Spurious center-of-mass mode as an S-matrix pole within the Jost-random-phase approximation
Abstract
Within the Jost-random-phase approximation (Jost-RPA), the spurious center-of-mass mode is a zero of the Jost determinant and hence a pole of the S matrix. A zero at zero excitation energy E, whether from self-consistency or from a calibration of the residual interaction, is a pole of exactly second order when it has a single independent solution, every unoccupied bound orbital lies above the holes, and each hole is paired with every allowed partial wave; the order follows from the position of the zero, not from self-consistency. The state of this double pole, given by the Autonne-Takagi factorization of its E−2 coefficient, is the zero-energy solution normalized by its inertia. In a self-consistent model of one energy density of the neutron and proton densities, every physical S-matrix element continued to E=0 carries the E−2 term, contrary to an earlier conclusion. Subtracting the mode's principal part from the response changes the strength at real E≠0 only through the smoothing and, in such a model, coincides with the projection of the ideal spurious state. In uncalibrated Woods-Saxon models of 16O and 208Pb the mode is a pair of poles on the imaginary axis.
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BibTeX
@misc{mizuyama2026spurious,
title = {{Spurious center-of-mass mode as an $S$-matrix pole within the Jost-random-phase approximation}},
author = {Kazuhito Mizuyama},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05858},
eprint = {2611.05858},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05858},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spurious center-of-mass mode as an S-matrix pole within the Jost-random-phase approximation
AU - Kazuhito Mizuyama
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.05858
UR - https://arxiv.org/abs/2611.05858
AB - Within the Jost-random-phase approximation (Jost-RPA), the spurious center-of-mass mode is a zero of the Jost determinant and hence a pole of the S matrix. A zero at zero excitation energy E, whether from self-consistency or from a calibration of the residual interaction, is a pole of exactly second order when it has a single independent solution, every unoccupied bound orbital lies above the holes, and each hole is paired with every allowed partial wave; the order follows from the position of the zero, not from self-consistency. The state of this double pole, given by the Autonne-Takagi factorization of its E^−2 coefficient, is the zero-energy solution normalized by its inertia. In a self-consistent model of one energy density of the neutron and proton densities, every physical S-matrix element continued to E=0 carries the E^−2 term, contrary to an earlier conclusion. Subtracting the mode's principal part from the response changes the strength at real E≠0 only through the smoothing and, in such a model, coincides with the projection of the ideal spurious state. In uncalibrated Woods-Saxon models of ^16O and ^208Pb the mode is a pair of poles on the imaginary axis.
ER -