Measuring Nuclear Shape In ³⁰Si Using Coulomb Excitation

The Coulomb excitation experimental method is a very effective means of studying nuclear structure.In this experiment,the Coulomb excitation method was used to investigate the nuclear structure by measuring the spectroscopic quadrupole moment Qs of the first excited state(2235 keV)of 30Si.The experiment was conducted at the Institute of Modern Physics,Lanzhou,using a 30Si beam with an energy of 129.4 MeV to bombard a stationary 196Pt target with a thickness of 1.31 mg/cm2.The beam energy was calculated to ensure that the closest distance of approach between the two nuclei was greater than 6.5 fm,effectively avoiding nuclear force interactions and satisfying the safety Coulomb excitation conditions.The experiment used an S3 double-sided silicon ring detector,placed 0.86 cm downstream of the target to detect scattered particles.The detector was divided into 24 rings and 32 sectors,enabling effective localization of the flight path of scattered particles.A high-purity germanium detector array was also used to detect the de-excitation γ-rays emitted by "Si scattered from the target.Particle-gamma coincidence techniques were used to correct for Doppler shift of the de-excitation γ-rays emitted by the high-speed 30Si and to extract the γ-ray yield corresponding to different scattering angles.The γ-ray yield associated with scattering angle is related to the matrix element of the nucleus-Therefore,we used the GOSIA program to analyze the distribution ofγ-ray yield as a function of scattering angle,and derived the value of the diagonal matrix element of the first 2+excited state of 30Si as-0.36 eb.The quadrupole moment Qs(2+)of the first 2+ excited state of 30Si can be obtained by simple calculation from the diagonal matrix element,and its value is-0.273 eb.This value indicates that the nucleus of 30Si has a prolate shape.The experimental results are consistent with the predictions of the rotational model and the 1979 measurement results of Fewell on the shape of the nucleus of 30Si,but the degree of deformation is greater than predicted.