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Register a new userShape of 13C studied by the real-time evolution method
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Background : Recently, Bijker et al. [Phys. Rev. Lett. 122, 162501 (2019)] explained the rotation-vibration spectrum of 13C by assuming triangular nuclear shape with D3h symmetry. Purpose : The purpose of this work is to test the shape and symmetry of 13C based on a microscopic nuclear model without assumption of nuclear shape. Method : We have applied the real-time evolution method to 13C. By using the equation-of-motion of clusters, the model describes the 3alpha+n system without any assumption of symmetry. Results : REM described the low-lying states more accurately than the previous cluster model studies. The analysis of the wave functions showed that the ground band has approximate triangular symmetry, while the excited bands deviate from it. Conclusion : This work confirmed that the ground band has the intrinsic structure with the triangular arrangement of three alpha particles.
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A new theoretical method is proposed to describe the ground and excited cluster states of atomic nuclei. The method utilizes the equation-of-motion of the Gaussian wave packets to generate the basis wave functions having various cluster configurations. The generated basis wave functions are superposed to diagonalize the Hamiltonian. In other words, this method uses the real time as the generator coordinate. The application to the $3alpha$ system as a benchmark shows that the new method works efficiently and yields the result consistent with or better than the other cluster models. Brief discussion on the structure of the excited $0^+$ and $1^-$ states is also made.
The cluster states in $^{13}{rm C}$ are investigated by antisymmetrized molecular dynamics. By investigating the spectroscopic factors, the cluster configurations of the excited states are discussed. It is found that the $1/2^+_2$ state is dominantly composed of the $^{12}{rm C}(0^+_2)otimes s_{1/2}$ configuration and can be regarded as a Hoyle analogue state. On the other hand, the p-wave states ($3/2^-$ and $1/2^-$) do not have such structure, because of the coupling with other configurations. The isoscalar monopole and dipole transition strengths from the ground to the excited states are also studied. It is shown that the excited $1/2^-$ states have strong isoscalar monopole transition strengths consistent with the observation. On the other hand, the excited $1/2^+$ states unexpectedly have weak isoscalar dipole transitions except for the $1/2^+_1$ state. It is discussed that the suppression of the dipole transition is attributed to the property of the dipole operator.
To identify the 3alpha BEC state with the excess neutron, we have investigated the monopole strength of the excited states of 13C by using the theoretical framework of the real-time evolution method. The calculations have revealed several candidates of the Hoyle-analog states in a highly excited region.
The low-lying cluster states of 6He (a+n+n) and 6Li (a+n+p) are calculated by the real-time evolution method (REM) which generates basis wave functions for the generator coordinate method (GCM) from the equation of motion of Gaussian wave packets. The 0+ state of 6He as well as the 1+, 0+ and 3+ states of 6Li are calculated as a benchmark. We also calculate the root-mean-square (r.m.s.) radii of the point matter, the point proton, and the point neutron of these states, particularly for the study of the halo characters of these two nuclei. It is shown that REM can be one constructive way for generating effective basis wave functions in GCM calculations.
We derive the rotation-vibration spectrum of a 3alpha+1 neutron (proton) configuration with triangular D(3h) symmetry by exploiting the properties of the double group D(3h), and show evidence for this symmetry to occur in the rotation-vibration spectra of 13C. Our results, based on purely symmetry considerations, provide benchmarks for microscopic calculations of the cluster structure of light nuclei.
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