We calculate the transition density for the overtone of the isosclar giant monopole resonance (ISGMR) from the response to an appropriate external field $\hat{f}_\xi(r)$ obtained using the seemiclassical fluid dynamic approximation and the Hartree-Fock (HF) based random phase approximation (RPA). We determine the mixing parameter $\xi$ by maximizing the ratio of the energy weighted sum for the overtone mode to the total energy weighted sum rule and derive a simple expression for the microscopic transition density associated with the overtone mode. This macroscopic transition density agrees well with that obtained from the HF-RPA calculations. We also point out that the ISGMR and its overtone can be clearly identified by considering the response to the electromagnetic external field $\hat{j}_o(qr)$ .
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机译：我们通过使用半经典流体动力学近似和Hartree-Fock获得的对适当外部场$ \ hat {f} _ \ xi（r）$的响应，计算出等腰大单极共振（ISGMR）的泛音的跃迁密度。 （HF）的随机相位近似（RPA）。我们通过最大化泛音模式的能量加权和与总能量加权和规则的比率来确定混合参数$ \ xi $，并得出与泛音模式相关的微观转变密度的简单表达式。该宏观转变密度与从HF-RPA计算获得的一致。我们还指出，通过考虑对电磁外部场$ \ hat {j} _o（qr）$的响应，可以清楚地确定ISGMR及其泛音。
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