Bonn Potential Research Articles

Unitary-model-operator approach to nuclear many-body theory

The structure of the unitary-model-operator approach (UMOA) is discussed in the framework of general effective interaction theory. The properties of the two-body effective interaction v ̃ 12 , introduced as a basic element in UMOA, are clarified. The effective interaction v ̃ 12 has some desirable features to be E-independent, Hermitian and decoupled between two spaces of two-particle states consisting of occupied and unoccupied orbits. It is noted that these properties of v ̃ 12 are advantageous over the usual Brueckner approach. The theory is applied to the calculation of the ground-state properties in 16O with various nucleon-nucleon potentials including the Bonn potential. The result is reasonable in comparison with those obtained in the usual Brueckner-Hartree-Fock calculation. The use of the Bonn potential with rather weaker tensor component leads to a better result. It is shown that the results for the saturation property, the binding energy versus charge radius, lie beyond the Coester band and get near to the experimental value.

Effective nuclear forces in free space

The energy dependence of effective nuclear forces in free space arising from the elimination of configurations outside a model space is discussed. This energy dependence provides the key to the understanding of why the best theoretical descriptions of the deuteron matter radius are given by energy-independent potentials and not by energy-dependent potentials such as the full Bonn potential.

Dynamical model for correlated two-pion exchange in the NN interaction.

A dynamical model for [ital S]- and [ital P]-wave correlated two-pion exchange between two nucleons is presented, starting from corresponding [ital N[bar N]][r arrow][pi][pi] amplitudes in the pseudophysical region, which have been constructed from nucleon and [Delta]-isobar exchange Born terms and a meson exchange model of [pi][pi] scattering which satisfactorily describes the empirical [pi][pi] data. It is demonstrated that the results have quite different characteristics, in both strength and range, compared to (sharp mass) [sigma][prime], [rho] exchange as used in the Bonn potential. Consequences for the description of high partial wave [ital NN] scattering phase shifts are discussed.

Nucleon-nucleon interaction with consistently soft form factors for one and two pion exchange.

It has recently proven possible to construct an acceptable one-boson-exchange potential in which the [ital NN][pi] form factor is quite soft. In order to do so it was necessary to add an effective [pi][prime] meson which increased the short-range tensor force. It is much less obvious that one can use such soft form factors if the two-pion-exchange diagrams are calculated explicitly rather than being parametrized as scalar meson exchange. Here we show that it is indeed possible to construct a model which describes nucleon-nucleon data with comparable quality as the original full Bonn potential, but in which the two pion exchange is included explicitly with consistently soft [ital NN][pi] and [Delta][ital N][pi] vertices.

Hadron-Hadron interactions from meson exchange

Several recent developments in the meson exchange theory of hadronic interactions are reviewed. After some introductory remarks about the relevance of the meson exchange concept in the era of QCD we will describe a dynamical model for correlated 2π-exchange in the NN as well as the πN interaction; for the NN system, it should replace the (sharp mass)σ′ andρ exchange used in the Bonn potential. Next we turn our attention to theπρ interaction. A recently proposed meson exchange model can resolve in a natural way apparent discrepancies occurring in the analysis of different experiments in connection with the A1 meson and leads to an appreciable softening of the πNN form factor.

Microscopic description of nucleon-nucleus scattering based on realistic nucleon-nucleon interactions

Based on the Bonn potential as the realisitic nucleon-nucleon (NN) interaction and the Dirac-Brueckner-Hartree-Fock (DBHF) approach for nuclear matter, we derive the microscopic nucleon-nucleus optical potential at intermediate energies. We calculate observables (differential cross sections, analysing powers, spin rotation functions and total cross sections) in nucleon-nucleus scattering and compare our predictions with experimental data as well as other calculations. Fairly good agreement is found between our microscopic results and experimental data. We also calculate the nucleon mean free path in nuclear medium starting from the bare NN interaction. The microscopic nucleon mean free path is in good agreement with the empirical value.

