Half-life measurements of highly charged radioisotopes by nuclear recoil in a Penning trap

We present a unique method for measuring the half-life of highly charged radioisotopes by nondestructive nuclear recoil detection in a Penning ion trap. A specific emphasis is placed on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mmultiscripts><a:mi>Be</a:mi><a:none/><a:mrow><a:mn>3</a:mn><a:mo>+</a:mo></a:mrow><a:mprescripts/><a:none/><a:mn>7</a:mn></a:mmultiscripts></a:math>, which plays a crucial role in stellar evolution and the production of solar neutrinos. The determination of the half-life is necessary to constrain the free electron capture rate in the solar environment, but is difficult to measure by existing techniques. Simulations of the sympathetic cooling of the recoiled daughter nuclei (<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mmultiscripts><b:mi>Li</b:mi><b:none/><b:mrow><b:mn>3</b:mn><b:mo>+</b:mo></b:mrow><b:mprescripts/><b:none/><b:mn>7</b:mn></b:mmultiscripts></b:math>) with the trapped cloud of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mmultiscripts><c:mi>Be</c:mi><c:none/><c:mrow><c:mn>3</c:mn><c:mo>+</c:mo></c:mrow><c:mprescripts/><c:none/><c:mn>7</c:mn></c:mmultiscripts></c:math> demonstrate a decay detection efficiency of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>99.5</d:mn><d:mo>%</d:mo></d:mrow></d:math>. A statistical analysis of half-life measurements on ensembles containing hundreds of ions shows that a final statistical uncertainty of less than <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>5</e:mn><e:mo>%</e:mo></e:mrow></e:math> is achieved with only 500 measured decays. By coherent control of hyperfine populations in trapped ions, the fidelity of the technique we describe enables the direct measurement and manipulation of state-dependent decay branching ratios for the first time.