962 achieved already some 60 years ago. We perceive this historical fact as concerning in view of the current emphasis on precision. We are able to trace the very large chi^2 as well as the apparent success of the potentials in nuclear structure to unrealistic predictions for P-wave states, in which the Delta-full NNLO potentials are off by up to 40 times the NNLO truncation errors. In fact, we show that, the worse the description of the P-wave states, the better the predictions in nuclear structure. Thus, these potentials cannot be seen as the solution to the outstanding problems in current miscroscopic nuclear structure physics.

An investigation of ab initio shell-model interactions derived by no-core shell model

The microscopic shell-model effective interactions are mainly based on the many-body perturbation theory (MBPT), the first work of which can be traced to Brown and Kuo’s first attempt in 1966, derived from the Hamada-Johnston nucleon-nucleon potential. However, the convergence of the MBPT is still unclear. On the other hand, ab initio theories, such as Green’s function Monte Carlo (GFMC), no-core shell model (NCSM), and coupled-cluster theory with single and double excitations (CCSD), have made many progress in recent years. However, due to the increasing demanding of computing resources, these ab initio applications are usually limited to nuclei with mass up to A = 16. Recently, people have realized the ab initio construction of valence-space effective interactions, which is obtained through a second-time renormalization, or to be more exactly, projecting the full-manybody Hamiltonian into core, one-body, and two-body cluster parts. In this paper, we present the investigation of such ab initio shell-model interactions, by the recent derived sd-shell effective interactions based on effective J-matrix Inverse Scattering Potential (JISP) and chiral effective-field theory (EFT) through NCSM. In this work, we have seen the similarity between the ab initio shellmodel interactions and the interactions obtained by MBPT or by empirical fitting. Without the inclusion of three-body (3-bd) force, the ab initio shell-model interactions still share similar defects with the microscopic interactions by MBPT, i.e., T = 1 channel is more attractive while T = 0 channel is more repulsive than empirical interactions. The progress to include more many-body correlations and 3-bd force is still badly needed, to see whether such efforts of ab initio shell-model interactions can reach similar precision as the interactions fitted to experimental data.

A short revisit to Kuo-Brown effective interactions

This paper is a short revisit to Kuo-Brown effective interaction derived from the Hamada-Johnston nucleon-nucleon potential, done by Gerry Brown and Tom Kuo. This effective interaction, derived in year 1966, is the first attempt to describe nuclear structure properties from the free nucleon-nucleon potential. Nowadays much progress has been achieved for the effective interactions in shell model. We would compare the effective interactions obtained in the 1966 paper with up-to-date shell-model interactions in sd-shell and pf-shell model space. Recent knowledge of effective interactions on nuclear structure, can also be traced in the Kuo- Brown effective interaction, i.e., the universal roles of central and tensor forces, which reminds us that such discovery should be noticed much earlier.

NUCLEON–NUCLEUS OPTICAL POTENTIAL FROM HARD- AND SOFT-CORE INTERNUCLEON POTENTIALS

We have compared the binding energy of nuclear matter and the nucleon–nucleus optical potential, calculated in Brueckner theory starting from both the soft-core Urbana V-14 and the hard-core Hamada–Johnston internucleon potentials. Our results show that the real central part of the optical potential calculated from V-14 is about 10 MeV deeper than from the hard-core potential in the energy region 1–200 MeV. This greater depth mainly comes from the internucleon S- and D-states. In these states, the V-14 and Hamada–Johnston potentials give different phase shifts, the V-14 being in better agreement with experimental data. This difference is further enhanced by the Pauli principle in the calculation of the optical potential. Our analysis of proton–40 Ca differential cross-section and polarization data, in the energy region 30–200 MeV, shows that the optical potential calculated using V-14 is in better agreement with the data as compared with the Hamada–Johnston potential.

Variational Method for Infinite Nuclear Matter with the Paris Potential

The energy per nucleon for infinite nuclear matter with the parametrized Paris potential is calculated using the variational method recently proposed by Takano and Yamada. Approximate energy expressions playing an important role in this variational method are refined for the Paris potential, and in particular for the quadratic momentum parts in it. Since this variational method without any constraints gives extreme overbinding, an effective theory also proposed in conjunction with the above-mentioned variational method is applied, in a modified manner, to the calculations for symmetric nuclear matter and neutron matter with the Paris potential, as well as the Hamada-Johnston and AV14 potentials. The obtained equation of state (EOS)for the Paris potential is, unlike the unrealistically soft EOS for the AV14 potential, capable of describing neutron stars with a reasonable maximum mass of 1.65 M� .

