May 13 – 17, 2019
Venice, Centro Culturale Don Orione Artigianelli
Europe/Rome timezone
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Alpha correlation in term of the hyper-Pfaffian

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SALA PALLADIO (Centro Culturale Don Orione Artigianelli)


Centro Culturale Don Orione Artigianelli


Prof. Takahiro Mizusaki (INS, Senshu University)


A new theoretical approach for alpha correlation in nuclei is investigated in term of the hyper-Pfaffian [1]. The Pfaffian has been recently investigated to formulate the pairing correlation and is useful in investigating the sign-problem of Onishi formula [2], Wick’s theorem, and the variational Monte Carlo [3]. While the hyper-Pfaffian, which is an extension of the Pfaffian for multi-dimensional tensor, is unfamiliar in physics.

In this contribution, we show that the overlap matrix element between M-scheme state and quartet wave function, which plays a key role in the variational Monte Carlo method, can be represented by the hyper-Pfaffian with k = 4. The hyper-Pfaffian, however, seems not to have many useful mathematical properties and is difficult for numerical computation. To overcome this difficulty, we found that the hyper-Pfaffian with k = 4 for the alpha-like quartet wave function can be calculated as the sum of usual Pfaffians, by which its numerical evaluation becomes faster and feasible. The first result will be shown in [4]. (See also [4], for relevant references concerning the Pfaffian and its applications, and definitions of the hyper-Pfaffian in mathematics.) We present its formula and show the alpha correlation in the nuclear shell model.

[1] For example, J.-G. Luque, J.-Y. Thibon, Advances in Applied Mathematics 29 4 620 (2002).
[2] For example, L. M. Robledo, Phys. Rev. C 79, 021302(R) (2009).
[3] M. Bajdich, L. Mitas, G. Drobny, L. K. Wagner, and K. E. Schmidt, Phys. Rev. Lett. 96, 130201 (2006). D. Tahara and M. Imada, J. Phys. Soc. Jpn. 77, 114701 (2008).
[4] Takahiro Mizusaki, Peter Schuck, Bulletin of the Institute of Natural Sciences Senshu University, No.50, (March 2019).

Primary authors

Prof. Takahiro Mizusaki (INS, Senshu University) Peter Schuck (Institut de Physique Nucleaire Orsay)

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