Grand unification, nuclear structure and the double beta-decay

Unification of the electroweak and the strong interaction prefers that the neutrino is a Majorana particle and therefore essentially identical with its own antiparticle. In such grand unified models the neutrino has also a finite mass and a slight right-handed weak interaction, since the model is left-right symmetric. These models have also left handed and right-handed vector bosons to mediate the weak interactions. If these models are correct the neutrinoless double beta-decay is feasable. Thus if one finds the neutrinoless double beta-decay one knows that the standard model can not be correct in which the neutrino is a Dirac particle and therefore different from its antiparticle. Although the neutrinoless double beta-decay has not been seen it is possible to extract from the lower limits of the lifetime against the double neutrinoless beta-decay upper limits for the effective electron-neutrino mass and for the effective mixing angle of the right-handed and the left-handed vector bosons mediating the weak interaction. One also can obtain an effective upper limit for the mass ratio of the light and the heavy vector bosons. The extraction of this physical quantities from the data is made difficult due to the fact that the weak interaction must not be diagonal in the representation of the mass matrix of the six neutrinos requested by such left-right symmetric models. A condition for obtaining reliable limits for these fundamental quantities from the measured lower limits of the half lifes of the 0νββ decay are correct calculations of the nuclear matrix elements involved. These nuclear structure calculations can be tested by calculating the two neutrino double beta decay (2νββ) for which we have experimental data and not only lower limits as for the 0νββ decay. The 2νββ decay is dominated by the Gamow Teller (GT) transitions. The intermediate 1 + states in the odd-odd mass nucleus are usually calculated within the Quasi-particle Random Phase Approcimation (QRPA). Since the proton-proton and neutron-neutron pairing correlations are treated in the BCS approach particle numbers are only conserved in average for the initial |0 i +〉 and the final vb0 f +〉 states. Particle number projection is used to improve on this point. Since QRPA with the physical particle-particle interaction from the Bonn potential is close to breakdown, where the excitation energy goes to zero, higher up to third order RPA is included, by allowing anharmonicities up to three bosons in the physical wave functions. Third order RPA which is the lowest order to allow modifications of the ground state correlations affect the results appreciably. Since the intermediate states are supperpositions of proton- neutron two quasi-particle states one expects that proton-neutron pairing affects these states. From the masses of the nuclei one can extract a proton-neutron (pn) pairing gap. Due to the finite basis and the inclusion of only T = 1 (and not also T = 0, J = 1) pn-pairing the bare Brückner matrix elements of the Bonn potential yield no pn-pairing gap in most nuclei. If one fits the experimental pn-pairing gap by renormalizing the pn J π = 0 + particle-particle Brückner matrix elements by a factor d pn ≈ 1.3 to 1.4 one obtains strong pn-pairing correlations, which reduce the GT strength. Since now part of the pn particle-particle correlations are already included in the BCS wave functions the 2νββ strength is reduced and the dependence on the 1 + particle-particle strength parameter g pp gets weaker. In heavier nuclei like 76Ge to 76Se this dependence on g pp of the second order GT matrix elements Σ α GT(0 i + → 1 α + → 0 f +) almost disappears. The upper limits derived from the neutrinoless double beta decay of 76Ge are for the effective neutrino mass 〈 m νe 〉≤ 0.88 eV, for the left-right mixing angle 〈 tgζ 〉≤ 1.55 × 10 −8 and for the mass ratio of the light over the heavy vector boson squared 〈 M 1 2 M 2 2 〉 ≤ 1.08 × 10 −6 .

Erratum: Self-consistent relativistic calculation of nucleon mean free path

We present a fully self-consistent and relativistic calculation of the nucleon mean free path in nuclear matter and finite nuclei. Starting from the Bonn potential, the Dirac-Brueckner-Hartree-Fock results for nuclear matter are parametrized in terms of an effective $\sigma$-$\omega$ Lagrangian suitable for the relativistic density-dependent Hartree-Fock (RDHF) approximation. The nucleon mean free path in nuclear matter is derived from this effective Lagrangian taking diagrams up to fourth-order into account. For the nucleon mean free path in finite nuclei, we make use of the density determined by the RDHF calculation in the local density approximation. Our microscopic results are in good agreement with the empirical data and predictions by Dirac phenomenology.

Microscopic nucleon-nucleus optical potentials at intermediate energies

Based on the Bonn potential as the realistic nucleon-nucleon (NN) interaction and the Dirac-Brueckner-Hartree-Fock (DBHF) approach for nuclear matter, we derive the microscopic nucleon-nucleus optical potential at intermediate energies. The present results are compared with those of the Dirac phenomenology, the relativistic impulse approximation and the Walecka model (QHD-I). The bulk properties of the optical potential are also compared with the available empirical data.

Self-consistent relativistic calculation of nucleon mean free path.

We present a fully self-consistent and relativistic calculation of the nucleon mean free path in nuclear matter and finite nuclei. Starting from the Bonn potential, the Dirac-Brueckner-Hartree-Fock results for nuclear matter are parametrized in terms of an effective \ensuremath{\sigma}-\ensuremath{\omega} Lagrangian suitable for relativistic density-dependent Hartree-Fock (RDHF) approximation. The nucleon mean free path in nuclear matter is derived from this effective Lagrangian taking diagrams up to the fourth order into account. For nucleon mean free path in finite nuclei, we make use of the density determined by the RDHF calculation in the local density approximation. Our microscopic results are in good agreement with the empirical data and the predictions of the Dirac phenomenology.