Quark Cluster Model of Baryon-Baryon Interaction

The quark cluster model of the baryon-baryon interaction is reviewed. The emphasis is on the foundation of the approach and the main features of the model. The origins of the short-range repulsion in the nuclear force and other baryonic interactions are discussed. The origin of the nuclear force is a central problem of nuclear physics. It has a long history since Yukawa 1) proposed the static one-pion exchange potential (OPEP) of the range of the pion Compton wave length. The discovery of the pion boosted both the experimental and theoretical investigation of the nuclear force. It was realized in the early stage that the short range part of the nuclear force requires further ingredients, including the two- and multi-pion exchange interactions. In order to study the shorter-range part, Taketani proposed to consider three regions of the nuclear force separately. 2) (I) The long-range part (R ≥ 2 fm) is described by OPEP. (II) The medium-range part (1 ≤ R ≤ 2 fm) is attributed to nonstatic part of the pion exchange, multipion exchanges and heavy meson exchanges. Finally, (III) the shortrange part (R ≤ 1 fm) is left for phenomenology as it is most “complicated”. The OPEP was firmly established since then and the region (II) was studied in various approaches that treat nonstatic contribution and heavy mesons. It is believed to give a strong attraction due mostly to exchange of two pions correlated in the S-wave, which is often represented by the exchange of a scalar sigma meson. It turned out that this strong attraction of the second region is crucial for the nuclear binding. The shortest range region (III) was found to have a strong repulsion as suggested from the medium-energy nucleon-nucleon ( NN ) scattering data. Thus the nuclear binding is on the balance between the attraction in the regions (I) and (II) and the repulsion in (III). Meanwhile, many phenomenological models have been constructed. Main source of information is the NN scattering observables as well as properties of the deuteron. The proposed models include the Hamada-Johnston potential, 3) the Reid soft core potential, 4) the Tamagaki potential, 5) all of which can explain the low energy observables fairly well. The real development in the study of region (II) was achieved in 1970’s resulting in two popular models of nuclear force, Bonn 6) and Paris 7) po

Variational Method for Infinite Nuclear Matter with Noncentral Forces

Approximate energy expressions are proposed for infinite zero-temperature neutron mat­ ter and symmetric nuclear matter by taking into account noncentral forces. They are explic­ itly expressed as functionals of spin-isospin-dependent radial distribution functions, tensor distribution functions and spin-orbit distribution functions, and can be used conveniently in the variational method. The two-body noncentral cluster terms are fully included in these expressions, while the degree of inclusion of the three-body cluster terms related to non­ central forces is less than that of the purely central three-body terms. The Euler-Lagrange equations are derived from these energy expressions and numerically solved for neutron mat­ ter and symmetric nuclear matter. The Hamada-Johnston and AV14 potentials are used as the two-body nuclear force. The results show that the noncentral forces cause the total en­ ergy of symmetric nuclear matter to be decreased too much with a saturation density which is too high. Discussion is given as to the reason for this disagreement with experiment, and the long tails of the noncentral distribution functions obtained in the numerical calculations are suspected to be the main reason. Then, an effective theory is proposed by introducing a density-dependent modification of the noncentral part of the energy expression to suppress the long tails of the noncentral distribution functions. With a suitable choice of the value of a parameter included in the modification, the saturation point (both the energy and the density) of symmetric nuclear matter can be reproduced with the Hamada-Johnston poten­ tial. Neutron stars are studied by use of this effective theory, and reasonable results are obtained.

The three-nucleon bound state with realistic soft- and hard-core potentials

The wave function of the three-nucleon bound state is decomposed in the LS coupling scheme and the radial amplitudes of all the channels considered are expanded on a set of correlated basis functions. Two different types of correlated expansions are investigated, namely the pair (PHH) and the Jastrow (CHH) correlated hyperspherical-harmonic expansions. The correlation factor includes only one pair-correlation function per channel in the PHH case, whilst it is a product of three pair-correlation functions per channel in the CHH case. The optimal dependence on the hyperradius is determined by means of a variational technique. For the Argonne AV14 potential the results given by the PHH expansion are in very close agreement with those of Kameyana et al. The CHH expansion allows for treating hard-core interactions too, and the results obtained for the Hamada-Johnston potential noticeably improve those obtained with other methods.

Spin-tensor analysis of realistic shell model interactions.

