Nuclear Force

The similarity renormalization group (SRG) is based on unitary transformations that suppress off-diagonal matrix elements, forcing the Hamiltonian toward a band-diagonal form. A simple SRG transformation applied to nucleon-nucleon interactions leads to greatly improved convergence properties while preserving observables and provides a method to consistently evolve many-body potentials and other operators.

The accuracy of the Lipkin-Nogami version of the BCS method is examined and compared with other methods, for the ground and 0 + excited states of a symmetric two-level model. Unlike many other methods which fail for either very weak or very strong couplings, the Lipkin-Nogami method works well for any value of the force strength.

Precise measurements of deuteron vector and tensor analyzing powers A y d , A xx , A yy , and A xz in d-p elastic scattering were performed via 1 H(d ជ ,d)p and 1 H(d ជ ,p)d reactions at three incoming deuteron energies of E d lab ϭ140, 200, and 270 MeV. A wide range of center-of-mass angles from Ϸ10°to 180°was covered. The cross section was measured at 140 and 270 MeV at the same angles. These high precision data were compared with theoretical predictions based on exact solutions of three-nucleon Faddeev equations and modern nucleonnucleon potentials combined with three-nucleon forces. Three-body interactions representing a wide range of present day models have been used: the Tucson-Melbourne 2-exchange model, a modification thereof closer to chiral symmetry, the Urbana IX model, and a phenomenological spin-orbit ansatz. Large three-nucleon force effects are predicted, especially at the two higher energies. However, only some of them, predominantly d/d⍀ and A y d , are supported by the present data. For tensor analyzing powers the predicted effects are in drastic conflict to the data, indicating defects of the present day three-nucleon force models.

The chiral low-energy constants cD and cE are constrained by means of accurate ab initio calculations of the A = 3 binding energies and, for the first time, of the triton β decay. We demonstrate that these low-energy observables allow a robust determination of the two undetermined constants, a result of the surprising fact that the determination of cD depends weakly on the short range correlations in the wave functions. These two-plus three-nucleon interactions, originating in chiral effective field theory and constrained by properties of the A = 2 system and the present determination of cD and cE, are successful in predicting properties of the A = 3, and 4 systems. 21.45.Ff, The fundamental connection between nuclear forces and the underlying theory of quantum chromodynamics (QCD) remains one of the greatest contemporary theoretical challenges, due to the non-perturbative character of QCD in the low-energy regime relevant to nuclear phenomena. However, the last two decades of theoretical developments provide us with a bridge to overcome this obstacle, in the form of chiral perturbation theory (χPT) [1]. The χPT Lagrangian, constructed by integrating out degrees of freedom of the order of Λ χ ∼ 1 GeV and higher (nucleons and pions are thus the only explicit degrees of freedom), is an effective Lagrangian of QCD at low energies. As such, it retains all conjectured symmetry principles, particularly the approximate chiral symmetry, of the underlying theory. Furthermore, it can be organized in terms of a perturbative expansion in positive powers of Q/Λ χ where Q is the generic momentum in the nuclear process or the pion mass [1]. Though the subject of an ongoing debate about its validity [2, 3], the naive extension of this expansion to non-perturbative phenomena provides a practical interface with existing manybody techniques, and clearly holds a significant value for the study of the properties of QCD at low energy and its chiral symmetry.

We show that the QCD van der Waals interaction due to multiple gluon exchange provides a new kind of attractive nuclear force capable of binding heavy quarkonia to nuclei. The parameters of the potential are estimated by identifying multi-gluon exchange with the pomeron contributions to elastic meson-nucleon scattering. The gluonic potential is then used to study the properties of CC nuclearbound states. In particular, we predict bound states of the qc with He3 and heavier nuclei. Production modes and rates are also discussed.

In the modern description of nuclear forces based on chiral effective field theory, four-nucleon operators with unknown coupling constants appear. These couplings can be fixed by a fit to the low partial waves of neutron-proton scattering. We show that the so determined numerical values can be understood on the basis of phenomenological one-boson-exchange models. We also extract these values from various modern high accuracy nucleon-nucleon potentials and demonstrate their consistency and remarkable agreement with the values in the chiral effective field theory approach. This paves the way for estimating the low-energy constants of operators with more nucleon fields and/or external probes.

