Coulomb energy differences in ⁹ B using a molecular model

Abstract Through the application of a molecular model to band-head states in 9 B, a prediction of the Coulomb energy difference relative to the 1/2 + analogue state in 9 Be is calculated. Under such treatment, a positive shift in energy of 0.605 MeV is found to emerge from molecular structures defined by replication of experimental rotational-band parameters. Given the relationship between the spatial arrangement of clusters within the nucleus and the obtained Coulomb energy, it is also possible to examine nuclear structures using known Thomas–Ehrman shifts. Molecular structures built using the α – α separation, 2 β , required to give Thomas–Ehrman shifts for both a 1.84 and 0.8 MeV candidate of the 9 B(1/2 + ) analogue state ( β = 1.89 fm and β = 3.18 fm respectively) are used to calculate state inertial parameters ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">A</mml:mi> </mml:math> ). From these structures, it is found that a 1.84 MeV state ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">A</mml:mi> </mml:math> = 0.407 MeV) agrees with the experimental K = 1/2 + rotational band inertial parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">A</mml:mi> </mml:math> = 0.41 ± 0.01 MeV) and a 0.8 MeV state does not ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">A</mml:mi> </mml:math> = 0.191 MeV). Thus, due to the large α – α spacing required to lower the Coulomb energy relative to 9 Be, the existence of a 0.8 MeV 9 B(1/2 + ) analogue state is highly unlikely. Indeed, excitation energies less than ≈1.25 MeV for a 1/2 + state, corresponding to a normal Thomas–Ehrman shift, can also be ruled out.