中文摘要：

考虑两核之间的相互作用,采用单中心展开方法和B-splines技术构建氢分子离子的径向和角向波函数,计算超强平行外磁场中氢分子离子的能级Eb（m=0,-1,-2,-3,-4,-5）和两核间的平衡距离2R.计算中,磁场强度从2.35×106T变到2.35×108T.对比绝热变分近似计算结果,计算精度提高的范围在0.00015Ry～0.0488Ry之间;对比变分近似计算结果,计算精度提高的范围在0.0029Ry～0.0257Ry之间.这些计算结果表明,用二重B-splines基函数展开方法使氢分子离子的波函数的完备性更好,并能得到比绝热变分近似和绝热近似方法更高的计算精度.

英文摘要：

With interaction between atomic nucleus in a hydrogen molecular ion,one-center expansion method and B-splines basis technology are used to build radial wave function and angular wave function of a hydrogen molecular ion.Energy levels Eb （m =0,-1,-2,-3,-4,-5） and equilibrium internuclear separations 2R are calculated in superstrong external parallel magnetic fields.Strength of magnetic field changes from 2.35 × 106 T to 2.35 × 108 T.Compared with results by adiabatic variational approximation,the precision increases to a range between 0.000 15Ry and 0.048 8Ry;Compared with results by variational approximation,ours increases to a range between 0.0029Ry and 0.0257Ry.It shows that the duplicate B-splines basis function expansion method can get better completeness of wave functions and higher calculation precisions.