We review the applications of quantum chxomodynamtca to nuclear nmHiquarlt systems. In particular, predictions are given for the deuteron reduced form factor in the high momentum transfer region, hidden color components in nuclear wavefunetions, and the short distance effective force between nucleons. A new antisymmatrisation technique is presented which allows a basis for relativistic multiquark wavefunctions and solutions to their evolution to short distances. Areas in which conventional nuclear theory conflicts with QCD are also briefly reviewed. 1. The representation of the unclear force in terms of quark and {loon eubprocesses. The unclear force between nucleons can in principle be represented at a fundamental level in QCD in terms of quark interchange (equivalent at large distances to pion and other meson exchange) and multiple-gluon exchange. Although calculations from first principles are still too complicated, recent results derived from effective potential, bag, and soliton models suggest that many of tbe bask features of the nuclear force can be understood from the underlying QCD substructure. At a more bask level we will show directly from QCD that the nudeon-nudeon force must be repulsive at short distances. At high momentum transfer the nucleon-nucleon interactions agree with the scaling laws predicted by the simplest constituent exchange processes. 2. The composition of the nudeon and nuclear state in terms of quark and gluon quanta. The light-cone quantisation formalism provides a consistent relativistic Fock state mo mentum space representation of multiquark and gluon color singlet bound states. 3. The propagation of quarks and gluons through nuclear matter: one is interested in the interplay between multiple scattering, induced radiation, the Landau-Pomeranchuk coherence effect, shadowing phenomena, and confinement. 4. Factorisation theorems for inclusive and exclusive reactions: for nuclear reactions one is particularly interested in the origin of the EMC non-additivity effect and other nuclear-induced effects in high transverse momentum reactions. |2 For a reeeni discussion of progress in tbe derivation of nuclear forces from QCD-based models, see K.

We discuss lattice simulations of light nuclei at leading order in chiral effective field theory. Using lattice pion fields and auxiliary fields, we include the physics of instantaneous one-pion exchange and the leading-order S-wave contact interactions. We also consider higher-derivative contact interactions which adjust the S-wave scattering amplitude at higher momenta. By construction our lattice path integral is positive definite in the limit of exact Wigner SU(4) symmetry for any even number of nucleons. This SU(4) positivity and the approximate SU(4) symmetry of the low-energy interactions play an important role in suppressing sign and phase oscillations in Monte Carlo simulations. We assess the computational scaling of the lattice algorithm for light nuclei with up to eight nucleons and analyze in detail calculations of the deuteron, triton, and helium-4.

We consider solutions to some of the difficulties which arise when Hartree-Fock-Bogoliubov equations are solved at high angular frequency. These are mainly associated with the fact that then instead of particles always decoupling in pairs, may do so singly and hence lead to quasiparticle wavefunctions containing an odd number of particle components in the quasiparticle wave function. These solutions then also lead to a satisfactory, reliable and fast method for connecting the upper and lower branches of the moment of inertia versus square of the angular frequency curve, and usually reproduce the typical S-shape of the curve. We also show the importance of higher (> 0) particle-particle channel coupled angular momentum of the nucleon-nucleon potential for the rotational spectrum of deformed nuclei at high angular momentum. Some unsolved problems and peculiar cases which arise during the solution of Hartree-Fock-Bogoliubov equations are mentioned in the end, which may be a reflection on the unsatisfactory nature of the present method of obtaining higher angular momentum rotational bands.

We follow our previous paper on possible cosmological variation of weak scale (quark masses) and strong scale, inspired by data on cosmological variation of the electromagnetic fine structure constant from distant quasar (QSO) absorption spectra. In this work we identify the strange quark mass ms as the most important quantity, and the sigma meson mass as the ingredient of the nuclear forces most sensitive to it. As a result, we claim significantly stronger limits on ratio of weak/strong scale (W = ms/ΛQCD) variation following from our previous discussion of primordial Big-Bang Nucleosynthesis (|δW/W | < 0.006) and Oklo natural nuclear reactor (|δW/W | < 1.2 • 10 −10 ; there is also a non-zero solution δW/W = (−0.56 ± 0.05) • 10 −9) .

We present new accurate measurements of the differential cross section σ(θ) and the proton analyzing power Ay for proton-3 He elastic scattering at various energies. A supersonic gas jet target has been employed to obtain these low energy cross section measurements. The σ(θ) distributions have been measured at Ep = 0.99, 1.59, 2.24, 3.11, and 4.02 MeV. Full angular distributions of Ay have been measured at Ep = 1.60, 2.25, 3.13, and 4.05 MeV. This set of high-precision data is compared to four-body variational calculations employing realistic nucleon-nucleon (N N) and threenucleon (3N) interactions. For the unpolarized cross section the agreement between the theoretical calculation and data is good when a 3N potential is used. The comparison between the calculated and measured proton analyzing powers reveals discrepancies of approximately 50% at the maximum of each distribution. This is analogous to the existing "Ay Puzzle" known for the past 20 years in nucleon-deuteron elastic scattering.

