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Makito Oi

Publications and source records attributed to Makito Oi.

17 recordsLinked to original sources
arXiv2018

Why does the sign problem occur in evaluating the overlap of HFB wave functions?

For the overlap matrix element between Hartree-Fock-Bogoliubov states, there are two analytically different formulae: one with the square root of the determinant (the Onishi formula) and the other with the Pfaffian (Robledo's Pfaffian formula). The former formula is two-valued as a complex function, hence it leaves the sign of the norm overlap undetermined (i.e., the so-called sign problem of the Onishi formula). On the other hand, the latter formula does not suffer from the sign problem. The derivations for these two formulae are so different that the reasons are obscured why the resultant formulae possess different analytical properties. In this paper, we discuss the reason why the difference occurs by means of the consistent framework, which is based on the linked cluster theorem and the product-sum identity for the Pfaffian. Through this discussion, we elucidate the source of the sign problem in the Onishi formula. We also point out that different summation methods of series expansions may result in analytically different formulae.

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arXiv2014

Toward extremes of angular momentum: Application of the Pfaffian algorithm in realistic calculations

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 $I \approx 34\hbar$, 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.

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arXiv2013

Grassmann integral and Balian-Brézin decomposition in Hartree-Fock-Bogoliubov matrix elements

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)).

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arXiv2012

A new formulation to calculate general HFB matrix elements through Pfaffian

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.

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arXiv2011

Norm-overlap formula of Hartree-Fock-Bogoliubov states with odd number parity

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.

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arXiv2007

Description of superdeformed bands in light N=Z nuclei using the cranked HFB method

Superdeformed states in light $N=Z$ nuclei are studied by means of the self-consistent cranking calculation (i.e., the P + QQ model based on the cranked Hartree-Fock-Bogoliubov method). Analyses are given for two typical cases of superdeformed bands in the $A \simeq 40$ mass region, that is, bands where backbending is absent ($^{40}$Ca) and present ($^{36}$Ar). Investigations are carried out, particularly for the following points: cross-shell excitations in the sd and pf shells; the role of the g$_{9/2}$ and d$_{5/2}$ orbitals; the effect of the nuclear pairing; and the interplay between triaxiality and band termination.

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arXiv2007

Cranked Hartree-Fock-Bogoliubov Calculation for Rotating Bose-Einstein Condensates

A rotating bosonic many-body system in a harmonic trap is studied with the 3D-Cranked Hartree-Fock-Bogoliubov method at zero temperature, which has been applied to nuclear many-body systems at high spin. This method is a variational method extended from the Hartree-Fock theory, which can treat the pairing correlations in a self-consistent manner. An advantage of this method is that a finite-range interaction between constituent particles can be used in the calculation, unlike the original Gross-Pitaevskii approach. To demonstrate the validity of our method, we present a calculation for a toy model, that is, a rotating system of ten bosonic particles interacting through the repulsive quadrupole-quadrupole interaction in a harmonic trap. It is found that the yrast states, the lowest-energy states for the given total angular momentum, does not correspond to the Bose-Einstein condensate, except a few special cases. One of such cases is a vortex state, which appears when the total angular momentum $L$ is twice the particle number $N$ (i.e., $L=2N$).

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arXiv2005

Semi-classical and anharmonic quantum models of nuclear wobbling motion

A semi-classical model for wobbling motion is presented as an extension to the Bohr-Mottelson model of wobbling motion. Using the resultant wobbling potential, a quantum mechanical equation is derived for anharmonic wobbling motion. We then attempt to explain the anharmonicity observed in the excited bands of two wobbling phonons in the A=160 region.

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arXiv2004

Nodal Lines in the Cranked HFB Overlap kernels

Norm overlap kernels of the cranked Hartree-Fock-Bogoliubov states are studied in the context of angular momentum projection. In particular, the geometrical distribution of nodal lines, i.e., one dimensional structures where the overlap kernels possess null value, is investigated in the three dimensional space defined by the Euler angles. It is important to know the distribution of these nodal lines when one attempts to determine the phase of norm overlap kernels.