In this paper various realistic shell model effective interactions are analyzed in terms of their central, vector, and tensor components. The effective forces were obtained from phenomenological (Hamada-Johnston) as well as from modern meson-exchange (Bonn-Juelich and Paris) nucleon-nucleon potentials and were calculated to various approximations within the framework of perturbation theory. For all forces examined, the dominant contribution comes from the central part. The vector component is small for the bare {ital G}-matrix interaction, especially for {ital T}=0, but is considerably modified by renormalization. The tensor component is somewhat larger than the vector component and is relatively larger for the Hamada-Johnston potential than for the Bonn-Juelich and Paris potentials. Centroids in {ital j}-{ital j} and SU(3) coupling were obtained with and without noncentral contributions; considerable sensitivity was observed in the SU(3) basis.

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.

Density dependence in the two-nucleon effective interaction at 135 MeV.

Differential cross sections and analyzing powers for scattering of 135-MeV protons by /sup 16/O have been measured for all narrow states below 12.1 MeV of excitation up to a momentum transfer of 3.2 fm/sup -1/. Calculations that employ accurate transition densities fitted to electroexcitation data are used to study medium modifications to the two-nucleon effective interaction with little residual uncertainty from nuclear structure. Definitive evidence for strong density dependence in the isoscalar spin-independent central component of the two-nucleon effective interaction has been found. The differential cross sections show that as the density increases, the strength of the central interaction is suppressed at low momentum transfer and enhanced at high momentum transfer. The analyzing powers exhibit strong negative excursions near 2.5 fm/sup -1/, which support enhanced repulsion at high density. The data are well described by the local-density approximation, which employs the nuclear-matter effective interaction appropriate to the density in the vicinity of the interacting nucleons. We find that the qualitative results are insensitive to ambiguities in the local-density prescription, the local-exchange approximation, and the choice of distorted waves. However, effective interactions based upon the Paris, Bonn, and Hamada-Johnston potentials do give substantially different results. Of these, the Paris-Hamburg effective interactionmore » provides the best description of normal-parity isoscalar transitions. The analysis also supports a rearrangement contribution to the effective interaction for inelastic scattering.« less

The use of off-shell potentials in Brueckner theory calculations of the nucleon optical potential

We calculate the nucleon optical potential from the Hamada-Johnston potential using first-order Brueckner theory. The new feature is that we use a fully complex off-shell potential in the energy denominator in the calculation of the -matrix in place of the usually used real part of the on-shell potential. We find that for bombarding energies near 30 MeV the agreement with experimental data is satisfactory while at higher energies the general results from the on- and off-shell potentials are very similar. The reason for the better agreement at the lower energies using the off-shell potential in the energy denominator is that the calculated optical potential in this case has a much smaller imaginary part.

Relativistic effects and deuteron photodisintegration with polarized and unpolarized gamma rays.

Angular distribution, asymmetry function, and polarization of the outgoing nucleons in deuteron photodisintegration are investigated employing the relativistic one-body charge density and two-body charge and current density effects with local and nonlocal contributions in pseudoscalar and pseudovector pion-nucleon couplings, and comparison is made with available experimental data. The angular distribution and polarization coefficients are reported for the super-soft core, Paris, Yale, and Hamada-Johnston potentials. The relativistic one-body and two-body corrections to the charge density increase the isotropic component of the angular distribution at lower energies but decrease it at higher energies. The changes in the polarization parameters are nearly the same for all the potentials, and all the potentials are found to reproduce the angular distribution, asymmetry function, and polarization of outgoing nucleons quite well at low and medium gamma ray energies.

Microscopic Lane-model calculations

Microscopic Lane-model calculations have been performed for 90Zr, 92Zr, 94Zr(p,n)IAS and 112Sn, 116Sn, 124Sn(p,n)IAS for Ep=25-80 MeV. The elastic and coupling potentials were calculated by folding the density-dependent interaction derived from the Hamada-Johnston potential. The ambiguity in the choice of a local momentum is avoided by noting that isospin local momenta for V> and Vp being well defined. The magnitude of the experimental cross sections conservation implies Vpn=(V>-Vp)/(2T)12/, the is well reproduced, but not the detailed structure. For the 80 MeV data agreement can be obtained if the coupling potential is surface dominated.

The effect of the quadratic spin-orbit interaction

The effect of the quadratic spin-orbit interaction on nuclear structure is tested. The quadratic spin-orbit terms in the Hamada-Johnston and Yale potentials are used to calculate the two-body matrix elements of identical equivalent particles in the f7/2 shell. The results show that the effect of the quadratic spin-orbit interaction on the spectra is, in general, larger than that of the Coulomb interaction, and cannot be neglected.

