论文标题
$^{31} $ NE的共振能量和波函数：使用超对称量子力学的计算
Resonance energy and wave functions of $^{31}$Ne: a calculation using supersymmetric quantum mechanics
论文作者
论文摘要
在这种交流中，我们提出了一种有效的方法，用于通过应用超对称量子力学（SSQM）（SSQM）和连续性（BIC）技术的结合状态来计算弱结合核的能量和波浪功能。作为一个案例研究，该方案将实施到两体（$^{30} $ ne + n）集群模型计算中子的富含中子核$^{31} $ ne。带有自旋轨道成分的Woods-Saxon Central电势用作核心核子相互作用。相对坐标中的两体schrödinger方程是通过数值求解的，以获得低洼结合状态的能量和波函数。在SSQM的代数之后，由界面解决方案构建了一个同一潜能（IP）的单参数家族（IP），以找到共振状态的能量和波功能。除2P $ _ {3/2^ - } $（-0.33 MEV）基态，两个绑定的激发状态：S $ _ {1/2} $（-0.30 MEV），$ P_ {1/2} $（-0.15 MEV）。很少有低洼共振状态：f $ _ {7/2_1} $（2.57 meV），f $ _ {7/2_2} $（4.59 meV），f $ _ {5/2_1} $（5.58 meV） MEV），P $ _ {3/2_1} $（1.431 MEV），P $ _ {3/2_2} $（4.205 MEV）。在预测的共鸣状态下，f $ _ {7/2^{ - }} $具有共振能量$ e_r \ simeq 4.59 $ MEV的状态与文献中发现的含量非常吻合。
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.
