t+t clustering in He isotopes is investigated by using two theoretical approaches. A role of the t+t cluster component in the ground state is examined with AMD triple-S, allowing the wider configuration space containing simultaneously the "t+t+valence neutrons" structure and "4 He +valence neutrons" structure. We understand the importance of the t + t component even for the ground state. Further, t + t resonances are investigated with RGM type approach. We obtained many t + t states as resonances near to t + t threshold.

In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasi-particles (qps). The problem can be solved by employing the Pfaffian algorithm generally applicable to calculations of matrix elements for Hartree-Fock-Bogoliubov states with any number of qps. This breakthrough in many-body techniques enables studies of high-spin states in a shell-model framework. As the first application of the Pfaffian algorithm, the configuration space of the Projected Shell Model is expanded to include 6-qp states for both positive and negative parities. Taking 166 Hf as an example, we show that 6-qp states become the main configuration of the yrast band beyond spin I ≈ 34 , which explains the observed third back-bending in moment of inertia. Structures of multi-qp high-K isomers in 176 Hf are analyzed as another example.PACS numbers: 21.10. Re, 21.60.Cs, 23.20.Lv, 27.70.+q All nucleons of even-even nuclei couple pairwise in their ground state. Nuclear rotation brings an effect into the system that tends to break the nucleon pairs. This effect due to the rotation of nuclei was suggested in 1960 [1] in analogy to the electron pair breaking in superconductivity due to the existence of external magnetic fields. However, it was soon after realized that a sharp phase transition with pair collapse does not occur in nuclear systems due to the fact that nuclei have a finite size [2]. Another reason is that nucleons have an orbital angular momentum in addition to spin. The nucleons in the vicinity of the Fermi surfaces belong to subshells with rather different j-values, and therefore, they feel the Coriolis force very differently. Pairs in those orbitals with the highest angular momentum j, as for instance the neutron i 13/2 shell in the rare earth region, feel a strong Coriolis force, and therefore, break first (the Stephens-Simon effect [3]). They contribute to formation of 2-quasiparticle (qp) state as the main configuration of the yrast state. The Stephens-Simon effect [3] successfully explained the experimental observations of backbending in moment of inertia for rotating nuclei [4]. As a nucleus rotates faster and faster, subsequent pair-breakings can occur for the pairs from the next highest j orbitals. In the rare earth region, proton pairs in the h 11/2 shell are expected to break next, which was observed experimentally [5]. Measurements for further pair breakings at higher angular momenta are difficult. However, there have been early [6] and recent evidences [7,8] of breaking of three nucleon pairs, which form 6-qp states as the main configuration of the yrast sequence.Pair-breaking in nuclei can lead to formation of another special group of excited states: nuclear isomers. In a deformed potential a j-shell splits up into 2 j+1 K-states. Two or more states with high K quantum numbers can couple to form a high-K multi-qp configuration. The selection rules of elec- * El...

A new formula is presented for the calculation of matrix elements between multi-quasiparticle Hartree-Fock-Bogoliubov (HFB) states. The formula is expressed in terms of the Pfaffian, and is derived by using the Fermion coherent states with Grassmann numbers. It turns out that the formula corresponds to an extension of generalized Wick's theorem and simplifies the combinatorial complexity resulting from practical applications of generalized Wick's theorem by unifying the transition density and the transition pairing tensor in the HFB theory. The resultant formula is simpler and more compact than the traditional description of matrix elements of general many-body operators. In addition, through the derivation of our new formula, we found that the Pfaffian version of the Lewis Carroll formula corresponds to the relation conjectrured by Balian and Brezin for the HFB theory in 1969.

We present a new formula to calculate matrix elements of a general unitary operator with respect to Hartree-Fock-Bogoliubov states allowing multiple quasi-particle excitations. The Balian-Brézin decomposition of the unitary operator (Il Nuovo Cimento B 64, 37 (1969)) is employed in the derivation. We found that this decomposition is extremely suitable for an application of Fermion coherent state and Grassmann integrals in the quasi-particle basis. The resultant formula is compactly expressed in terms of the Pfaffian, and shows the similar bipartite structure to the formula that we have previously derived in the bare-particles basis (Phys. Lett. B 707, 305 (2012)). dξ←−The integral over η * ν (ν ∈ J) gives rise to a product of η's aswhere n = M − n. Then the integral over η ν (ν ∈ J) in the Eq.(32) can be carried out aswhere {η} J stands for the Grassmann variables η ν 1 , · · · , η ν n . After the integrals over η ν (ν ∈ J) and η * ν are performed, the integral over η ν (ν ∈ J) remains. Then, Eq.(30) is represented by the integrals over ξ , ξ * and η ν (ν ∈ J) as

A formula to calculate a norm overlap between Hartree-Fock-Bogoliubov (HFB) states with the odd number parity (one quasi-particle excited states) is derived with help of the Grassmann numbers and the Fermion coherent states. The final form of the formula is expressed in terms of a product of the Pfaffian for a neighboring even-even system (the zero quasi-particle state), and an extra factor consisting of the Bogoliubov transformation matrix and the anti-symmetric matrix in Thouless' HFB ansatz for the even-even system. I. INTRODUCTIONThe Hartree-Fock-Bogoliubov (HFB) method has been a powerful method in descriptions of nuclear states [1]. The reason is that the method can deal with the two most important correlations in interacting many-body nuclear systems, that is, deformation and pairing.These correlations are effectively taken into account by breaking relevant symmetries (the rotational and gauge symmetries). As a consequence, however, the conservation laws of angular momentum and the particle numbers are violated.Restorations of these broken symmetries are achieved through quantum number projections, but there have been difficulties to overcome in carrying out practical calculations of the projection. The major problem lies in the calculation of the so-called norm overlap kernels, which is necessary in the projections. The evaluation of the norm overlap is particularly difficult in angular momentum projection because the rotational symmetry is associated with the non-Abelian SO(3) group. * Electronic address: m.oi@isc.senshu-u.ac.jp