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“How can we determine the two-bodyt-matrix?”

“Как определяетсяt-Матрица Двух тел?”

  • Published:
Acta Physica Academiae Scientiarum Hungaricae

Abstract

We start with an assumed shape for the wavefunction of the ground state of the two-nucleon system. This wavefunction gives us the residue of thet-matrix at the bound-state pole-and using the unitary pole approximation (UPA) provides a good extrapolation procedure for other off-shell values of thet-matrix. (E. Harms has verified the accuracy of the UPA using the anti-bound state for theReid soft-core singlet potential.)

We now face the problem: what bound-state wavefunction should we assume? In the next several years it should be possible to determine the deuteron wavefunction experimentally, by measuring elastic electron-deuteron scattering from polarized deuterons, or equivalently by measuring the polarization of the recoil deuteron. (The wavefunction at large neutron-proton separation should also be checked by using it in the Schrödinger equation to give a local potential which should agree well with that for one pion exchange.) Angular distribution measurements provide a separation of the deuteron form factor into a charge form factor and a magnetic moment form factor. Polarization measurements separate the charge form factor into a monopole form factorG 0 and a quadrupole form factorG 2.T. Brady has found that values ofG 2(q) at momentum transfersq of order 3F −1 are quite sensitive to the percentage ofD-state (p D) in the deuteron. At present the lack of knowledge ofpD is the main source of uncertainty in calculation of the energy of the trinucleon.

Резюме

Сначала предлагаем определенную форму волновой функции основного состояния системы двух ядер. Эта волновая функция дает остатокt-матрицы в полюсе связанного состояния, и использование приближения единичного полюса дает хорошую экстраполяцию для значенийt-матрицы в неэнергетической поверхности. Сейчас возникает проблема, какую волнову функцию связанного состояния мы должны подобрать? В течение следующих лет становится возможным экспериментальным путем определить волновую функцию дейтерия путем измерения упругого рассеяния электрона и действия в поляризованном дейтерии или аналогичным путем измерить поляризацию отраженного дейтерия.

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Authors and Affiliations

  1. Rensselaer Polytechnic Institute, 12181, Troy, New York, USA

    J. S. Levinger

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  1. J. S. Levinger
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Travel supported in part by the National Science Foundation.

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Levinger, J.S. “How can we determine the two-bodyt-matrix?”. Acta Physica 33, 135–150 (1973). https://doi.org/10.1007/BF03158002

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