Frontiers and challenges of the nuclear shell model

Two recent developments of the nuclear shell model are presented. One is a breakthrough in computational feasibility owing to the Monte Carlo Shell Model (MCSM). By the MCSM, the structure of low-lying states can be studied with realistic interactions for a wide, nearly unlimited basically, variety of nuclei. The magic numbers are the key concept of the shell model, and are shown to be different in exotic nuclei from those of stable nuclei. Its novel origin and robustness will be discussed. Received: 1 May 2001 / Accepted: 4 December 2001     

Nuclear forces with <Emphasis Type="Italic">Δ</Emphasis> excitations up to next-to-next-to-leading order,part I: Peripheral nucleon-nucleon waves

We study the two-nucleon force at next-to-next-to-leading order in a chiral effective field theory with explicit Δ degrees of freedom. Fixing the appearing low-energy constants from a next-to-leading-order calculation of pion-nucleon threshold parameters, we find an improved convergence of most peripheral nucleon-nucleon phases compared to the theory with pions and nucleons only. In the delta-full theory, the next-to-leading-order corrections are dominant in most partial waves considered.     

Overview of hadronic parity violation

The subject of hadronic parity violation is nearly fifty years old, but a good deal of uncertainty remains, despite many efforts both theoretical and experimental. A brief summary of the field is presented and a plan is proposed for new experimental work which, when combined with a new theoretical tack based on effective field theory, should lead to resolution of the present difficulties.     

Production of a0 +-mesons in the reaction pp↦da0 +

We investigate the reaction pp↦da ₀ ⁺ at COSY and SIS energies together with accompanying background reactions and inclusive particle yields. The a ₀ ⁺ is considered as a usual u quark model state with two decay channels a ₀ ⁺↦K ⁺ and a ₀ ⁺↦π⁺η. Calculated cross-sections for a ₀ ⁺ production as well as for the corresponding non-resonant channels pp↦dK ⁺ and pp↦dπ⁺η are compared. Especially, in case of the final channel dπ⁺η, high statistics measurements are necessary to extract the a ₀ ⁺ signal from the high non-resonant background. Received: 20 December 2000 / Accepted: 7 May 2001     

Higher order two step mechanisms in nucleon antinucleon annihilation and the OZI rule

We evaluate three meson doorway mechanisms for nucleon-antinucleon annihilation at rest for the first time. Detailed results are presented for the final state φπ⁰ originating from the ³S₁ initial state and for the φρ channel originating from ¹S₀. The results presented also include the improved contributions from two meson doorway states and from the tree diagrams. For all the channels considered a consistent explanation of large and small OZI violations emerges. Received: 22 December 1999     

Nonlinearity of strong interaction and doorway states for one-nucleon transfer reactions

The experimental data on the doorway states for one-nucleon transfer reactions permit to reveal the many-particle nucleon-nucleon forces resulting from the nonlinearity of strong interaction. The three-particle and four-particle forces are found to be of the same magnitude as the two-particle ones in contrast to the finding from the few-nucleon systems. The origin of this difference is explained. Received: 14 May 2002 / Accepted: 4 June 2002 / Published online: 19 November 2002 RID="a" ID="a"e-mail: birbrair@thd.pnpi.spb.ru Communicated by V.V. Anisovich     

First measurements of the 16O(e, e'pn)14N reaction

This paper reports on the first measurement of the ¹⁶O(e, e'pn)¹⁴N reaction. Data were measured in kinematics centred on a super-parallel geometry at energy and momentum transfers of 215MeV and 316MeV/c. The experimental resolution was sufficient to distinguish groups of states in the residual nucleus but not good enough to separate individual states. The data show a strong dependence on missing momentum and this dependence appears to be different for two groups of states in the residual nucleus. Theoretical calculations of the reaction using the Pavia code do not reproduce the shape or the magnitude of the data. An erratum to this article is available at.     

Renormalizing the Lippmann-Schwinger equation for the one-pion exchange potential

We address the question whether the cut-off dependence, which has to be introduced in order to properly define the Lippmann-Schwinger equation for the one-pion exchange potential plus local (δ-function) potentials, can be removed (up to inverse powers of it) by a suitable tuning of the various (bare) coupling constants. We prove that this is indeed so both for the spin singlet and for the spin triplet channels. However, the latter requires, in the limit when the cut-off is taken to infinity, such a strong cut-off dependence of the coupling constant associated to the non-local term which breaks orbital angular momentum conservation, that the renormalized amplitude lacks from partial-wave mixing. We argue that this is an indication that this term must be treated perturbatively. Received: 7 October 2002 / Accepted: 15 January 2003 / Published online: 5 May 2003     

Pseudo-spin as a relativistic symmetry

The existence of broken pseudo-spin symmetry in the Pb nucleus has been studied in the relativistic mean field approach using realistic Lagrangian parameters. Its relationship to spin orbit splitting and the vanishingly small surface delta character of the mean spin orbit potential are investigated. In the ²⁰⁸Pb nucleus the broken pseudo-spin doublets are found to exist above the neutron (proton) Fermi surfaces. Received: 16 April 1998 / Revised version: 26 June 1998     

Regularization of singular terms in the N¯ potential model

We suggest a method of singular terms regularization in a potential model of the N¯ interaction. This method is free from uncertainties related to the usual cut-off procedure and is based on the fact that, in the presence of sufficiently strong short-range annihilation, N and ¯ never approach close enough to each other. In such a case the low-energy scattering is shown to be fully determined by the OBEP tail, while any details of the short-range core of the N¯ interaction are excluded from the observables. The obtained results for S- and P-wave scattering lengths are in agreement with the well-established theoretical models.     

