We have studied the competition between different decay modes such as alpha decay, beta decay, electron capture and proton decay for lanthanide nuclei. This study enable us to identify the dominant decay mode. By studying the different decay properties, we have predicted 79 new isotopes in the lanthanide region. Twenty-four new \(\beta ^+\) emitting isotopes such as \(^{119,120,122}Ce\), \(^{120-125}Nd\), \(^{126-128,130}Sm\), \(^{132-134,136}Gd\), \(^{145}Tb\), \(^{136-138,140}Dy\), \(^{143}Ho\), \(^{145}Er\) and \(^{148}Yb\) were identified. Also, 55 new \(\beta ^-\) emitting isotopes such as \(^{157-160}La\), \(^{159-162}Ce\), \(^{161-164}Pr\), \(^{163-166}Nd\), \(^{164-167}Pm\), \(^{167-170}Sm\), \(^{169-171}Eu\), \(^{171-174}Gd\), \(^{173-176}Tb\), \(^{174-177}Dy\), \(^{176-179}Ho\), \(^{177-180}Er\), \(^{182-183}Tm\), \(^{148,186}Yb\) and \(^{185-188}Lu\) were identified. The predicted new isotopes have the decay energies in the range 4 MeV to 12 MeV and life times from few minutes to seconds. The predicted \(\beta ^-\) and \(\beta ^+\) decay emitters will find potential applications in the radiotherapy and diagnosis.

我们已经研究了镧系原子核的不同衰变模式（例如，α衰变，β衰变，电子俘获和质子衰变）之间的竞争。这项研究使我们能够确定主要的衰减模式。通过研究不同的衰变特性，我们预测了镧系元素区域中的79个新同位素。二十四个新的发射（\ {\ beta ^ + \）同位素，例如\（^ {119,120,122} Ce \），\（^ {120-125} Nd \），\（^ {126-128,130} Sm \），\（^ {132-134,136} Gd \），\（^ {145} Tb \），\（^ {136-138,140} Dy \），\（^ {143} Ho \），\（^ {145} Er \）和\（^ {148} Yb \）被识别。还有55个新\（\ beta ^-\）发射同位素，例如\（^ {157-160} La \），\（^ {159-162} Ce \），\（^ {161-164} Pr \），\（ ^ {163-166} Nd \），\（^ {164-167} Pm \），\（^ {167-170} Sm \），\（^ {169-171} Eu \），\（^ { 171-174} Gd \），\（^ {173-176} Tb \），\（^ {174-177} Dy \），\（^ {176-179} Ho \），\（^ {177- 180} Er \），\（^ {182-183} Tm \），\（^ {148,186} Yb \）和\（^ {185-188} Lu \）被确定。预测的新同位素的衰变能量范围为4 MeV至12 MeV，寿命为数分钟至数秒。预测的\（\ beta ^-\）和\（\ beta ^ + \）衰减发射器将在放射治疗和诊断中找到潜在的应用。