How the Pauli principle governs the decay of three-cluster systems

Filippov

2012

Phys. Atom. Nuclei

For the example of the 5 H = 3 H + n + n nucleus, the effect of the Pauli exclusion principle on the asymptotic behavior of wave functions for the continuous spectrum of three-cluster systems is studied within a microscopic approach. It is shown that, in the asymptotic limit, the Schr¨odinger equation for the wave function that describes the relative motion of tritium and two neutrons reduces to the multichannel problem of valence-neutron scattering on the 4 H subsystem. The single-channel approximation within which the phase shift for neutron scattering on the 4 H subsystem occurring in the lowest energy state is the only feature that characterizes the continuous spectrum of the 5 H nucleus is proposed and implemented.

Section: Allowed States Of the Systemmentioning

confidence: 66%

Section: Resultsmentioning

confidence: 99%

Section: Allowed States Of the Systemmentioning

confidence: 94%

Section: Allowed States Of the Systemmentioning

confidence: 98%

“…In [4], we have shown that, in the limiting case of ν k, it is reasonable to go over from the asymptotic functions of the SU (3) basis,…”

Section: Allowed States Of the Systemmentioning

confidence: 99%

See 3 more Smart Citations

Continuous spectrum of three-cluster systems

Filippov

2012

Phys. Atom. Nuclei

How the antisymmetrization affects a cluster–cluster interaction: Two-cluster systems

Vasilevsky

2020

Annals of Physics

We study effects of the antisymmetrization on the potential energy of twocluster systems. The object of the investigation is the lightest nuclei of p-shell with a dominant alpha-cluster channel. For this aim we construct matrix elements of two-cluster potential energy between cluster oscillator functions with and without full antisymmetrization. Eigenvalues and eigenfunctions of the potential energy matrix are studied in detail. Eigenfunctions of the potential energy operator are presented in oscillator, coordinate and momentum spaces. We demonstrate that the Pauli principle affects more strongly the eigenfunctions than the eigenvalues of the matrix and leads to the formation of resonance and trapped states.

The role of the Pauli principle in three-cluster systems composed of identical clusters

Filippov

2009

Nuclear Physics A

Self Cite

Within the microscopic model based on the algebraic version of the resonating group method the role of the Pauli principle in the formation of continuum wave function of nuclear systems composed of three identical s-clusters has been investigated. Emphasis is placed upon the study of the exchange effects contained in the genuine three-cluster norm kernel. Three-fermion, three-boson, three-dineutron (3d ′ ) and 3α systems are considered in detail. Simple analytical method of constructing the norm kernel for 3α system is suggested. The Pauli-allowed basis functions for the 3α and 3d ′ systems are given in an explicit form and asymptotic behavior of these functions is established. Complete classification of the eigenfunctions and the eigenvalues of the 12 C norm kernel by the 8 Be= α+α eigenvalues has been given for the first time. Spectrum of the 12 C norm kernel is compared to that of the 5 H system.The question of the role of the Pauli principle in three-cluster systems goes back a long way in history. The 12 C nucleus has been established to exhibit three-alpha-cluster structure forty years ago. Since then many microscopic, macroscopic and semi-microscopic cluster models have been applied to analyze the structure of the ground and excited states of this nucleus. In particular, microscopic 3α calculation was performed within the resonating group method (RGM) by Kamimura [1] and within the generator coordinate method (GCM) by Uegaki [2]. Both calculations give reasonable results for the ground state of the 12 C and some excited states. However, wave functions provided by these models are very complicated and heavy to handle. Furthermore, although RGM ensures correct account of nucleon exchange between different clusters, an antisymmetry requirement on the total wave function can be violated by the improper truncation of model space. The measure of this violation is lacking. For example, in Ref.[1] the RGM calculation was performed with truncation to a space where the angular momentum l of α − α relative wave function was fixed to be equal to zero. At the same time, even the lowest Pauli-allowed state of the 12 C represents the mixture of l = 0, 2 and 4. This raises the question as to whether such truncation is consistent with the requirements of ⋆ This work was partly supported by the Program the Pauli principle. As for the GCM, seven-dimensional numerical integrals are involved in the calculation and the integration over generator coordinate is replaced into summation over some mesh-points. However, the generator coordinate is chosen to be real and its domain is not well-defined, while only complex generator parameters ensure the existence of inverse transition from the generator parameter space to the coordinate space [3].A number of macroscopic models were also applied to studying the 12 C nucleus (see, for example, Refs. [4,5]). Within such models, clusters are considered to be structureless particles interacting via local potentials, which reproduce experimental α − α phase shifts. But the antisymmetrization ...