We benchmark angular-momentum projected-after-variation Hartree–Fock calculations as an approximation to full configuration-interaction results in a shell model basis. For such a simple approximation we find reasonably good agreement between excitation spectra, including for many odd-A and odd–odd nuclides. We frequently find shape coexistence, in the form of multiple Hartree–Fock minima; mixing in shape coexistence, the first step beyond single-reference projected Hartree–Fock, demonstrably improves the spectrum in the sd- and pf-shells. The complex spectra of germanium isotopes present a challenge: for even A the spectra are only moderately good and those of odd A bear little resemblance to the configuration-interaction results. Despite this failure we are able to broadly reproduce the odd–even staggering of ground state binding energies, save for germanium isotopes with N > 40. To illustrate potential applications, we compute the spectrum of the recently measured dripline nuclide ⁴⁰Mg. All in all, projected Hartree–Fock often provides a better description of low-lying nuclear spectra than one might expect. Key to this is the use of gradient descent and unrestricted shapes.

我们将角动量投影后变化 Hartree-Fock 计算作为对壳模型基础的完整配置相互作用结果的近似值进行基准测试。对于这样一个简单的近似，我们发现激发光谱之间相当好的一致性，包括许多奇数A和奇数核素。我们经常发现形状共存，以多个 Hartree-Fock 最小值的形式存在；混合形状共存，超越单参考投影 Hartree-Fock 的第一步，明显改善了sd - 和pf -壳中的频谱。锗同位素的复杂光谱提出了一个挑战：对于偶数A的光谱只是中等好，而对于奇数A的光谱与配置交互结果几乎没有相似之处。尽管失败了，我们还是能够广泛地重现基态结合能的奇偶惊人，除了N > 40 的锗同位素。为了说明潜在的应用，我们计算了最近测量的滴线核素⁴⁰ Mg的光谱。总而言之，投影的 Hartree-Fock 通常比人们想象的更好地描述低洼核光谱。关键是使用梯度下降和不受限制的形状。