We parameterize the recently proposed generalized Skyrme effective force (GSEF) containing extended density dependence. The parameters of the GSEF are determined by the fit to several properties of the normal and isospin-rich nuclei. We also include in our fit a realistic equation of state for the pure neutron matter up to high densities so that the resulting Skyrme parameters can be suitably used to model the neutron star with the "canonical" mass (∼ 1.4M ⊙). For the appropriate comparison we generate a parameter set for the standard Skyrme effective force (SSEF) using exactly the same set of the data as employed to determine the parameters of the GSEF. We find that the GSEF yields larger values for the neutron skin thickness which are closer to the recent predictions based on the isospin diffusion data. The Skyrme parameters so obtained are employed to compute the strength function for the isoscalar giant monopole, dipole and quadrupole resonances. It is found that in the case of GSEF, due to the the larger value of the nucleon effective mass the values of centroid energies for the isoscalar giant resonances are in better agreement with the corresponding experimental data in comparison to those obtained using the SSEF. We also present results for some of the key properties associated with the neutron star of "canonical" mass and for the one with the maximum mass.

We measured cross sections and analyzing powers for the 2H(n,n)2H and 2H(n,pn)n reactions at 189 MeV at the Indiana University Cyclotron Facility (IUCF). These measurements are designed to search for evidence of three-body forces in the nuclear force and have the advantage that the Coulomb force is not involved. The analyzing-power measurements for the 2H(n,n)2H reaction are in close agreement with those from the analog 2H(p,p)2H reaction at nearby energies and do not agree quantiatively with available three-body, Faddeev calculations, either with or without three-body forces included. The 2H(n,pn)n measurements are still under analysis.

In this work we revisit the Okamoto-Nolen-Schiffer (ONS) anomaly in the context of four parametrizations of effective hadronic models, two of them with constant couplings between the nucleons and the mesons and two with density-dependent couplings. A Thomas-Fermi approximation is performed and the effects of the isovector-scalar virtual δ(a 0(980)) mesons are investigated since they influence directly the proton and neutron effective masses in opposite ways. The ρ-ω mixing term is claimed to be important in the explanation of the ONS anomaly and is added in our calculations. We have concluded that as far as the ρ-ω mixing term is included, ΔM (Z, N) is clearly larger in models with δ than in models where this meson is not considered, which is not always the case if the coupling is discarded. None of the models is good enough to describe all experimental data, but the models that better describe the experimental values include the δ mesons.

Excluded volume effects are incorporated in the quark meson coupling model to take into account in a phenomenological way the hard core repulsion of the nuclear force. The formalism employed is thermodynamically consistent and does not violate causality. The effects of the excluded volume on in-medium nucleon properties and the nuclear matter equation of state are investigated as a function of the size of the hard core. It is found that in-medium nucleon properties are not altered significantly by the excluded volume, even for large hard core radii, and the equation of state becomes stiffer as the size of the hard core increases.

Shell effects in nuclei about the stability line are investigated within the framework of the Relativistic Hartree-Bogoliubov (RHB) theory with self-consistent finiterange pairing. Using 2-neutron separation energies of Ni and Sn isotopes, the role of σ-and ω-meson couplings on the shell effects in nuclei is examined. It is observed that the existing successful nuclear forces (Lagrangian parameter sets) based upon the nonlinear scalar coupling of σ-meson exhibit shell effects which are stronger than suggested by the experimental data. We have introduced nonlinear vector self-coupling of ω-meson in the RHB theory. It is shown that the inclusion of the vector self-coupling of ω-meson in addition to the nonlinear scalar coupling of σmeson provides a good agreement with the experimental data on shell effects in nuclei about the stability line. A comparison of the shell effects in the RHB theory is made with the Hartree-Fock Bogoliubov approach using the Skyrme force SkP. It is shown that the oft-discussed shell quenching with SkP is not consistent with the available experimental data.

