Cluster structure of a low-energy resonance in tetraneutron
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NUCLEI Theory
Cluster Structure of a Low-Energy Resonance in Tetraneutron* Yu. A. Lashko** and G. F. Filippov*** Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine Received April 24, 2007
Abstract—We theoretically investigate the possibility for a tetraneutron to exist as a low-energy resonance state. We explore a microscopic model based on the assumption that the tetraneutron can be treated as a compound system, where 3 n + n and 2 n + 2 n coupled cluster configurations coexist. The influence of the Pauli principle on the kinetic energy of the relative motion of the neutron clusters is shown to result in their attraction. The strength of such attraction is high enough to ensure the existence of a low-energy resonance in the tetraneutron, provided that the oscillator length is large enough. PACS numbers: 21.60.Gx DOI: 10.1134/S1063778808020014
1. INTRODUCTION The first claim of experimental observation of the nuclear stable tetraneutron was made in [1]. Since then, all other experimental attempts to find either a bound or a resonance state in the system of four neutrons have not met with success. However, in a recently reported experiment with the breakup of 14 Be [2], six events consistent with the formation of a bound tetraneutron were revealed. Unfortunately, several other experiments [3–5] undertaken to verify these results failed to prove or refute completely the existence of the tetraneutron because of poor statistics. An overall conclusion of a number of theoretical papers on this subject [6– 9] is that it does not seem possible to change modern nuclear Hamiltonians to bind a tetraneutron without destroying many other successful predictions of those Hamiltonians. For instance, calculations within the hyperspherical-functions method (HSFM) [7] suggest that a very strong phenomenological four-nucleon force is needed in order to bind the tetraneutron. And yet neither theoretical nor experimental results exclude the possible existence of a tetraneutron as a low-energy resonance (see [6, 9, 10]). There are only few cases of theoretical treatment of the resonant tetraneutron. In [9], the continuum states of the 4 n system were studied in the framework of the approach which combines concepts of the HSFM and the resonating-group method (RGM). ∗
The text was submitted by the authors in English. E-mail: [email protected] *** E-mail: [email protected] **
Along with the lowest order hyperharmonic, the authors of [9] invoked the hyperharmonics with hypermomenta K = Kmin + 2 and K = Kmin + 4, which reproduce 2 n + 2 n clustering of the tetraneutron. The analysis of the energy behavior of the eigenphases led those authors to the conclusion that 4 n has a resonance state at an energy of about 1–3 MeV. But a clear indication of such a resonance was obtained only for the Volkov effective N N potential, which is known to be inappropriate for studying multineutron systems as it binds a dineutron. The most systematic study of four-neutron resonances was performed in [8], where configuration space Faddeev–Yakubovsky
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