The 2π-exchange potential for pseudovector coupling of pions and nucleons

A 2 pi -exchange (TPE) potential for pseudovector coupling of pions and nucleons is derived by transforming the Dirac equation into a Schrodinger-like form. The resulting TPE potential is spin dependent and attractive in all states of the NN and NN systems and describes part of the intermediate-range interaction. A comparison is made with the Hamada-Johnston potential and with the TPE potential obtained from different approaches.

Two-body effects and deuteron photodisintegration with polarized and unpolarized gamma rays

Employing the two-body charge effects owing to $\ensuremath{\pi}$ exchange and the current effects owing to $\ensuremath{\pi}$-, $\ensuremath{\rho}$-, and $\ensuremath{\omega}$-exchange processes, the angular distribution, asymmetry function, and polarization of nucleons from the $^{2}\mathrm{H}{(\ensuremath{\gamma},n)}^{1}\mathrm{H}$ reaction are investigated. The cross section and polarization parameters are reported for the Paris, Yale, super-soft-core B, and Hamada-Johnston potentials. The changes in the parameters owing to exchange effects are found to be nearly the same for all the potentials, and all the potentials are found to reproduce the low energy angular distribution data provided a suitable normalization factor is chosen.[NUCLEAR REACTIONS $^{2}\mathrm{H}{(\ensuremath{\gamma},n)}^{1}\mathrm{H}$. Two-body exchange effects, total and differential cross section, polarization, asymmetry function with realistic nucleon-nucleon interactions.]

Two-body effects in the sum rules for thed(γ, p)nreaction

The integrated and bremsstrahlung-weighted cross sections have been calculated including the one-pion-exchange contributions to the charge density for the Paris, super-soft-core, Yale, Hamada-Johnston, and modified Hamada-Johnston potentials. The contribution of the two-meson exchange to the integrated cross section has been estimated. For velocity independent potentials the change in the enhancement factor due to the meson exchange is found to be approximately the same, but it is a little larger for the velocity dependent (Paris) potential. It is found that contrary to the claim made in the literature the integrated cross section cannot distinguish between the various two-nucleon potentials.NUCLEAR REACTIONS $d(\ensuremath{\gamma}, p)n$, calculated integrated and bremsstrahlung-weighted cross sections; included one- and two-pion exchange contribution.

Wave functions for low-lying states of light deformed nuclei using a “realistic” hamiltonian and their test by inelastic scattering: The case of 20Ne

Nuclear structure wave functions for the ground and low-lying excited states of 20Ne, obtained from the angular momentum projected deformed particle-hole model using a “realistic” many-nucleon hamiltonian (kinetic energy plus a Brueckner G-matrix based on the Hamada-Johnston potential), are used as input to microscopic antisymmetrised DWBA analyses of inelastic proton scattering from 20Ne. This nuclear structure model, which has been previously shown able to describe the essential features of the giant multipole resonances of both 20Ne and 28Si, predicts angular distributions for inelastic proton scattering, exciting a number of states below 9 MeV in 20Ne, in qualitative agreement with the available data; a somewhat surprising result given the nuclear structure model's completely microscopic formulation. Anomalies observed in the assignment of some predicted levels to experimental states suggest some shortcomings in the form adopted for the hamiltonian.

Analyses of the energy-dependent single-separable-potential models for the $$\mathcal{N}\mathcal{N}$$ scattering

By starting from a systematic study of the salient features regarding the quantum-mechanical two-particle scattering off an energy-dependent (ED) single separable potential and its connection with the rank-2 energy-independent (EI) separable potential in theT-(K-) amplitude formulation, the present status of the ED single-separable-potential models due to Tabakin (M1), Garcilazo (M2) and Ahmad (M3) has been discussed. It turned out that the incorporation of a self-consistent optimization procedure improves considerably the results of the1S0 and3S1 scattering phase shifts for the models (M2) and (M3) up to the c.m. wave numberq=2.5 fm−1, although the extrapolation of the results up toq=10 fm−1 reveals that the two models follow the typical behaviour of the well-known supersoft-core potentials. It has been found that a variant of (M3)—i.e. (M4) involving one more parameter—gives phase-shift results which are generally in excellent agreement with the data up toq=2.5 fm−1 and the extrapolation of the results for the1S0 case in the higher wave number range not only follows the corresponding data qualitatively, but also reflects a behaviour similar to the Reid soft-core and Hamada-Johnston potentials together with a good agreement with the recent [4/3] Pade fits. A brief discussion regarding the features resulting from the variations in the ED parts of all the four models under consideration and their correlations with the inverse-scattering theory methodology concludes the paper.