Measured and calculated cross sections for spin-exchange between alkali atoms and noble gases (specifically sodium and helium) are used to constrain anomalous spin-dependent forces between nuclei at the atomic scale (∼ 10 −8 cm). Combined with existing stringent limits on anomalous shortrange, spin-dependent couplings of the proton, the dimensionless coupling constant for a heretofore undiscovered axial vector interaction of the neutron arising from exchange of a boson of mass < ∼ 100 eV is constrained to be g n A / √ 4πhc < 2 × 10 −3. Constraints are established for a velocityand spin-dependent interaction ∝ (I • v)(K • v), where I and K are the nuclear spins of He and Na, respectively, and v is the relative velocity of the atoms. Constraints on torsion gravity are also considered.

We consider 1 S0 pairing in infinite neutron matter and nuclear matter and show that in the lowest order approximation, where the pairing interaction is taken to be the bare nucleon-nucleon (NN) interaction in the 1 S0 channel, the pairing interaction and the energy gap can be determined directly from the 1 S0 phase shifts. This is due to the almost separable character of the nucleonnucleon interaction in this partial wave. Since the most recent NN interactions are charge-dependent, we have to solve coupled gap equations for proton-proton, neutron-neutron, and neutron-proton pairing in nuclear matter. The results are, however, found to be close to those obtained with charge-independent potentials.

We are looking for a holographic explanation of nuclear forces, especially the attractive forces. Recently, the repulsive hard core of a nucleon-nucleon potential was obtained in the Sakai-Sugimoto model, and we show that a generalized version of that model-with an asymmetric configuration of the flavor D8 branes-also has an attractive potential. While the repulsive potential stems from the Chern-Simons interactions of the U(2) flavor gauge fields in 5D, the attractive potential is due to a coupling of the gauge fields to a scalar field describing fluctuations of the flavor branes' geometry. At intermediate distances r between baryons-smaller than R KK = O(1)/M ω meson but larger than the radius ρ ∼ R KK / √ λ′ t Hooft of the instanton at the core of a baryon-both the attractive and the repulsive potentials behave as 1/r 2 , but the attractive potential is weaker: Depending on the geometry of the flavor D8 branes, the ratio C a/r = −V attr (r)/V rep (r) ranges from 0 to 1 9. The 5D scalar fields also affect the isovector tensor and spin-spin forces, and the overall effect is similar to the isoscalar central forces, V (r) → (1 − C a/r) × V (r). At longer ranges r R KK , we find that the attractive potential decays faster than the repulsive potential, so the net potential is always repulsive. This unrealistic behavior may be peculiar to the Sakai-Sugimoto-like models, or it could be a general problem of the N c → ∞ limit inherent in holography.

The short-range properties of the KN interaction are studied within the meson-exchange model of the Jülich group. Specifically, dynamical explanations for the phenomenological short-range repulsion, required in this model for achieving agreement with the empirical KN data, are explored. Evidence is found that contributions from the exchange of a heavy scalar-isovector meson (a 0 (980)) as well as from genuine quark-gluon exchange processes are needed. Taking both mechanisms into account a satisfactory description of the KN phase shifts can be obtained without resorting to phenomenological pieces.

Quark-model descriptions of the nucleon-nucleon interaction contain two main ingredients, a quark-exchange mechanism for the short-range repulsion and meson-exchanges for the medium-and long-range parts of the interaction. We point out the special role played by higher partial waves, and in particular the 1 F 3 , as a very sensitive probe for the meson-exchange part employed in these interaction models. In particular, we show that the presently available models fail to provide a reasonable description of higher partial waves and indicate the reasons for this shortcoming.

We study the effect of strong magnetic fields, of the order of 10 18 − 10 19 G, on the instability region of nuclear matter at subsaturation densities. Relativistic nuclear models both with constant couplings and with density dependent parameters are considered. It is shown that a strong magnetic field can have large effects on the instability regions giving rise to bands of instability and wider unstable regions. As a consequence we predict larger transition densities at the inner edge of the crust of compact stars with strong magnetic field. The direction of instability gives rise to a very strong distillation effect if the last Landau level is only partially filled. However, for almost completed Landau levels an anti-distillation effect may occur.

We start from a low-energy effective field theory for interacting fermions on the lattice and expand in the hopping parameter to derive the nearest-neighbor interactions for a lattice gas model. In this model the renormalization of couplings for different lattice spacings is inherited from the effective field theory, systematic errors can be estimated a priori, and the breakdown

Observables in elastic proton-deuteron scattering are sensitive probes of the nucleon-nucleon interaction and three-nucleon force effects. The present experimental data base for this reaction is large, but contains a large discrepancy between data sets for the differential cross section taken at 135 MeV/nucleon by two experimental research groups. This paper reviews the background of this problem and presents new data taken at KVI. Differential cross sections and analyzing powers for the 2 H(p, d)p and H(d, d)p reactions at 135 MeV/nucleon and 65 MeV/nucleon, respectively, have been measured. The data differ significantly from previous measurements and consistently follow the energy dependence as expected from an interpolation of published data taken over a large range at intermediate energies.

