$^{31}$ Ne的共振能和波函数：超对称量子力学计算
Resonance energy and wave functions of $^{31}$Ne: a calculation using supersymmetric quantum mechanics
摘要：
本文利用超对称量子力学（SSQM）和连续束缚态（BIC）技术，提出了一种计算弱束缚核能量和波函数的有效方法。作为计算实例，将该方案应用于丰中子核$^{31}$ Ne的二体（$^{30}$ Ne + n）团簇模型计算。核-核子相互作用采用具有自旋-轨道分量的Woods-Saxon中心势。数值求解了相对坐标下的两体薛定谔方程，得到了低束缚态的能量和波函数。从束缚态解出发，根据SSQM代数构造单参数等谱势族，求出共振态的能量和波函数。除了2 p $_{3/2^-}$（-0.33 MeV）基态外，还得到了两个束缚激发态：s $_{1/2}$（-0.30 MeV），$p_{1/2}$（-0.15 MeV）.预测了几个低共振态：f $_{7/2_1}$（2.57 MeV），f $_{7/2_2}$（4.59 MeV），f $_{5/2_1}$（5.58 MeV），p $_{1/2_1}$（1.432 MeV），p $_{1/2_2}$（4.165 MeV），p $_{3/2_1}$（1.431 MeV），p $_{3/2_2}$（4.205 MeV）.在预测的共振态中，具有共振能量$E_R \simeq 4.59$ MeV的f $_{7/2^{-}}$态与文献中发现的状态非常一致。
英文摘要：
In this communication, we present an efficient method for computation of energy and wave function of weakly bound nuclei by the application of supersymmetric quantum mechanics (SSQM) and bound states in continuum (BIC) technique. As a case study the scheme is implemented to the two-body ($^{30}$Ne + n) cluster model calculation of neutron-rich nucleus $^{31}$Ne. Woods-Saxon central potential with spin-orbit component is used as the core-nucleon interaction. The two-body Schrödinger equation in relative coordinate is solved numerically to get the energy and wave function of the low-lying bound states. A one-parameter family of isospectral potential (IP) is constructed from the bound state solutions following algebra of SSQM to find energies and wave functions of the resonance states. In addition to the 2p$_{3/2^-}$ (-0.33 MeV) ground state, two bound excited states: s$_{1/2}$ (-0.30 MeV), $p_{1/2}$ (-0.15 MeV) are also obtained. Few low-lying resonance states: f$_{7/2_1}$ (2.57 MeV), f$_{7/2_2}$ (4.59 MeV), f$_{5/2_1}$ (5.58 MeV), p$_{1/2_1}$(1.432 MeV), p$_{1/2_2}$ (4.165 MeV), p$_{3/2_1}$ (1.431 MeV), p$_{3/2_2}$ (4.205 MeV) are predicted. Among the predicted resonance states, the f$_{7/2^{-}}$ state having resonance energy $E_R \simeq 4.59$ MeV is in excellent agreement with the one found in the literature.
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