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Register a new userFew-body universality in the deuteron-alpha system
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We treat ${}^6$Li as an effective three-body ($n$-$p$-$alpha$) system and compute the $d$-$alpha$ $S-$wave scattering length and three-body separation energy of ${}^6$Li for a wide variety of nucleon-nucleon and $alpha$-nucleon potentials which have the same (or nearly the same) phase shifts. The Coulomb interaction in the $p$-$alpha$ subsystem is omitted. The results of all calculations lie on a one-parameter curve in the plane defined by the $d$-$alpha$ $S-$wave scattering length and the amount by which ${}^6$Li is bound with respect to the $n$-$p$-$alpha$ threshold. We argue that these aspects of the $n$-$p$-$alpha$ system can be understood using few-body universality and that ${}^6$Li can thus usefully be thought of as a two-nucleon halo nucleus.
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Using realistic wave functions, the proton-neutron and proton-proton momentum distributions in $^3He$ and $^4He$ are calculated as a function of the relative, $k_{rel}$, and center of mass, $K_{CM}$, momenta, and the angle between them. For large values of ${k}_{rel}gtrsim 2,,fm^{-1}$ and small values of ${K}_{CM} lesssim 1.0,,fm^{-1}$, both distributions are angle independent and decrease with increasing $K_{CM}$, with the $pn$ distribution factorizing into the deuteron momentum distribution times a rapidly decreasing function of $K_{CM}$, in agreement with the two-nucleon (2N) short range correlation (SRC) picture. When $K_{CM}$ and $k_{rel}$ are both large, the distributions exhibit a strong angle dependence, which is evidence of three-nucleon (3N) SRC. The predicted center-of-mass and angular dependence of 2N and 3N SRC should be observable in two-nucleon knock-out processes $A(e,epN)X$.
Hadronic composite states are introduced as few-body systems in hadron physics. The $Lambda(1405)$ resonance is a good example of the hadronic few-body systems. It has turned out that $Lambda(1405)$ can be described by hadronic dynamics in a modern technology which incorporates coupled channel unitarity framework and chiral dynamics. The idea of the hadronic $bar KN$ composite state of $Lambda(1405)$ is extended to kaonic few-body states. It is concluded that, due to the fact that $K$ and $N$ have similar interaction nature in s-wave $bar K$ couplings, there are few-body quasibound states with kaons systematically just below the break-up thresholds, like $bar KNN$, $bar KKN$ and $bar KKK$, as well as $Lambda(1405)$ as a $bar KN$ quasibound state and $f_{0}(980)$ and $a_{0}(980)$ as $bar KK$.
A comparative analysis of the astrophysical S factor and the reaction rate for the direct $ alpha(d,gamma)^{6}{rm Li}$ capture reaction, and the primordial abundance of the $^6$Li element, resulting from two-body, three-body and combined cluster models is presented. It is shown that the two-body model, based on the exact-mass prescription, can not correctly describe the dependence of the isospin-forbidden E1 S factor on energy and does not reproduce the temperature dependence of the reaction rate from the direct LUNA data. It is demonstrated that the isospin-forbidden E1 astrophysical S factor is very sensitive to the orthogonalization procedure of Pauli-forbidden states within the three-body model. On the other hand, the E2 S factor does not depend on the orthogonalization method. This insures that the orthogonolizing pseudopotentials method yields a very good description of the LUNA collaborations low-energy direct data. At the same time, the SUSY transformation significantly underestimates the data from the LUNA collaboration. On the other hand, the energy dependence of the E1 S factor are the same in both methods. The best description of the LUNA data for the astrophysical S factor and the reaction rates is obtained within the combined E1(three-body OPP)+E2(two-body) model. It yields a value of $(0.72 pm 0.01) times 10^{-14}$ for the $^6$Li/H primordial abundance ratio, consistent with the estimation $(0.80 pm 0.18) times 10^{-14}$ of the LUNA collaboration. For the $^6{rm Li}/^7{rm Li}$ abundance ratio an estimation $(1.40pm 0.12)times 10^{-5}$ is obtained in good agreement with the Standard Model prediction.
A convenient framework for dealing with hadron structure and hadronic physics in the few-GeV energy range is relativistic quantum mechanics. Unlike relativistic quantum field theory, one deals with a fixed, or at least restricted number of degrees of freedom while maintaining relativistic invariance. For systems of interacting particles this is achieved by means of the, so called, Bakamjian-Thomas construction, which is a systematic procedure for implementing interaction terms in the generators of the Poincare group such that their algebra is preserved. Doing relativistic quantum mechanics in this way one, however, faces a problem connected with the physical requirement of cluster separability as soon as one has more than two interacting particles. Cluster separability, or sometimes also termed macroscopic causality, is the property that if a system is subdivided into subsystems which are then separated by a sufficiently large spacelike distance, these subsystems should behave independently. In the present contribution we discuss the problem of cluster separability and sketch the procedure to resolve it.
{bf Background} Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. {bf Purpose} Faddeev-AGS equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that observables calculated based on separable interactions agree exactly with those based on nonseparable forces. {bf Methods} Momentum space AGS equations are solved with separable and nonseparable forces as coupled integral equations. {bf Results} Deuteron-alpha scattering is calculated via momentum space AGS equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-$^4$He force, for which the Pauli-forbidden S-wave bound state is projected out. Elastic as well as breakup observables are calculated and compared to results in which the interactions in the two-body sub-systems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. {bf Conclusions} We find that the calculations based on the separable representation of the interactions and the original interactions give results that are in excellent agreement. Specifically, integrated cross sections and angular distributions for elastic scattering agree within $approx$ 1%, which is well below typical experimental errors. In addition, the five-fold differential cross sections corresponding to breakup of the deuteron agree extremely well.
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