Effective two-body model for spectra of clusters of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">H</mml:mi><mml:mrow/></mml:mrow><mml:mprescripts/><mml:none/><mml:mn>2</mml:mn></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">H</mml:mi><mml:mrow/></mml:mrow><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>4</mml:mn></mml:mmultiscripts></mml:math> with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>4</mml:mn></mml:mmultiscripts></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">H</mml:mi><mml:mrow/></mml:mrow><mml:mprescripts/><mml:none/><mml:mn>2</mml:mn></mml:mmultiscripts><mml:mtext>−</mml:mtext><mml:mmultiscripts><mml:mi mathvariant="normal">He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>4</mml:mn></mml:mmultiscripts></mml:mrow></mml:math> scattering
Abstract
Four light-mass nuclei are considered by an effective two-body clusterization method: $^{7}\mathrm{Li}$ as $^{3}\mathrm{H}+^{4}\mathrm{He},^{7}\mathrm{Be}$ as $^{3}\mathrm{He}+^{4}\mathrm{He},^{8}\mathrm{Be}$ as $^{4}\mathrm{He}+^{4}\mathrm{He}$, and $^{6}\mathrm{Li}$ as $^{2}\mathrm{H}+^{4}\mathrm{He}$. The low-energy spectra of the first three are determined from single-channel Lippmann-Schwinger equations. For the last, two uncoupled sets of equations are considered: those involving the $\underset{1}{^{3}\mathrm{S}}$ and those of the posited ${}^{1}{S}_{0}$ states of $^{2}\mathrm{H}$. Low-energy elastic scattering cross sections are calculated from the same $^{2}\mathrm{H}+^{4}\mathrm{He}$ Hamiltonian, for many angles and energies for which data are available. While some of these systems may be more fully described by many-body theories, this work establishes that a large amount of data may be explained by these two-body clusterizations.
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