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arXiv2003

Three-dimensional rotation of even-even triaxial nuclei

With the self-consistent three-dimensional cranked Hartree-Fock-Bogoliubov (3d-cranked HFB) method, various types of rotational motion near the yrast line are investigated in an even-even nucleus in the $A\simeq 130$ mass region ($^{134}_{58}$Ce$_{76}$). The possibilities of chiral rotations, tilted-rotations, and dynamical aspects of these rotations are discussed through the analysis of the 3d-cranked HFB solutions. Although a stable planar solution of the chiral rotation is obtained, an aplanar chiral configuration is found to be unstable when triaxial deformation is treated self-consistently.

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arXiv2001

Wobbling motion coupled to gamma vibration at high spin

We report a solution of the tilted-axis cranked HFB equation for $^{164}$Hf, which shows wobbling motion coupled to gamma vibration at high spin ($J\simeq 60\hbar$). Possible anharmonicity and splitting of energy levels are also discussed as a consequence of the wobbling motion with large amplitude.

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arXiv2001

A self-consistent quantal description of high-K states in the tilted-axis cranking model

A self-consistent and quantal description of high-$K$ bands is given in the framework of the tilted-axis cranking model. (With a $θ=90^{\circ}$ tilt angle with respect to $x$-axis, this cranking model is equivalent to the $z$-axis cranking.) The numerical results of the HFB calculations in this framework are compared with experimental data for two quasi-particle excited bands with $K^π=6^+$ in $^{178}$W.

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arXiv2001

Shape coexistence and tilted-axis rotation in neutron-rich hafnium isotopes

We have performed tilted-axis-cranked Hartree-Fock-Bogoliubov calculations for a neutron-rich hafnium isotope ($^{182}$Hf) whose proton and neutron numbers are both in the upper shell region. We study whether the shell effects play a role in producing high-$K$ isomers or highly gamma-deformed states at high spin. In particular, the possibility of shape coexistence and the effect of wobbling motion are discussed.

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arXiv2000

Wobbling motion in the multi-bands crossing region

The backbending in the A=180 mass region is expected to be caused by multi-bands crossing between low-K (g- and s-bands) and high-K bands. % We analyze a mechanism of coupling of these bands in terms of a dynamical treatment for nuclear rotations, i.e., the wobbling motion. The wobbling states are produced through the generator coordinate method after angular momentum projection, in which the intrinsic states are constructed through the 2d-cranked HFB calculations.

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arXiv1998

Band Structures of $^{182}$ Os Studied by GCM based on 3D-CHFB

Band structure properties of $^{182}$Os are investigated through a particle number and angular momentum constrained generator coordinate(GCM) calculation based on self-consistent three-dimensional cranking solutions. From the analysis of the wave function of the lowest GCM solution, we confirm that this nucleus shows a tilted rotational motion in its yrast states, at least with the present set of force parameters of the pairing-plus-quadrupole interaction Hamiltonian. A close examination of behavior of other GCM solutions reveals a sign of a possible occurrence of multi-band crossing in the nucleus. Furthermore, in the course of calculations, we have also found a new potential curve along the prime meridian on the globe of the $J=18\hbar$ sphere. Along this new solution the characters of proton and neutron gap parameters get interchanged. Namely, $Δ_p$ almost vanishes while $Δ_n$ grows to a finite value close to the one corresponding to the principal axis rotation(PAR). A state in the new solution curve at the PAR point turns out to have almost the same characteristic features of an yrare $s$-band state which gets located just above the $g$-band in our calculation. This fact suggests a new type of seesaw vibrational mode of the proton and the neutron pairing, occurring through a wobbling motion. The mode is considered to bridge the $g$-band states and the $s$-band states in the backbending region.

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arXiv1997

Signature and Angular Momentum in 3d-Cranked HFB states

In terms of the exaxt angular momentum projection, properties of the three dimensional cranked HFB (3d-CHFB) states are analyzed quantitatively in the context of the relation between the signature of an intrinsic symmetry and the parity of angular momentum, (-1)^I. We found that the tilted states have favorable features to describe states involved with high-K quantum number and/or odd total angular momentum. This implies that 3d-CHFB can describe properly the backbending phenomena like a "t-band and g-band" crossing, which is suggested in N=106 isotopes.

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