| Summary: | The shake-off processes and charge-state fractions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> were studied following the beta decay of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>He in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><msup><mi>s</mi><mn>2</mn></msup><msup><mspace width="0.277778em"></mspace><mn>1</mn></msup><msub><mi>S</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>s</mi><mn>2</mn><mi>s</mi><msup><mspace width="0.277778em"></mspace><mn>1</mn></msup><msub><mi>S</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>s</mi><mn>2</mn><mi>s</mi><msup><mspace width="0.277778em"></mspace><mn>3</mn></msup><msub><mi>S</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> initial states. The sudden approximation was used, together with fully correlated Hylleraas wave functions and pseudostates. A projection operator method was introduced to separate the charge-state fractions in the positive energy region of overlapping continua. The results show that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></semantics></math></inline-formula> (single-ionisation) remains dominant, even in the energy range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, where the formation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> (double-ionisation) is energetically allowed. The results reduce disagreements with the experiment for the fraction of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> by nearly an order of magnitude, but substantial disagreements remain that are inconsistent with the sudden approximation widely used in other similar work.
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