AUTHOR=Nannini Alessia , Marcucci Laura E. 

TITLE=Non-symmetrized Hyperspherical Harmonics Method for Non-equal Mass Three-Body Systems

JOURNAL=Frontiers in Physics

VOLUME=6

YEAR=2018

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2018.00122

DOI=10.3389/fphy.2018.00122

ISSN=2296-424X

ABSTRACT=<p>The non-symmetrized hyperspherical harmonics method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle, is reviewed and applied to the <sup>3</sup>H, <sup>3</sup>He nuclei, and <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mtext>H</mml:mtext><mml:mprescripts /><mml:mo>Λ</mml:mo><mml:mn>3</mml:mn></mml:mmultiscripts></mml:mrow></mml:math></inline-formula> hyper-nucleus, seen respectively as <italic>nnp</italic>, <italic>ppn</italic>, and <italic>NNΛ</italic> three-body systems. The convergence of the method is first tested in order to estimate its accuracy. Then, the difference of binding energy between <sup>3</sup>H and <sup>3</sup>He due to the difference of the proton and the neutron masses is studied using several central spin-independent and spin-dependent potentials. Finally, the <inline-formula><mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mtext>H</mml:mtext><mml:mprescripts /><mml:mo>Λ</mml:mo><mml:mn>3</mml:mn></mml:mmultiscripts></mml:mrow></mml:math></inline-formula> hypernucleus binding energy is calculated using different <italic>NN</italic> and Λ<italic>N</italic> potential models. The results have been compared with those present in the literature, finding a very nice agreement.</p>