Using the idea of the instanton approach to quantum tunneling we try to obtain a method of calculating spontaneous fission rates for nuclei with the odd number of neutrons or protons. This problem has its origin in the failure of the adiabatic cranking approximation which serves as the basis in calculations of fission probabilities. Selfconsistent instanton equations, with and without pairing, are reviewed and then simplified to non-selfconsistent versions with phenomenological single-particle potential and seniority pairing interaction. Solutions of instanton-like equations without pairing and actions they produce are studied for the Woods-Saxon potential along realistic fission trajectories. Actions for unpaired particles are combined with cranking actions for even-even cores and fission hindrance for odd-$A$ nuclei is studied in such a hybrid model. With the assumed equal mass parameters for neighbouring odd-A and even-even nuclei, the model shows that freezing the $K^{\pi }$ configuration leads to a large overestimate of the fission hindrance factors. Actions with adiabatic configurations mostly show not enough hindrance; instanton-like actions for blocked nucleons correct this, but not sufficiently.

中文翻译：

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瞬时激发的奇核自发裂变研究

使用瞬时子方法进行量子隧穿的思想，我们尝试获得一种计算具有奇数个中子或质子的原子核自发裂变率的方法。这个问题的根源是绝热曲柄近似的失败，而绝热曲柄近似是计算裂变概率的基础。审查具有和不具有配对的自洽瞬时子方程，然后将其简化为具有现象学单粒子势能和资历配对相互作用的非自洽版本。对于沿现实裂变轨迹的Woods-Saxon势，研究了没有配对和它们产生的作用的类瞬时子方程的解。未配对粒子的作用与偶数核的起动作用以及奇数轴的裂变阻碍相结合$\mathrm{一种}$在这种混合模型中研究了原子核。假设相邻奇数A和偶数偶数核的质量参数相等，该模型显示冻结${ķ}^{\pi }$构造导致对裂变阻碍因素的高估。绝热形态的动作大多没有足够的阻碍。对于被阻止的核子，类似瞬时子的动作可以纠正这一点，但是还不够。