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铀同位素链α衰变的研究

Alpha Decay for Uranium Isotopes

  • 摘要: 利用传输矩阵方法计算了铀同位素链\alpha衰变的穿透几率,并且与常用于计算势垒穿透几率的Wenzel Kramers Brillouin(WKB)近似方法进行了比较,发现由WKB近似方法得到的穿透几率比精确值小40%左右,而且WKB方法带来的误差与\alpha衰变的衰变能有很好的抛物线关系。基于结团模型,利用传输矩阵方法得到\alpha粒子穿透势垒的精确几率,计算了铀同位素链\alpha衰变的半衰期。还研究了势阱深度V_0、弥散宽度a和主量子数G对半衰期的影响。结果表明,考虑一组同位旋依赖的势阱深度和弥散宽度参数,结团模型能够较好地再现铀同位素链\alpha衰变的半衰期。

     

    Abstract: Both the transfer matrix approach and the Wentzel Kramers Brillouin(WKB) approximation are used to calculate the penetrability of \alpha decay for uranium isotopes. It is found that the penetrability obtained with WKB approximation is about 40% smaller than the accurate result obtained with the transfer matrix approach, and a parabolic relationship between this underestimation and the decay energy can be observed. Based on the cluster model, the half-lives of \alpha decay for uranium isotopes are calculated in which the transfer matrix approach is used to obtain the penetrability. In addition, the influences of potential depth V_0, the diffuseness parameter a, and the global quantum number G on the calculated half-life are also investigated. Furthermore, with considering an isospin-dependent potential depth parameter, the \alpha decay half-lives of uranium isotopes can be fairly well reproduced by the cluster model.

     

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