Microscopic Calculation of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts><mml:mo stretchy="false">(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mmultiscripts><mml:mi>Be</mml:mi><mml:mprescripts/><mml:none/><mml:mn>7</mml:mn></mml:mmultiscripts></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="bold">H</mml:mi><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts><mml:mo stretchy="false">(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts/><mml:none/><mml:mn>7</mml:mn></mml:mmultiscripts></mml:math>Capture Cross Sections Using Realistic Interactions

The radiative capture cross sections for the $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ and $^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Li}$ reactions are calculated in the fully microscopic fermionic molecular dynamics approach using a realistic effective interaction that reproduces the nucleon-nucleon scattering data. At large distances bound and scattering states are described by antisymmetrized products of $^{4}\mathrm{He}$ and $^{3}\mathrm{He}/^{3}\mathrm{H}$ ground states. At short distances the many-body Hilbert space is extended with additional many-body wave functions needed to represent polarized clusters and shell-model-like configurations. Properties of the bound states are described well, as are the scattering phase shifts. The calculated $S$ factor for the $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ reaction agrees very well with recent experimental data in both absolute normalization and energy dependence. In the case of the $^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Li}$ reaction the calculated $S$ factor is larger than available experimental data by about 15%.

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