Application of a molecular model to band-head states in ⁹B

Abstract Clarification of the apparent double 1/2 + analogue states in 9 B through the R -matrix formalism has allowed experimentally observed states to be fitted into rotational bands through a least squares fitting method. From such experimental fits, the moment of inertia for the three rotational bands in 9 B, K π = 3/2 − , 1/2 + and 1/2 − , in addition to Coriolis decoupling parameters, a , for the 1/2 + and 1/2 − bands, are extracted. Values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>ℏ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mi>ℑ</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">A</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> = 0.494 ± 0.002 MeV, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">A</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> = 0.378 ± 0.004 MeV and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> = 2.27 ± 0.04, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">A</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> = 0.688 ± 0.013 MeV and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> = 0.186 ± 0.041 are obtained. Due to a lack of theoretical predictions for 9 B, these structural parameters are compared to theoretically obtained values for analogue bands in 9 Be and show remarkable agreement. Using the linear combination of nuclear orbital approach, the structures of each band-head state are examined in order to reproduce the observed properties of the respective rotational bands. It is found that without modification to the underlying 8 Be substructure, these orbitals struggle to correctly generate the expected moment of inertia.