Determination of dipole polarization effects in 7Li and 11Li

The structure of 6Li, 7Li and 11Li nuclei is investigated in a model space which includes all configurations with oscillator energy up to 3khω above the ground-state configuration. The energy spectra and electromagnetic properties of the low-lying states are determined with various two-body interactions, which are derived from the Bonn potential. The results of these shell-model calculations depend on the strength of the tensor component contained in the NN interaction and also on the treatment of the Dirac spinors for the nucleons in the nuclear medium. In addition, the calculation determines the dipole polarizability of 7Li and 11Li caused from virtual El excitations to the positive-parity states of these nuclei. It is demonstrated that the BAGEL scheme provides a very powerful tool to consider contributions from virtual excitations up to large energies.

Neutron-proton pairing in light nuclei and two-neutrino double-beta decay

We have investigated neutron-proton (np) pairing in light nuclei (2p-lf shell) using a specialized Hartree-Fock-Bogoliubov (HFB) method. For the pairing interaction we used the constant Kisslinger-Sorensen interaction and the realistic G-matrix obtained by solving the Bethe-Goldstone equation with the Bonn one-boson-exchange potential. Our results show that there are at least two minima of the total energy corresponding to two solutions of the HFB equation. The lower solution shows large np pairing. This is confirmed by a recent empirical determination of the np pairing gap, which turns out to be surprisingly large in agreement with our theoretical result. If one renormalizes the Brueckner reaction matrix elements of the Bonn potential by a factor g np multiplying the neutron-proton particle-particle matrix elements to reproduce the experimental np gaps δ np, one obtains large T = 1 np pairing. Preliminary results indicate that the np pairing increases even more if particle-number projection is included. These effects are expected to affect strongly the double-beta decay. The 2 v double-beta decay in 20 48Ca 28 → 22 48Ti 26 is calculated. The Gamow-Teller matrix elements are reduced remarkably by the large np pairing compared to the results without np pairing. The sensitivity of the 2 tv double-beta decay transition on the particle-particle force strength parameter g pp is also reduced compared with the results without np pairing correlations.

Ground-State Properties of 16O in Unitary-Model-Operator Approach with Bonn Potential

The unitary-model-operator approach (UMOA) is applied to the calculation of the ground-state energy, the charge radius and the single-particle energies of occupied states in 16O with the Bonn potential. The calculation reproduces the experimental saturation property fairly well beyond the Coester band.

Hermitian effective interactions derived from the Paris and Bonn potentials

The relationship between the non-hermitian ( R) and hermitian ( W) forms of the effective interaction and the corresponding eigenvectors is discussed. We calculate the exact hermitian effective interaction in the sd and pf shells using the Bonn-A and Paris potentials. We comment upon the fact that W can be well approximated by 1 2 (R + R †)

Ground-State Properties of 16O in Unitary-Model-Operator Approach with Bonn Potential

Ground-State Properties of 16O in Unitary-Model-Operator Approach with Bonn Potential

Phase-shift analysis of NN scattering below 160 MeV: Indication for a strong tensor force.

A new phase-shift analysis of NN scattering in the energy range 15--160 MeV is presented. The analysis is based on the carefully reviewed world pp+np data, including recent results for higher-order spin observables in n-p scattering. The latter are essential to determine the mixing parameter ${\mathrm{\ensuremath{\varepsilon}}}_{1}$ which is directly related to the isoscalar tensor force. ${\mathrm{\ensuremath{\varepsilon}}}_{1}$ displays a high trend, in agreement with recent analyses above 140 MeV, and is only reproduced by potential models with a strong tensor force. The prediction of the full Bonn potential is too low by 20% for energies above 40 MeV. All other I=0 phase shifts show agreement with potential models; in particular, the notorious problem with $^{1}$${\mathit{P}}_{1}$ around 50 MeV has disappeared. Around 25 MeV a ten parameter fit based purely on np data agrees with the corresponding fit to the pp data and reveals no indication of anomalous charge independence breaking.

Two-body photodisintegration of 3H and 3He near the giant resonance : (I). Plane-wave approximation

A concise survey of the current status of two-body photodisintegration of the trinucleons in the region of the giant resonance is presented. Calculations neglecting both final-state interactions (FSI) and M1 transitions are presented using the Reid soft-core, Paris and Bonn potentials. D-wave contributions to these reactions are not in agreement in the literature. The present results indicate that approximately (10±4)% of the cross section is due to constructive transitions involving the D-waves. Furthermore, E2 contributions at a photon excitation energy of ∼ 12.5 MeV are found to be approximately 2% for 3He(γ,p)d and 0.1% for 3H(γ,n)d. In addition, fore-aft asymmetry calculations indicate markedly different contributions from E1–E2 interference in a comparison of the 3He and 3H systems.