An inspection game is a mathematical model of a situation in which an inspector verifies the adherence of an inspectee to some legal obligation, such as an arms control treaty, where the inspectee may have an interest in violating that obligation. The mathematical analysis ...

The effect of the inclusion of ground state correlations into the QRPA equation of motion for the two-neutrino double beta (ββ 2ν) decay is carefully analyzed. The resulting model, called renormalized QRPA (RQRPA), does not collapse near the physical value of the nuclear force strength in the particle-particle channel, as happens with the ordinary QRPA. Still, the ββ 2ν transition amplitude is only slightly less sensitive on this parameter in the RQRPA than that in the plain QRPA. It is argued that this fact reveals once more that the characteristic behaviour of the ββ 2ν transition amplitude within the QRPA is not an artifact of the model, but a consequence of the partial restoration of the spin-isospin SU(4) symmetry. It is shown that the price paid for bypassing the collapse in the RQRPA is the violation of the Ikeda sum rule.

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.

Systematic calculations of ground-state spin and parity of odd-mass nuclei have been performed within the Hartree-Fock-BCS (HFBCS) approach and the Finite-Range Droplet Model for nuclei for which experimental data are available. The unpaired nucleon has been treated perturbatively, and axial and left-right reflection symmetries have been assumed. As for the HFBCS approach, three different Skyrme forces have been used in the particle-hole channel, whereas the particle-particle matrix elements have been approximated by a seniority force. The calculations have been done for the 621 nuclei for which the Nubase 2003 data set give assignments of spin and parity with strong arguments. The agreement of both spin and parity in the self-consistent model reaches about 80% for spherical nuclei, and about 40% for well-deformed nuclei regardless of the Skyrme force used. As for the macroscopic-microscopic approach, the agreement for spherical nuclei is about 90% and about 40% for well-deformed nuclei, with different sets of spherical and deformed nuclei found in each model.

Cross sections were measured for the near-threshold electrodisintegration of 3 He at momentum transfer values of q = 2.4, 4.4, and 4.7 fm −1. From these and prior measurements the transverse and longitudinal response functions RT and RL were deduced. Comparisons are made against previously published and new non-relativistic A = 3 calculations using the best available NN potentials. In general, for q < 2 fm −1 these calculations accurately predict the threshold electrodisintegration of 3 He. Agreement at increasing q demands consideration of two-body terms, but discrepancies still appear at the highest momentum transfers probed, perhaps due to the neglect of relativistic dynamics, or to the underestimation of high-momentum wave-function components.

We study the many-body effects in the propagation of the scalar meson in the nuclear medium arising from its coupling to two pion states. We identify the source of the medium effects as the influence of the individual nucleon response arising from their pion clouds. The same modification applies to the QCD scalar susceptibility. It reflects the reshaping of the scalar strength observed in 2π production experiments. While large modifications of the σ propagator occur, we show that the NN scalar potential remains instead unaffected.

V eff = t0 + t1k 2 + t2k • k + t3/6ρ perturbative (no loops); saturation by three-body force Bender, Heenen, Reinhard, RevModPhys 2003 Nucleon-Nucleon interaction and few-nucleon systems: Effective field theory Epelbaum, Hammer, Meißner RevModPhys 2009

The suitability of density and momentum dependent delta function forces in nuclear calculations is studied using Hartree-Fock calculations in the 2s-ld shell. The effect of the compressibility upon deformation and rms radius is investigated.

The data from the DISTO Collaboration on the exclusive pp → pK + Λ production acquired at T p = 2.85 GeV have been re-analysed in order to search for a deeply bound K − pp(≡ X) state, to be formed in the binary process pp → K + X. The preliminary spectra of the ∆M K + missingmass and of the M pΛ invariant-mass show, for large transverse-momenta of protons and kaons, a distinct broad peak with a mass M X = 2265 ± 2 MeV/c 2 and a width Γ X = 118 ± 8 MeV/c 2 .

A recently developed formulation for treating two-and three-nucleon bound states in a threedimensional formulation based on spin-momentum operators is extended to nucleon-nucleon scattering. Here the nucleon-nucleon t-matrix is represented by six spin-momentum operators accompanied by six scalar functions of momentum vectors. We present the formulation and provide numerical examples for the deuteron and nucleon-nucleon scattering observables. A comparison to results from a standard partial wave decomposition establishes the reliability of this new formulation.