Differences between pairing and zero-range effective interactions for nuclear binding energies

In this paper, we show that, although the spectroscopic properties of the monopole pairing force and a zero-range delta-function interaction are very similar, their saturation properties are quite different. In particular, the predictions for binding energies when filling up a major shell are radically different past mid-shell. This has significant consequences for understanding the masses and binding energies of long isotopic chains of nuclei that will be accessible with advanced exotic beam facilities. Received: 29 November 2001 / Accepted: 13 February 2002     

Systematics of collective correlation energies from self-consistent mean-field calculations

We study nucleon-nucleon scattering on the lattice at next-to-leading order in chiral effective field theory. We determine phase shifts and mixing angles from the properties of two-nucleon standing waves induced by a hard spherical wall in the center-of-mass frame. At fixed lattice spacing we test model independence of the low-energy effective theory by computing next-to-leading-order corrections for two different leading-order lattice actions. The first leading-order action includes instantaneous one-pion exchange and same-site contact interactions. The second leading-order action includes instantaneous one-pion exchange and Gaussian-smeared interactions. We find that in each case the results at next-to-leading order are accurate up to corrections expected at higher order.     

On the NN final-state interaction in the <Superscript>16</Superscript>O (e,e<Superscript>′</Superscript>pp) reaction

The influence of the mutual interaction between the two outgoing nucleons (NN-FSI) in the ¹⁶O(e, e'pp) reaction has been investigated. Results for various kinematics are discussed. In general, the effect of NN-FSI depends on kinematics and the chosen final state in the excitation spectrum of ¹⁴C. Received: 19 December 2002 / Accepted: 6 February 2003 / Published online: 15 April 2003     

Antiproton-deuteron scattering at 600 MeV/ c

Using Glaubers multiple-scattering theory, the elementary ¯p-neutron scattering amplitude has been obtained from an analysis of ¯p-deuteron elastic-scattering data at 600 MeV/c. The plane-wave expansion in the double-scattering amplitudes is treated more accurately than in earlier work. It is found that this leads to significantly better agreement with the data at high momentum transfer.     

Role of Δ exchange for p annihilation into two-pion and three-pion channels

p annihilation into two pions and three pions is studied in a baryon exchange model. Annihilation diagrams involving nucleon as well as Δ-resonance exchanges are included consistently in the two- and three-pion channels. Effects from the initial-state interaction are fully taken into account. A comparison of the influence of the Δ exchange on the considered annihilation channels is made and reveals that its importance for three-pion annihilation is strongly reduced as compared to two-pion annihilation. It is found that annihilation into three uncorrelated pions can yield up to 10% of the total experimentally observed three-pion annihilation cross-section. Received: 16 January 2002 / Accepted: 20 February 2002     

Microscopic three-body force for asymmetric nuclear matter

Brueckner calculations including a microscopic three-body force have been extended to isospin-asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β = (N - Z)/A is fulfilled in the whole asymmetry range 0≤β≤1 up to high densities. The three-body force provides a strong enhancement of the symmetry energy which increases with density in good agreement with the predictions of relativistic approaches. The Lane's assumption that proton and neutron mean fields linearly vary vs. the isospin parameter is violated at high density due to the three-body force, while the momentum dependence of the mean fields turns out to be only weakly affected. Consequently, a linear isospin split of the neutron and proton effective masses is found for both cases with and without the three-body force. The isospin effects on multifragmentation events and collective flows in heavy-ion collisions are briefly discussed along with the conditions for direct URCA processes to occur in the neutron star cooling. Received: 18 February 2002 / Accepted: 16 May 2002     

Dynamics of low-energy nuclear forces for electromagnetic and weak reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei

A dynamics of low-energy nuclear forces is investigated for low-energy electromagnetic and weak nuclear reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei by example of the neutron-proton radiative capture (M1-capture) n + p → D + γ, the photomagnetic disintegration of the deuteron γ + D → n + p and weak reactions of astrophysical interest. These are the solar proton burning p + p → D + e⁺ + ν _e, the pep-process p + e⁻ + p → D + ν _e and the neutrino and antineutrino disintegration of the deuteron caused by charged ν _e + D → e⁻ + p + p, + D → e⁺ + n + n and neutral ν _e() + D → ν _e() + n + p weak currents.     

Two-particle scattering on the lattice: Phase shifts,spin-orbit coupling,and mixing angles

We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any non-relativistic effective theory of point particles on the lattice. In the center-of-mass frame of the two-particle system we impose a hard spherical wall at some fixed large radius. For channels without partial-wave mixing the partial-wave phase shifts are determined from the energies of the nearly spherical standing waves. For channels with partial-wave mixing further information is extracted by decomposing the standing wave at the wall boundary into spherical harmonics, and we solve coupled-channels equations to extract the phase shifts and mixing angles. The method is illustrated and tested by computing phase shifts and mixing angles on the lattice for spin-1/2 particles with an attractive Gaussian potential containing both central and tensor force parts.