Recent developments in ab-initio few-body scattering calculations including the Coulomb interaction

Recent progress on the solution of ab-initio three- and four-nucleon scattering equations in momentum space that include the correct treatment of the Coulomb interaction is reviewed; results for specific observables in reactions initiated by p + d, p + ³He and n + ³He are shown. In addition three-body calculations of d + ¹²C reactions are compared with equivalent CDCC calculations.     

Efimov Physics with {1/2} Spin-Isospin Fermions

The structure of few-fermion systems having \({1/2}\) spin-isospin symmetry is studied using potential models. The strength and range of the two-body potentials are fixed to describe low energy observables in the angular momentum \({L=0}\) state and spin \({S=0,1}\) channels of the two-body system. Successively the strength of the potentials are varied in order to explore energy regions in which the two-body scattering lengths are close to the unitary limit. This study is motivated by the fact that in the nuclear system the singlet and triplet scattering lengths are both large with respect to the range of the interaction. Accordingly we expect evidence of universal behavior in the three- and four-nucleon systems that can be observed from the study of correlations between observables. In particular we concentrate in the behavior of the first excited state of the three-nucleon system as the system moves away from the unitary limit. We also analyze the dependence on the range of the three-body force of some low-energy observables in the three- and four-nucleon systems.     

Four-nucleon system with Δ-isobar excitation

The four-nucleon bound state and scattering below three-body breakup threshold are described based on the realistic coupled-channel potential CD Bonn+Δ$\text{Bonn}+\mathrm{\Delta }$ which allows the excitation of a single nucleon to a Δ isobar. The Coulomb repulsion between protons is included. In the four-nucleon system the two-baryon coupled-channel potential yields effective two-, three- and four-nucleon forces, mediated by the Δ isobar and consistent with each other and with the underlying two-nucleon force. The effect of the four-nucleon force on the studied observables is much smaller than the effect of the three-nucleon force. The inclusion of the Δ isobar is unable to resolve the existing discrepancies with the experimental data.     

Analysis of the Effects of Three-nucleon Forces in A = 3, 4 Systems

It is not possible to reproduce both the three- and four-nucleon binding energies using the available two-nucleon potentials. This is one manifestation of the need to include a three-nucleon force in the corresponding Hamiltonian. In this paper we will analyze the capability of a three-nucleon force model to describe not only the aforementioned binding energies but also some N ? d low energy scattering observables.     

Quasifree processes and FEW-body systems

The progress achieved during the last two years in the understanding of quasifree processes in three- and four-nucleon systems and evidence for quasifree reaction mechanisms in more complex systems are presented. Some applications of quasifree processes are discussed.     

Testing Nucleon–nucleon Potentials in Three- and Four-nucleon Scattering Observables

We present a theoretical study of three- and four-nucleon continuum within the hyperspherical harmonics method, using a representative variety of realistic nucleon–nucleon potential models, i.e. one of phenomenological type, the Argonne v ₁₈ (AV18), one obtained within chiral effective field theory up to next-to-next-to-next-leading order, the Idaho N3LO (I-N3LO), and a “low-k” model derived from the CD-Bonn potential. In particular, the convergence pattern for the four-nucleon system is found to be problematic for the P-waves phase-shifts in the case of the AV18 potential at higher energies. An extrapolation procedure is presented and discussed. Finally, we present the theoretical results for p?d and p?³ scattering observables at two selected energies, and we compare these with the available experimental data. In particular, some spread in the unpolarized cross section and in some polarization observables has been observed using the three potential models, in particular for A =  4. Furthermore the well known discrepancy in the vector polarization observables remains for the three potential models.     

Isobar configurations in nuclei

A comprehensive review of the role of nucleon resonances in nuclear structure is given with emphasis on the two-, three-, and four-nucleon systems and nuclear matter.     

Selected Topics in Correlated Hyperspherical Harmonics

Correlated hyperspherical-harmonic basis functions are used to expand the three- and four-nucleon wave functions. Bound and scattering states are considered. Results for the binding energies of ³H, ³He, and ⁴He calculated using modern two- and three-nucleon forces are given and discussed. For scattering states, results for N-d differential cross section and vector analyzing powers are shown. The importance of the Coulomb and magnetic moment effects are discussed.     

Global-vector representation of the angular motion of few-particle systems II

The angular motion of a few-body system is described with global vectors which depend on the positions of the particles. The previous study using a single global vector is extended to make it possible to describe both natural and unnatural parity states. Numerical examples include three- and four-nucleon systems interacting via nucleon-nucleon potentials of AV8 type and a 3α system with a nonlocal αα potential. The results using the explicitly correlated Gaussian basis with the global vectors are shown to be in good agreement with those of other methods. A unique role of the unnatural parity component, caused by the tensor force, is clarified in the 0^? ₁ state of ⁴He. The two-particle correlation function is calculated in the coordinate and momentum spaces to show different characteristics of the interactions employed.     

