Few-Body Systems

Chúng tôi báo cáo về bốn trạng thái Σ và ba trạng thái Λ trong vùng năng lượng 1500–1800 MeV, như là những cộng hưởng S-wave (1/2)+ của hai meson—một baryon, được tìm thấy bằng cách giải phương trình Faddeev trong cách tiếp cận kênh liên kết, có thể tương ứng với các cộng hưởng baryon thấp S = −1, JP = 1/2+ hiện có. Mặt khác, chúng tôi cũng báo cáo về một trạng thái N* mới, ẩn chứa tính lạ, chủ yếu được cấu thành từ K̄ N, với khối lượng khoảng 1920 MeV, mà chúng tôi nghĩ có thể chịu trách nhiệm cho đỉnh tìm thấy trong quá trình γp → K+ Λ xung quanh năng lượng này. Cuối cùng, chúng tôi đề cập đến một chủ đề rất mới trong đó chúng tôi thể hiện cách mà các hệ thống chứa vài meson ρ có thể được sản xuất, với các spin của chúng được căn chỉnh lên tới J = 6, và cách mà những trạng thái này được tìm thấy lý thuyết có thể liên hệ với nhiều meson đã biết với các spin J = 2, 3, 4, 5, 6.

The first microscopic calculation of inelastic reactions on nuclei with mass number A = 6 is presented. In particular, we consider the total photoabsorption cross section of 6He and 6Li. It is shown that the halo nucleus 6He exhibits two types of dipole resonances, the normal giant dipole resonance and a low-energy soft dipole resonance associated with the excitation of the outer neutrons. Comparing our results with available experimental data we note the role of P-wave interaction. Calculations are performed using the Lorentz integral transform (LIT) method and the effective interaction in the hyperspherical harmonics formalism (EIHH).

Based on the investigation of the asymptotic behaviour of the polarization loop function for scalar charged particles in an external gauge field we determine the interaction Hamiltonian including the nonperturbative corrections of the relativistic character of motion and the large coupling constant. The mass spectrum of the bound state is analytically derived. The mechanism for arising of the constituent mass of the bound-state forming particles is explained. The change of the bound-state mass and of the constituent mass of particles is analyzed by varying the coupling constant. The mass spectrum of the two-gluon glueball is calculated taking into account spin-orbit and spin-spin interactions.

Tôi trình bày một phép tính Lattice-QCD trực tiếp đầu tiên về sự phụ thuộc Bjorken-x của các hàm cấu trúc hadrôn. Bằng cách lấy một hadrôn có mức gia tốc động lượng lớn, chúng tôi có thể kết nối các đại lượng mặt phẳng ánh sáng với các phần tử ma trận phi địa phương nhưng không thay đổi theo thời gian trong Lattice-QCD. Vì động lượng lớn nhất có thể đạt được là có hạn, chúng tôi điều chỉnh một cách hệ thống cho sự phụ thuộc động lượng hàng đầu đáng kể. Trong bài nói chuyện này, tôi trình bày một nghiên cứu khám phá về mật độ quark nucleon, phân bố helicity và transversity.

Scattering of two spin- $${\frac{1}{2}}$$ particles is formulated in a three-dimensional approach based on a simple three-dimensional momentum-spin basis. Both cases of identical and nonidentical particles are considered. The azimuthal behaviour of the potential and of the T-matrix elements leads to a set of integral equations for the T-matrix elements in two variables, i.e. the momentum magnitude and the scattering angle. Observables can be directly calculated from these T-matrix elements. Some symmetry relations for the T-matrix elements reduce the number of equations to be solved.

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this progress report, we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.

The LIT approach is tested for the calculation of astrophysical S-factors. As an example the S-factor of the reaction $$^2\hbox {H}(p,\gamma )^3\hbox {He}$$ is considered. It is discussed that a sufficiently high density of LIT states at low energies is necessary for a precise determination of S-factors. In particular it is shown that the hyperspherical basis is not very well suited for such a calculation and that a different basis system is much more advantageous. A comparison of LIT results with calculations, where continuum wave functions are explicitly used, shows that the LIT approach leads to reliable results. It is also shown how an error estimate of the LIT inversion can be obtained.

Different approaches to solve the spinor–spinor Bethe–Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve numerically the resulting system of equations with realistic interaction kernels. Other representations can be obtained by performing proper unitary transformations. A generalization of the iteration method for finding the energy spectrum of the BS equation is discussed and examples of concrete calculations are presented. Comparison of relativistic calculations with available experimental data and with corresponding non relativistic results together with an analysis of the role of Lorentz boost effects and relativistic corrections are presented. A novel method related to the use of hyperspherical harmonics is considered for a representation of the vertex functions suitable for numerical calculations.

Recent studies of clustering in light nuclei with an initial energy above 1 A GeV in a nuclear track emulsion are overviewed. The results of investigations of the relativistic 9Be nuclei fragmentation in emulsion, which entails the production of α particles, are presented. It is shown that most precise angular measurements provided by this technique play a crucial role in the restoration of the excitation spectrum of the α particle system. In peripheral interactions 9Be → 2α nuclei are dissociated practically totally through the 0+ and 2+ states of the 8Be nucleus.

This is the second in a pair of articles that classify the configuration space and kinematic symmetry groups for N identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies. The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in terms of the one-particle observables. Symmetry also determines the degree to which the algebraic expressions for energy level shifts by weak interactions or nearly–unitary interactions are universal, i.e. independent of trap shape and details of the interaction. Identical fermions and bosons with and without spin are considered. This article analyzes the symmetries of N particles in asymmetric, symmetric, and harmonic traps; the prequel article treats the one, two and three particle cases.