Infinite-rank separable expansion for the three-body<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math>matrix at energies in the continuous spectrum region

Matsui, Yoshiko

doi:10.1103/physrevc.26.2620

Cited by 6 publications

(3 citation statements)

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“…This fact that the eigenvalue becomes complex may be regarded due to the repulsive part contained in the Tabakin potential. Consequently, we must perform numerical analysis which extend to the range of the complex values, as if the energy is in the continuous spectrum region, by operating the dilation group and using the Schmidt expansion 3 ) instead of the HS expansion. Including the first four eigenstates of the 3 + 1 and 2 + 2 subsystems in the Schmidt expansion, the result for the bound state energy of the four-particle system is given in Table I.…”

Section: Ref 3)mentioning

confidence: 99%

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Nucleon-Trinucleon Scattering in Terms of the Schmidt Expansion. III: Integral Equation

Matsui

1992

Progress of Theoretical Physics

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The practical theory of the four•nucleon scattering is presented by generalizing our formalism for the rank one separable potential to the rank n(;;:;;2) case. The Schmidt expansion is used to express the 3+ 1 and 2+2 subamplitudes at energies in the continuous spectrum region as an infinite series of separable terms. Employing the pole term decomposition for these subamplitudes in terms of the Schmidt expansion we can define, in conformity with Faddeev's residue prescription, respective four-nucleon amplitudes that describe elastic/rearrangement, partial breakup and full breakup scattering processes. Acquired simultaneous equations of these amplitudes take the form of multichannel two-particle Lippmann-Schwinger type equations. The four-nucleon binding energy and the nucleon-trinucleon elastic amplitude are obtained by numerical analysis of these equations for the Tabakin potential. Also was verified that this amplitude satisfies the unitarity relation.

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Section: Ref 3)mentioning

confidence: 99%

“…Ak'k(P', q'; p, q; z) Bk'k(P', q'; p, q; z) =( Ifr TjPf)JVk'k"(P', 8 1; S')rk"(Zl)Wk"k(8z, p; s) +(lfr TjPf)JjVk'k"(p', 81; s')rk,,(zs)Ak"k(8z, q"; p, q; z)dq" , (3) where the momentum variables Q, Rand S are shown in Ref. 5).…”

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Nucleon-Trinucleon Scattering in Terms of the Schmidt Expansion. III: Integral Equation

Matsui

1992

Progress of Theoretical Physics

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“…He determined two 0 + bound states of the four-nucleon system; one of them was assigned to the ground state and the other to the first excited state of 4 He. Although the 0 + excited state is expected to show up in the continuum as a resonance from the experimental point of view, his results for the 0 + excited state both for the spinless case and for spin dependent forces are found to be a state bound just under the 3+1-threshold, because of the strong effect of the attractive force of the Yamaguchi potential.…”

Section: §1 Introductionmentioning

confidence: 99%

Boson-Triboson Scattering with Yamaguchi Potential. I: Restriction to s-Wave Contribution from the 3+1-Subamplitude

Matsui

1999

Progress of Theoretical Physics

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For the investigation of the S-wave boson-triboson phase shift, the Faddeev-Osborn equation is solved numerically by assuming a rank-one separable potential of the Yamaguchi type for the two-particle interaction. The calculation is performed in the exact approach based on rigorous Faddeev theory of the scattering problem. As a first step of the investigation, to gain insight into the origin of a four-body resonance, the contribution from the 3+1-subamplitude is limited to the s-wave only. The calculated phase shift behaves generally like a standard two-body one for a potential that causes one loosely bound state; this phase shift has further characteristic behavior resulting from fine structure consisting of a valley and a peak. The result of the partial cross section indicates the presence of two resonant states in the four-boson system with the Yamaguchi potential. §1. IntroductionMore than twenty years have passed since Narodetsky 1) calculated the binding energies of a four-nucleon system for a rank-one separable potential of the Yamaguchi type by applying a systematic method based on using integral equations of the Faddeev type. He determined two 0 + bound states of the four-nucleon system; one of them was assigned to the ground state and the other to the first excited state of 4 He. Although the 0 + excited state is expected to show up in the continuum as a resonance from the experimental point of view, his results for the 0 + excited state both for the spinless case and for spin dependent forces are found to be a state bound just under the 3+1-threshold, because of the strong effect of the attractive force of the Yamaguchi potential. He concluded from his results as follows: the excited 0 + state for these two cases lies very close to the 3+1-threshold, despite the fact that the ground states for both cases based on corresponding thresholds differ by approximately 30 MeV. He further remarked that, although the physical meaning of this phenomenon is far from clear, it may be caused by the threshold anomaly.After that time, for the practical application of Faddeev's scattering theory 2) established in the mathematical framework, various treatments have gradually been devised, such as the contour rotation method, 3) the Schmidt expansion theorem 4) and the pole term decomposition. 5) These treatments enable us to perform the numerical analysis for the four-body scattering problem.From the calculation of the eigenvalues of the homogeneous four-body integral equations, we found 6) that the bound states of the four-nucleon system with the Tabakin potential are limited to one, namely the ground state of the 4 He nucleus. As the Tabakin potential includes the repulsive force in addition to an attractive

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Recent developments in few-particle scattering theory

Kowalski

1984

Nuclear Physics A

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Infinite-rank separable expansion for the three-bodyTmatrix at energies in the continuous spectrum region

Cited by 6 publications

References 15 publications

Nucleon-Trinucleon Scattering in Terms of the Schmidt Expansion. III: Integral Equation

Nucleon-Trinucleon Scattering in Terms of the Schmidt Expansion. III: Integral Equation

Boson-Triboson Scattering with Yamaguchi Potential. I: Restriction to s-Wave Contribution from the 3+1-Subamplitude

Recent developments in few-particle scattering theory

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