The evaluation of short range contributions to neutrinoless double beta decay has been challenged due to critics of the ansatz of the nuclear matrix element calculations. We comment on the critics and uncertainties of these calculations and the effect on the derived limits. Neutrinoless double beta decay corresponds to the lepton-number converting process A Z X → A Z+2 X + 2e − .

The Similarity Renormalization Group (SRG) is a continuous series of unitary transformations that can be implemented as a flow equation. When the relative kinetic energy (T rel) is used in the SRG generator, nuclear structure calculations have shown greatly improved convergence with basis size because of the decoupling of high-energy and low-energy physics. However this generator can sometimes be problematic. A test case is provided by a study of initial interactions from chiral effective field theories with large cutoffs, which can lead to spurious deep bound states. We would like the SRG to decouple these from the physical shallow bound states. However, with T rel the high-and low-energy bound states are not decoupled in the usual sense. Replacing T rel by the momentum-space diagonal of the Hamiltonian (H d) in the SRG generator does produce decoupling, such that the shallow states are in the low-momentum region and the deep bound states are at higher momentum. The flow toward universal low-momentum interactions is also restored.

Optical model potentials for elastic nucleon nucleus scattering are calculated for a number of target nuclides from a full-folding integral of two different realistic target density matrices together with full off-shell nucleonnucleon t-matrices derived from two different Bonn meson exchange models. Elastic proton and neutron scattering observables calculated from these full-folding optical potentials are compared to those obtained from 'optimum factorized' approximations in the energy regime between 65 and 400 MeV projectile energy. The optimum factorized form is found to provide a good approximation to elastic scattering observables obtained from the full-folding optical potentials, although the potentials differ somewhat in the structure of their nonlocality.

High-precision tensor analyzing power T 20 data of the 1 H(d,pp)n reaction at 130 MeV beam energy have been determined for 81 kinematical configurations. They are compared to theoretical predictions based on various approaches to describe the dynamics of the three-nucleon (3N) system. The calculations are performed using modern realistic nucleon-nucleon potentials combined with three-nucleon force (3NF) models or with an effective 3NF resulting from the explicit treatment of the Δ-isobar in coupled-channels (CC) calculations. Alternatively, the framework of chiral perturbation theory is used to generate consistent two-nucleon and three-nucleon potentials at the currently numerically attainable order. Results of the CC calculations with the Δ degrees of freedom and including long-range Coulomb force are also shown. In general all predictions are consistent with each other and describe the experimental T 20 results quite well. In a few configurations small inconsistencies between the data and the results of all approaches are observed. Predicted effects of the 3NF are not big and in most cases do not lead to an improved description of the data. The Coulomb force effects are also small in size and often opposite to the effects of TM99 3NF.

We consider various forms of the mass term that can be used in the Skyrme model and their implications on the properties of baryonic states. We show that, with an appropriate choice for the mass term, without changing the asymptotic behaviour of the profile functions at large r, we can considerably reduce or increase the mass term's contribution to the classical mass of the solitons. We find that multibaryon configurations can be classically bound at large baryon numbers for some choices of this mass term.

Euclidean point-to-point propagators or wall-to-wall correlators related to exchange by an unstable particle (σ, ρ, ω-mesons) are modified by presence of particle width. In particular, the usual method of deriving particle masses from logarithmic derivatives need to be modified. Similarly Yukawalike potentials of nuclear physics due to exchange of those mesons are significantly modified since the coupling to the decay products is strong. For example, the large distance asymptotic changes, ∼ exp(−Mminr), where Mmin is the sum of the decay product masses (2mπ, 2me, 2mν). In the area Mminr < 1 the potential has a long-range tail ∼ 1/r 3. Similar effects appear due to the virtual decays in the elecroweak sector of the Standard model. The Z − γ mixing via electron loop gives the parity violation potential with the range 1/2me, i.e. the range of the weak interaction increases 10 5 times.

Rich sets of high precision cross sections, vector and tensor analyzing powers for the [Formula: see text] breakup reaction were measured at 130 and 100 MeV beam energy with the use of detection systems covering large parts of the phase space. The cross section data allowed to establish evidences for three-nucleon force contributions and to confirm predictions of sizable effect of the Coulomb force in the breakup reaction. Analyzing power data are generally quite well described by theoretical predictions even with pure nucleon-nucleon interactions. However, in some regions discrepancies has been observed for tensor analyzing powers at 130 MeV.