Modern Nuclear Force Predictions for theαParticle

Abstract

We present new calculations of the α-particle which are based on the most modern nucleon-nucleon interactions alone and combined with the Tucson-Melbourne or the Urbana IX three-nucleon interaction. Results for the binding energies and some properties of the wave function are given. On that phenomenological level little room is left for the action of a possible four-nucleon force.PACS numbers: 21.10.-h, 21.45.+v, 27.10.+h,21.30.-x Few nucleon bound states have received increasing attention in recent years. The possibility of solving increasingly complex systems allows to probe the underlying dynamics directly (for a detailed review, see [1] [8]. The 4N system is an important test ground for both, the NN and the 3N nuclear interactions, because of its strong binding. In this article we want to address the question whether at least the ground state energy of the α-particle can be described by the most modern nuclear Hamiltonians.In recent years NN forces have been tuned very well to the rich NN data base, which led to a new generation of so called realistic NN forces: Nijm I, II [9], AV18 [10] and CD-Bonn [11]. While Nijm II and AV18 are purely local, Nijm I has a weak nonlocality in form of a ∇ 2 -dependence and CD-Bonn is quite nonlocal keeping the underlying Dirac structure of the one-boson-exchange without p/m expansions. All potentials describe the NN data base with a χ 2 /data very close to 1. But they also have a large phenomenological character with a typical number of 40 fit parameters. The AV18 and CD-Bonn forces distinguish nn, pp and np interactions and thus include charge symmetry(CSB) and charge-independence(CIB) breaking. The interaction AV18 has in addition a whole set of electromagnetic corrections built in.It is well known that the two 3N bound states, 3 H and 3 He, are theoretically underbound using only NN forces [12][13][14][15]. We compare our latest theoretical results based on fully converged Faddeev calculations to the experimental binding energies in Table I. The two nonlocal potentials lead to less underbinding than the local ones. The 3N calculations take the full CSB and CIB of the NN force into account including the isospin T = 3/2 admixtures. In case of 3 He and 4 He the Coulomb interaction is included and, in addition, we use also the electromagnetic corrections in case of AV18. Because of an implementation error the results for Nijm I, II changed with respect to [13]. Table I includes also the strongly model dependent kinetic energies which are correlated to the NN correlations. The local potentials have a somewhat harder core [13] leading to a higher kinetic energy.There are two additional dynamical ingredients, which should cure that underbinding, relativistic effects and three-nucleon forces (3NF). Though one can in principle always find an unitary (but very complex) transformation to a Hamiltonian without any 3NF [16], we keep the given 2N interactions for practical reasons and because of their generally accepted physical origin. In relation to those forces one or both of th...

Nuclear structure in the framework of the Unitary Correlation Operator Method

“…Exact benchmark calculations for the three-and four-body system [8,9,10,11,12] were very helpful in this respect. They also showed that three-body forces are needed, though different ones for different phase-shift equivalent two-body potentials.…”

“…Matrix elements of one-, two-, or three-body operators in A-body space can be calculated easily using an occupation number representation. Modern computers and numerical techniques can tackle A-body Hilbert spaces dimensions up to about 10 10 . These numbers are impressive but by far not sufficient.…”

Current Status of Nuclear Physics Research

“…For example, a particular interaction coined as V low−k is shown to parameterize a high-order chiral effective field theory two-nucleon force. In the theory, a cutoff dependence can be used as a tool to assess the error in the truncation of nuclear forces to two-nucleon interactions and introduce low-momentum three-nucleon forces [71][72][73][74][75][76][77][78][79].…”

Three-Nucleon Force in the 4He Scattering System

“…In order to avoid fake effects the relative thresholds in 4 He should be reproduced well, therefore we used also a 35-dimensional modelspace, called large,by allowing additional configurations with two orbital angular momenta on the two Jacoby coordinates yielding -6.69 MeV binding energy. This must be compared to −6.92MeV known from Faddeev calculations [18]. For the deuteron we use the structure given in [2], yielding a binding energy of -1.921 MeV, which could be easily improved.…”