Effects of isospin mixing in the A=32 quintet

For the A=32 T=2 quintet we provide a unified theoretical description for three related aspects of isospin mixing: the necessity of more than three terms in the isobaric mass multiplet equation, isospin-forbidden proton decay, and a correction to the allowed Fermi beta decay. We demonstrate for the first time that all three effects observed in experiment can be traced to a common origin related to isospin mixing of the T=2 states with T=1 states

Renormalized interactions with a realistic single particle basis

Neutron-rich isotopes in the sdpf space with Z < 15 require modifications to derived effective interactions to agree with experimental data away from stability. A quantitative justification is given for these modifications due to the weakly bound nature of model space orbits via a procedure using realistic radial wavefunctions and realistic NN interactions. The long tail of the radial wavefunction for loosely bound single particle orbits causes a reduction in the size of matrix elements involving those orbits, most notably for pairing matrix elements, resulting in a more condensed level spacing in shell model calculations. Example calculations are shown for 36Si and 38Si.Comment: 6 page

Hegel on Indian Philosophy: Spinozism, Romanticism, Eurocentrism

This study examines nineteenth-century German philosopher G.W.F. Hegel’s appraisal of philosophies of India. In Hegel’s time, classical Indian texts such as the Vedas, Upaniṣads, and Bhagavadgītā had only recently been translated into European languages, and were generating tremendous controversy. Hegel carved out a unique and hugely influential position by devotedly reading fledgling translations of source texts alongside European interpretations, attempting to comprehend the philosophical significance of Indian thought. Hegel’s legacy proved deeply problematic, however, both because his views were not entirely consistent or unambiguous over time, and because his evident relegation of Indian ideas to pre- or unphilosophical status became the dominant practice among Europeans and Westerners through the twentieth century even while Hegel’s star, relatively speaking, went into a period of decline. While Hegel spent much more time and space discussing Indian philosophy in detail than did many philosophers who succeeded him in Europe and elsewhere, today his philosophy is too-frequently either reflexively labeled Eurocentric to legitimize ignoring or summarily dismissing it, or studied and written about exclusively in the context of “Western” ideas as if India were of little or no serious concern to him. This work first situates Hegel’s interest in and attention to Indian ideas in the context of the philosophical trends of Spinozism and Romanticism that he sought to navigate from his earliest forays into theology and philosophy. It then interrogates his analyses and judgments of Indian philosophical systems over the course of his career, revealing the increasing depth and innovation in his engagement with India over time while also critiquing his readings of Indian texts and his characterizations of Indian thought and culture. In doing so, it endeavors to supply the complete account of Hegel’s approach to Indian philosophy in its full complexity

Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Ab initio many-body methods address closed-shell nuclei up to mass A ~ 130 on the basis of realistic two- and three-nucleon interactions. Several routes to address open-shell nuclei are currently under investigation, including ideas which exploit spontaneous symmetry breaking. Singly open-shell nuclei can be efficiently described via the sole breaking of $U(1)$ gauge symmetry associated with particle number conservation, to account for their superfluid character. The present work formulates and applies Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wavefunction of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in $m$-scheme, which will eventually permit the treatment of doubly open-shell nuclei. Proof-of-principle calculations in an $N_{\text{max}}=6$ spherical harmonic oscillator basis are performed for $^{16,18,20}$O, $^{18}$Ne, $^{20}$Mg in the BCCD approximation with a chiral two-nucleon interaction, comparing to results obtained in standard coupled cluster theory when applicable. The breaking of $U(1)$ symmetry is monitored by computing the variance associated with the particle-number operator. The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e. potentially to reach several hundred additional mid-mass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei.Comment: 22 pages, 13 figure

Ab-initio coupled-cluster effective interactions for the shell model: Application to neutron-rich oxygen and carbon isotopes

We derive and compute effective valence-space shell-model interactions from ab-initio coupled-cluster theory and apply them to open-shell and neutron-rich oxygen and carbon isotopes. Our shell-model interactions are based on nucleon-nucleon and three-nucleon forces from chiral effective-field theory. We compute the energies of ground and low-lying states, and find good agreement with experiment. In particular our calculations are consistent with the N=14, 16 shell closures in oxygen-22 and oxygen-24, while for carbon-20 the corresponding N=14 closure is weaker. We find good agreement between our coupled-cluster effective-interaction results with those obtained from standard single-reference coupled-cluster calculations for up to eight valence neutrons

Quasiparticle Coupled Cluster Theory for Pairing Interactions

We present an extension of the pair coupled cluster doubles (p-CCD) method to quasiparticles and apply it to the attractive pairing Hamiltonian. Near the transition point where number symmetry gets spontaneously broken, the proposed BCS-based p-CCD method yields significantly better energies than existing methods when compared to exact results obtained via solution of the Richardson equations. The quasiparticle p-CCD method has a low computational cost of $\mathcal{O}(N^3)$ as a function of system size. This together with the high quality of results here demonstrated, points to considerable promise for the accurate description of strongly correlated systems with more realistic pairing interactions