Bonn potential and sd-shell nuclei.

Using a G-matrix folded diagram method and the Bonn nucleon-nucleon potential, the s-d shell effective interaction is derived and applied to evaluate the spectra of some light sd-shell nuclei. Due to the relatively weak tensor-force characteristic for the Bonn potential, the effective interaction matrix elements, particularly those with isospin T=0, come out generally more attractive than in earlier derivations in which local, strong tensor-force potentials were used. As a consequence of this, our results for the effective interaction and the spectra are in considerably better agreement with empirical determinations and experimental data. The sensitivity of the above nuclear structure calculations to the strength of the nuclear tensor force is demonstrated systematically and the dependence of the s-d shell matrix elements on the nuclear mass number is studied.

Beta beta decay of 128Te, 130Te, and 76Ge with renormalized effective interactions derived from Paris and Bonn potentials.

We perform 2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta} and 0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta} calculations for $^{76}\mathrm{Ge}$, $^{128}\mathrm{Te}$, and $^{130}\mathrm{Te}$ using effective interactions derived from the Paris and Bonn-A potentials. Extended model spaces are employed in setting up the quasiparticle random phase approximation (QRPA) equations, on which our present calculations are based. For $^{76}\mathrm{Ge}$ the model space consists of nine orbits, the two major shells from 0${\mathit{f}}_{7/2}$ to 2${\mathit{s}}_{1/2}$, and for the tellurium case we include eleven orbits spanning three major shells from 1${\mathit{p}}_{3/2}$ to 1${\mathit{f}}_{7/2}$. The bare-G-matrix elements are first calculated, with the Pauli exclusion operator carefully treated with a matrix inversion method, so that double counting between the calculated effective interaction and the above model spaces is strictly avoided. We then calculate the renormalized effective interaction, including corrections from core polarizations and folded diagrams. The effect of core polarization is found to be highly significant, especially for $^{76}\mathrm{Ge}$. There appears to be a compensating effect from the folded diagrams; the net results with core polarizations and folded diagrams both included become rather close to the bare-G results. Unlike earlier QRPA calculations, our calculated ${\mathit{M}}_{\mathrm{GT}}$ matrix elements for 2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta} do not seem to exhibit strong dependence on ${\mathit{g}}_{\mathrm{pp}}$, the particle-particle interaction strength parameter, in the vicinity of ${\mathit{g}}_{\mathrm{pp}}$=1.0.For 0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta} decays, our calculated values for ${\mathit{T}}_{1/2}^{0\ensuremath{\nu}}$〈${\mathit{m}}_{\ensuremath{\nu}}$${\mathrm{〉}}^{2}$ are typically 5\ifmmode\times\else\texttimes\fi{}${10}^{23}$ yr ${\mathrm{eV}}^{2}$ for $^{76}\mathrm{Ge}$, 2\ifmmode\times\else\texttimes\fi{}${10}^{24}$ yr ${\mathrm{eV}}^{2}$ for $^{128}\mathrm{Te}$, and 9\ifmmode\times\else\texttimes\fi{}${10}^{22}$ yr ${\mathrm{eV}}^{2}$ for $^{130}\mathrm{Te}$. Although the Bonn-A potential gives generally more pairing force, the final results for \ensuremath{\beta}\ensuremath{\beta} decays given by the Paris and Bonn-A potentials are rather close to each other.

Enhancement in axial-charge matrix elements from meson-exchange currents

The enhancement factor ϵ mec = 1 + δ mec, defined as the ratio of the axial-charge matrix element in first-forbidden beta decay to its impulse-approximation value, is calculated in a meson-exchange model for both light and heavy nuclei. Pion-exchange processes are computed from a chiral-symmetric phenomenological lagrangian and compared with results obtained in the soft-pion approximation. Heavy-meson pair graphs are included, with coupling constants determined from the Bonn potential. Non-relativistic reductions are carried out to leading order and to next-to-leading order. The results are sensitive to the choice of the short-range correlation function used in conjunction with harmonic-oscillator wavefunctions. A ratio of transition matrix elements however is less sensitive to this uncertainty. Our main result comparing a heavy-mass transition with a light-mass one is r ≡ δ mec (A = 208; lg 9 2 → 0 h 9 2 ) δ mec (A = 16; 1 s 1 2 → 0 p 1 2 ) = 1.38 . This result is smaller than the value of 1.58 ± 0.09 deduced by Warburton in a fit between shell-model impulse-approximation matrix elements and experiment.