A new cluster model interpretation of the anomalous lifetime of <Superscript>14</Superscript>C

A new cluster model solution to the long-standing nuclear structure problem of describing the anomalously long lifetime of ¹⁴C is presented. Related beta-decay data for ¹⁴O to states in ¹⁴N, gamma-decay data between low-lying positive parity states in ¹⁴N and the elastic and inelastic magnetic dipole electron scattering from ¹⁴N data are all shown to be very accurately described by the model. The shapes of the beta spectra for the A = 14 system are also well reproduced by the model. The model invokes four-nucleon tetrahedral symmetric spatial correlations arising from three- and four-nucleon interactions, which yields a high degree of SU(4) singlet structure for the clusters and a tetrahedral intrinsic shape for the doubly magic ¹⁶O ground state. The large quadrupole moment of the ¹⁴N ground state is obtained here for the first time and arises because of the almost 100% d-wave deuteron-like-hole cluster structure inherent in the model.     

Recent Progress in the Theory of Nuclear Forces

During the past two decades, it has been demonstrated that chiral effective field theory represents a powerful tool to deal with nuclear forces in a systematic and model-independent way. Two-, three-, and four-nucleon forces have been derived up to next-to-next-to-next-to-leading order (N³LO) and (partially) applied in nuclear few- and many-body systems—with, in general, a good deal of success. This may suggest that we are finally done with the nuclear force problem; but that would be too optimistic. There are still some pretty basic open issues that have been swept under rug and, finally, need our full attention, like the proper renormalization of the two-nucleon potential. Moreover, the order-by-order convergence of the many-body force contributions is at best obscure at this time.     

Transfer reactions by heavy ions and finite-range DWBA calculations

Experimental data of one-, three- and four-nucleon transfer reactions induced by the heavy-ion projectiles ¹⁶O and ¹⁹F on the targets ¹¹B and ¹²C are analyzed within the framework of finite-range DWBA. In many-nucleon transfer reactions, the cross section is composed of the coherent sum of amplitudes corresponding to the transfer of clusters with different intrinsic states. The spectroscopic amplitudes are calculated using the results of the intermediate-coupling shell model. The calculated cross sections can reproduce the experiments fairly well in most cases. The method is compared with other approximations from the viewpoint of the selection rules for the angular-momentum transfer.     

Alpha-like four nucleon correlations in superfluid phases of atomic nuclei

α-like four-nucleon correlations are included in the structure of superfluid ground and low-lying excited states of atomic nuclei within a BCS-like approach. New metastable superfluid and normal states are predicted. These states could be associated with some of the recently discovered I^π = 0⁺ states in different regions of atomic nuclei. A new type of elementary excitations may be constructed on these metastable states in the same way as those constructed on the BCS superfluid ground states. The region of superfluid cold nuclei is enlarged due to the fact that the neutron and proton superfluidity can mutually be induced via the α-like four-nucleon ineractions. This type of correlations lead to a further enhancement of the probabilities of the favoured α-clusterization processes (such as α-decay or α-transfer reactions), two-nucleon transfer reactions and other clusterization processes such as e.g. the heavy cluster decay.     

Inequalities for light nuclei in the Wigner symmetry limit

Using effective field theory we derive inequalities for light nuclei in the Wigner symmetry limit. This is the limit where isospin and spin degrees of freedom can be interchanged. We prove that the energy of any three-nucleon state is bounded below by the average energy of the lowest two-nucleon and four-nucleon states. We show how this is modified by lowest-order terms breaking Wigner symmetry and prove general energy convexity results for SU(N). We also discuss the inclusion of Wigner-symmetric three- and four-nucleon force terms.     

Charge independence breaking and charge symmetry breaking in the nucleon–nucleon interaction from effective field theory

We discuss charge symmetry and charge independence breaking in an effective field theory approach for few-nucleon systems. We systematically introduce strong isospin-violating and electromagnetic operators in the theory. The charge dependence observed in the nucleon–nucleon scattering lengths is due to one-pion exchange and one electromagnetic four-nucleon contact term. This gives a parameter free expression for the charge dependence of the corresponding effective ranges, which is in agreement with the rather small and uncertain empirical determinations. We also compare the low energy phase shifts of the nn and the np system. We present a classification scheme for corrections to the leading order results and show that power counting explains previously made phenomenological observations.     

A new many-particle variational method

The results of calculation of the properties of three- and four-particle systems within the framework of the recently suggested stochastic variational method (SVM) are presented. The 3N, 4N and 3α model systems with two-particle S-wave central forces have been investigated. The results of all calculations are compared with similar results of other workers, and a higher efficiency of the method proposed as compared with other methods is demonstrated.     

A new projected basis in the theory of five-dimensional quasi-spin

The procedure for constructing the non-canonical basis corresponding to the reduction SO(5)?SU₂(T)×U₁ valid for the arbitrary irreducible representations of the group SO(5) is developed. The proof of the completeness of this basis is given and the matrix elements of the generators are calculated in this basis. The matrix of the operator B introduced by Flowers and Szpikovsky, and specifying the effective number of alpha-like four-nucleon cluster in a nucleus is obtained and some of its general properties are discussed.